50576969 acca p4 class notes june 2011 version

ACCA Paper P4

Advanced Financial Management

Class Notes

June 2011

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© Ken Preece January 2011

All rights reserved. No part of this publication may be reproduced, stored in a

retrieval system, or transmitted, in any form or by any means, electronic,

mechanical, photocopying, recording or otherwise, without the prior written

permission of Ken Preece.



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Contents PAGE

INTRODUCTION TO THE PAPER 5

FORMULAE & TABLES PROVIDED IN THE EXAMINATION PAPER 7

CHAPTER 1: ISSUES IN CORPORATE GOVERNANCE 13

CHAPTER 2: ADVANCED INVESTMENT APPRAISAL – SECTION 1 39

CHAPTER 3: ADVANCED INVESTMENT APPRAISAL – SECTION 2 63

CHAPTER 4: COST OF CAPITAL 97

CHAPTER 5: EFFICIENT MARKET HYPOTHESIS 121

CHAPTER 6: THEORIES OF GEARING 129

CHAPTER 7: PORTFOLIO THEORY AND THE CAPITAL ASSET PRICING MODEL 147

CHAPTER 8: ADJUSTED PRESENT VALUE 191

CHAPTER 9: VALUATIONS, ACQUISITIONS AND MERGERS – SECTION 1 205



CHAPTER 12: CORPORATE RECONSTRUCTION AND REORGANISATION 281

CHAPTER 13: CORPORATE DIVIDEND POLICY 291

CHAPTER 14: MANAGEMENT OF INTERNATIONAL TRADE AND FINANCE 301

CHAPTER 15: HEDGING FOREIGN EXCHANGE RISK 317

CHAPTER 16: FUTURES AND OPTIONS 345

CHAPTER 17: HEDGING INTEREST RATE RISK 375

CHAPTER 18: SWAPS 407

CHAPTER 19: INTERNATIONAL INVESTMENT APPRAISAL 423




Introduction to the

paper



INTRODUCTION TO THE PAPER


Aim of the Paper

The aim of the paper is to apply relevant knowledge, skills and exercise

professional judgement as expected of a senior financial executive or advisor, in

taking or recommending decisions relating to the financial management of an

organisation.

Outline of the syllabus

A. Role and responsibility towards stakeholders

B. Economic environment for multinationals

C. Advanced investment appraisal

D. Acquisitions and mergers

E. Corporate reconstruction and re-organisation

F. Treasury and advanced risk management techniques

G. Emerging issues in finance and financial management

Format of the Exam Paper

The examination will be a three-hour paper (with the additional 15 minutes reading

and planning time) of 100 marks in total, divided into two sections:

Section A

Section A will contain two compulsory questions, comprising between 50

and 70 marks in total.

Section A will normally cover significant issues relevant to the senior financial

manager or advisor and will be set in the form of a short case study or scenario.

The requirements of the section A questions are such that candidates will be

expected to show a comprehensive understanding of issues from across the

syllabus. Each question will contain a mix of computational and discursive

elements. Each question in section A will comprise of between 25 and 40

marks. Candidates will be expected to provide answers in a specified form such as

a short report or board memorandum commensurate with the professional level of

the paper.

Section B

In section B candidates will be asked to answer two from three questions,

comprising of between 15 and 25 marks each.

Section B questions are designed to provide a more focused test of the syllabus

with, normally, one question being wholly discursive.

Candidates will be provided (within the examination paper) with a

formulae sheet as well as present value, annuity and standard normal

distribution tables.




Formulae & tables

provided in the examination paper



FORMULAE & TABLES PROVIDED IN THE EXAMINATION PAPER


Formulae

Modigliani and Miller Proposition 2 (with tax)

ke = kie + (1 – T)(ki

e – kd) e

d

V

V

Two asset portfolio

sp = baabba2

b2

b2

a2

a s s r w w 2 + s w + s w

The Capital Asset Pricing Model

E(rj) = Rf + βj (E(rm) – Rf)

The asset beta formula

βa =

β

+ ede

e

))T-1(VV(

V +

β

+ dde

d

))T-1(VV(

)T-1(V

The Growth Model

P0 = g) - (r

g) + (1 D

e

0

Gordon’s growth approximation

g = bre

The weighted average cost of capital

WACC =

+ de

e

VV

V ke +

+ de

d

VV

V kd(1–T)

The Fisher formula

(1 + i) = (1 + r) (1 + h)

Purchasing power parity and interest rate parity

S1 = S0 × )h(1

)h(1

b

c

+

+ Fo = So ×

)i(1

)i(1

b

c

+

+





Modified Internal Rate of Return

MIRR = n

1

I

R

PV

PV

(1 + re) – 1

The Black Scholes Option

Pricing Model

c = Pa N(d1) − Pe N(d 2) e-rt

Where:

d1 = ts

)t0.5s +(r + )/Pln(P 2ea

and

d2 = d1 – ts

The Put Call Parity relationship

p = c − Pa + Pe e -rt





Present value table

Present value of 1 i.e. (1 + r)-n

Where r = discount rate

n = number of periods until payment

Discount rate (r)

Periods

(n) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

________________________________________________________________________________

1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 1 2 0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826 2 3 0.971 0.942 0.915 0.889 0.864 0.840 0.816 0.794 0.772 0.751 3 4 0.961 0.924 0.888 0.855 0.823 0.792 0.763 0.735 0.708 0.683 4 5 0.951 0.906 0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621 5

6 0.942 0.888 0.837 0.790 0.746 0.705 0.666 0.630 0.596 0.564 6 7 0.933 0.871 0.813 0.760 0.711 0.665 0.623 0.583 0.547 0.513 7 8 0.923 0.853 0.789 0.731 0.677 0.627 0.582 0.540 0.502 0.467 8 9 0.914 0.837 0.766 0.703 0.645 0.592 0.544 0.500 0.460 0.424 9 10 0.905 0.820 0.744 0.676 0.614 0.558 0.508 0.463 0.422 0.386 10

11 0.896 0.804 0.722 0.650 0.585 0.527 0.475 0.429 0.388 0.350 11 12 0.887 0.788 0.701 0.625 0.557 0.497 0.444 0.397 0.356 0.319 12 13 0.879 0.773 0.681 0.601 0.530 0.469 0.415 0.368 0.326 0.290 13 14 0.870 0.758 0.661 0.577 0.505 0.442 0.388 0.340 0.299 0.263 14 15 0.861 0.743 0.642 0.555 0.481 0.417 0.362 0.315 0.275 0.239 15

________________________________________________________________________________

(n) 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%

________________________________________________________________________________

1 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833 1 2 0.812 0.797 0.783 0.769 0.756 0.743 0.731 0.718 0.706 0.694 2 3 0.731 0.712 0.693 0.675 0.658 0.641 0.624 0.609 0.593 0.579 3 4 0.659 0.636 0.613 0.592 0.572 0.552 0.534 0.516 0.499 0.482 4 5 0.593 0.567 0.543 0.519 0.497 0.476 0.456 0.437 0.419 0.402 5

6 0.535 0.507 0.480 0.456 0.432 0.410 0.390 0.370 0.352 0.335 6 7 0.482 0.452 0.425 0.400 0.376 0.354 0.333 0.314 0.296 0.279 7 8 0.434 0.404 0.376 0.351 0.327 0.305 0.285 0.266 0.249 0.233 8 9 0.391 0.361 0.333 0.308 0.284 0.263 0.243 0.225 0.209 0.194 9 10 0.352 0.322 0.295 0.270 0.247 0.227 0.208 0.191 0.176 0.162 10

11 0.317 0.287 0.261 0.237 0.215 0.195 0.178 0.162 0.148 0.135 11 12 0.286 0.257 0.231 0.208 0.187 0.168 0.152 0.137 0.124 0.112 12 13 0.258 0.229 0.204 0.182 0.163 0.145 0.130 0.116 0.104 0.093 13 14 0.232 0.205 0.181 0.160 0.141 0.125 0.111 0.099 0.088 0.078 14 15 0.209 0.183 0.160 0.140 0.123 0.108 0.095 0.084 0.074 0.065 15





Annuity table

Present value of an annuity of 1 i.e. r

r) + (1 - 1 -n

Where r = discount rate

n = number of periods

Discount rate (r)

Periods

(n) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

________________________________________________________________________________

1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 1 2 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.736 2 3 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 2.487 3 4 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170 4 5 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791 5

6 5.795 5.601 5.417 5.242 5.076 4.917 4.767 4.623 4.486 4.355 6 7 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033 4.868 7 8 7.652 7.325 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.335 8 9 8.566 8.162 7.786 7.435 7.108 6.802 6.515 6.247 5.995 5.759 9 10 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145 10

11 10.37 9.787 9.253 8.760 8.306 7.887 7.499 7.139 6.805 6.495 11 12 11.26 10.58 9.954 9.385 8.863 8.384 7.943 7.536 7.161 6.814 12 13 12.13 11.35 10.63 9.986 9.394 8.853 8.358 7.904 7.487 7.103 13 14 13.00 12.11 11.30 10.56 9.899 9.295 8.745 8.244 7.786 7.367 14 15 13.87 12.85 11.94 11.12 10.38 9.712 9.108 8.559 8.061 7.606 15 ________________________________________________________________________________

(n) 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%

________________________________________________________________________________

1 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833 1 2 1.713 1.690 1.668 1.647 1.626 1.605 1.585 1.566 1.547 1.528 2 3 2.444 2.402 2.361 2.322 2.283 2.246 2.210 2.174 2.140 2.106 3 4 3.102 3.037 2.974 2.914 2.855 2.798 2.743 2.690 2.639 2.589 4 5 3.696 3.605 3.517 3.433 3.352 3.274 3.199 3.127 3.058 2.991 5

6 4.231 4.111 3.998 3.889 3.784 3.685 3.589 3.498 3.410 3.326 6 7 4.712 4.564 4.423 4.288 4.160 4.039 3.922 3.812 3.706 3.605 7 8 5.146 4.968 4.799 4.639 4.487 4.344 4.207 4.078 3.954 3.837 8 9 5.537 5.328 5.132 4.946 4.772 4.607 4.451 4.303 4.163 4.031 9 10 5.889 5.650 5.426 5.216 5.019 4.833 4.659 4.494 4.339 4.192 10

11 6.207 5.938 5.687 5.453 5.234 5.029 4.836 4.656 4.486 4.327 11 12 6.492 6.194 5.918 5.660 5.421 5.197 4.988 4.793 4.611 4.439 12 13 6.750 6.424 6.122 5.842 5.583 5.342 5.118 4.910 4.715 4.533 13 14 6.982 6.628 6.302 6.002 5.724 5.468 5.229 5.008 4.802 4.611 14 15 7.191 6.811 6.462 6.142 5.847 5.575 5.324 5.092 4.876 4.675 15





Standard normal distribution table

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0

0.0000 0.0398 0.0793 0.1179 0.1554 0.1915 0.2257 0.2580 0.2881 0.3159 0.3413 0.3643 0.3849 0.4032 0.4192 0.4332 0.4452 0.4554 0.4641 0.4713 0.4772 0.4821 0.4861 0.4893 0.4918 0.4938 0.4953 0.4965 0.4974 0.4981 0.4987

0.0040 0.0438 0.0832 0.1217 0.1591 0.1950 0.2291 0.2611 0.2910 0.3186 0.3438 0.3665 0.3869 0.4049 0.4207 0.4345 0.4463 0.4564 0.4649 0.4719 0.4778 0.4826 0.4864 0.4896 0.4920 0.4940 0.4955 0.4966 0.4975 0.4982 0.4987

0.0080 0.0478 0.0871 0.1255 0.1628 0.1985 0.2324 0.2642 0.2939 0.3212 0.3461 0.3686 0.3888 0.4066 0.4222 0.4357 0.4474 0.4573 0.4656 0.4726 0.4783 0.4830 0.4868 0.4898 0.4922 0.4941 0.4956 0.4967 0.4976 0.4982 0.4987

0.0120 0.0517 0.0910 0.1293 0.1664 0.2019 0.2357 0.2673 0.2967 0.3238 0.3485 0.3708 0.3907 0.4082 0.4236 0.4370 0.4484 0.4582 0.4664 0.4732 0.4788 0.4834 0.4871 0.4901 0.4925 0.4943 0.4957 0.4968 0.4977 0.4983 0.4988

0.0160 0.0557 0.0948 0.1331 0.1700 0.2054 0.2389 0.2703 0.2995 0.3264 0.3508 0.3729 0.3925 0.4099 0.4251 0.4382 0.4495 0.4591 0.4671 0.4738 0.4793 0.4838 0.4875 0.4904 0.4927 0.4945 0.4959 0.4969 0.4977 0.4984 0.4988

0.0199 0.0596 0.0987 0.1368 0.1736 0.2088 0.2422 0.2734 0.3023 0.3289 0.3531 0.3749 0.3944 0.4115 0.4265 0.4394 0.4505 0.4599 0.4678 0.4744 0.4798 0.4842 0.4878 0.4906 0.4929 0.4946 0.4960 0.4970 0.4978 0.4984 0.4989

0.0239 0.0636 0.1026 0.1406 0.1772 0.2123 0.2454 0.2764 0.3051 0.3315 0.3554 0.3770 0.3962 0.4131 0.4279 0.4406 0.4515 0.4608 0.4686 0.4750 0.4803 0.4846 0.4881 0.4909 0.4931 0.4948 0.4961 0.4971 0.4979 0.4985 0.4989

0.0279 0.0675 0.1064 0.1443 0.1808 0.2157 0.2486 0.2794 0.3078 0.3340 0.3577 0.3790 0.3980 0.4147 0.4292 0.4418 0.4525 0.4616 0.4693 0.4756 0.4808 0.4850 0.4884 0.4911 0.4932 0.4949 0.4962 0.4972 0.4979 0.4985 0.4989

0.0319 0.0714 0.1103 0.1480 0.1844 0.2190 0.2517 0.2823 0.3106 0.3365 0.3599 0.3810 0.3997 0.4162 0.4306 0.4429 0.4535 0.4625 0.4699 0.4761 0.4812 0.4854 0.4887 0.4913 0.4934 0.4951 0.4963 0.4973 0.4980 0.4986 0.4990

0.0359 0.0753 0.1141 0.1517 0.1879 0.2224 0.2549 0.2852 0.3133 0.3389 0.3621 0.3830 0.4015 0.4177 0.4319 0.4441 0.4545 0.4633 0.4706 0.4767 0.4817 0.4857 0.4890 0.4916 0.4936 0.4952 0.4964 0.4974 0.4981 0.4986 0.4990

This table can be used to calculate N(di), the cumulative normal distribution

functions needed for the Black-Scholes model of option pricing.

If di > 0, add 0.5 to the relevant number above.

If di < 0, subtract the relevant number above from 0.5




Chapter 1

Issues in corporate governance



CHAPTER 1 – ISSUES IN CORPORATE GOVERNANCE


CHAPTER CONTENTS

FINANCIAL OBJECTIVES ------------------------------------------------ 15

THE UK CORPORATE GOVERNANCE CODE ----------------------------- 17

CODE OF BEST PRACTICE 17

INTERNATIONAL COMPARISONS OF CORPORATE GOVERNANCE -- 36

UNITED STATES OF AMERICA 36

GERMANY 36

JAPAN 37





FINANCIAL OBJECTIVES

Advanced Financial Management is concerned with the following key decisions:

- What to invest in (INVESTMENT DECISIONS)

- How to finance the investment (FINANCING DECISIONS)

- The level of dividend distributions (DIVIDEND DECISIONS).

Objectives

Primary objective: to maximise the wealth of shareholders. A positive NPV equates

(in theory) to an increase in shareholder wealth.

Secondary objectives may be e.g. meeting financial targets (say satisfactory

ROCE), meeting productivity targets, establishing brands and quality standards and

effective communication with customers, suppliers, employees.

As an alternative to maximising the wealth of shareholders a company must in

reality consider satisficing objectives for each of the major stakeholders.

Stakeholders (user groups) and their goals

These include:

● Shareholders

Ownership is separate from control. Institutional investors may have different

requirements from private shareholders. Information is provided to

shareholders via published financial statements, forecasts by directors

responding to takeover bids, investment analysts and the financial press.

● Directors

The key decisions are made by directors, who are the stakeholders with the

most to lose – their jobs, their investments and their reputation. Does this

influence their decisions? Hence the extensive work on corporate governance

matters.

● Management and employees

Obviously they require long-term security and appropriate rewards

(pay/benefits). Should performance related incentives be offered e.g. share

options, long-term incentive plans (LTIPs)?

● Loan creditors

Covenants in loan agreements may restrict gearing and dividend levels and

the sale of assets. Loan creditors would have remedies if the company

defaults.

● Customers

No doubt these should be the most important interest group of all.

● Suppliers

Must be reliable – if not, consider internal production (vertical integration)

● The government

● Environmental pressure groups

● The general public

Many of these groups may have conflicting objectives, which need to be reconciled.





Corporate governance

Clearly the executive directors of a listed company are both decision-makers and

major stakeholders. They are therefore open to the accusation of making key

decisions for their own benefit. Following a number of notable financial scandals in

the UK during the late 20th century (e.g the Maxwell affair and the collapse of the

BCCI) the Cadbury Committee was set up to investigate procedures for appropriate

corporate governance.

The Cadbury Code (1992) defined corporate governance as “the system by which

companies are directed and controlled”. This initial document has been subject to

subsequent amendments by the Greenbury, Hampel and Higgs Reports. The

Financial Services Authority requires listed companies to confirm that they have

complied with the Code provisions or – in the event of non-compliance – to provide

an explanation of their reasons for departure.





THE UK CORPORATE GOVERNANCE CODE

Code of best practice

Section A: Leadership

A.1 The Role of the Board

Main Principle: Every company should be headed by an effective board

which is collectively responsible for the long-term success of the company.

Supporting Principles

The board’s role is to provide entrepreneurial leadership of the company

within a framework of prudent and effective controls which enables risk to be

assessed and managed. The board should set the company’s strategic aims,

ensure that the necessary financial and human resources are in place for the

company to meet its objectives and review management performance. The

board should set the company’s values and standards and ensure that its

obligations to its shareholders and others are understood and met.

All directors must act in what they consider to be the best interests of the

company, consistent with their statutory duties (as set out in the Companies

Act 2006).

Code Provisions

1.1 The board should meet sufficiently regularly to discharge its duties effectively.

There should be a formal schedule of matters specifically reserved for its

decision. The annual report should include a statement of how the board

operates, including a high level statement of which types of decisions are to

be taken by the board and which are to be delegated to management.

1.2 The annual report should identify the chairman, the deputy chairman (where

there is one), the chief executive, the senior independent director and the

chairmen and members of the board committees. It should also set out the

number of meetings of the board and its committees and individual

attendance by directors.

1.3 The company should arrange appropriate insurance cover in respect of legal

action against its directors.

A.2 Division of Responsibilities

Main Principle: There should be a clear division of responsibilities at the

head of the company between the running of the board and the executive

responsibility for the running of the company’s business. No one individual

should have unfettered powers of decision.

Code Provision

2.1 The roles of chairman and chief executive should not be exercised by the

same individual. The division of responsibilities between the chairman and

chief executive should be clearly established, set out in writing and agreed by

the board.





A.3 The Chairman

Main Principle: The chairman is responsible for leadership of the board and

ensuring its effectiveness on all aspects of its role.

Supporting Principle

The chairman is responsible for setting the board’s agenda and ensuring that

adequate time is available for discussion of all agenda items, in particular

strategic issues. The chairman should also promote a culture of openness and

debate by facilitating the effective contribution of non-executive directors in

particular and ensuring constructive relations between executive and non-

executive directors.

The chairman is responsible for ensuring that the directors receive accurate,

timely and clear information. The chairman should ensure effective

communication with shareholders.

Code Provision

3.1 The chairman should on appointment meet the independence criteria set out

in B.1.1 below. A chief executive should not go on to be chairman of the

same company. If, exceptionally, a board decides that a chief executive

should become chairman, the board should consult major shareholders in

advance and should set out its reasons to shareholders at the time of the

appointment and in the next annual report. (Compliance or otherwise with

this provision need only be reported for the year in which the appointment is

made).

A.4 Non-executive Directors

Main Principle: As part of their role as members of a unitary board, non-

executive directors should constructively challenge and help develop

proposals on strategy.


Non-executive directors should scrutinise the performance of management in

meeting agreed goals and objectives and monitor the reporting of

performance. They should satisfy themselves on the integrity of financial

information and that financial controls and systems of risk management are

robust and defensible. They are responsible for determining appropriate

levels of remuneration of executive directors and have a prime role in

appointing and, where necessary, removing executive directors, and in

succession planning.

Code Provisions

4.1 The board should appoint one of the independent non-executive directors to

be the senior independent director to provide a sounding board for the

chairman and to serve as an intermediary for the other directors when

necessary. The senior independent director should be available to

shareholders if they have concerns which contact through the normal

channels of chairman, chief executive or other executive directors has failed

to resolve or for which such contact is inappropriate.

4.2 The chairman should hold meetings with the non-executive directors without

the executives present. Led by the senior independent director, the non-





executive directors should meet without the chairman present at least

annually to appraise the chairman’s performance and on such other occasions

as are deemed appropriate.

4.3 Where directors have concerns which cannot be resolved about the running of

the company or a proposed action, they should ensure that their concerns are

recorded in the board minutes. On resignation, a non- executive director

should provide a written statement to the chairman, for circulation to the

board, if they have any such concerns.

Section B: Effectiveness

B.1 The Composition of the Board

Main Principle: The board and its committees should have the appropriate

balance of skills, experience, independence and knowledge of the company

to enable them to discharge their respective duties and responsibilities

effectively.


The board should be of sufficient size that the requirements of the business

can be met and that changes to the board’s composition and that of its

committees can be managed without undue disruption, and should not be so

large as to be unwieldy.

The board should include an appropriate combination of executive and non-

executive directors (and, in particular, independent non-executive directors)

such that no individual or small group of individuals can dominate the board’s

decision taking.

The value of ensuring that committee membership is refreshed and that

undue reliance is not placed on particular individuals should be taken into

account in deciding chairmanship and membership of committees.

No one other than the committee chairman and members is entitled to be

present at a meeting of the nomination, audit or remuneration committee, but

others may attend at the invitation of the committee.

Code Provisions

1.1 The board should identify in the annual report each non-executive director it

considers to be independent. The board should determine whether the

director is independent in character and judgement and whether there are

relationships or circumstances which are likely to affect, or could appear to

affect, the director’s judgement. The board should state its reasons if it

determines that a director is independent notwithstanding the existence of

relationships or circumstances which may appear relevant to its

determination, including if the director:

● has been an employee of the company or group within the last five

years;

● has, or has had within the last three years, a material business

relationship with the company either directly, or as a partner,

shareholder, director or senior employee of a body that has such a

relationship with the company;





● has received or receives additional remuneration from the company

apart from a director’s fee, participates in the company’s share option or

a performance-related pay scheme, or is a member of the company’s

pension scheme;

● has close family ties with any of the company’s advisers, directors or

senior employees;

● holds cross-directorships or has significant links with other directors

through involvement in other companies or bodies;

● represents a significant shareholder; or

● has served on the board for more than nine years from the date of their

first election.

1.2 Except for smaller companies (i.e. those below the FTSE 350 throughout the

year immediately prior to the reporting year), at least half the board,

excluding the chairman, should comprise non-executive directors determined

by the board to be independent. A smaller company should have at least two

independent non-executive directors.

B.2 Appointments to the Board

Main Principle: There should be a formal, rigorous and transparent

procedure for the appointment of new directors to the board.


The search for board candidates should be conducted, and appointments

made, on merit, against objective criteria and with due regard for the benefits

of diversity on the board, including gender.

The board should satisfy itself that plans are in place for orderly succession

for appointments to the board and to senior management, so as to maintain

an appropriate balance of skills and experience within the company and on

the board and to ensure progressive refreshing of the board.

Code Provisions

2.1 There should be a nomination committee which should lead the process for

board appointments and make recommendations to the board. A majority of

members of the nomination committee should be independent non-executive

directors. The chairman or an independent non-executive director should

chair the committee, but the chairman should not chair the nomination

committee when it is dealing with the appointment of a successor to the

chairmanship. The nomination committee should make available its terms of

reference, explaining its role and the authority delegated to it by the board.

(This requirement would be met by including the information on the company

website).

2.2 The nomination committee should evaluate the balance of skills, experience,

independence and knowledge on the board and, in the light of this evaluation,

prepare a description of the role and capabilities required for a particular

appointment.

2.3 Non-executive directors should be appointed for specified terms subject to re-

election and to statutory provisions relating to the removal of a director. Any

term beyond six years for a non-executive director should be subject to





particularly rigorous review, and should take into account the need for

progressive refreshing of the board.

2.4 A separate section of the annual report should describe the work of the

nomination committee, including the process it has used in relation to board

appointments. An explanation should be given if neither an external search

consultancy nor open advertising has been used in the appointment of a

chairman or a non-executive director.

B.3 Commitment

Main Principle: All directors should be able to allocate sufficient time to the

company to discharge their responsibilities effectively.

Code Provisions

3.1 For the appointment of a chairman, the nomination committee should prepare

a job specification, including an assessment of the time commitment

expected, recognising the need for availability in the event of crises. A

chairman’s other significant commitments should be disclosed to the board

before appointment and included in the annual report. Changes to such

commitments should be reported to the board as they arise, and their impact

explained in the next annual report.

3.2 The terms and conditions of appointment of non-executive directors should be

made available for inspection (at the company’s registered office and at the

AGM). The letter of appointment should set out the expected time

commitment. Non-executive directors should undertake that they will have

sufficient time to meet what is expected of them. Their other significant

commitments should be disclosed to the board before appointment, with a

broad indication of the time involved and the board should be informed of

subsequent changes.

3.3 The board should not agree to a full time executive director taking on more

than one non-executive directorship in a FTSE 100 company nor the

chairmanship of such a company.

B.4 Development

Main Principle: All directors should receive induction on joining the board

and should regularly update and refresh their skills and knowledge.


The chairman should ensure that the directors continually update their skills

and the knowledge and familiarity with the company required to fulfil their

role both on the board and on board committees. The company should

provide the necessary resources for developing and updating its directors’

knowledge and capabilities.

To function effectively, all directors need appropriate knowledge of the

company and access to its operations and staff.





Code Provisions

4.1 The chairman should ensure that new directors receive a full, formal and

tailored induction on joining the board. As part of this, directors should avail

themselves of opportunities to meet major shareholders.

4.2 The chairman should regularly review and agree with each director their

training and development needs.

B.5 Information and Support

Main Principle: The board should be supplied in a timely manner with

information in a form and of a quality appropriate to enable it to discharge

its duties.


The chairman is responsible for ensuring that the directors receive accurate,

timely and clear information. Management has an obligation to provide such

information but directors should seek clarification or amplification where

necessary.

Under the direction of the chairman, the company secretary’s responsibilities

include ensuring good information flows within the board and its committees

and between senior management and non-executive directors, as well as

facilitating induction and assisting with professional development as required.

The company secretary should be responsible for advising the board through

the chairman on all governance matters.

Code Provisions

5.1 The board should ensure that directors, especially non-executive directors,

have access to independent professional advice at the company’s expense

where they judge it necessary to discharge their responsibilities as directors.

Committees should be provided with sufficient resources to undertake their

duties.

5.2 All directors should have access to the advice and services of the company

secretary, who is responsible to the board for ensuring that board procedures

are complied with. Both the appointment and removal of the company

secretary should be a matter for the board as a whole.

B.6 Evaluation

Main Principle: The board should undertake a formal and rigorous annual

evaluation of its own performance and that of its committees and

individual directors.


The chairman should act on the results of the performance evaluation by

recognising the strengths and addressing the weaknesses of the board and,

where appropriate, proposing new members be appointed to the board or

seeking the resignation of directors.

Individual evaluation should aim to show whether each director continues to

contribute effectively and to demonstrate commitment to the role (including

commitment of time for board and committee meetings and any other duties).





Code Provisions

6.1 The board should state in the annual report how performance evaluation of

the board, its committees and its individual directors has been conducted.

6.2 Evaluation of the board of FTSE 350 companies should be externally facilitated

at least every three years. A statement should be made available of whether

an external facilitator has any other connection with the company. (This

requirement would be met by including the information on the company

website).

6.3 The non-executive directors, led by the senior independent director, should be

responsible for performance evaluation of the chairman, taking into account

the views of executive directors.

B.7 Re-election

Main Principle: All directors should be submitted for re-election at regular

intervals, subject to continued satisfactory performance.

Code Provisions

7.1 All directors of FTSE 350 companies should be subject to annual election by

shareholders. All other directors should be subject to election by shareholders

at the first annual general meeting (AGM) after their appointment, and to re-

election thereafter at intervals of no more than three years. Non-executive

directors who have served longer than nine years should be subject to annual

re-election. The names of directors submitted for election or re-election

should be accompanied by sufficient biographical details and any other

relevant information to enable shareholders to take an informed decision on

their election.

7.2 The board should set out to shareholders in the papers accompanying a

resolution to elect a non-executive director why they believe an individual

should be elected. The chairman should confirm to shareholders when

proposing re-election that, following formal performance evaluation, the

individual’s performance continues to be effective and to demonstrate

commitment to the role.

Section C: Accountability

C.1 Financial and Business Reporting

Main Principle: The board should present a balanced and understandable

assessment of the company’s position and prospects.


The board’s responsibility to present a balanced and understandable

assessment extends to interim and other price-sensitive public reports and

reports to regulators as well as to information required to be presented by

statutory requirements.

Code Provisions

1.1 The directors should explain in the annual report their responsibility for

preparing the annual report and accounts, and there should be a statement by

the auditor about their reporting responsibilities.





1.2 The directors should include in the annual report an explanation of the basis

on which the company generates or preserves value over the longer term (the

business model) and the strategy for delivering the objectives of the company

(This explanation would ideally be located within the Business Review required

by CA 2006).

1.3 The directors should report in annual and half-yearly financial statements that

the business is a going concern, with supporting assumptions or qualifications

as necessary.

C.2 Risk Management and Internal Control

(The Turnbull Guidance, last updated in October 2005, suggests means of

applying this part of the Code)

Main Principle: The board is responsible for determining the nature and

extent of the significant risks it is willing to take in achieving its strategic

objectives. The board should maintain sound risk management and

internal control systems.

Code provision

2.1 The board should, at least annually, conduct a review of the effectiveness of

the company’s risk management and internal control systems and should

report to shareholders that they have done so. The review should cover all

material controls, including financial, operational and compliance controls.

C.3 Audit Committee and Auditors

(The FRC ‘Guidance on Audit Committees’ - formerly referred to as the Smith

Guidance - suggests means of applying this part of the Code)

Main Principle: The board should establish formal and transparent

arrangements for considering how they should apply the corporate

reporting and risk management and internal control principles and for

maintaining an appropriate relationship with the company’s auditor.

Code provisions

3.1 The board should establish an audit committee of at least three, or in the case

of smaller companies (i.e. those below the FTSE 350 throughout the year

immediately prior to the reporting year) two, independent non-executive

directors. In smaller companies the company chairman may be a member of,

but not chair, the committee in addition to the independent non-executive

directors, provided he or she was considered independent on appointment as

chairman. The board should satisfy itself that at least one member of the

audit committee has recent and relevant financial experience.

3.2 The main role and responsibilities of the audit committee should be set out in

written terms of reference and should include:

● to monitor the integrity of the financial statements of the company and

any formal announcements relating to the company’s financial

performance, reviewing significant financial reporting judgements

contained in them;

● to review the company’s internal financial controls and, unless expressly

addressed by a separate board risk committee composed of independent





directors, or by the board itself, to review the company’s internal control

and risk management systems;

● to monitor and review the effectiveness of the company’s internal audit

function;

● to make recommendations to the board, for it to put to the shareholders

for their approval in general meeting, in relation to the appointment, re-

appointment and removal of the external auditor and to approve the

remuneration and terms of engagement of the external auditor;

● to review and monitor the external auditor’s independence and

objectivity and the effectiveness of the audit process, taking into

consideration relevant UK professional and regulatory requirements;

● to develop and implement policy on the engagement of the external

auditor to supply non-audit services, taking into account relevant ethical

guidance regarding the provision of non-audit services by the external

audit firm, and to report to the board, identifying any matters in respect

of which it considers that action or improvement is needed and making

recommendations as to the steps to be taken.

3.3 The terms of reference of the audit committee, including its role and the

authority delegated to it by the board, should be made available (e.g. by

including the information on the company website). A separate section of the

annual report should describe the work of the committee in discharging those

responsibilities.

3.4 The audit committee should review arrangements by which staff of the

company may, in confidence, raise concerns about possible improprieties in

matters of financial reporting or other matters. The audit committee’s

objective should be to ensure that arrangements are in place for the

proportionate and independent investigation of such matters and for

appropriate follow-up action.

3.5 The audit committee should monitor and review the effectiveness of the

internal audit activities. Where there is no internal audit function, the audit

committee should consider annually whether there is a need for an internal

audit function and make a recommendation to the board, and the reasons for

the absence of such a function should be explained in the relevant section of

the annual report.

3.6 The audit committee should have primary responsibility for making a

recommendation on the appointment, re-appointment and removal of the

external auditor. If the board does not accept the audit committee’s

recommendation, it should include in the annual report, and in any papers

recommending appointment or re-appointment, a statement from the audit

committee explaining the recommendation and should set out reasons why

the board has taken a different position.

3.7 The annual report should explain to shareholders how, if the auditor provides

non-audit services, auditor objectivity and independence is safeguarded.





Section D: Remuneration

D.1 The Level and Components of Remuneration

Main Principle: Levels of remuneration should be sufficient to attract,

retain and motivate directors of the quality required to run the company

successfully, but a company should avoid paying more than is necessary

for this purpose. A significant proportion of executive directors’

remuneration should be structured so as to link rewards to corporate and

individual performance.


The performance-related elements of executive directors’ remuneration should

be stretching and designed to promote the long-term success of the company.

The remuneration committee should judge where to position their company

relative to other companies. But they should use such comparisons with

caution, in view of the risk of an upward ratchet of remuneration levels with

no corresponding improvement in performance.

They should also be sensitive to pay and employment conditions elsewhere in

the group, especially when determining annual salary increases.

Code Provisions

1.1 In designing schemes of performance-related remuneration for executive

directors, the remuneration committee should follow the provisions in

Schedule A to this Code.

1.2 Where a company releases an executive director to serve as a non-executive

director elsewhere, the remuneration report (required by UK legislation)

should include a statement as to whether or not the director will retain such

earnings and, if so, what the remuneration is.

1.3 Levels of remuneration for non-executive directors should reflect the time

commitment and responsibilities of the role. Remuneration for non-executive

directors should not include share options or other performance- related

elements. If, exceptionally, options are granted, shareholder approval should

be sought in advance and any shares acquired by exercise of the options

should be held until at least one year after the non-executive director leaves

the board. Holding of share options could be relevant to the determination of

a non-executive director’s independence (as set out in provision B.1.1).

1.4 The remuneration committee should carefully consider what compensation

commitments (including pension contributions and all other elements) their

directors’ terms of appointment would entail in the event of early termination.

The aim should be to avoid rewarding poor performance. They should take a

robust line on reducing compensation to reflect departing directors’

obligations to mitigate loss.

1.5 Notice or contract periods should be set at one year or less. If it is necessary

to offer longer notice or contract periods to new directors recruited from

outside, such periods should reduce to one year or less after the initial period.





D.2 Procedure

Main Principle: There should be a formal and transparent procedure for

developing policy on executive remuneration and for fixing the

remuneration packages of individual directors. No director should be

involved in deciding his or her own remuneration.


The remuneration committee should consult the chairman and/or chief

executive about their proposals relating to the remuneration of other

executive directors. The remuneration committee should also be responsible

for appointing any consultants in respect of executive director remuneration.

Where executive directors or senior management are involved in advising or

supporting the remuneration committee, care should be taken to recognise

and avoid conflicts of interest.

The chairman of the board should ensure that the company maintains contact

as required with its principal shareholders about remuneration.

Code Provisions

2.1 The board should establish a remuneration committee of at least three, or in

the case of smaller companies two, independent non-executive directors. In

addition the company chairman may also be a member of, but not chair, the

committee if he or she was considered independent on appointment as

chairman. The remuneration committee should make available its terms of

reference, explaining its role and the authority delegated to it by the board.

Where remuneration consultants are appointed, a statement should be made

available of whether they have any other connection with the company (This

requirement would be met by including the information on the company

website).

2.2 The remuneration committee should have delegated responsibility for setting

remuneration for all executive directors and the chairman, including pension

rights and any compensation payments. The committee should also

recommend and monitor the level and structure of remuneration for senior

management. The definition of ‘senior management’ for this purpose should

be determined by the board but should normally include the first layer of

management below board level.

2.3 The board itself or, where required by the Articles of Association, the

shareholders should determine the remuneration of the non-executive

directors within the limits set in the Articles of Association. Where permitted

by the Articles, the board may however delegate this responsibility to a

committee, which might include the chief executive.

2.4 Shareholders should be invited specifically to approve all new long-term

incentive schemes (as defined in the Listing Rules) and significant changes to

existing schemes, save in the circumstances permitted by the Listing Rules.





Section E: Relations with shareholders

E.1 Dialogue with Shareholders

Main Principle: There should be a dialogue with shareholders based on the

mutual understanding of objectives. The board as a whole has

responsibility for ensuring that a satisfactory dialogue with shareholders

takes place.


Whilst recognising that most shareholder contact is with the chief executive

and finance director, the chairman should ensure that all directors are made

aware of their major shareholders’ issues and concerns.

The board should keep in touch with shareholder opinion in whatever ways

are most practical and efficient.

Code Provisions

1.1 The chairman should ensure that the views of shareholders are communicated

to the board as a whole. The chairman should discuss governance and

strategy with major shareholders. Non-executive directors should be offered

the opportunity to attend scheduled meetings with major shareholders and

should expect to attend meetings if requested by major shareholders. The

senior independent director should attend sufficient meetings with a range of

major shareholders to listen to their views in order to help develop a balanced

understanding of the issues and concerns of major shareholders.

1.2 The board should state in the annual report the steps they have taken to

ensure that the members of the board, and, in particular, the non-executive

directors, develop an understanding of the views of major shareholders about

the company, for example through direct face-to-face contact, analysts’ or

brokers’ briefings and surveys of shareholder opinion.

E.2 Constructive Use of the AGM

Main Principle: The board should use the AGM to communicate with

investors and to encourage their participation.

Code Provisions

2.1 At any general meeting, the company should propose a separate resolution on

each substantially separate issue, and should, in particular, propose a

resolution at the AGM relating to the report and accounts. For each

resolution, proxy appointment forms should provide shareholders with the

option to direct their proxy to vote either for or against the resolution or to

withhold their vote. The proxy form and any announcement of the results of

a vote should make it clear that a ‘vote withheld’ is not a vote in law and will

not be counted in the calculation of the proportion of the votes for and against

the resolution.

2.2 The company should ensure that all valid proxy appointments received for

general meetings are properly recorded and counted. For each resolution,

where a vote has been taken on a show of hands, the company should ensure

that the following information is given at the meeting and made available as





soon as reasonably practicable on a website which is maintained by or on

behalf of the company:

● the number of shares in respect of which proxy appointments have been

validly made;

● the number of votes for the resolution;

● the number of votes against the resolution; and

● the number of shares in respect of which the vote was directed to be

withheld.

2.3 The chairman should arrange for the chairmen of the audit, remuneration and

nomination committees to be available to answer questions at the AGM and

for all directors to attend.

2.4 The company should arrange for the Notice of the AGM and related papers to

be sent to shareholders at least 20 working days before the meeting.

Schedule A: The design of performance-related

remuneration for executive directors

The remuneration committee should consider whether the directors should be

eligible for annual bonuses. If so, performance conditions should be relevant,

stretching and designed to promote the long-term success of the company. Upper

limits should be set and disclosed. There may be a case for part payment in shares

to be held for a significant period.

The remuneration committee should consider whether the directors should be

eligible for benefits under long-term incentive schemes. Traditional share option

schemes should be weighed against other kinds of long-term incentive scheme.

Executive share options should not be offered at a discount save as permitted by

the relevant provisions of the Listing Rules.

In normal circumstances, shares granted or other forms of deferred remuneration

should not vest, and options should not be exercisable, in less than three years.

Directors should be encouraged to hold their shares for a further period after

vesting or exercise, subject to the need to finance any costs of acquisition and

associated tax liabilities.

Any new long-term incentive schemes which are proposed should be approved by

shareholders and should preferably replace any existing schemes or, at least, form

part of a well considered overall plan incorporating existing schemes. The total

potentially available rewards should not be excessive.

Payouts or grants under all incentive schemes, including new grants under existing

share option schemes, should be subject to challenging performance criteria

reflecting the company’s objectives, including non-financial performance metrics

where appropriate. Remuneration incentives should be compatible with risk policies

and systems.

Grants under executive share option and other long-term incentive schemes should

normally be phased rather than awarded in one large block.

Consideration should be given to the use of provisions that permit the company to

reclaim variable components in exceptional circumstances of misstatement or

misconduct.

In general, only basic salary should be pensionable. The remuneration committee

should consider the pension consequences and associated costs to the company of





basic salary increases and any other changes in pensionable remuneration,

especially for directors close to retirement.

Schedule B: Disclosure of corporate governance

arrangements

Corporate governance disclosure requirements are set out in three places:

● FSA Disclosure and Transparency Rules, which set out certain mandatory

disclosures;

● FSA Listing Rules, which include the ‘comply or explain’ requirement; and

● The UK Corporate Governance Code (in addition to providing an explanation

where they choose not to comply with a provision, companies must disclose

specified information in order to comply with certain provisions).

These requirements are summarised below. There is some overlap between the

mandatory disclosures required under the Disclosure and Transparency Rules and

those expected under the UK Corporate Governance Code. Areas of overlap are

summarised in the Appendix to this Schedule. In respect of disclosures relating to

the audit committee and the composition and operation of the board and its

committees, compliance with the relevant provisions of the Code will result in

compliance with the relevant Rules.

Disclosure and Transparency Rules

The Disclosure and Transparency Rules (DTR) concern audit committees or bodies

carrying out equivalent functions.

DTR set out requirements relating to the composition and functions of the

committee or equivalent body:

● An issuer must have a body which is responsible for performing the functions

set out below, and at least one member of that body must be independent

and at least one member must have competence in accounting and/or

auditing.

● The requirements for independence and competence in accounting and/or

auditing may be satisfied by the same member or by different members of the

relevant body.

● An issuer must ensure that, as a minimum, the relevant body must:

(1) monitor the financial reporting process;

(2) monitor the effectiveness of the issuer’s internal control, internal audit

where applicable, and risk management systems;

(3) monitor the statutory audit of the annual and consolidated accounts;

(4) review and monitor the independence of the statutory auditor, and in

particular the provision of additional services to the issuer.

The following disclosures are required:

● The issuer must make a statement available to the public disclosing

which body carries out the above functions and how it is composed.

This can be included in the corporate governance statement as described

below.





● Compliance with the relevant provisions of the UK Corporate Governance

Code (as set out in the Appendix to this Schedule) will result in

compliance with much of the DTR.

● Issuers are required to produce a corporate governance statement that

must be either included in the directors’ report; or in a separate report

published together with the annual report; or on the issuer’s website, in

which case there must be a cross-reference in the directors’ report.

● DTR requires that the corporate governance statements must contain a

reference to the corporate governance code to which the company is

subject (for companies with a Premium listing this is the UK Corporate

Governance Code). DTR requires that, to the extent that it departs from

that code, the company must explain which parts of the code it departs

from and the reasons for doing so. Compliance with the ‘comply or

explain’ rule will also satisfy these requirements.

● DTR sets out certain information that must be disclosed in the corporate

governance statement i.e. the statement must contain:

o A description of the main features of the company’s internal control

and risk management systems in relation to the financial reporting

process. DTR states that an issuer which is required to prepare a

group directors’ report must include in that report a description of

the main features of the group’s internal control and risk

management systems in relation to the process for preparing

consolidated accounts.

o The information required by SI 2008 No. 410 [The Large and

Medium-sized Companies and Groups (Accounts and Reports)

Regulations 2008], where the issuer is subject to its requirements.

o A description of the composition and operation of the issuer’s

administrative, management and supervisory bodies and their

committees. Compliance with the provisions of the UK Corporate

Governance Code (as set out in the Appendix to this Schedule) will

satisfy the requirements of DTR.

Listing Rules

The Listing Rules state that in the case of a company that has a Premium listing of

equity shares, the following items must be included in its annual report and

accounts:

● a statement of how the listed company has applied the Main Principles set out

in the UK Corporate Governance Code, in a manner that would enable

shareholders to evaluate how the principles have been applied;

● a statement as to whether the listed company has:

o complied throughout the accounting period with all relevant provisions

set out in the UK Corporate Governance Code; or

o not complied throughout the accounting period with all relevant

provisions set out in the UK Corporate Governance Code, and if so,

setting out:

(i) those provisions, if any, it has not complied with;





(ii) in the case of provisions whose requirements are of a continuing

nature, the period within which, if any, it did not comply with some

or all of those provisions; and

(iii) the company’s reasons for non-compliance.

The UK Corporate Governance Code

In addition to the ‘comply or explain’ requirement in the Listing Rules, the Code

includes specific requirements for disclosure which must be provided in order to

comply.

The annual report should include:

● a statement of how the board operates, including a high level statement of

which types of decisions are to be taken by the board and which are to be

delegated to management;

● the names of the chairman, the deputy chairman (where there is one), the

chief executive, the senior independent director and the chairmen and

members of the board committees;

● the number of meetings of the board and those committees and individual

attendance by directors;

● where a chief executive is appointed chairman, the reasons for their

appointment (this only needs to be done in the annual report following the

appointment);

● the names of the non-executive directors whom the board determines to be

independent, with reasons where necessary;

● a separate section describing the work of the nomination committee, including

the process it has used in relation to board appointments and an explanation

if neither external search consultancy nor open advertising has been used in

the appointment of a chairman or a non-executive director;

● any changes to the other significant commitments of the chairman during the

year;

● a statement of how performance evaluation of the board, its committees and

its directors has been conducted;

● an explanation from the directors of their responsibility for preparing the

accounts and a statement by the auditors about their reporting

responsibilities;

● an explanation from the directors of the basis on which the company

generates or preserves value over the longer term (the business model) and

the strategy for delivering the objectives of the company;

● a statement from the directors that the business is a going concern, with

supporting assumptions or qualifications as necessary;

● a report that the board has conducted a review of the effectiveness of the

company’s risk management and internal control systems;

● a separate section describing the work of the audit committee in discharging

its responsibilities;

● where there is no internal audit function, the reasons for the absence of such

a function;





● where the board does not accept the audit committee’s recommendation on

the appointment, re-appointment or removal of an external auditor, a

statement from the audit committee explaining the recommendation and the

reasons why the board has taken a different position;

● an explanation of how, if the auditor provides non-audit services, auditor

objectively and independence is safeguarded;

● a description of the work of the remuneration committee as required under

the Large and Medium-Sized Companies and Groups (Accounts and Reports)

Regulations 2008 including, where an executive director serves as a non-

executive director elsewhere, whether or not the director will retain such

earnings and, if so, what the remuneration is;

● the steps the board has taken to ensure that members of the board, in

particular the non-executive directors, develop an understanding of the views

of major shareholders about their company.

The following information should be made available (which may be met by placing

the information on a website that is maintained by or on behalf of the company):

● the terms of reference of the nomination, audit and remuneration committees,

explaining their role and the authority delegated to them by the board;

● the terms and conditions of appointment of non-executive directors;

● where performance evaluation has been externally facilitated, a statement of

whether the facilitator has any other connection with the company; and

● where remuneration consultants are appointed, a statement of whether they

have any other connection with the company.

The board should set out to shareholders in the papers accompanying a resolution

to elect or re-elect directors:

● sufficient biographical details to enable shareholders to take an informed

decision on their election or re-election;

● why they believe an individual should be elected to a non-executive role; and

● on re-election of a non-executive director, confirmation from the chairman

that, following formal performance evaluation, the individual’s performance

continues to be effective and to demonstrate commitment to the role.

The board should set out to shareholders in the papers recommending appointment

or reappointment of an external auditor:

● if the board does not accept the audit committee’s recommendation, a

statement from the audit committee explaining the recommendation and from

the board setting out reasons why they have taken a different position.

Additional guidance

The Turnbull Guidance and FRC Guidance on Audit Committees contain further

suggestions as to information that might usefully be disclosed in the internal control

statement and the report of the audit committee respectively.





Appendix: Overlap between the disclosure and transparency rules and the UK Corporate Governance Code

DISCLOSURE AND TRANSPARENCY

RULES

UK CORPORATE GOVERNANCE CODE

Sets out minimum requirements on

composition of the audit committee or

equivalent body.

Provision C.3.1

Sets out recommended composition of

the audit committee.

Sets out minimum functions of the audit

committee or equivalent body.

Provision C.3.2

Sets out the recommended minimum

terms of reference for the audit

committee.

The composition and function of the

audit committee or equivalent body must

be disclosed in the annual report.

Provision A.1.2

The annual report should identify

members of the board committees.

Provision C.3.3

The annual report should describe the

work of the audit committee. Further

recommendations on the content of the

audit committee report are set out in

the FRC Guidance on Audit Committees.

The corporate governance statement

must include a description of the main

features of the company’s internal

control and risk management systems in

relation to the financial reporting

process.

Provision C.2.1

The Board must report that a review of

the effectiveness of the risk

management and internal control

systems has been carried out. Further

recommendations on the content of the

internal control statement are set out in

the Turnbull Guidance.

The corporate governance statement

must include a description of the

composition and operation of the

administrative, management and

supervisory bodies and their

committees.

This requirement overlaps with a

number of different provisions of the

Code:

A.1.1: the annual report should include

a statement of how the board operates.

A.1.2: the annual report should identify

members of the board and board

committees.





B.2.4: the annual report should

describe the work of the nomination

committee.

C.3.3: the annual report should

describe the work of the audit

committee.

D.2.1: a description of the work of the

remuneration committee should be

made available. [Note: in order to

comply with DTR this information will

need to be included in the corporate

governance statement].

Schedule C: Engagement principles for institutional

shareholders

This schedule has been superseded by the “Stewardship Code” for institutional

investors.

Principle 1: Dialogue with companies

Main Principle: Institutional shareholders should enter into a dialogue

with companies based on the mutual understanding of objectives.

Principle 2: Evaluation of Governance Disclosures

Main Principle: When evaluating companies’ governance arrangements,

particularly those relating to board structure and composition, institutional

shareholders should give due weight to all relevant factors drawn to their

attention.

Principle 3: Shareholder Voting

Main Principle: Institutional shareholders have a responsibility to make

considered use of their votes.





INTERNATIONAL COMPARISONS OF CORPORATE

GOVERNANCE

The broad principles of corporate governance are similar in the UK, the USA and

Germany, but there are significant differences in how they are applied. Whereas

the UK and Germany have voluntary corporate governance codes, the US system is

based upon legislation within the Sarbanes-Oxley Act.

United States of America

Whereas the UK has historically relied upon a system of self-regulation and

voluntary codes of best practice, the USA corporate governance structure is more

formalised, with legally enforceable controls.

In the US, statutory requirements for publicly-traded companies are set out in the

Sarbanes-Oxley Act. These requirements include the certification of published

financial statements by the CEO and the chief financial officer (CFO), faster public

disclosures by companies, legal protection for whistleblowers, a requirement for an

annual report on internal controls, and requirements relating to the audit

committee, auditor conduct and avoiding ‘improper’ influence of auditors.

The Act also requires the Securities and Exchange Commission (SEC) and the main

stock exchanges to introduce further rules, relating to matters such as the

disclosure of critical accounting policies, the composition of the Board and the

number of independent directors. The Act has also established an independent

body to oversee the accounting profession, which is known as the Public Company

Accounting Oversight Board. Managers must be careful to comply with regulations

to avoid possible legal action against the company or themselves individually.

Germany

As both the UK and Germany are members of the EU, they must both follow EU

directives on company law. A major difference that exists in the board structure for

companies is that the UK has a unitary board (consisting of both executive and

non-executive directors), whereas German companies have a two-tier board of

directors. The Supervisory Board of non-executives (Aufsichtsrat) has

responsibility for corporate policy and strategy and the Management Board of

executive directors (Vorstand) has responsibility primarily for the day-to-day

operations of the company.

The Supervisory Board typically includes representatives from major banks that

have historically been large providers of long-term finance to German companies

(and are often major shareholders). The Supervisory Board does not have full

access to financial information, is meant to take an unbiased overview of the

company, and is the main body responsible for safeguarding the external

stakeholders’ interests. The presence on the Supervisory Board of representatives

from banks and employees (trade unions) may introduce perspectives that are not

present in some UK boards. In particular, many members of the Supervisory Board

would not meet the criteria under UK Corporate Governance Code for their

independence.





Japan

Although there are signs of change in Japanese corporate governance, much of the

system is based upon negotiation or consensual management rather than upon a

legal or even a self-regulatory framework. Banks as well as representatives of

other companies (in their capacity as shareholders) also sit on the Boards of

Directors of Japanese companies.

It is not uncommon for Japanese companies to have cross holdings of shares with

their suppliers, customers and banks etc., all being represented on each others

Board of Directors. There are often three boards of directors: Policy Boards,

responsible for strategy and comprised of directors with no functional responsibility;

Functional Boards, responsible for day to day operations; and largely symbolic

Monocratic Boards. The interests of the company as a whole should dictate the

actions of these boards. This is in contrast to the UK or USA systems where, at

least in theory, the board should act primarily in the best interests of the

shareholders, being the owners of the company.




Chapter 2

Advanced investment

appraisal – section 1



CHAPTER 2 – ADVANCED INVESTMENT APPRAISAL: SECTION 1


CHAPTER CONTENTS

INVESTMENT APPRAISAL TECHNIQUES ------------------------------- 41

1. ACCOUNTING RATE OF RETURN 41

2. PAYBACK PERIOD 42

3. DISCOUNTED CASH FLOW 42

CONGO LTD --------------------------------------------------------------- 44

INFLATION AND DISCOUNTED CASH FLOW -------------------------- 48

‘MONEY’ CASH FLOWS 48

‘REAL’ CASH FLOWS 48

RELATIONSHIP BETWEEN MONEY INTEREST RATES AND REAL INTEREST RATES 48

TAXATION AND INVESTMENT APPRAISAL ---------------------------- 50

CAPITAL RATIONING ---------------------------------------------------- 52

WHAT ARE THE 2 TYPES OF CAPITAL RATIONING? 52

CAPITAL RATIONING AND TIME 52

SINGLE PERIOD CAPITAL RATIONING 53

MULTI-PERIOD CAPITAL RATIONING 56





INVESTMENT APPRAISAL TECHNIQUES

Assumed objective is –

Selection of those projects which will maximise the wealth of the owners (or

shareholders) of the enterprise. Involves a consideration of FUTURE events, not

PAST performance.

Accepted techniques are –

1. Accounting Rate of Return (alternatively called Return on Investment)

2. Payback Period

3. Discounted Cash Flow, of which there are two major variants:

(a) Net Present Value

(b) Internal Rate of Return (alternatively called Yield)

1. Accounting rate of return

The ARR (or ROI) is a measure of relative project profitability, which expresses:

1. The expected average annual profit (after allowing for depreciation, but before

taxation) emerging from a project,

AS A PERCENTAGE OF

2. The investment involved. Normally the average investment over the life of the

project is used, but initial investment is sometimes employed.

Advantages

● It is relatively easy to understand

● The required figures are readily available from accounting data.

● The ROI technique is frequently used as an assessment of management’s

actual (hindsight) performance.

● It gives an indication as to whether available projects are meeting target

returns on capital employed.

Disadvantages

● Based on accounting profits not cash flows - the success of an enterprise

depends on its ability to generate cash. The ability to invest depends on

availability of cash.

● Ignores the time value of money

● It is relative rate of return, thus ignores the size of the project

● No set rules (theoretical or practical) for determining the cut-off rate of

return.





2. Payback period

The Payback Period demonstrates how long an enterprise must expect to wait

before the after-tax cash flows generated by the project allow it to recoup the initial

amount invested. Thus it gives an investor an idea of “how long their money will

be at risk”; a short payback period is taken to reveal low risk, and a long payback -

high risk.

Advantages

● The most tried and tested of all methods

● Easy to calculate and understand

● An enterprise with limited cash resources is obviously concerned with speed of

return.

● Some companies combine DCF techniques with the payback method.

Disadvantages

● Does not measure profitability nor increases in shareholders wealth, since it

ignores cash flows expected to arise beyond the payback period.

● Ignores the time value of money (but discounted payback sometimes used).

● No set rules (theoretical or practical) for determining the minimum acceptable

payback period.

● May be difficult to measure the initial amount invested when e.g. net outlays

arise in both the initial and final years of a project.

3. Discounted cash flow

DCF is a method of capital investment appraisal which takes account of:

1. The overall cash flows arising from projects, and

2. The timing of those cash flows.

Only relevant cash flows are considered (i.e. those future cash flows which arise as

a result of those projects) and the timing effect is incorporated by means of the

discounting technique.

Both the Accounting Rate of Return and the Payback approaches are surpassed by

the DCF methods. The basic arguments are:

● it is better to consider cash rather than profits because cash is how investors

will eventually see their rewards (i.e. dividends, interest, or the proceeds from

the sale of the shares or debentures).

● the timing of the cash flows is important because early cash receipts can be

reinvested to earn interest.

● it is important to consider the cash flows arising over the entire life of a

project.

The technique of discounting reduces all future cash flows to current equivalent

values (present values) by allowing for the interest which could have been earned if

the cash had been received immediately.

There are two common techniques, net present value and internal rate of return,

but net terminal value can be used.





DCF – Net present value

The NPV of a project is the net value of a project’s cash flows after discounting (i.e.

allowing for reinvestment) at the company’s cost of capital. Projects with a negative

NPV should be rejected.

N.B. Cost of capital is the average required return which is set by the market for

the company in view of the risk associated with its operations.

Provided that:

1. The project under consideration is of average risk for the company, and

2. There is no restriction on access to capital,

a positive NPV provides the best theoretical estimate of the total absolute increase

in wealth which accrues to an enterprise as a result of accepting that project.

However in the short run the use of the NPV rule may not lead to good profits being

reported in the published accounts of the enterprise – although in the long term

cash flows and reported profits should move in tandem.

The NPV rule has a sound theoretical basis and is likely to produce investment

decision advice of consistently good quality.

DCF – Internal rate of return (economic return/yield)

The IRR (or Economic return) of a project is that discount rate which when applied

to a projects cash flows provides an NPV of zero. The IRR is therefore the expected

“earning rate” of an investment. If the IRR of a project exceeds the cost of capital

of that enterprise, that project is acceptable.

When considering a single project in isolation IRR will give the same decision as

NPV (i.e. if the NPV of a project is positive, its IRR will exceed the cost of capital).

However, when choosing between mutually exclusive projects, the two techniques

may conflict and (subject to the provisos set out above) NPV always provides the

correct solution.

Disadvantages of IRR

1. IRR provides a relative (as opposed to an absolute) result, and may give

incorrect decision advice if mutually exclusive projects:

o Are of different size, or

o Have unequal lives.

2. May be multiple IRRs or no IRR

3. Cannot adapt to expected changes in cost of capital during the life of a

project.

4. Makes an inconsistent assumption about the rate at which cash surpluses can

be reinvested; it assumes they are reinvested at whatever the IRR happens to

be. The company’s cost of capital is a more appropriate reinvestment rate i.e.

the assumption underlying NPV.

5. More difficult to calculate than the theoretically more sound NPV approach.





Congo Ltd

Congo Ltd is considering the selection of one of a pair of mutually exclusive

investment projects. Both would involve purchase of machinery with a life of five

years

Project 1 would generate annual cash flows (receipts less payments) of £200,000;

the machinery would cost £556,000 and have a scrap value of £56,000.

Project 2 would generate annual cash flows of £500,000; the machinery would cost

£1,616,000 and have a scrap value of £301,000.

Congo uses the straight-line method for providing depreciation.

Its cost of capital is 15 per cent per annum. Assume that annual cash flows arise

on the anniversaries of the initial outlay, that there will be no price changes over

the project lives and that acceptance of one of the projects will not alter the

required amount of working capital.

Requirements

(i) Calculate for each project

(a) the accounting rate of return (i.e. the percentage of the average

accounting profit to the average book value of investment) to the

nearest 1%.

(b) the net present value

(c) the internal rate of return (Yield or Economic return) to the nearest 1%,

and

(d) the payback period to one decimal place.

Ignore taxation.

(ii) WITHOUT ANY REFERENCE TO THE INCREMENTAL YIELD METHOD, briefly

explain which one of the discounted cash flow techniques used in part (i) of

this question should be used by the management of Congo Ltd, in deciding

whether Project 1 or Project 2 should be undertaken.





Suggested solution to Congo Ltd

(i) Summary of results

Project 1 2

a) Accounting rate of return 33% 25%

b) Net present value (£000) 142 210

c) Internal rate of return (Economic return) 25% 20%

d) Payback period (years) 2.8 or 3 3.2 or 4

Summary of rankings

Better project

a) Accounting rate of return 1

b) Net present value 2

c) Internal rate of return 1

d) Payback period 1

WORKINGS

Project 1 Project 2

(a) Accounting rate of return £000 £000

Initial investment 556 1,616

Scrap value (56) (301)

Total depreciation 500 1,315

Annual depreciation 100 263

Cash flows 200 500

Depreciation (see above) (100) (263)

Average accounting profit 100 237

Project 1 Project 2

£000 £000

Average book value of investment (£000)

½ (556 + 56) 306

½ (1,616 + 301) 958

Accounting rate of return 33% 25%





(b) Net present value

£000 £000

Year

0 Initial outlay (556) (1,616)

1 – 5 Cash flows

200 x 3.352 670

500 x 3.352 1,676

5 Residual value

56 x 0.497 28

301 x 0.497 ___ 150

Net present value (£000) 142 210

(c) Internal rate of return (Economic return)

£000 £000

By trial and error

Try 20%

Initial outlays (556) (1,616)

Cash flows 598 1,495

Residual values _22 _121

NPV (£000) 64 NIL

Try 25%

Initial outlays (556) (1,616)

Cash flows 538 1,345

Residual values __18 __99

NPV (£000) NIL £(172)

IRR 25% 20%

(d) Payback period

£000 £000

Annual cash flows 200 500

Initial investment 556 1,616

Payback period in years

If cash flows arose during each year 2.8 3.2

If cash flows arose at year end (as in this

question)

3 4

(ii) Investment Decision

This example illustrates the conflict which will often be found between the two

discounted cash flow appraisal techniques in a ranking decision.

Under the net present value criterion, project 2 is preferred because it has a

higher net present value when the project cash flows are discounted at the

cost of capital. On the other hand project 1 has the higher internal rate of

return.

To decide which method of ranking is correct it is necessary to consider the

assumed objective of the firm, which is to maximise the wealth of the

providers of finance. Both projects earn more than the required rate of return

but project 2 generates larger cash surpluses in excess of the required

amounts than project 1, as can be seen from the net present value





calculations. It is these cash surpluses which improve the wealth of the

owners of the firm.

IRR provides a relative (as opposed to an absolute) result, and may give

incorrect decision advice if mutually exclusive projects are of different size (as

in this instance) or have unequal lives.

IRR makes an inconsistent assumption about the rate at which cash surpluses

can be reinvested; it assumes they are reinvested at whatever the IRR

happens to be. The company’s cost of capital is a more appropriate

reinvestment rate i.e. the assumption underlying NPV.

Accordingly PROJECT 2 IS PREFERRED TO PROJECT 1 and this can be justified

by the following argument:

Project 1 is relatively more profitable than project 2, but it is smaller. The

two projects are mutually exclusive, which means that only one of them can

be accepted. It is better for the owners of the company to receive the large

cash surpluses from a large adequately profitable project than to receive the

smaller cash surpluses from a small very profitable project. Taken to

extremes, a return of ten per cent on £1,000 is better than a return of one

thousand per cent on a penny.

Tutorial Note

This question examines the conflicting rankings sometimes given by the NPV

and IRR technique. You may wish to “add a graph” to amplify your solution to

part (c).





INFLATION AND DISCOUNTED CASH FLOW

The mechanics of allowing for inflation are basically easy to handle in DCF

calculations. The real difficulty is one of predicting what the rate will be. At this

point we will discuss the mechanics.

There are two possible techniques:

1. discount ‘money’ (nominal) cash flows at the ‘money’ (nominal) discount rate.

2. discount ‘real’ cash flows at the ‘real’ discount rate.

‘Money’ cash flows

These are the predictions of the actual sums of money which will be received and

paid taking into account predicted inflation levels. The ‘money’ rate of interest is

the interest rate which is normally quoted and contains an allowance for inflation

(for example, a 20% discount rate may contain an allowance for expected inflation

of 5%).

‘Real’ cash flows.

These are cash flows expressed in today’s prices. A ‘real’ discount rate is the real

required rate of return after adjusting the money discount rate for the inflation

allowance.

Relationship between money interest rates and real

interest rates

Suppose we can invest money in a bank to earn 7% per annum interest. However,

we expect inflation to be 4% per annum next year. If I invest £1 this must grow to

£1.04 to keep pace with inflation. So, if I have £1.07 cash in the bank after one

year, the real interest I have received is £1.07 - £1.04 = 3p. When compared with

the capital required to keep pace with inflation (£1.04), this shows a return of

0.03/1.04 = 2.9%.

The formula which relates real and money interest rates is as follows:

1 + r = 1 + m or, according to the ACCA Formula Sheet, (1 + i) = (1 + r)(1 + h)

1 + i

Where r is the real interest rate, m is the money interest rate and i is the rate of

inflation.

Thus 1 + r = 1.07/1.04 in the above example, giving r = 0.029 or 2.9%.





Example

A project requires an outlay of £1.5m in year 0 and will repay cash flows in real

terms (today’s prices) as follows:

Year £’000

1 670

2 500

3 1,200

The company’s money cost of capital is 15½%. Appraise the project if inflation is

estimated to remain at 5% per annum.

Method 1: Compute the real discount rate and discount the real cash flows

1 + r = 1+ m = 1.155 = 1.1

1 + i 1.05

Thus r = 0.1 or 10%

‘Real’ cash flow 10% factor Present value

Year

0 (1,500) 1 (1,500)

1 670 1/1.1 609.1

2 500 1/1.12 413.2

3 1,200 1/1.13 901.6

NPV 423.9

Method 2: Compute the money cash flows, using the rate of inflation and discount

at the money discount rate.

‘Money’ cash flow 15.5% factor Present value

Year

0 (1,500) 1 (1,500)

1 670 x 1.05 = 703.5 1/1.155 609.1

2 500 x 1.052 = 551.25 1/1.1552 413.2

3 1,200 x 1.053 =1,389.15 1/1.1553 901.6

NPV 423.9

Please note that discount rates have been computed as opposed to looked up in

tables, to ensure that accuracy is obtained for the reconciliation.





TAXATION AND INVESTMENT APPRAISAL

Example 1

A company buys a fixed asset for £10,000 at the beginning of an accounting

period (1 January 2001) to undertake a two year project.

Net trading revenues at t1 and t2 are £5,000 per annum.

The company sells the fixed asset on the last day of the second year for £6,000.

Corporation tax = 33%. Writing down allowance = 25% reducing balance.

Required

Calculate the net cashflows for the project.

Solution to example 1

t0 t1 t2 t3

£ £ £ £

Net trading revenue 5,000 5,000

Tax at 33% (1,650) (1,650)

Fixed asset (10,000)

Scrap proceeds 6,000

Tax savings on WDAs _____ ____ 825 495

Net cashflow (10,000) 5,000 10,175 (1,155)

WORKING

Tax savings on writing down allowances

Tax relief

at 33%

Timing

£ £

t0 Investment in fixed asset 10,000

t1 WDA @ 25% (2,500) 825 t2

7,500

t2 Proceeds (6,000)

Balancing allowance (1,500) 495 t3

Example 2

A company buys a fixed asset for £10,000 at the end of the previous accounting

period (31 December 2000) to undertake a two year project.

Net trading revenues at t1 and t2 are £5,000 per annum.

The fixed asset has zero scrap value when it is disposed of at the end of year 2.

Corporation tax = 33%. Writing down allowance = 25% reducing balance.

Required

Calculate the net cashflows for the project.





Solution to example 2

t0 t1 t2 t3

£ £ £ £

Net trading revenue 5,000 5,000

Tax at 33% (1,650) (1,650)

Fixed asset (10,000)

Tax savings on

WDAs

_____ 825 619 1,856

Net cashflow (10,000) 5,825 3,969 206

WORKING

Tax savings on writing down allowances

Tax relief at 3% Timing

£ £

t0 Investment in fixed asset 10,000

t0 WDA @ 25% (2,500) 825 t1

7,500

t1 WDA @25% (1,875) 619 t2

5,625

t2 Proceeds ____

Balancing allowance (5,625) 1,856 t3





CAPITAL RATIONING

Where the finance available for capital expenditure is limited to an amount which

prevents acceptance of all new projects with a positive NPV, the company is said to

experience “capital rationing”.

What are the 2 types of capital rationing?

They are:

1. Hard capital rationing

This applies when a company is restricted from undertaking all worthwhile

investment opportunities due to external factors over which it has no control.

These factors may include government monetary restrictions and the general

economic and financial climate (eg, a depressed stock market, which precludes a

rights issue of ordinary shares).

2. Soft capital rationing

This applies when a company decides to limit the amount of capital expenditure

which it is prepared to authorise. Segments of divisionalised companies often have

their capital budgets imposed by the main board of directors. A company may

purposely curtail its capital expenditure for a number of reasons eg, it may consider

that it has insufficient depth of management expertise to exploit all available

opportunities without jeopardising the success of both new and ongoing operations.

Capital rationing and time

Capital rationing may exist in a:

1. Single period

i.e. available finance is only in short supply during the current period, but will

become freely available in subsequent periods.

Projects may be:

(i) Divisible – An entire project or any fraction of that project may be

undertaken. In this event projects may be ranked by means of a

profitability index, which can be calculated by dividing the present value (or

NPV) of each project by the capital outlay required during the period of

restriction.

Projects displaying the highest profitability indices will be preferred. Use of

the profitability index assumes that project returns increase in direct

proportion to the amount invested in each project.

(ii) Indivisible – An entire project must be undertaken, since it is impossible to

accept part of a project only. In this event the NPV of all available projects

must be calculated. These projects must then be combined on a trial and

error basis in order to select that combination which provides the highest total

NPV within the constraints of the capital available. This approach will

sometimes result in some funds being unused.





2. Multi-period

i.e. available finance is limited not only during the current period, but also during

subsequent periods.

Projects may be:

(i) Divisible - In this event, linear programming is used to determine the

optimal combination of projects. Two techniques, which both result in

identical project selections can be used i.e. the objective is to either:

● Maximise the total NPV from the investment in available projects, or

● Maximise the present value (PV) of cash flows available for dividends.

(ii) Indivisible - In this event, integer programming would be required to

determine the optimal combination of investments.

Single period capital rationing

Example of single period capital rationing

Banden Ltd is a highly geared company that wishes to expand its operations. Six

possible capital investments have been identified, but the company only has access

to a total of £620,000. The projects are not divisible and may not be postponed

until a future period. After the projects end, it is unlikely that similar investment

opportunities will occur.

Expected net cash inflows (including salvage value)

Initial

Project Year 1 2 3 4 5 outlay

£ £ £ £ £ £

A 70,000 70,000 70,000 70,000 70,000 246,000

B 75,000 87,000 64,000 180,000

C 48,000 48,000 63,000 73,000 175,000

D 62,000 62,000 62,000 62,000 180,000

E 40,000 50,000 60,000 70,000 40,000 180,000

F 35,000 82,000 82,000 150,000

Projects A and E are mutually exclusive. All projects are believed to be of similar

risk to the company’s existing capital investments.

Any surplus funds may be invested in the money market to earn a return of 9% per

year. The money market may be assumed to be an efficient market. Banden’s cost

of capital is 12% per year.

Required

(a) Calculate:

(i) The expected net present value;

(ii) The expected profitability index associated with each of the six projects.

Rank the projects according to both of these investment appraisal methods

and explain briefly why these rankings differ.

(b) Give reasoned advice to Banden Ltd recommending which projects should be

selected.





Solution to single period capital rationing example

(a) (i) Calculation of expected Net Present value

Project NPV

A. £70,000 x 3.605 - £246,000 = £6,350

B. £75,000 x 0.893 + £87,000 x 0.797 + £64,000

x 0.712 - £180,000 = £1,882

C. £48,000 x 0.893 + £48,000 x 0.797 + £63,000

x 0.712 + £73,000 x 0.636 - £175,000 = (£2,596)

D. £62,000 x 3.037 - £180,000 = £8,294

E. £40,000 x 0.893 + £50,000 x 0.797 + £60,000

x 0.712 + £70,000 x 0.636 + £40,000 x 0.567

- £180,000 = £5,490

F. £35,000 x 0.893 + £82,000 x 0.797 + £82,000

x 0.712 - £150,000 = £4,993

(ii) Calculation of Profitability Index

Present value of cash inflows ÷ initial outlay:

Project PI

A. £252,350/£246,000 = 1.026

B. £181,882/£180,000 = 1.010

C. £172,404/£175,000 = 0.985

D. £188,294/£180,000 = 1.046

E. £185,490/£180,000 = 1.031

F. £154,993/£150,000 = 1.033

Ranking NPV P.I

1 D D

2 A F

3 E E

4 F A

5 B B

6 C C





The rankings differ because NPV is an absolute measure of the benefit from a

project, whilst profitability index is a relative measure, and shows the benefit

per £ of outlay. Where the initial outlays vary in size the two methods may

give different rankings.

(b) In a capital rationing situation, the projects should be selected which give the

greatest total NPV from the limited outlay available.

A and E are mutually exclusive.

C is not considered as it has a negative NPV.

Total outlay is limited to £620,000.

Possible selections are:

Projects Expected NPV Total NPV Outlay in £’000

£ £

A, B, D (6,350 + 1,882 + 8,294) 16,526 (246 + 180 + 180) 606

A, B, F (6,350 + 1,882 + 4,993) 13,225 (246 + 180 + 150) 576

A, D, F (6,350 + 8,294 + 4,993) 19,637 (246 + 180 + 150) 576

B, D, E (1,882 + 8,294 + 5,490) 15,666 (180 + 180 + 180) 540

B, D, F (1,882 + 8,294 + 4,993) 15,169 (180 + 180 + 150) 510

B, E, F (1,882 + 5,490 + 4,993) 12,365 (180 + 180 + 150) 510

D, E, F (8,294 + 5,490 + 4,993) 18,777 (180 + 180 + 150) 510

The recommended selection is projects A, D and F

Tutorial note: Neither the NPV nor PI rankings will necessarily be appropriate

because of the sheer size of these indivisible investments. In this particular

instance, because of the similarity in size of the projects, only three can be

undertaken, and the NPV ranking clearly leads to A, D and E. Profitability

index will not work if projects are indivisible or where multiple limiting factors

exist. The PI might lead to the incorrect solution of D, E and F.





Multi-period capital rationing

Please remember that you are only likely to be asked to set up the

equations for both the linear programming and integer programming

formulations and then to interpret the output. The actual solving of these

equations are computer-based calculations.

Example of multi-period capital rationing using linear programming

The management team of Barney Ltd has identified the following independent

investment projects, all of which are divisible.

No project can be delayed or performed on more than one occasion. The projected

cash flows during the life of each project are as follows:

Year 0 Year 1 Year 2 Year 3 Year 4

£’000 £’000 £’000 £’000 £’000

Project A (25) (50) 25 50 50

Project B (25) (25) 75 - -

Project C (12.5) 5 5 5 5

Project D - (37.5) (37.5) 50 50

Project E (50) 25 (50) 50 50

Project F (20) (10) 37.5 25 -

The capital available at Year 0 is only £50,000 and only £12,500 is available at Year

1, together with any cash inflows from the projects undertaken at Year 0. From

Year 2 onwards there is no restriction on the access to capital. The appropriate

cost of capital is 10%.

Formulate both:

1. The NPV linear programme, and

2. The PV of dividends linear programme.

Multi-period capital rationing solutions for divisible projects

NPV formulation

Since the objective is to maximise the total NPV from these projects, it is initially

necessary to calculate the NPV of each project at a discount rate of 10%:

Year 0 Year 1 Year 2 Year 3 Year 4 Total

NPV

Discount factor

(10%) 1.000 0.909 0.826 0.751 0.683

£’000 £’000 £’000 £’000 £’000 £’000

Project A (25) (45.45) 20.65 37.55 34.15 +21.90

Project B (25) (22.73) 61.95 - - +14.22

Project C (12.5) 4.55 4.13 3.75 3.42 +3.35

Project D - (34.09) (30.97) 37.55 34.15 +6.64

Project E (50) 22.73 (41.30) 37.55 34.15 +3.13

Project F (20) (9.09) 30.98 18.77 - +20.66





The combination of projects, which will maximise the total NPV can now be

specified, where:

a = the proportion of Project A to be undertaken

b = the proportion of Project B to be undertaken

c = the proportion of Project C to be undertaken

d = the proportion of Project D to be undertaken

e = the proportion of Project E to be undertaken

f = the proportion of Project F to be undertaken

The objective function, which represents the maximum NPV that can be earned, is:

z = 21.90a + 14.22b + 3.35c + 6.64d + 3.13e + 20.66f

This is subject to the following constraints:

Year 0 : 25a + 25b + 12.5c + 50e + 20f ≤ 50

Year 1 : 50a + 25b + 37.5d + 10f ≤ 12.5 + 5c + 25e

Furthermore : 0 ≤ a, b, c, d, e, f ≤ 1

When solved, the linear programme will provide the proportions of each project

which should be undertaken in order to establish the value of z, which represents

the maximum NPV achievable in view of the limitation of available capital.

Notice that the first constraint relates to the limited capital available at Year 0. The

second constraint concerns the capital limitation at Year 1, which is of course eased

by the Project C and E cash inflows, which can also be used to fund investment

needs at that time.

The third constraint shows that each project can only be undertaken once and that

it is impossible to undertake a negative quantity of any project. This non-negative

rule is essential, since if it were excluded a computer model may well establish that

negative quantities of a project could make cash inflows available that would be

included within the solution!!

PV of dividends formulation

The combination of projects, which will maximise the PV of cash flows available for

dividends must be specified, where:

a = the proportion of Project A to be undertaken

b = the proportion of Project B to be undertaken

c = the proportion of Project C to be undertaken

d = the proportion of Project D to be undertaken

e = the proportion of Project E to be undertaken

f = the proportion of Project F to be undertaken

The objective function will be based upon the premise that:

z = the PV of dividends.

The dividend flows need to be defined for each year up to the point where the

investment with the longest life ceases – in this case up to the end of Year 4 i.e.

d0 = the dividend flow generated at Year 0 by the projects selected









Therefore the objective function, which represents the present value of the

maximum dividends, discounted at the cost of capital of 10% is:

z = d0 + 1.1

d1 + 2

2

1.1

d +

3

3

1.1

d +

4

4

1.1

d

alternatively

z = d0 + 0.909 d1 + 0.826 d2 + 0.751 d3 + 0.683 d4

This is subject to the following constraints:

Year 0 : 25a + 25b + 12.5c + 50e + 20f + d0 ≤ 50

Year 1 : 50a + 25b + 37.5d + 10f + d1 ≤ 12.5 + 5c + 25e

Year 2 : 37.5d + 50e + d2 ≤ 25a + 75b + 5c + 37.5f

Year 3 : d3 ≤ 50a + 5c + 50d + 50e + 25f

Year 4 : d4 ≤ 50a + 5c + 50d + 50e

Furthermore : 0 ≤ a, b, c, d, e, f ≤ 1

Additionally : d0, d1, d2, d3, d4 ≥ 0

When solved, the linear programme will provide the proportions of each project

which should be undertaken in order to establish the value of z, which represents

the maximum PV of dividends earned in view of the capital constraints.

With an NPV formulation, we only have constraints for the periods during which

capital rationing exists (in this instance, Years 0 and 1), whereas under the

dividend formulation we have a constraint for every year of potential project cash

flows (in this case, Years 0 to 4).

The available funds are the same as in the NPV formulation (i.e. available capital

together with cash inflows from the projects); however the dividend flow for each

period must also be included. Furthermore an additional non-negative constraint is

used, since the dividends must be greater than or equal to zero. If this constraint

were excluded, a computer model may specify negative dividend payments, which

make cash inflows available that could be used to finance more projects!!

One advantage of the PV of dividends formulation is that it removes the need to

even calculate the NPV of each investment opportunity, since the discounting

process is carried out by the linear programme as part of the calculation of the

solution.

Notice the only difference in the value of z in these formulations is as follows:

● Under the NPV formulation, z provides the NPV of the project returns,

whereas

● Under the PV of dividends formulation, z provides the PV of the project

returns.

Dual values

Dual values (also referred to as “shadow prices”) reflect the change in the objective

function as a result of having one more or one less unit of scarce resource. In the

context of capital rationing the scarce resource is available cash, so that the dual

price states the change in the objective function if one more unit of currency (e.g.

£1) becomes available or if one less GB pound is invested.

Shadow prices can therefore be used to calculate the impact of raising additional

finance for further investment or the effect of diverting capital away from current

projects into newly discovered investments.





The dual price depends upon which method is used to formulate the linear

programme i.e.

● Under the NPV formulation, it reflects the change in the NPV if £1 more or

£1 less is available

● Under the PV of dividends formulation, it reflects the change in the PV of

cash available for dividend payments if £1 more or £1 less capital is available.

Dual prices relate only to marginal changes in the availability of capital. Thus,

suppose that a dual value of £1.25 arises under the PV of dividends method, this

means that if an additional £1 of funds became available, the total value of the

objective function would rise by £1.25. It does not necessarily mean that if an

additional £10,000 became available, that the value of the objective function would

increase by (£10,000 x 1.25) £12,500.

Shadow prices can therefore be used to test the validity of new investments which

emerge. The cash flows generated by the new project can be compared with the

cash flows lost by diverting funds from existing investments, thereby calculating the

effect of diversion of that finance.

Example of the use of dual values in linear programming

Bruno Ltd is experiencing capital rationing during both Year 0 and Year 1 in relation

to a number of divisible projects. It has used linear programming to develop an

investment strategy over its three year planning horizon for dividend payments,

using a cost of capital of 10%.

Shadow prices have been calculated under the NPV formulation for the two years of

capital constraints and under the PV of dividends formulation for the three year

planning horizon. The dual prices per £1 of capital available are as follows:

NPV method PV of dividends method

£ £

Year 0 0.1 (1 + 0.1) = 1.1

Year 1 0.08 (0.909 + 0.08) = 0.989

Year 2 0 (0.826 + 0) = 0.826

A new investment opportunity has emerged with the following cash flows:

Cash flow

£’000

Year 0 (75)

Year 1 50

Year 2 50

Appraise the new project using both the NPV dual prices and the PV of dividend

shadow prices.





Solution to example of the use of dual values in linear programming

Appraisal using NPV dual values

The NPV of the new investment project is:

Year Cash flow Discount

factor Present value

£000 @ 10% £000

0 (75) 1 (75)

1 50 0.909 45.45

2 50 0.826 41.3

NPV 11.75

The net dual value of the new investment project (i.e. the impact of diverting funds

from the current investment strategy) is:

Year Cash flow Shadow price Opportunity cost

£000 £000

0 (75) 0.1 (7.5)

1 50 0.08 4

2 50 0 - _

Net dual value (3.5)

Accordingly, the NPV of the current investment strategy would fall by £3,500 if the

new project were accepted. However, Bruno Ltd would benefit from the positive

NPV of that new investment opportunity. Therefore:

£’000

NPV of new project 11.75

Net dual value (3.5)

Net benefit of undertaking new project 8.25

This indicates that this project is worth further consideration, since if it were

accepted in full (and in doing so does not violate the marginality assumption of dual

values) it would result in the value of the objective function increasing by £8,250.

Appraisal using PV of dividends dual values

The net dual value of the new investment project (i.e. the impact of diverting funds

from the current investment strategy) is:

Year Cash flow Shadow price Opportunity cost

£000 £000

0 (75) 1.1 (82.5)

1 50 0.989 49.45

2 50 0.826 41.3

Net dual value (i.e. net benefit of undertaking new

project) 8.25

The two techniques will always provide the same result, but as can be seen the PV

of dividends dual prices technique is far quicker and simpler to solve.

Again, the project is worth considering; the linear programme should therefore be

reformulated (by including the new project) and then re-solved.





Example of multi-period capital rationing using integer programming

The management team of Toby Ltd has identified four indivisible projects, which

require funds to be invested over the next few years, as set out below:

Project A Project B Project C Project D

£ £ £ £

Year 0 17,500 22,500 - 12,500

Year 1 25,000 - 15,000 15,000

Year 2 10,000 30,000 20,000 17,500

The board of directors of that company has approved the following capital

expenditure programme for those same accounting periods:

£

Year 0 40,000

Year 1 35,000

Year 2 42,500

The four projects are expected to produce the following positive net present values:

Project A Project B Project C Project D

Project NPV +£20,000 +£27,500 +£15,000 +£10,000

You are required to discuss the approach for calculating the optimum mix

of projects.





Multi-period capital rationing solution for indivisible projects

The problem is to identify that combination of investment projects which will

produce the highest possible total NPV (within the annual funding limitations).

For instance, if Projects C and D were undertaken, they would satisfy the annual

capital constraints, because the combined investment for Year 0 is £12,500, for

Year 1 is £30,000 and for Year 2 is £37,500, whilst achieving a total positive NPV of

£25,000.

On the other hand, if Projects A and B were selected, they would also remain within

the annual capital limitations. The combined investment for Year 0 is £40,000, for

Year 1 is £25,000 and for Year 2 is £40,000, whilst achieving a total positive NPV of

£47,500. This amount exceeds the NPV earned by the combination of Projects C

and D.

This problem can be solved by an integer programming formulation. The

procedures would be to establish the value of variables YA, YB, YC and YD for each of

the four projects, which maximise the total net present value i.e.

Maximise: 20,000 YA + 27,500 YB + 15,000 YC + 10,000 YD

Subject to three annual capital investment constraints:

Year 0 : 17,500 YA + 22,500 YB + 0 YC + 12,500 YD ≤ 40,000

Year 1 : 25,000 YA + 0 YB + 15,000 YC + 15,000 YD ≤ 35,000

Year 2 : 10,000 YA + 30,000 YB + 20,000 YC + 17,500 YD ≤ 42,500

The solution to the above problem would result in YA = 1, YB = 1, YC = 0, YD = 0.

In other words, both Project A and Project B would be selected, whilst the other two

projects would be rejected and the positive NPV of the entire investment strategy

would be £47,500.

Notice that the above solution is superior to the combination of YA = 0, YB = 0, YC

= 1, YD = 1, since the combined positive NPV of Project C and Project D is only

£25,000, as already stated.




Chapter 3

Advanced investment

appraisal – section 2





CHAPTER CONTENTS

MODIFIED INTERNAL RATE OF RETURN ------------------------------ 65

CALCULATING THE MIRR 65

FREE CASH FLOW -------------------------------------------------------- 68

DEFINITION OF FREE CASH FLOW 68

FREE CASH FLOW TO EQUITY 69

RISK AND UNCERTAINTY ----------------------------------------------- 74

SENSITIVITY ANALYSIS 74

PROBABILITY AND EXPECTED VALUES 75

MONTE CARLO SIMULATION 75

PROJECT VALUE AT RISK 76

DURATION ---------------------------------------------------------------- 78

GENTO LTD --------------------------------------------------------------- 80

HULME LTD --------------------------------------------------------------- 85

BAILEY PLC --------------------------------------------------------------- 91





MODIFIED INTERNAL RATE OF RETURN

To assist in remedying some of the deficiencies of IRR, a technique called Modified

Internal Rate of Return (MIRR) has been developed. MIRR has certain advantages

in that it:

● Eliminates the possibility of multiple internal rates of return.

● Addresses the reinvestment rate issue i.e. it does not make the assumption

that the company’s reinvestment rate is equal to whatever the project IRR

happens to be.

● Provides rankings which are consistent with the NPV rule (which is not always

the case with IRR).

● Provides a % rate of return for project evaluation. It is claimed that non-

financial managers prefer a % result to a monetary NPV amount, since a %

helps measure the “headroom” when negotiating with suppliers of funds.

Calculating the MIRR

The MIRR assumes a single outflow at time 0 and a single inflow at the end of the

final year of the project. The procedures are as follows:

● Convert all investment phase outlays as a single equivalent payment at time

0. Where necessary, any investment phase outlays arising after time 0 must

be discounted back to time 0 using the company’s cost of capital.

● All net cash flows generated by the project after the initial investment (i.e. the

return phase cash flows) are converted to a single net equivalent terminal

receipt at the end of the project’s life, assuming a reinvestment rate equal to

the company’s cost of capital.

● The MIRR can then be calculated employing one of a number of methods, as

illustrated in the following example.

Example

Carter plc is considering an investment in a project, which requires an immediate

payment of £15,000, followed by a further investment of £5,400 at the end of the

first year. The subsequent return phase net cash inflows are expected to arise at

the end of the following years:

Net cash inflows

Year £

1 6,500

2 7,750

3 5,750

4 4,750

5 3,750

You are required to calculate the modified internal rate of return of this

project assuming a reinvestment rate equal to the company’s cost of

capital of 8%.





Solution

Single equivalent payment discounted to year 0 at an 8% discount rate:

Year £

0 15,000

1 (£5,400 x 0.926) _5,000

Present Value (PV) of investment phase cash flows 20,000

Single net equivalent receipt at the end of year 5, using an 8% compound rate:

Year £ 8% compound factors £

1 6,500 1.3605 8,843

2 7,750 1.2597 9,763

3 5,750 1.1664 6,707

4 4,750 1.08 5,130

5 3,750 1 3,750

Terminal Value (TV) of return phase cash flows £34,193

The above compound factors are produced with a calculator.

A five year PV factor can now be established i.e.(£20,000 ÷ £34,193) = 0.585

Using present value tables, this 5 year factor falls between the factors for 11% and

12% i.e. 0.593 and 0.567. Using linear interpolation:

MIRR = 11% + 0.567) - (0.593

0.585) - 0.593( x (12% - 11%) = 11.3%

Alternatively, the MIRR may be calculated as follows;

MIRR = 000,20

193,34£

5 − 1 = 11.3%

Furthermore, in examples where the PV of return phase net cash flows has already

been calculated, there is yet another formula for computing MIRR (which is given

on the ACCA formulae sheet). This formula avoids having to establish the Terminal

Value of those return phase net cash flows i.e.

PV of return phase net cash flows

(6,500 x 0.926) + (7,750 x 0.857) + (5,750 x 0.794) + (4,750 x 0.735) + (3,750 x

0.681) = £23,271

MIRR = 1 - 1.08 000,20

271,23£

5

× = 11.3%





The reservations which are often cited concerning the MIRR technique include:

● In what are claimed to be the very exceptional circumstances where the

reinvestment rate exceeds the company’s cost of capital, the MIRR will

underestimate the project’s true rate of return.

● The determination of the life of a project can have a significant effect on the

actual MIRR, if the difference between the project’s IRR and the company’s

cost of capital is large.

● Like IRR, the MIRR is biased towards projects with short payback periods and

large initial cash inflows.

● The extent to which this method is being used in industry is unclear and only

time will tell whether it eventually becomes popular.





FREE CASH FLOW

Definition of free cash flow

Free cash flow is cash that is not retained and reinvested in the business.

Unfortunately, there is dispute as to what is included within free cash flow, as can

be seen from the following typical definitions:

1. The free cash flow to the company is the cash flow derived from operations,

after adjustment for working capital changes, for investment and for taxes

and it represents the funds available for distribution to the providers of

capital, i.e. shareholders and lenders.

2. Free cash flow is the cash flow available to a company from operations after

tax, any changes in working capital and capital spending on assets needed to

continue existing operations (i.e. replacement capital expenditure equivalent

to economic depreciation).

As can be seen, the main difference between the two definitions is whether or not

to deduct capital expenditure required to expand operations. Throughout these

notes the treatment will be varied as a reminder of the inconsistency. In addition,

some authorities suggest that no adjustment is made for working capital changes in

respect of short-term measures of free cash flow.

Example

Hawthorns plc has earnings before interest and tax of £225,000 for the current

year. Depreciation charges for the year have been £15,000 and working capital

has increased by £2,500. The company needs to invest £22,500 to acquire non-

current assets. Profits are subject to taxation @ 30% p.a.

Calculate free cash flow.

Solution

£

EBIT 225,000

Less: Corporation tax @ 30% (67,500)

157,500

Add back: Depreciation (non-cash amount) 15,000

Deduct: Capital expenditure (22,500)

Working capital increases (2,500)

Free cash flow £147,500





Free cash flow to equity

The dividend capacity of a company is measured by its free cash flow to equity.

Free cash flow to equity can be calculated by establishing the free cash flow

described above, and then:

● Deducting any interest payments and any loan repayments; and

● Adding any cash inflows arising from the issue of debt.

Free cash flow to equity is thought by some authorities to provide a superior

measure of dividend cover i.e.

Example

The following data relates to Molineux Ltd:

Forecast Income statement for 2010

£m

Revenue 1,950.00

Cost of sales (1,314.00)

Gross profit 636.00

Operating expenses (322.50)

Earnings before interest and tax 313.50

Interest charges (24.00)

Profit before tax 289.50

Corporation tax(@ 35%) (101.32)

Profit after tax 188.18

During the year loan repayments are expected to amount to £69 million,

depreciation charges to £30 million and capital expenditure to £60 million.

You are required to calculate:

(a) Free cash flow;

(b) Free cash flow to equity.

Dividend cover (in terms of free cash flow) Free cash flow to equity

Dividends paid =





Solution

(a) Free cash flow

£m

EBIT 313.50

Less: Corporation tax (@ 35% thereon) (109.72)

203.78

Add back: Depreciation (non-cash amount) 30.00

Deduct: Capital expenditure (60.00)

Free cash flow 173.78

(b) Free cash flow to equity

Method One

£m

Free cash flow (as above) 173.78

Deduct: Loan repayments (69.00)

Interest charges, net of tax [£24m x (1 – 0.35)] (15.60)

Free cash flow to equity 89.18

Method Two

£m


Add back: Depreciation (non-cash amount) 30.00

Deduct: Capital expenditure (60.00)

Loan repayments (69.00)

Free cash flow to equity 89.18





Example

The following information relates to the forecasts of Bescot plc for the forthcoming

year:

£000

Capital expenditure for expansion 100

Capital expenditure to replace existing non-current assets 240

Depreciation charges 300

Amounts raised from fresh bond issue 120

Increase in working capital 220

Interest paid 40

Repayment of loans 60

Profit from operations 1,880

Corporation tax paid (@ 30%) 552

Ordinary share capital (@ 25p par value) 1,840

Dividend paid for the year is expected to be 5p per share

You are required to calculate:

(a) Free cash flow;

(b) Free cash flow to equity;

(c) Dividend cover based upon free cash flow to equity.





Solution

(a) Free cash flow

£000

Profit from operations (EBIT) 1,880

Deduct: Corporation tax (@ 30% thereon) (564)

1,316

Add back: Depreciation (non-cash amount) 300

Deduct: Capital expenditure to replace existing non-current assets (240)

Capital expenditure for expansion (ARGUABLY, THIS SHOULD NOT

BE DEDUCTED IN ARRIVING AT FREE CASH FLOW)

(100)

Increase in working capital (220)

Free cash flow 1,056

(b) Free cash flow to equity

Method One

£000

Free cash flow (as above) 1,056

Deduct: Loan repayments (60)

Interest charges, net of tax [£40,000 x (1 – 0.3)] (28)

Add: Proceeds of bond issue 120

Free cash flow to equity 1,088

Method Two

£000

EBIT 1,880

Interest charges (40)

Corporation tax (552)

Profit after tax (i.e. Earnings after interest and tax) 1,288

Add back: Depreciation (non-cash amount) 300

Deduct: Increase in working capital (220)

Capital expenditure [£240,000 + £100,000] (340)

Loan repayments (60)

Add: Amounts raised from bond issue 120

Free cash flow to equity 1,088

(c) Dividend cover

ie, = 000,368£

000,288,1£ = 3.5 times

WORKING:

Dividends for the year:

Number of shares in issue = 25.0£

£1,840,000 = 7,360,000

Dividends for the year = 7,360,000 x £0.05 = £368,000

The normal dividend cover calculation is:Earnings after interest and tax

Dividends for the year





The above result is thought by some authorities to be misleading, since it is

cash (and not earnings) that is used to pay dividends. Therefore, dividend

cover based upon free cash flow to equity may be used, as follows:

ie = 000,368£

000,088,1£ = 2.96 times

This would be considered a satisfactory level of assurance for ordinary

shareholders.

Dividend cover (in terms of free cash flow) Free cash flow to equity

Dividends paid =





RISK AND UNCERTAINTY

Risk occurs where there are several possible outcomes for each component of a

decision and probabilities can be assigned for each possible outcome. This allows

for the calculation of an expected value based upon the probability of each

outcome.

Uncertainty occurs where there are several possible outcomes, but the probability

attaching to each cannot be established.

Sensitivity analysis

A technique which assesses the effect on an overall decision if a single constituent

variable were to change i.e. how sensitive is the investment decision to a change in

a single aspect (e.g. sales revenue, material price, project life, etc). This allows for

the consideration of a range of possible outcomes. Sadly the technique does not

take into account the interdependence of the variables i.e. the technique ignores

the interaction of the constituent variables.

Procedure

Firstly, calculate the expected NPV, using the best estimates available.

Then, calculate for each input factor (e.g. initial investment, sales price, wage rate,

discount rate, residual value, etc) the necessary percentage change which would

cause the NPV to become zero.

To find the percentage change required to achieve an NPV of zero, the calculation is

as follows:

% change = 100variable the by affected flows cash of PV

project of NPV×

Illustration

An expected NPV has already been calculated for the following project:

Year Cash flow 10% discount factor Present value

£000 £000

0 Initial investment (100) 1 (100.00)

1-3 Revenues 40 2.487 99.48

3 Scrap value 10 0.751 7.51

NPV +6.99

From these results, the sensitivity to each variable, which would create an NPV of 0

is:

Initial investment: 100

99.6 x 100 = an increase of 7%

Annual revenues: 48.99

99.6 x 100 = a decrease of 7%

Scrap value: 51.7

99.6 x 100 = a decrease of 93%





Discount factor: (this requires the calculation of the IRR, since this would cause the

NPV to be 0. The IRR is, of course, established by trial and error),

ie:

Year Cash flow Try 13% Try 14%

£000 DF £000 DF £000

0 (100) 1 (100) 1 (100)

1-3 40 2.361 94.44 2.322 92.88

3 10 0.693 6.93 0.675 6.75

NPV +1.37 -0.37

IRR = 13% + ( )%13%1437.037.1

37.1−×

+ = 13.79%

Cost of capital will have to increase by 37.9% (i.e. from 10% to 13.79%) for an

NPV of 0 to arise.

Project life: Clearly if the project life were for a shorter period than 3 years an NPV

of 0 would at some point arise. Accurate calculations are in this case not possible,

since at a life of less than 3 years, the scrap value would be greater, but the precise

amount is unknown.

Probability and expected values

A probability distribution of expected cash flows could be estimated and used to

calculate the expected value of the NPV and measure risk (normally the standard

deviation of that NPV). This aspect will be demonstrated during the lectures

dealing with Project Value at Risk (VAR) and the Capital Asset Pricing Model

(CAPM).

This expected value is unlikely to be the same amount as one of the specific

outcomes, since it is based upon a weighted average calculation. Whilst the

expected value is simple to calculate and easy to understand, it does suffer from

the following limitations:

● Probabilities usually have to be estimated and therefore may be inaccurate or

unreliable;

● Expected values are long-term averages, which assume repetition of the task

and may clearly be inappropriate for one-off projects;

● Does not take into account the decision makers attitude to risk – think of a

banker!;

● May not take into account the time value of money.

Monte Carlo simulation

Sensitivity analysis assesses the effect on an overall decision if a single constituent

variable were to change. Monte Carlo simulation is a mathematical model which

will include all combinations of the potential variables associated with the project. It

results in the creation of a distribution curve of all possible cash flows which could

arise from the investment and allows for the probability of the different outcomes

to be calculated. The steps involved are as follows:

1. Specify all major variables

2. Specify the relationship between those variables

3. Using a probability distribution, simulate each environment.





The advantage of this technique is it includes all foreseeable outcomes. The

disadvantages are the difficulty in formulating the probability distribution and the

model becoming very complex.

Project value at risk

Value at risk (VaR) is the value which can be attached to the downside of a value or

price distribution of known standard deviation and within a given confidence level.

VaR and related measures give an indication of the potential loss in monetary value

which is likely to occur with a given level of confidence. The setting of the

confidence level is necessary because in principle, if a price distribution is normally

distributed for example, the downside loss is potentially infinite.

Confidence levels are often set at either 95% (in which case the VaR will provide

the amount that has only a 5% chance of decline) or at 99% (when the VaR

considers a 1% chance of loss of value).

Example

Andrews plc estimates the expected NPV of a project to be £100 million, with a

standard deviation of £9.7 million.

Establish the value at risk using both a 95% and also a 99% confidence

level.





Solution

Using Z = σ

µ - X and establishing Z from the normal distribution tables i.e. at a

95% confidence level, 1.65 is the value for a one tailed 5% probability of decline

(i.e. 0.4505) and at a 99% confidence level, 2.33 is the value for a one tailed 1%

probability of loss of NPV (i.e.0.4901).

At 95% confidence level, Z = 9.7

100 - X = –1.65;

therefore X = (9.7 x – 1.65) + 100 = 84.

At 99% confidence level, Z = 9.7

100 - X = –2.33;

therefore X = (9.7 x – 2.33) + 100 = 77.4.

There is a 5% chance of the expected NPV falling to £84 million or less and a 1%

probability of it falling to £77.4 million or below.





DURATION

Duration is the average time taken to recover the cash flows on an investment.

The average is taken as the value weighted average of the number of the year (1 to

n) in which the cash flows arise. In capital investment, the duration can be

calculated using either the firm’s original outlay, or the present value of its future

cash flows as the basis for the annual weighting.

If duration is based upon the average time to recover the initial capital investment:

1. Calculate the value of each future net cash flow, discounted at the IRR of the

project;

2. Calculate each year’s discounted cash flow as a proportion of the original

capital outlay;

3. Take the time from investment to each discounted cash flow and multiply by

the respective proportion. Finally, sum the weighted year values.

If duration is based upon the average time taken to recover the present value of

the project:

1. Calculate the value of each future net cash flow, discounted at the chosen

hurdle rate;

2. Calculate each year’s discounted cash flow as a proportion of the PV of total

cash inflows;



Example

The forecast cash flows relating to a proposed project are:

Year 0 1 2 3 4

Incremental cash flows (£34,000) £7,600 £16,500 £13,000 £6,600

Establish both the duration to recover the original investment (using the IRR of this

project of 11.13%) and the duration to recover the present value of the project (at

an 8% hurdle rate).





Solution

Duration taken to recover the original investment

Year 1 2 3 4

1. Discount cash inflows @ 11.13% £6,839 £13,361 £9,473 £4,327

2. Proportion of initial outlay (£34,000) 0.201 0.393 0.279 0.127

3. Proportion multiplied by year number 0.201 0.786 0.837 0.508

Finally, sum these to provide the duration i.e. on average the company will take

2.332 years to recover the initial investment i.e. an indication of project

uncertainty (see below).

Duration taken to recover the present value of the project

Year 1 2 3 4

1. Discount cash inflows @ 8% £7,037 £14,146 £10,320 £4,851

2. Proportion of project PV (£36,354) 0.194 0.389 0.284 0.133

3. Proportion multiplied by year number 0.194 0.778 0.852 0.532

Finally, sum these to provide the duration i.e. on average the company will take

2.356 years to recover half the present value of the project i.e. a different

indication of project uncertainty. The longer the duration, the greater the

uncertainty attaching to future returns!!





Gento Ltd

Gento Ltd has been invited to make a tender for a contract to manufacture six

special processing machines. Manufacture would take a total of three years,

commencing immediately (1st August 2005), and the contract price would be

payable in two equal instalments, the first on 1st August 2005 and the second on

31st July 2008. The company would manufacture two machines each year.

The following estimates are available about the resources required to produce the

special processing machines:

(1) Materials

Type of

material

Quantity

per

machine

Amount in

stock now

Original

cost of

stock per

ton

Current

purchase

price per

ton

Current

realisable

value per

per ton

tons tons £ £ £

Gamma 20 60 700 1,000 800

Zeta 10 20 500 750 see below

Gamma is used regularly by the company on many contracts. Zeta is used

rarely and if the existing stock is not applied to this contract it will have to be

disposed of immediately at a net cost of £100 per ton. Materials required for

the contract must be purchased and paid for annually in advance.

Replacement costs of Gamma and Zeta and the realisable value of Gamma

are expected to increase at an annual compound rate of 20%.

(2) Labour

Each of six machines will require 3,000 hours of skilled labour and 5,000 hours

of unskilled labour. Current wage rates are £4 per hour for skilled labour and

£3 per hour for unskilled labour.

Gento Ltd expects to suffer a shortage of skilled labour during the year to 31st

July 2006 so that acceptance of the contract would make it necessary to give

up other work on which a contribution of £7 per hour, net of skilled labour

costs, would be earned. (The “other work” would require no unskilled labour).

For the year to 31st July 2006 only, the company expects to have 20,000

surplus unskilled labour hours. Gento Ltd has an agreement with its labour

force whereby it lays off employees for whom there is no work and pays them

two-thirds of their normal wages during the layoff period.

All wage rates are expected to increase at an annual compound rate of 15%.

(3) Overheads

Overhead costs are currently allocated to contracts at a rate of £14 per skilled

labour hour, calculated as follows:

£

Fixed overheads (including equipment depreciation of £5) 11.00

Variable overheads 3.00

14.00





Special equipment will be required for this contract, and will be purchased on 1st

August 2005 at a cost of £200,000 payable immediately. It will be sold on 31st

July 2008 for £50,000. Both fixed and variable overheads are expected to increase

in line with the Retail Price Index.

Gento Ltd has a cost of capital of 20% per annum in money terms. The Retail Price

Index is expected to increase in the future at an annual compound rate of 15%.

Assume that all payments will arise on the last day of the year to which they relate

except where otherwise stated. Assume also that input prices will change annually

at midnight on 31st July.

You are required to:

(a) Calculate the minimum price at which Gento Ltd should be willing to

undertake the contract to manufacture the six special processing machines

based on the information given above.

(b) Provide brief explanations of the figures you have used, and

(c) Comment on other factors, not reflected in your calculations, which may affect

the minimum acceptable price.





Gento Ltd solution

(a) Calculation of minimum price

Present value of costs

Date 1.8.05 31.7.06 31.7.07 31.7.08

Year 0 1 2 3

Reference to workings

£’000 £’000 £’000 £’000

Equipment (200) - - 50

Materials

Gamma 1 (40) (48) (57.6) -

Zeta 2 2 (18) (21.6) -

Labour

Skilled 3 - (66) (27.6) (31.74)

Unskilled 4 - (10) (34.5) (39.67)

Variable

overheads

5

-

(18)

(20.7)

(23.81)

Net cash

outflows

(238) (160) (162.0) (45.22)

Money

Discount Factor

20%

1.0 0.833 0.694 0.579

(238) (133.28) (112.43) (26.18)

Total PV of costs = (509.89)

The minimum contract price will be such that the PV of the cash received just

covers the total PV of the costs, i.e. £509,890.

If £X = Total price paid

2

Xwill be received on 1.8.05 (Year 0) and

2

X on 31.7.08 (year 3)

The PV of these cash inflows will be 2

X +

2

X579.0 = 0.7895X

For the minimum price therefore

0.7895X = £509,890

X = £645,839

The minimum total contract price is £645,839

WORKINGS

(1) Material Gamma

2 machines p.a. each requiring 20 tons at current price.

Cost for 2006 = 2 x 20 x £1,000 = £40,000 (paid in advance – Year 0)

2007 = £40,000 x 1.20 = £48,000 (Year 1)

2008 = £40,000 x (1.20)2 = £57,600 (Year 2)





(2) Material Zeta

2 machines p.a. requiring 10 tons each.

Costs for 2006

20 tons used from stock produce a cost saving of 20 x £100 = £2,000

(Year 0)

Costs for 2007 = 20 x £750 x 1.20 = £18,000 (Year 1)

2008 = 20 x £750 x (1.20)2 = £21,600 (Year 2)

(3) Skilled Labour

Annual requirement = 2 x 3,000 hours = 6,000 hours.

Year 1 – 6,000 hours at opportunity cost (£4 + £7) = £66,000

Year 2 – 6,000 hours at normal wage rate 6,000 x £4 x

1.15 = £27,600

Year 3 – 6,000 x £4 x (1.15)2 = £31,740

(4) Unskilled Labour

Annual requirement 2 x 5,000 hours = 10,000 hours.

Year 1 only: 20,000 surplus hours

Extra wages payable for 10,000 hours worked = 10,000 x £3 x 1/3 =

£10,000

Year 2 10,000 x £3 x 1.15 = £34,500

Year 3 10,000 x £3 x 1.152 = £39,675.

(5) Variable Overheads

6,000 x £3 p.a. = £18,000 p.a. rising by 15%.

(b) Brief explanation of the figures used

(1) General approach

The general approach is to estimate the relevant “money” cash flows

associated with each cost, that is the cash flows after allowing for

expected rates of inflation. These cash flows are then discounted at the

“money” cost of capital which contains an element of inflation.

(2) Material – Gamma

This material is used on many contracts. The extra requirement on this

contract will therefore be met by purchasing extra material at current

replacement cost.

(3) Material – Zeta

If existing stock is not applied to this contract, it will have to be disposed

of immediately at a net cost of £100 per ton. The 20 tons now in stock

will therefore be valued as a cash inflow of £100 per ton, because the

use of this material will actually produce cost savings to the organisation

as a whole.





(4) Skilled Labour

In year one the use of skilled labour does not in fact produce any extra

cash outlay on labour, because the men would be employed on other

work if this contract was not accepted. However the use of skilled

labour on this contract means that revenues from the other work are

lost. The measure of this loss is £7 contribution per skilled labour hour,

but since this contribution is after deducting £4 per hour for labour, the

total relevant opportunity cost per hour is £7 + £4 = £11.

(5) Unskilled Labour

In year one the incremental cost to the organisation is the payment of

the remaining one-third of normal wage rates for 10,000 hours to the

men who are at present laid off.

(6) Overheads

It is assumed that fixed overheads will be unchanged as a result of the

decision. Accordingly, only variable overheads are relevant costs.

(c) Discussion of other factors affecting the minimum acceptable price

(1) It has been assumed that all estimates of cash flows, inflation rates etc

can be made with certainty. This is unrealistic. Allowance for

uncertainty can be incorporated into the appraisal in various ways. An

assessment can be made of the sensitivity of the project to a number

of variables (e.g. price level changes). Alternatively several estimates

can be made for each variable and subjective probabilities attached

to each with a view to quantifying the uncertainty.

(2) The relationship between the risk characteristics of the project and

the present portfolio of projects being undertaken by Gento Ltd must be

taken into account with a view to a possible reduction in the overall risk

of the firm.

(3) Taxation should be included in the analysis to obtain a realistic

minimum price.

(4) The availability of working capital to finance the project has been

assumed. The first instalment received at 1st August 2005 will cover

the cost of the equipment and materials required at this date but extra

cash will be required in Years 1 and 2.

(5) This project must be appraised in relation to any other alternatives

which might be available in competition for the scarce resources of the

firm.

(6) The effect of accepting the project on future trading should be

considered, particularly in two respects:

(i) the possibility of losing future trade from present customers

perhaps affected by the transfer of the skilled labour.

(ii) the desirability of influencing the proposed customer on the

present contract, by offering a lower tender, in the hope of

obtaining more lucrative contracts later.





Hulme Ltd

Hulme Ltd is considering the manufacture of a new product, the Champ, to add to

its existing range. Manufacture would commence on 1 January 2007 and 100,000

Champs would be produced and sold each year for three years. The directors of

Hulme Ltd expect to be able to charge a price of £6 per Champ during 2007 and to

increase the price during 2008 and 2009 in line with increases in the Retail Price

Index. The Index is expected to increase in the future at an annual compound rate

of 10%.

The following costs are involved in producing Champs.

Labour. Each Champ requires ¼ hour of skilled labour and ½ hour of unskilled

labour (1 January 2007) wage rates are £3 per hour for skilled labour and £2 per

hour for unskilled labour. For 2007 only Hulme Ltd expects to have 100,000

surplus hours of unskilled labour. Whether or not Champs are manufactured, the

employees concerned will be retained and paid by the company. All labour costs


Materials. Each Champ requires 2kgs of Alpha and 1 kg of Beta. Hulme Ltd

currently holds in stock 200,000 kgs of Alpha and 100,000 kgs of Beta. The stock

of Alpha originally cost £0.40 per kg and has a current realisable value of £0.30 per

kg. The current buying price is £0.50 per kg. The stock of Beta originally cost

£0.80 per kg and has a current realisable value of £0.90 per kg. The current

buying price is £1.10 per kg. Alpha is used regularly by the company on many

products. Beta is used rarely and the only use for the existing stock, if it is not

applied to the manufacture of Champs, is to sell it immediately.

Materials required to manufacture Champs must be purchased and paid for

annually in advance. Replacement costs and realisable values of Alpha and Beta


Overheads. It is the policy of the company to allocate all overhead costs to its

various products. The calculated overhead cost per unit for Champs, at current

price, is as follows:

£

Allocated head office fixed costs (rent, rates, administration, etc) 0.70

Depreciation £30,000 ÷ 100,000 0.30

Variable overheads 0.50

£1.50

Head office costs and variable overheads are expected to increase in line with the

Retail Price Index. The machine required to manufacture Champs was bought

some years ago. Its current book value is £90,000, and the above depreciation

charge is based on a remaining life of three years at the end of which the machine

will have no scrap or re-sale value. If it is not used to produce Champs the

machine will be sold immediately for £150,000.

Hulme Ltd has a cost of capital of 20% per annum in money terms.

Assume that all receipts and payments (except costs of materials and machine sale

proceeds) will arise on the last day of the year to which they relate.

Assume also that input prices will change annually on 31 December.





Requirements

(a) Prepare calculations showing whether Hulme Ltd should undertake production

of the Champ.

(b) Provide brief explanations of the figures you have used.

(c) Comment on factors which are not included in your calculations but which

may affect the decision.

Ignore taxation.





Hulme Ltd solution

(a) Cash flows resulting from manufacture and sale of champs

Ref. to

Workings Time 0 Time 1 Time 2 Time 3

£000 £000 £000 £000

Machine (150) - - -

Labour (1) - (75) (210) (252)

Materials

Alpha (2) (100) (110) (121) -

Beta (3) (90) (121) (133) -

Overheads (4) - (50) (55) (61)

Total outflows (340) (356) (519) (313)

Sales (5) - 600 660 726

Net inflow/(outflow) (340) 244 141 413

20% discount factor 1.000 0.833 0.694 0.579

Present value (340) 203 98 239

Net present value = +£200,000

On the basis of the estimates given, production of Champs is worthwhile.

Note Time 0 is taken to be the date on which manufacture would

commence, i.e. 1 January 2007; time 1 is 31 December 2007, etc

WORKINGS

For explanations of the figures used, see part (b)

(1) Labour cost

Year 1 Skilled 25,000 hours @ £3 75,000

Unskilled No cost incurred

£75,000

Year 2 Skilled 25,000 x (£3 x 1.2) 90,000

Unskilled 50,000 x (£2 x 1.2) 120,000

£210,000

Year 3 Year 2 cost x 1.2 £252,000

(2) Material Alpha

Current buying price is 50p per kg, rising at 10% per annum.

Time 0 cost 50p x 200,000 = £100,000

Time 1 cost £100,000 x 1.1 = £110,000

Time 2 cost £110,000 x 1.1 = £121,000

(3) Material Beta

Quantity held is enough for one year

Time 0 realisable value 100,000 x 90p = £90,000

Time 1 buying price 100,000 x £1.10 x 1.1 = £121,000

Time 2 buying price £121,000 x 1.1 = £133,100





(4) Overheads

The only relevant cost are variable overheads, which rise at 10% per

annum.

Year 1 cost 100,000 x 50p = £50,000

Year 2 cost £50,000 x 1.1 = £55,000

Year 3 cost £55,000 x 1.1 = £60,500

(5) Sales

The selling price rises at 10% per annum

Year 1 100,000 x £6 = £600,000

Year 2 £600,000 x 1.1 = £660,000

Year 3 £660,000 x 1.1 = £726,000

(b) Brief explanations of figures used

(1) Machine

Although the machine is owned already, it has an opportunity cost if

used on this project, which is the revenue foregone if it is not sold now

for £150,000.

(2) Labour

In the first year of the project the company will have to pay for extra

skilled labour only, as there is enough surplus unskilled labour to cover

the necessary 50,000 hours on the project. As this unskilled labour is

paid whether or not the Champs are produced, there is no relevant

unskilled labour cost in year 1 of the project.

In years 2 and 3 of the project the company will have to pay for extra

skilled and unskilled labour.

(3) Material Alpha

Alpha is used regularly by the company on many projects. If existing

stocks are used to manufacture Champs, the company will have to buy

in more stocks of Alpha for its other projects. The relevant cost of Alpha

is thus always its buying price, which is expected to rise by 10% per

annum.

(4) Material Beta

Present stocks of Beta are sufficient for the first year’s production of

Champs. Since there is no alternative use for Beta within the company,

the opportunity cost of existing stocks is the realisable value of 90p per

kg.

After one year present stocks will be exhausted, and the relevant cost of

further supplies of Beta will be the buying price.





(5) Overheads

Fixed costs allocated from head office will be irrelevant to this decision

as they will be incurred whether or not Champs are produced.

Depreciation is irrelevant to a project appraisal based on cash flows.

The only relevant cost is, therefore, the variable overhead.

(c) Factors not included in the calculations which may affect the decision

(i) Availability of more profitable projects

The project has been appraised in its own right, but it should be

compared with alternative uses for the funds employed, particularly if

there are constraints on capital or other resources.

(ii) Scarcity of resources

The calculations assume that there is no scarcity in supply of the

resources used on the project, e.g. that sufficient supplies of Alpha or

skilled labour are available at the prices stated and that the use of them

will not affect the quantities available for the company’s normal

operations. If there is a scarcity in supply, the opportunity cost of these

resources will include the lost contribution through not using the

resources on alternative projects.

(iii) Risk and uncertainty of estimates

Most of the figures used in the project appraisal are subject to

uncertainty. The decisions might be affected by revised estimates of the

following:

(1) The sales price/sales volume relationship. Marketing of the Champ

may encourage others to compete with the new product, leading to

reduced sales, or to reduced selling price, or to a combination of

the two.

(2) The rate of inflation, which could lead to revised forecasts for costs

and the cost of capital.

(3) The length of the project

(4) Whether head office fixed costs would be unaltered by the new

project. In practice, the addition of a new line is likely to increase

fixed costs. Additional staff may be employed in accounts,

despatch or stores (for example) not directly connected with the

new product line, but ultimately resulting from the increased

turnover. The need for additional storage area may require the

utilisation of space which could otherwise have been sub-let. If so,

the rental income foregone would be treated as a relevant cash

outflow.

Other more general possibilities, such as a change of government or a

change in fiscal policy, may affect the profitability of the project.





(iv) Management and labour skills

The calculation assumes that the necessary skills exist for this new

project or that they can be quickly acquired without any initial problems.

In practice this would be a major factor in the decision.

(v) Technological change

Changing technology may render the Champ obsolete before the end of

three years.





Bailey plc

Bailey plc is developing a new product, the Oakman, to replace an established

product, the Shepard, which the company has marketed successfully for a number

of years. Production of the Shepard will cease in one year whether or not the

Oakman is manufactured. Bailey plc has recently spent £75,000 on research and

development relating to the Oakman. Production of the Oakman can start in one

year’s time.

Demand for the Oakman is expected to be 5,000 units per annum for the first three

years of production and 2,500 units per annum for the subsequent two years. The

product’s total life is expected to be five years.

Estimated unit revenues and costs for the Oakman, at current prices, are as

follows.

£ £

Selling price per unit 35.00

Costs per unit

Materials and other consumables 8.00

Labour (see (1) below) 6.00

Machine depreciation and overhaul (see (2) below) 12.50

Other overheads (see (3) below) _9.00

35.50

Loss per unit £0.50

(1) Each Oakman requires two hours of labour, paid £3 per hour at current prices.

The labour force required to produce Oakmans comprises six employees, who

are at present employed to produce Shepards. If the Oakman is not

produced, these employees will be made redundant when production of the

Shepard ceases. If the Oakman is produced, three of the employees will be

made redundant at the end of the third year of its life, when demand halves,

but the company expects to be able to find work for the remaining three

employees at the end of the Oakman’s five year life. Any employee who is

made redundant will receive a redundancy payment equivalent to 1,000

hours’ wages, based on the most recent wage rate at the time of the

redundancy.

(2) A special machine will be required to produce the Oakman. It will be

purchased in one year’s time (just before production begins). The current

price of the machine is £190,000. It is expected to last for five years and to

have no scrap or resale value at the end of that time. A major overhaul of the

machine will be necessary at the end of the second year of its life. At current

prices the overhaul will cost £60,000. As the machine will not produce the

same quantity of Oakmans each year, the directors of Bailey plc have decided

to spread its original cost and the cost of the overhaul equally between all

Oakmans expected to be produced (i.e. 20,000 units). Hence the combined

charge per unit for depreciation and overhaul is £12.50 [£(190,000 + 60,000)

÷ 20,000 units].

(3) Other overheads at current prices comprise variable overheads of £4.00 per

unit and head office fixed costs of £5.00 per unit, recovered on the basis of

labour time.





All wage rates are expected to increase at an annual compound rate of 15%. The

selling price per unit and all costs other than labour are expected to increase in line

with the Retail Price Index. The Index is expected to increase in the future at an

annual compound rate of 10%.

Corporation tax at 35% on net cash income is payable in full one year after the

income arises. 25% writing down tax allowances are available on the machine.

Bailey plc has a money cost of capital, net of corporation tax, of 20% per annum.

Assume that all receipts and payments will arise on the last day of the year to

which they relate. Assume also that all “current prices” given above have been

operative for one year and are due to change shortly. Subsequently all prices will

change annually.

Requirements:

(a) Prepare calculations, with explanations, showing whether Bailey plc should

undertake production of the Oakman.

(b) Discuss the particular investment appraisal problems created by the existence

of high rates of inflation.





Bailey plc solution

(a) Investment appraisal of production of Oakmans

Year 1 2 3 4 5 6 7

£ £ £ £ £ £ £

Contribution before

labour costs 139,150 153,065 168,371 92,604 101,865

Labour cost (39,675) (45,626) (52,470) (30,170) (34,696)

Redundancy

payments (15,741)

Redundancy

payments avoided 20,700

Machine overhaul (79,860)

_____ ______ ______ ______ _____ ______ ______

20,700 99,475 27,579 100,160 62,434 67,169

Tax at 35% (7,245) (34,816) (9,653) (35,056) (21,852) (23,509)

Cost of machine (209,000)

Tax saved on

WDAs ______ 18,288 13,716 10,287 7,715 5,786 17,359

Net cash flows £(188,300) £110,518 £6,479 £100,794 £35,093 £51,103 £(6,150)

20% factors 0.833 0.694 0.579 0.482 0.402 0.335 0.279

Present value (156,854) 76,699 3,751 48,583 14,107 17,120 (1,716)

Net present value = +£1,690

Conclusion

Bailey plc should, on the basis of the positive net present value, undertake

production of the Oakman. However, the decision is fairly marginal, and the

estimate of all variables should be carefully reviewed to ensure that the

decision to produce is the correct one.

Explanatory notes

If the current date (per question) is taken as year 0, production will

commence and the machine will be purchased one year later at the end of

year 1. Revenue and costs will arise initially during year 2. Current (year 0)

prices are due to change shortly and therefore two price increases will occur

before the start of production (year 0 and year 1 increases).

(1) Contribution from sales before labour costs

These cash flows have been grouped as they all inflate at 10% per

annum. At current values the cash flow per unit is as follows:

£

Sales price 35

Material and other consumables (8) (It is assumed that there is

no change in head office

fixed costs if Oakman is

produced)

Variable overheads (4)

Net contribution before labour

costs £23





Year Production units Contribution before labour costs

Unit/£ Total/£

2 5,000 23 x (1.1)2 139,150

3 5,000 23 x (1.1)3 153,065

4 5,000 23 x (1.1)4 168,371

5 2,500 23 x (1.1)5 92,604

6 2,500 23 x (1.1)6 101,865

(2) Labour cost

At current prices the labour cost per unit of 2 hours x £3 is included as

the six employees would not be paid if the Oakman were not produced.

Year Production units Labour costs

Unit/£ Total/£

2 5,000 6 x (1.15)2 39,675

3 5,000 6 x (1.15)3 45,626

4 5,000 6 x (1.15)4 52,470

5 2,500 6 x (1.15)5 30,170

6 2,500 6 x (1.15)6 34,696

(3) Redundancy payment

This is the payment to the three redundant employees in four years’

time.

Year 4: 3 men x 1,000 hours x £3 x (1.15)4 = £15,741 outflow.

(4) Redundancy payments avoided

If the Oakman were not produced, there would be a payment to the six

employees who would be made redundant. This is avoided and hence is

an incremental cash inflow.

Year1: 6 men x 1,000 hours x £3 x 1.15 = £20,700 inflow.

(5) Purchase and maintenance of machine

These are the cash flows that will be incurred at year 1 and two years

later at year 3

Purchase cost at year 1: £190,000 x 1.1 = £209,000.

Overhaul cost at year 3: £60,000 x (1.1)3 = £79,860.

(6) Overhead costs

It is assumed that the overhead costs will be allowed for tax in the year

in which they are incurred.

(7) Taxation

All tax paid on accounting profit is based on the previous year’s cash

flow at 35%.





(8) Writing down allowances and tax savings

WDA Tax

saved

Timing

£ £ £

Cost – paid at end of first

year (t1)

209,000

WDA year 1 (52,250) 52,250 18,288 t2

156,750

WDA year 2 (39,188) 39,188 13,716 t3

117,563

WDA year 3 (29,391) 29,391 10,287 t4

88,172

WDA year 4 (22,043) 22,043 7,715 t5

66,129

WDA year 5 (16,532) 16,532 5,786 t6

49,597

Proceeds – end of year 6 -__

Balancing allowance £49,597 49,597 17,359 t7

(9) The production of Oakman has been evaluated by considering the

incremental change in the company’s cash flows caused by a decision to

produce. These have been valued at the actual cash flow in each year

after allowing for the differing effects of inflation on each item. These

money cash flows have then been discounted at the money cost of

capital (net of corporation tax).

The £75,000 already spent on research and development is a sunk cost

and is therefore irrelevant to our calculations.

(b) Discussion of investment appraisal problems caused by high inflation

rates.

The existence of high rates of inflation creates problems in investment

appraisal by contributing to the uncertainty attached both to the cash flows

themselves and the appropriate discount rate. It is unlikely that in any

investment appraisal situation each cash flow stream will be affected in the

same way by specific price changes. The budget must predict as accurately

as possible the anticipated level of inflation.

Higher rates of inflation will tend to be more volatile than lower rates,

especially as government action will be directed to reducing them. With

different inflation rates applying to each item (e.g. materials and labour) the

value of an investment could be highly sensitive to changes in those rates.

The extent to which the effect of inflation can be passed on by income

increases (e.g. raising product selling price) must also become less certain as

government controls, competitors’ reactions and the elasticity of demand

become more important.

The conventional treatment of inflation is to discount the anticipated money

cash flows at a money discount rate. This money rate would normally be

derived from the so-called “dividend valuation model”, to give the

shareholders’ required rate of return and the required rate of return for other

suppliers of capital such as debenture holders. Such a required rate of return

will consist of both a real rate reflecting the “time value of money” to the

providers of funds, plus an additional return to compensate for the decrease

in purchasing power caused by inflation.





Clearly, with higher anticipated inflation rates, such a money rate will be

higher than with lower rates. However, the company must anticipate such a

required rate of return when evaluating capital projects. With high inflation

rates this anticipation becomes more difficult, as again the expectations of the

shareholders as to the effect of inflation on them will become more diverse.

Also with the increased probability of changes in inflation in the future, the

required rate of return is unlikely to be constant over the life of the project.

The company will be faced with increasing uncertainty as to whether it is

acting in the best interests of shareholders by accepting or rejecting a

particular project.

Finally, it should be noted that the above comments refer to the problems

presented to investment appraisal by expected or anticipated inflation. The

correct treatment in capital budgeting of unanticipated inflation has so far

defied a workable solution, and this represents a serious gap in the theory of

financial decision making.




Chapter 4

Cost of capital



CHAPTER 4 – COST OF CAPITAL


CHAPTER CONTENTS

PURPOSE OF COST OF CAPITAL ---------------------------------------- 99

CALCULATING THE COMPONENT COSTS OF CAPITAL --------------- 100

1. COST OF EQUITY SHARE CAPITAL 100

2. COST OF PREFERENCE SHARE CAPITAL 102

3. COST OF DEBT 102

CALCULATING THE WEIGHTED AVERAGE COST OF CAPITAL ------- 104

MAIN ASSUMPTIONS UNDERLYING USE OF WACC AS THE DISCOUNT RATE --------------------------------------------------------------------- 107

JUSTIFICATION FOR THE USE OF WACC ----------------------------- 108

SOURCES OF FINANCE ------------------------------------------------- 109

SOURCES OF SHORT-TERM FINANCE 109

SOURCES OF LONG-TERM FINANCE 110

SMALL AND MEDIUM-SIZED ENTITIES (SMES) 110

QUESTION (NEVADA PLC) --------------------------------------------- 112

QUESTION (CRYSTAL PLC) -------------------------------------------- 114

QUESTION (NILE PLC) ------------------------------------------------- 117





PURPOSE OF COST OF CAPITAL

As a “discount rate” for NPV or “cut-off rate” for IRR.

(N.B. Cost of Capital is sometimes denoted by the letter “r”, whilst in other texts it

is denoted by the letter “k”. The note which follows uses the latter notation).





CALCULATING THE COMPONENT COSTS OF CAPITAL

1. Cost of equity share capital

(a) Retained earnings (an opportunity cost)

Ke = div)-(ex P

D

0

Example 1 (Naylor plc)

Naylor plc is expected to pay a constant annual net dividend of 30p per ordinary

share. The current market price per share is £2.30 (cum-div). The dividend is

about to be paid.

What is Ke?

Solution 1 (Naylor plc)

Ke = p30p230

p30

− = 15%

(b) Fresh issue of equity

Two views:

(i) Ke = fP

D

0 −

Example 2 (Goodman plc)

Goodman plc wishes to finance a new project by the issue 40,000 ordinary shares

of £2.50 each, out of which share issue (flotation) costs of 8% of issue price have

to be paid. New shareholders expect constant annual dividends of 32.2p per share.

What is Ke?

Solution 2 (Goodman plc)

Ke = 50.2£ x %92

p2.32 = 14%

(ii) Carsberg recommends that share issue costs are treated as a year 0 cash

outflow of the project for which the share capital is raised. Thus share issue

costs do not affect Ke. In Example 2, Ke would be calculated as follows:

Ke = 50.2£

p2.32 = 12.9%





(c) Growth

The Dividend Growth model is:

Ke = g P

)g1( D

0

0 ++

= g P

D

0

1 +

Example 3

Current cum-div price £2.20

Impending dividend 20p

Expected growth p.a. 10%

Calculate Ke

Solution 3

Ke = %102£

p22+ = 21%

Two methods of estimating future growth

(i) Historical growth in dividends

Example 4 (Talbot plc)

The dividends of Talbot plc over the last five years have been:

Year Annual Net Dividends

2004 £150,000

2005 £172,000

2006 £195,380

2007 £230,100

2008 £262,350

Estimate the historical growth rate as a prediction of future growth.

Solution 4 (Talbot plc)

Dividend in 2004 (1 + g)4 = Dividend in 2008

(1 + g)4 = 2004 in Dividend

2008 in Dividend

= 000,150£

350,262£ = 1.749

(1 + g) = 4 749.1 = 1.15

g = 15%





(ii) Use of Gordon growth approximation

g = br

where: b = proportion of earnings retained p.a.

r = average return on reinvested funds.

Strictly only applicable to all-equity companies, but is often used for geared

companies as an approximation of growth rates.

Example 5

Establish an estimate of future growth and of Ke if:

Proportion of earnings distributed p.a. 60%

Average return on reinvested funds 10%

Current cum-div price £1.08

Impending dividend 12p

Solution 5

g = 40% x 10% = 4%

Ke = p96

p48.12 + 4% = 17%

2. Cost of preference share capital

Kps = div)-(ex P

)net( D

0

3. Cost of debt

(a) Irredeemable

Kb = int)-(ex debt of Value Market

)tl( Interest −

(b) Redeemable

IRR exercise

Example 6

A 5% debenture is currently quoted at £95.84 (ex-int). It is redeemable at the end

of 3 years at £100.

Taking corporation tax at 50%, and ignoring the timing lag for tax savings,

calculate Kd.





Solution 6

Year £ Try DF @ 4% £

0 Cost (95.84) 1.00 (95.84)

1 Interest £5(0.5) 0.962 2.41

2 Interest £2.50 0.925 2.31

3 Interest & Redemption £102.50 0.889 91.12

NPV NIL

Therefore, Kb = IRR = 4%

NB Try 3% (NPV + £2.74) and 5% (NPV - £2.63), then by linear interpolation

Kb = 3% + 37.5£

74.2£ x 2% = 4.02%

i.e. linear interpolation tends to overstate the IRR of “normal” cash flows

(c) Convertible

The cost of convertible debt is calculated in a similar manner to the calculation of

the cost of redeemable debt, EXCEPT that in the final year, one must include the:

- redemption value of the debt, or

- conversion value of the debt

whichever is the GREATER.

(d) Floating rate debt

The cost of floating rate debt (e.g. most bank loans and overdrafts) is the current

interest rate being charged on such funds.

Accordingly, if a company is paying interest at LIBOR + 8%, when LIBOR is set at

5% p.a. and corporation tax rates are at 30%, Kd will be calculated as follows:

Kd = (5% + 8%) x (1 – 0.3) = 9.1%





CALCULATING THE WEIGHTED AVERAGE COST OF

CAPITAL (WACC)

Difficult to associate a project with a specific source of finance, as a pool of

resources are available in order to invest in projects. Thus a WACC is an

appropriate discount rate/cut off rate.

Example 7 (Whyte plc)

Whyte plc has on issue:

(a) 500,000 ordinary shares of £1 each, whose ex-div share price is £2. A

constant dividend of 36p per share will be paid on these for several years

hence.

(b) 500,000 6% preference shares of £1 each, whose ex-div share price is 50p.

(c) £1,000,000 10% irredeemable debentures, quoted at 75 (ex-interest).

Calculate K0 (i.e. the WACC) assuming Corporation Tax at 40%.

Solution 7 (Whyte plc)

Market Value Component Cost

£ £

Equity (½m @ £2) 1,000,000 18% 180,000

Prefs (½m @ 50p) 250,000 12% 30,000

Debt (£1m @ 75) 750,000 8%* 60,000

£2,000,000 £270,000

K0 = 000,000,2£

000,270£ = 13.5%

*Kb = £75

)4.01( 10£ − = 8%





Comprehensive example (Hunt plc)

The management of Hunt plc is trying to decide upon a cost of capital discount rate

to apply to the evaluation of investment projects.

The company has an issued share capital of 500,000 ordinary £1 shares, with a

current market value cum div of £1.17 per share. It has also issued £200,000 of

10% debentures, which are redeemable at par in 2 years and have a current

market value of £105.30 per cent and £100,000 of 6% preference shares, currently

priced at 40p per share. The preference dividend has just been paid, and the

ordinary dividend and debenture interest are due to be paid in the near future.

(The preference dividend is shown net).

The ordinary share dividend will be £60,000 this year, and the directors have

publicised their view that earnings and dividends will increase by 5% per annum

into the indefinite future.

The fixed assets and working capital of the company are financed by:

£

Ordinary shares of £1 500,000

6% £1 Preference shares 100,000

Debentures 200,000

Reserves 380,000

1,180,000

Calculate the WACC. Assume corporation tax at 50% per annum, payable

one year in arrears





Solution to comprehensive example (Hunt plc)

Ke = %5p1217.1£

)05.1( p12+

− = 17%

Kps = p40

p6 = 15%

Kb

Year Capital Interest Tax Net Try DF @ 8% Net

£ £ £ £ £

0 (95.30) (95.30) 1.00 (95.30)

1 10 10 0.926 9.26

2 100 10 (5) 105 0.857 89.99

3 (5) (5) 0.794 (3.97)

-0.02

Therefore, Kb = IRR = 8%

WACC

Market Value Component Cost

£ £

Equity (½m @ £1.05) 525,000 17% 89,250

Prefs (100K @ 40p) 40,000 15% 6,000

Debt (£200K @ 95.30) 190,600 8% 15,248

£755,600 £110,498

Ko = 600,755£

498,110£ = 14.6%





MAIN ASSUMPTIONS UNDERLYING USE OF WACC AS THE

DISCOUNT RATE

1. Only under conditions of perfect capital markets will the costs of capital

calculated represent the true opportunity cost of funds used.

2. The project must be small relative to the size of the company (i.e. it

represents a marginal investment). This is because the costs of capital

calculated refer to the minimum required return of marginal investors and

therefore are only appropriate for the evaluation of marginal changes in the

company’s total investment.

3. Using the existing market value mix of funds as weights in the calculation

assumes that in the long run funds will be raised in this proportion (i.e. in the

long run the capital structure of the company will remain unchanged). This

implies that the current gearing ratio is thought to be optimal.

4. No attempt is made to match a project with a particular source of funds. All

funds are regarded as forming a pool out of which all projects are financed

(the ‘pool’ concept).

5. The project is of average risk for the firm and will cause no change in the risk

of the company as perceived by investors. This is because the cost of capital

estimates are only valid for the existing level of risk in the enterprise.





JUSTIFICATION FOR THE USE OF WACC

NOTE. For simplicity of explanation, the following example uses the IRR technique

of investment appraisal. It is emphasised that most authorities would advocate use

of the NPV approach.

Illustration

Whyte plc has the following capital costs:

Ko = 13.5%

Ke = 18%

Kb = 8%

Suppose that in March 2008 the company proposes to raise debt at 8% to finance

Project A whose IRR is 12%. Whyte plc accepts Project A since IRR > Kb.

Subsequently in June 2008 Whyte plc considers the issue of equity at 18% to

finance Project B whose IRR is 17%. However the company rejects Project B since

IRR < Ke.

Is it logical to reject a project yielding 17%, whilst accepting one yielding 12%?

The use of WACC (at 13.5%) would have provided the logical answer i.e.

Reject Project A (with an IRR of 12%), and

Accept Project B (with an IRR of 17%)

Therefore generally do not test the viability of a project by reference to its specific

financing source, but by reference to WACC.

The only exception to this rule is when the finance is provided (by e.g. a local

authority or government department) to assist in the financing of a specific project

undertaken for that agency.





SOURCES OF FINANCE

Sources of short-term finance

Bank overdrafts

If cash outflows from a bank current account exceed inflows for a temporary period,

a clearing bank may provide an overdraft. Overdrafts may be arranged speedily,

but are subject to review by the bank, may be renewable and offer a level of

flexibility, whilst interest is only paid on the overdrawn amount.

Overdrafts are technically repayable on demand and may require some form of

security or guarantee. Interest is often payable at a variable rate (ie benchmark

rate plus a premium) and an arrangement fee is normally payable upon the initial

grant of the facility.

Short-term loans

Bank loans are an agreement for the provision of a specific fixed sum for a

predetermined period at an agreed interest rate. A term loan is provided in full at

the start of the loan period and is repaid at a specified time or in instalments over a

period of agreed dates.

Bank loans are only repayable on the agreed dates, but are more expensive and

less flexible than overdrafts. The terms of the loan must be adhered to and the

bank may impose loan covenants with which the borrower must comply.

Trade credit

Raw materials are normally purchased on credit and this effectively represents an

interest free short-term loan. It is important to remember that payment delays

would worsen the credit rating of the company and that additional credit may then

be difficult to obtain. The loss of settlement discounts that suppliers may offer for

early payment must be considered.

Lease finance

Instead of the outright purchase of a non-current asset, a company may choose to

obtain the temporary use of that asset by means of an operating lease, whereby

the risks and rewards of ownership are retained by the lessor (ie the legal owner).

An operating lease contract between a lessor and lessee is for the hire of a specific

asset, whereby the lessee has possession and use of equipment for a period which

is shorter than the economic useful life of the asset, but the lessee is committed to

pay specified rentals during the period of the lease. The lessor is normally

responsible for repairs and maintenance and the lease can sometimes be cancelled

at short notice.





Sources of long-term finance

The main sources are:

● Fixed interest capital (i.e. debt finance) and preference share capital;

● Equity finance, which is commonly raised by rights issues, placings, offers for

sale or public issues following a stock exchange introduction. Details may be

found in your Study Manual.

Two other long-term sources of finance available to businesses are:

Lease finance

A long-term leasing arrangement is likely to be finance lease, ie a lease that

transfers substantially all the risks and rewards incidental to the ownership of an

asset to the lessee. Legal title may or may not eventually be transferred.

The lessor is likely to be a bank or other financial institution, which does not

normally trade in the type of asset concerned. The lessee normally becomes

responsible for the cost of repairs and maintenance.

The substance of a finance lease arrangement is that the lessee is effectively

borrowing in order to have use of a non-current asset for substantially the whole of

its useful economic life and thereby becomes liable for all lease payments. In

contrast, an operating lease is equivalent to the short-term rental of an asset from

an organisation which normally trades in that type of asset.

Venture capital

Venture capital is the provision of risk bearing capital, normally provided in return

for an equity stake in companies with high growth potential.

The 3i Group (a member of the FTSE 100 Index) is one of the world’s oldest

venture capital organisations and is involved in schemes in Europe, the USA and

the Far East. The 3i Group is prepared to invest in companies with a highly

motivated management team, having a well defined strategy and target market,

which are committed to innovation and a proven ability to outperform competitors.

Venture capitalists may provide finance for business start-ups, the development of

existing businesses, management buyouts and the realisation of the investments of

existing owners who wish to exit their companies.

Where company directors seek assistance from a venture capitalist they must

expect that the institution will require an equity stake in the company, need

convincing that the business will be successful, seek representation on the

company’s board of directors, demand exceptional returns on their investment and

expect an obvious ultimate exit route.

Small and medium-sized entities (SMEs)

The funding gap

SMEs normally have difficulty obtaining equity finance from third parties. They

normally rely on finance from retentions, bank borrowings and rights issues. Such

companies are often considered risky, since they may not have an established track

record, lack the necessary assets to offer as security, have inexperienced

management and inadequate financial control systems.





The funding (or equity) gap becomes crucial when they wish to expand beyond

their limited sources of finance, but are not yet mature enough for a stock market

quotation.

A major problem for SMEs in obtaining equity finance is their inability to offer an

easy exit route for any investors wishing to dispose of their shares. The company

could, of course, purchase its own shares back from shareholders, but this uses

cash that could be more profitably employed elsewhere in the business of the

company.

The maturity gap

This presents a further problem for SMEs, who may ideally wish to obtain medium-

term loans. This arises due to the mismatching of the maturity of assets and

liabilities. Since the SME can secure long-term loans with mortgages against their

property assets, they find that longer term borrowing is much easier to obtain than

the medium term loans that they require.

Investors

Due to lack of security and a risk-averse attitude, banks have been reluctant to

make large investments in SMEs. However, investment has become more readily

available from:

● Venture capitalists (as above)

● Business Angels – These are wealthy private individuals prepared to invest in

start-up or expanding companies. Business Angels provide more modest

sums than venture capitalists. They normally wish to obtain an equity holding

and this will permit the company to gain access to the Angel’s network of

contacts and accumulated business experience.





Question (Nevada plc)

(i) Nevada plc has issued 10 million ordinary shares of a nominal value of £1

each. Details of the company’s earnings and dividends per share during the

past four years are as follows:

Year ended31 December Earnings per share Dividend per share

2003 35p 26p

2004 33p 27p

2005 43p 29p

2006 42p 30p

The current (December 2006) market value of each ordinary share of Nevada

plc is £2.35 cum div. The 2006 dividend of 30p per share is due to be paid in

January 2007.

Required

Estimate the cost of capital for Nevada plc’s ordinary share capital.

(ii) Ten years ago California plc issued £2.5 million 6% redeemable debentures at

a price of £98 per cent. The debentures are redeemable six years from now

at a price of £102 per cent. They are currently quoted at £59 per cent, ex

interest.

Required

Estimate the cost of capital for California plc’s redeemable debentures.

(iii) The following figures are from the current balance sheet of Delaware plc

£000

Ordinary share capital

Authorised: 10,000,000 shares of £1 10,000

Issued: 8,000,000 shares of £1 8,000

Share premium account 2,000

Revenue reserves _6,000

Shareholders funds 16,000

12% Irredeemable debentures 4,000

An annual ordinary dividend of 20p per share has just been paid. In the past,

ordinary dividends have grown at a rate of 10% per annum and this rate of

growth is expected to continue. Annual interest has recently been paid on the

debentures. The ordinary shares are currently quoted at £2.75 and the

debentures at £80 per cent.

Required

Estimate the weighted average cost of capital for Delaware plc.





Solution (Nevada plc)

(i) Cost of ordinary shares

Growth rate in dividend = 126

303 − = 0.049 (i.e. 4.9%)

Cost of equity = gP

D

0

1 +

= 049.030-235

049.1 x 30+

= 0.2025 (i.e. 20.25%)

(ii) Cost of redeemable debentures

Time Flow 20% factor PV 15% factor PV

£ £ £

0 (59) 1 (59.000) 1 (59.000)

1-6 6 3.326 19.956 3.784 22.704

6 102 0.335 34.170 0.432 44.064

(4.874) 7.768

By interpolation:

IRR = )1520( x 874.4768.7

768.715 −

++ = 18.07

Cost of debentures = 18.07%

(iii) Weighted average cost of capital

Cost of equity = 1.0275

1.1 20+

× = 0.18 (i.e. 18%)

Cost of debenture = 80

12 = 15%

Weighted average cost of capital = 0.80)(4m + 2.75)(8m

15%)0.80(4m + 18%) 2.758m

××

××××

= 520,2

444 = 17.6%





Question (Crystal plc)

The following figures have been extracted from the most recent accounts of Crystal

plc.

Balance sheet as on 30 June 2007

£000 £000

Fixed assets 10,115

Investments 821

Current assets 3,658

Less current liabilities 1,735

_1,923

12,859

Ordinary share capital

Authorised: 4,000,000 ordinary shares of £1

Issued: 3,000,000 ordinary shares of £1 3,000

Reserves 6,542

Shareholders’ funds 9,542

7% Debentures 1,300

Corporation tax _2,017

12,859

Summary of profits and dividends

Year ended 30 June: 2003 2004 2005 2006 2007

£000 £000 £000 £000 £000

Profit after interest and before tax 1,737 2,090 1,940 1,866 2,179

Less tax 573 690 640 616 719

Profit after interest and tax 1,164 1,400 1,300 1,250 1,460

Less dividends 620 680 740 740 810

Added to reserves 544 720 560 510 650

The current (1 July 2007) market value of Crystal plc’s ordinary shares is £3.27 per

share cum div. An annual dividend of £810,000 is due for payment shortly. The

debentures are redeemable at par in ten years time. Their current market value is

£77.10 per cent. Annual interest has just been paid on the debentures. There

have been no issues or redemptions of ordinary shares or debentures during the

past five years.

The current rate of corporation tax is 33%, and the current basic rate of income tax

is 25%. Assume that there have been no changes in the system or rates of

taxation during the last five years.

Required

(a) Estimate the cost of capital which Crystal plc should use as a discount rate

when appraising new investment opportunities.

(b) Discuss any difficulties and uncertainties in your estimates.





Solution (Crystal plc)

(a) The post-tax weighted average cost of capital

(i) Ordinary shares £

Market value of shares cum div 3.27

Less dividend per share (810 ÷3,000) 0.27

£3.00

The formula for calculating the cost of equity when there is dividend

growth is

Ke = gP

)g1( D

0

0 ++

In this case we can estimate the future rate of growth (g) from the

average growth in dividends over the past four years.

810 = 620(1 + g)4

(1 + g)4 = 620

810 = 1.3065

(1 + g) = 1.069

g = 0.069 = 6.9%

Ke = 069.03

1.0690.27=

× = 16.5%

(ii) 7% Debentures

In order to find the post-tax cost of the debentures, which are

redeemable in ten years time, it is necessary to find the discount rate

(IRR) which will give the future post-tax cash flows a present value of

£77.10.

The relevant cash flows are:

1. annual interest payments, net of tax, which are £100 x 7% x 67%

= £4.69 (for ten years);

2. a capital repayment of £100 (in ten years time)

It is assumed that tax relief on the debenture interest arises at the same

time as the interest payment. In practice the cash flow effect is unlikely

to be felt for about a year, but this will have no significant effect on the

calculations.

Try 8% PV £

Current market value of debentures (77.10)

Annual interest payments net of tax £4.69 x 6.710 31.47

Capital repayment £100 x 0.463 46.30

NPV 0.67

Try 9% PV £

Current market value of debentures (77.10)

Annual interest payments net of tax £4.69 x 6.418 30.10

Capital repayment £100 x 0.422 42.20

NPV (4.80)





IRR = % )89( x 80.467.0

67.0%8

−

++ = 8.12%

(iii) The weighted average cost of capital

Market value Cost

£’000 % £’000

Equity 9,000 16.50 1,485

7% Debentures 1,002 8.12 81

10,002 1,566

WACC (Ko) = 100 x 002,10

566,1 = 15.7%

The above calculations suggest that a discount rate in the region of 16%

might be appropriate.

(b) Difficulties and uncertainties arise in a number of areas.

(i) The cost of equity. The above calculation assumes that all shareholders

have the same marginal cost of capital and the same dividend

expectations, which is unrealistic. In addition, it is assumed that

dividend growth has been and will be at a constant rate of 6.9%. In

fact, actual growth in the years 2003/04 and 2006/07 was in excess of

9%, while in the year 2005/2006 there was no dividend growth. 6.9%

is merely the average rate of growth for the past four years. The rate of

future growth will depend more on the return from future projects

undertaken than on the past dividend record.

(ii) The use of the weighted average cost of capital. Use of the weighted

average cost of capital as a discount rate is only justified where the

company in question has achieved what it believes to be the optimal

capital structure (the mix of debt and equity) and where it intends to

maintain this structure in the long term.

(iii) The projects themselves. The weighted average cost of capital makes

no allowance for the business risk of individual projects. In practice

some companies, having calculated the WACC, then add a premium for

risk. This risk premium should vary from project to project, since not all

projects are equally risky. In general, the riskier the project the higher

the discount rate which should be used. Ideally, the use of the capital

asset pricing model should provide a suitable risk adjusted discount rate,

which is obviously preferable to the result of the dividend growth model,

which has been used in the solution to part a) of this question





Question (Nile plc)

Nile plc is considering an investment in projects, which will be financed from the

issue of new ordinary shares and debentures in a mix, which will hold its gearing

ratio approximately constant. It wishes to estimate the cost of capital for purposes

of appraising the projects, which would be small in relation to the company’s

present scale of operations.

The company has an issued share capital of 1 million ordinary shares of £1 each; it

has also issued £800,000 of 8% debentures. The market price of ordinary shares is

£4.76 per share and debentures are priced at £79.40 per cent. Dividends and

interest are payable annually. An ordinary dividend has just been paid; and the

next instalment of interest is payable in the near future. Debentures are

redeemable at par in eight years time.

Dividends relating to the last five years have been as follows:

Year 2002 2003 2004 2005 2006

£000 £000 £000 £000 £000

Total dividends 200 230 230 260 300

Assume that there have been no changes in the system or rates of taxation during

the last five years and that the current rate of corporation tax is 40 per cent.

Ignore personal taxation.

Required:

(a) Estimate the cost of capital which Nile plc should use as a discount rate for

purposes of investment appraisal, and

(b) Discuss any difficulties and uncertainties in your estimation.





Solution (Nile plc)

(a) Estimate of cost of capital

(i) Cost of equity, based on assumed constant growth rate

Ke = gP

)g1( D

0

0 ++

The future expected growth in dividends may be estimated from the

historical growth rate which can be seen to be approximately 10.7%, i.e.

Average growth rate, g, may be calculated as follows:

2002 Dividend (1 + g)4 = 2006 Dividend

(1 + g)4 = Dividend 2002

Dividend 2006 =

£200,000

£300,000

= 1.5

Now, g can be found by use of compound interest tables, or by the use

of a calculator:

1 + g = 4 5.1

= 1.107

g = 10.7%

Now the growth model can be employed:

Ke = 107.0p476

107.1( p30+

= 107.0476p

33.21p=

= 17.68%

(ii) Cost of debt (after corporation tax)

The effective cost of the debentures to the company allowing for

corporation tax of 40% on interest paid (an allowable charge against

profits) can be calculated by the following IRR method.

Try 10% Try 11%

Year Cash flow DF £ DF £

0 (71.40)* 1.0 (71.40) 1.0 (71.40)

1-8 (£8 x 60%) 4.80 5.335 25.61 5.146 24.70

8 100 0.467 46.70 0.434 43.40

+0.91 -3.30

Kb =

++ %1 x

30.391.0

91.0%10

= 10% + 0.22%

= 10.22%

* Ex-interest price = £79.40 - £8 = £71.40





(iii) Calculation of WACC

Using market value weightings:

Market value K% £

Ordinary shares:

1m @ £4.76

= 4,760,000 x 17.68 = 841,568

Debentures:

100

4.71 x 000,800

= 571,200 x 10.22 = 58,377

£5,331,200 £899,945

WACC (Ko) = £5,331,200

£899,945 = 16.88% (say 17%)

(b) Difficulties and uncertainties in estimating WACC

The concept of the cost of capital is perhaps the most difficult of all the DCF

concepts and one about which there is still considerable controversy.

The approach taken above employs the weighted average cost of capital

concept. It is based on the following basic principles:

(i) The cost of capital required for investment appraisal is the cost of raising

more capital in the market. The historical cost of existing capital is

irrelevant. It is for this reason that current yields (returns related to

current market prices) are used.

(ii) It is assumed that the company will maintain approximately the same

mix of capital as hitherto and that the consequent weighted average

cost of capital is an appropriate measure of the future cost. This is

management’s declared intention in this case, although it is probably

unrealistic in practice.

The difficulties and uncertainties in the estimation of the cost of capital are as

follows:

(i) Growth rate – the expected future growth rate of dividends has been

obtained from the historical average growth rate of the last five years.

(ii) Current share price – it is assumed that the current share price is a

reflection on logical investor behaviour in the market and reflects the

market’s anticipation of future dividends unaffected by extraneous

events or influences. This will frequently not be the case.

(iii) Corporation tax – it is assumed that the future rate of corporation tax

will remain at 40%. Any change in the rate, or for that matter in the

system of taxation, would affect the earnings available for distribution

and therefore the future dividend growth rate.

(iv) Risk class – it is assumed that the project to be appraised is of the same

risk class as existing project.




Chapter 5

Efficient market hypothesis



CHAPTER 5 – EFFICIENT MARKET HYPOTHESIS


CHAPTER CONTENTS

EFFICIENT MARKET HYPOTHESIS------------------------------------- 123

1. DEFINITION AND FORMS OF EFFICIENCY 123

2. THE IMPLICATIONS OF THE EMH FOR FINANCIAL MANAGERS 124

EFFICIENT MARKET HYPOTHESIS ILLUSTRATION ------------------ 125

EFFICIENT MARKET HYPOTHESIS SOLUTION ----------------------- 126

FUNCTIONS PERFORMED BY THE CAPITAL MARKET 126

EFFICIENT MARKET HYPOTHESIS 126





EFFICIENT MARKET HYPOTHESIS

1. Definition and forms of efficiency

Definition

An efficient market is one in which the market price of all securities traded on it

instantly and perfectly reflect all new information as it becomes available.

If this is correct, a company’s real financial position, with respect to both current

and future profitability, will be reflected in its share price.

The implication for an investor is that he can rarely outperform the market,

because it will already have anticipated developments in the future and have

reflected these in the share price. Therefore the best course of action for an

investor is to hold a well-diversified portfolio of shares to reduce overall risk.

Other areas of financial management, such as the dividend valuation model,

Modigliani and Miller’s arbitrage “proof”, the dividend irrelevancy hypothesis and

aspects of mergers and takeovers rely on the existence of an efficient market.

Forms of Market Efficiency

(i) Weak form

Share prices reflect all the information contained in the record of past prices and

past trading volumes. As a result it is not possible to predict future share price

movements by reference to past trends. Share prices follow a ‘random walk’.

Accordingly a chartist (technical analyst) must regard the stock market as being

totally inefficient.

(ii) Semi-strong form

Share prices also reflect all current publicly available information. Therefore prices

will change only when new information is published. As a result it would only be

possible to predict share price movements if unpublished information were known

(insider dealing). Accordingly fundamental analysis is a waste of effort if the stock

market is semi-strong efficient.

(iii) Strong form

Share prices reflect all information which is relevant to the company.

If this is the case then share price movements can never be predicted.

Gains through insider dealing are not possible because shares are priced absolutely

fairly. The government must not consider the stock market to be strong form

efficient, because of its attempts to outlaw insider dealing.





2. The implications of the EMH for financial managers

In their book “Principles of Corporate Finance”, Richard Brealey, Stewart Myers and

Franklin Allen describe six lessons of market efficiency as follows:

Lesson 1 - Markets Have No Memory.

The weak form of the EMH states that a study of past price changes will not be

helpful in predicting future price changes, i.e. markets have no memory. This

means that there is no right time to issue shares and the common reluctance of

managers to make a new issue after a price fall has no basis in theory.

Lesson 2 - Trust Market Prices.

In an efficient market the price of a security is reliable and allows for all available

information about that security. This means that it is not possible for most

investors to achieve consistently above average returns, i.e. you cannot beat the

market.

Lesson 3 - Read the Entrails.

If the market is efficient, the current price incorporates all available information

about the future. Therefore, a careful study of security prices will provide a lot of

information about investors’ expectations of the future, since investors are heavily

influenced by economic prospects.

Lesson 4 - There Are No Financial Illusions.

Attempts to improve the image of the company through such cosmetic operations

as bonus issues and changes in accounting policies or methods (e.g. depreciation

methods) are unlikely to have any material effects on market values in the long-

run. In fact they may be regarded as a sign of weakness and not of strength.

Lesson 5 - The Do-It-Yourself Alternative.

Rational investors operating in an efficient market will not pay others to do what

they can do equally well themselves. Diversification for its own sake will not

enhance market values, because shareholders could achieve the same results for

themselves, much more cheaply, by holding shares in a variety of companies.

Lesson 6 - Seen One Stock, Seen Them All.

In buying shares investors are simply buying an expected return for a given level of

risk. Where two shares have the same risk and return characteristics they will be

seen by the market as perfect substitutes one for the other (just like similar brands

of coffee). The homogeneous nature of many securities results in the demand for

the company’s shares being very elastic.

N.B. Most studies of this subject have been based on Wall Street or the London

Stock Exchange, which are surely more efficient than most other stock markets.





EFFICIENT MARKET HYPOTHESIS ILLUSTRATION

Company A has 2 million shares in issue and company B, 6 million.

On day 1 the market value per share is £2 for A and £3 for B.

On day 2 the management of B decides, at a private meeting, to make a cash

takeover bid for A at a price of £3.00 per share. The takeover will produce large

operating savings with a present value of £3.2 million.

On day 4 B publicly announces an unconditional offer to purchase all shares of A at

a price of £3.00 per share with settlement on day 15. Details of the large savings

are not announced and are not public knowledge.

On day 10 B announces details of the savings which will be derived from the

takeover.

Requirements

(a) Briefly outline the major functions performed by the capital market and

explain the importance of each function for corporate financial management.

How does the existence of a well functioning capital market assist financial

management?

(b) Describe the efficient market hypothesis and explain the difference between

the three forms of the hypothesis which have been distinguished.

(c) Ignoring tax and the time-value of money between day 1 and 15, and

assuming the details given are the only factors having an impact on the share

price of A and B, determine the day 2, day 4 and day 10 share price of A and

B if the market is:

1. semi-strong form efficient, and

2. strong form efficient,

in each of the following separate circumstances:

(i) the purchase consideration is cash as specified above, and

(ii) the purchase consideration, decided upon on day 2 and publicly

announced on day 4, is one newly issued share of B for each share of A.





EFFICIENT MARKET HYPOTHESIS SOLUTION

Functions performed by the capital market

Important points are as follows:

1. Functions

● a source of new finance (the primary market)

● provides a market for those who already hold securities (a secondary market).

2. Importance of each function

(1) The primary market

Provides a focal point for would-be borrowers and lenders and enables the

typically small sums provided by lenders to be combined into the large

amounts required by borrowers.

An efficient primary market enables companies to raise finance quickly and

with relatively low transaction costs.

(2) The secondary market

Provides liquidity for investors.

An efficient (perfect) market is a precondition for the application of many of

the financial management decision rules.

Efficient market hypothesis

Important points to make are:

(i) The EMH - states that the current share price reflects all available information

about a security and that the market will react correctly and immediately to

new information which emerges.

(ii) The weak form - the current price reflects all information about past prices

and past trading volumes.

(iii) The semi-strong form - the current share price reflects all publicly available

information (e.g. published accounts).

(iv) The strong form - the current price reflects all available information - both

public and private.





Illustration – continuation of solution

The important thing in answering this type of question is to be methodical. The

first step is to get a clear idea of what is required. Here the question is asking for

the prices of two different shares on three different days with two forms of the

efficient market hypothesis and two alternative forms of purchase consideration, a

total of 2 x 3 x 2 x 2 = 24 prices! Set up a series of grids that will show the

eventual answers.

(i) Cash consideration

(1) Semi-strong form

Day Share A Share B Note

2 £2.00 £3.00 1

4 £3.00 £2.67 2

10 £3.00 £3.20 3

Notes

1 Only publicly available information affects share prices under the

semi-strong form. No information is publicly available until day 4

so prices remain unaltered from day 1 levels.

2 Offer made known so A rises to offer price. B is apparently paying

£6m for assets worth £4m. The apparent loss of £2m spread over

6 million shares causes the price to fall by 33p.

3 News of savings publicly available so price of B increases by £3.2m

spread over 6 million shares, i.e. increase of 53p.

(2) Strong form


2 £3.00 £3.20 4

4 £3.00 £3.20 4

10 £3.00 £3.20 4

4 Strong form so all information, public and private, is immediately

reflected in share price. Final price, as per note 3, operates from

day 2.





(ii) Share issue

1. Semi-strong form


2 £2.00 £3.00 1

4 £2.75 £2.75 5

10 £3.15 £3.15 6

5 The best way to see this is to think of a new merged company A

and B with 8 million shares. The share price will be the market’s

view of the total value of the company divided by the number of

shares. On day 4 savings are not public so total value is (£2m x

£2) + (6m x £3) = £22m. The share price is therefore £22m ÷ 8m

= £2.75.

6 Savings known so total value increases to £22m + £3.2m =

£25.2m and the share price = £25.2m ÷ 8m = £3.15.

2. Strong form


2 £3.15 £3.15 7

4 £3.15 £3.15 7

10 £3.15 £3.15 7

7 As with note 4, all information reflected immediately so final price

calculated in note 6 is in effect from day 2.




Chapter 6

Theories of gearing



CHAPTER 6 – THEORIES OF GEARING


CHAPTER CONTENTS

THE TRADITIONAL VIEW ---------------------------------------------- 131

MODIGLIANI & MILLER – TAX IGNORED (1958) ------------------- 132

GRAPH 132

FORMULAE 132

ASSUMPTIONS 133

ARBITRAGE IN A WORLD WITH NO TAXES 133

MODIGLIANI & MILLER – INCLUDING CORPORATION TAX (1963)135

GRAPH 135

CORPORATION TAX POSITION (U AND G IN WORLD WITH TAXES) 135

EQUILIBRIUM POSITION – M & M 136

FORMULAE 136

WHY DO COMPANIES NOT ATTEMPT A 99.9% DEBT STRUCTURE? 137

PECKING ORDER THEORY ---------------------------------------------- 139

STATIC TRADE-OFF THEORY ------------------------------------------- 140

SOLVENCY RATIOS ----------------------------------------------------- 141

1. GEARING RATIO 141

2. INTEREST COVER 141

BERLAN AND CANALOT ------------------------------------------------ 142





THE TRADITIONAL VIEW





MODIGLIANI AND MILLER – TAX IGNORED (1958)

All companies with the same earnings in the same risk class have the same future

income stream and should therefore have the same value, independent of capital

structure.

Graph

Modigliani & Miller (no tax)

Formulae

Vg = Vu

Keg = E

D)KbKeu(Keu −+

Kog = Keu

N.B. These formulae may be derived from the expressions which include the effect

of corporation tax treating t = 0





Assumptions

● Investors are rational

● Investors have the same view of the future

● Personal and corporate gearing are perfect substitutes

● Information is freely available

● No transaction costs

● No tax

● Firms can be grouped into similar risk classes.

The arbitrage “proof”, which incorporates these assumptions, can be used to

support this M & M proposition.

Arbitrage in a world with no taxes

Assume two companies, identical in every respect, except G is financed by £1,000

of 10% irredeemable debt trading at par. The above assumptions hold. The

traditional view of the two companies would be:

U (ungeared) G (geared)

£ £

EBIT 500 500

Interest -_ (100)

Dividends 500 400

Cost of Equity (assumed) 20% 25%

£ £

E (equity) 2,500 1,600

D (debt) - _ 1,000

V (total) 2,500 2,600

WACC 20% 19.2%

If an investor owned 1% of G’s equity (income £4) he should arbitrage i.e.

1. Sell his stake in G for £16

2. Adopt same financial risk as in G by borrowing personally a proportional

amount at 10% i.e. £1,000 x 1% = £10.

3. Invest £26 in U to obtain 1.04% of U’s equity (£26 ÷ £2,500)

4. £

Dividends from U (1.04% x £500) 5.20

Interest on borrowings (10% x £10) (1.00)

Net income £4.20

i.e. the investor is better off as a result of arbitrage





If one person makes the switch, many other investors will sell their shares in G and

purchase equity shares in U. G’s share price will fall, whilst U’s share price will

rise. Assuming G’s share price is the only one which changes, then the equilibrium

will arise where the net income from the two equity investments is identical.

£

i.e. Dividends from U (balance) 5.00

Interest (1.00)

Net 4.00

£5 dividend from U = 1% of shares

1% represents a £25 investment, of which £10 is borrowed. Therefore sales

proceeds from G’s shares in equilibrium must be £15

Accordingly all G’s shares are worth £1,500 in equilibrium

Thus: Vg = Vu

(£1,500 + £1,000) = £2,500

Ke in G is now 500,1£

400£ = 26.7%

and WACC is 500,2£

500£ = 20%

Therefore: Kog = Keu = 20%





MODIGLIANI AND MILLER – INCLUDING CORPORATION

TAX (1963)

The values of companies with the same earnings in the same risk class are no

longer independent. Companies with a higher gearing ratio have a greater net

future income stream (purely due to corporation tax relief on interest payments)

and therefore a higher value.

Graph

D

E

Corporation tax position (U and G in world with taxes)

Assume corporation tax rate is 35%. The net of tax distributions to investors are

shown in the following table:

£ £

EBIT 500 500

Interest - (100)

Profit before tax 500 400

Tax (35%) (175) (140)

Dividends £325 £260





Equilibrium position – M & M

M & M argue that as G pays less tax it can distribute more to its investors. The

difference in equilibrium values is explained by the present value of the tax shield

on debt interest available to G. As G’s debt is irredeemable this difference can be

measured by

Kb

t x Kb x D = Dt

therefore Vg = Vu + Dt

where Vu = value of an equivalent ungeared company

Assuming U is correctly valued and its cost of equity is 20%, then we calculate the

equilibrium value of G with reference to U

£

Value of U =

20.0

325£

= 1,625

Dt = £1,000 x 0.35 = 350

Value of G £1,975

CONCLUSION: a 99.9% debt structure is optimal!!!

Formulae

Vg = Vu + Dt

Keg = E

)t1(D*)KbKeu(Keu

−−+ or

e

dde

ie

i

V

V)k-T)(k-(1+k

*Kb or kd is the PRE-TAX COST OF DEBT for this formula.

N.B. The formula on the right-hand side is provided on the ACCA P4 Formulae sheet

Kog =

+−

DE

Dt1 Keu

Capital structure illustration (Grant plc)

Grant plc (an all equity company) has on issue 6,000,000 £1 ordinary shares at

market value of £2.50 each.

Bell plc (a geared company) has on issue:

17,000,000 25p ordinary shares; and

£8,000,000 15% debentures (quoted at 125)

Taking corporation tax at 35%, and assuming that:

1. The companies are in all other respects identical; and

2. The market value of Grant’s equity and the market value of Bell’s debt

are “in equilibrium”;

Calculate the equilibrium price per share of Bell’s equity.





Solution

Vg = Vu + Dt

N.B. D = 100

125 x 000,000,8£ = £10m

£m

Vu = 6,000,000 @ £2.50 = 15

Dt = £10,000,000 x 35% = 3.5

Vg = £18.5m

£m

E = (balancing figure) 8.5

D (as above) 10_

Vg (as above) £18.5m

Price per share =

m17

m5.8£

= 50p

Why do companies not attempt a 99.9% debt structure?

1. Bankruptcy costs

The higher the level of gearing the greater the risk of bankruptcy with the

associated “COSTS OF FINANCIAL DISTRESS”.

Vg = Vu + Dt − Present value of costs of financial distress

2. Agency costs

Costs of restrictive covenants to protect the interests of debt holders at high levels

of gearing.

3. Tax exhaustion

The value of the company will be reduced if advantage cannot be taken of the tax

relief associated with debt interest.

4. Debt capacity

Generally loans must be secured against a company’s assets and clearly some

assets (e.g. property) provide better security for loans than other assets (e.g. high-

tech equipment which may become obsolescent overnight). The depth of the

asset’s second hand market and its rate of depreciation are important

characteristics.





5. Personal taxes (MILLER’S CRITIQUE 1977)

Investors will be concerned with returns net of all taxes

● If a firm’s income is paid out as debt interest, corporation tax savings are

made (see M & M 1963) but investors will have to pay income tax on debt

interest.

● If a firm’s income is paid out as an equity return, corporation tax has to be

paid but personal tax can be saved (e.g. by avoidance of capital gains tax

using exemptions).

● In deciding its gearing level, a firm should consider its corporation tax position

and the personal tax position of its investors if it wishes to maximise their

wealth.

● In his 1977 article, Miller argues that firms will gear up until marginal

investors face a personal tax cost of holding debt equal to the corporation tax

saving. At this point there is no further advantage of gearing.





PECKING ORDER THEORY

The Pecking Order Theory is that a company’s capital structure decision is not

determined by the costs and benefits of using a combination of debt and equity

finance to minimise the cost of capital.

The theory suggests that a company has a well defined order of preference in

relation to available sources of finance i.e.

(a) The first preference is the use of retained earnings, since internal finance is

readily accessible, has no issue costs and does not involve negotiating with

third parties, such as banks.

(b) If external finance has to be used (because the company has identified more

positive NPV projects than can be financed by retentions alone), bank

borrowings, loan stock and debentures are the initial preferred source of

external finance. The cost of issuing new debt is normally much smaller than

the cost of equity issues. Furthermore it is possible to raise smaller amounts

of debt than of equity.

When raising debt, initially it is advisable to issue low risk secured debt, and

when there are no more assets available as security, then to issue unsecured

debt with a consequent higher risk and higher cost.

(c) If, after the company’s level of debt capacity is reached, there remain further

positive NPV projects that remain to be financed, the final and least preferred

source of finance is the issue of new equity capital.

Accordingly there appears to exist a financing pecking order i.e. first use retained

profits, then secured debt, then unsecured debt and finally equity.

A more sophisticated explanation of the Pecking Order Theory was developed in

1984, when it was suggested that the order of preference stemmed from the

existence of “asymmetry of information” between the company and the capital

markets. This term refers to the fact that company management are likely to have

a much better idea of the true worth of the company’s shares than do outside

investors.

Accordingly if a company wishes to raise new project finance and the capital market

has underestimated the benefits of the project, company management (with their

inside information) will be aware that the market has undervalued the company.

They would therefore choose to finance the project through retentions, so that

when the market discovers the true value of the project, existing shareholders will

benefit. If retained earnings are inadequate, the company would choose to raise

debt finance in preference to a new equity issue (since they would not wish to issue

new equity shares which are undervalued by the market).

However if the company’s management believe that investors are overvaluing the

benefits of the new project and therefore placing too high value on the company’s

shares, they would prefer to issue new equity at that overvalued price.





STATIC TRADE-OFF THEORY

This variation on the 1963 with corporate tax theory of Modigliani and Miller arrives

at a conclusion, which is similar to that of the traditional theory of gearing i.e. there

exists an optimum level of leverage that companies should attempt to attain.

Provided a company is in a static position i.e. not in a period of extreme growth, it

is likely to have a gearing policy that is stable over time. This is achieved by

striking a balance between the benefits and the costs of raising debt.

The benefits of debt relate to the tax relief that is enjoyed when interest payments

are made – the cheaper debt finance will reduce the weighted average cost of

capital and increase corporate value.

The costs of debt relate to the increases in the costs of financial distress (e.g.

bankruptcy costs) and increases in agency costs that arise when the company

exceeds its optimum gearing levels. The resultant increase in required returns

demanded by investors cause the weighted average cost of capital of the company

to increase and hence corporate value to fall.

There is accordingly, in theory, a trade-off between these two effects and hence the

cost of capital and the value of the company will be optimised. However,

subsequent research suggests that there is little evidence of the static trade-off

theory operating in the real world.





SOLVENCY RATIOS

1. Gearing Ratio

This indicates the relationship between:

Equity : Fixed return securities (or Debt) on issue

It may be based upon balance sheet values (in which case “Equity” will comprise

ordinary share capital and reserves) or upon stock exchange values (in which event

the shares and debentures on issue are valued at mid market price).

Illustration

Called-up Share Capital:

£250,000 of ordinary shares of 25p, quoted price 53p – 55p

£500,000 of 7% preference shares of £1, quoted price 71p – 73p

Reserves £100,000

Loans: £200,000 of 12% irredeemable debentures – market yield currently 10%

You are required to calculate the Capital Gearing Ratio, based upon

(a) Book values

(b) Market values

Solution to illustration

(a) Book values = (250,000 + 100,000) : (500,000 + 200,000) = 0.5 : 1

(b) Market values = 540,000 : (360,000 + 240,000) = 0.9 : 1

N.B. Gearing ratios are expressed in a number of ways e.g.

Equity

Debt

DebtEquity

Debt

+

Debt may include long-term borrowings only or both short and long-term debt.

A further problem is the classification of hybrid securities e.g preference shares. In

the above illustration they have been classified as debt, but this is open to debate

when the ratio is calculated for the benefit of lenders.

2. Interest cover

ie Interest Gross

Taxand Interest before Earnings





Berlan and Canalot

Berlan plc

Berlan plc has annual earnings before interest and tax of £15m. These earnings

are expected to remain constant. The market price of the company’s ordinary

shares is 86 pence per share cum.div. and of debentures £105.50 per debenture

ex-interest. An interim dividend of six pence per share has been declared.

Corporate tax is at the rate of 35% and all available earnings are distributed as

dividends.

Berlan’s long-term capital structure is shown below:

£’000

Ordinary shares (25 pence par value) 12,500

Reserves 24,300

36,800

16% debentures 31.12.2007 (£100 par value) 23,697

60,497

Required:

Calculate the cost of capital of Berlan plc according to the traditional theory of

capital structure. Assume that it is now 31 December 2004.

Canalot plc

Canalot plc is an all-equity company with an equilibrium market value of £32.5

million and a cost of capital of 18% per year.

The company proposes to repurchase £5 million of equity and to replace it with

13% irredeemable loan stock.

Canalot’s earnings before interest and tax are expected to be constant for the

foreseeable future. Corporate tax is at the rate of 35%. All profits are paid out as

dividends.

Required:

(a) Using the assumptions of Modigliani and Miller, explain and demonstrate how

this change in capital structure will affect:

(i) the market value

(ii) the cost of equity

(iii) the cost of capital

of Canalot plc.

(b) Explain any weakness of both the traditional and Modigliani and Miller theories

and discuss how useful they might be in the determination of the capital

structure for a company.





Berlan and Canalot solution

Berlan’s weighted average cost of capital

Cost of equity

£’000

Earnings before interest and tax 15,000

Interest (16% x 23,697) 3,792

11,208

Tax (35% x 11,208) _3,923

Earnings 7,285

Dividend (full distribution) 7,285

NIL

Number of shares = £12.5 million x 4 = 50 million

Pence

Market price per share: cum div 86

Less interim dividend declared _6

Ex div 80p

Value of shares = 50 million x 80p = £40 million

Cost of equity capital, using the dividend valuation model and assuming constant

dividends

= 000,40

7285 = 18.21%

Cost of debt

A market value higher than redemption value implies that the cost (pre-tax) is less

than the nominal rate of 16%.

Using 8% and 9% as discount rates.

Year £ 8%

factors PV

9%

factors PV

0 Market value (105.50) 1 (105.50) 1 (105.50)

1-3 Interest (net of tax) 10.40 2.577 26.80 2.531 26.32

3 Redemption 100.00 0.794 79.40 0.772 77.20

+0.70 −1.98

Cost of debt = %1 X 98.17.0

7.0%8

++ = 8.26%

Market value of debt = 100

50.105 x million697.23£ = £25 million

Value of debt plus equity = £(25 + 40) million = £65 million

Weighted average cost of capital

WACC = 65

25 x %26.8

65

40 x %21.18 + = 14.38%





Changes to capital structure: Canalot plc

(a) (i) Market value

Using a Modigliani-Miller formula for the value of a geared company

(with irredeemable debt):

Vg = Vu + Dt

When Canalot replaces equity with loan stock, the company will increase

in value by the tax shield, Dt.

= £5 million debt issued x 35% tax rate

= £1.75 million

The market value of the company increases to

£32.5 million + £1.75 million = £34.25 million

The market value of equity becomes

£34.25 million − £5 million = £29.25 million

(ii) The cost of equity

This can be computed

- from first principles, or

- by using the MM formula for Ke

From first principles

Consider the distribution of profits before and after the change in capital

structure.

Before the change, equity earnings = 18% x market value of

£32.5 million = £5.85 million.

Pre-tax profits = 65

100 x million 85.5£ = £9 million.

After the debt issue:

£’000

Earnings before interest and tax 9,000

Less interest: £5m x 13% _650

8,350

Tax (35% x 8,350) 2,922

Equity earnings (= dividend) 5,428

Cost of equity = 250,29

428,5 = 18.56%

The cost of equity has increased by 0.56% because of the increased

financial risk experienced by shareholders.





Using the MM formula for Ke:

Keg = E

)t1(D)KbKeu(Keu

−−+

= 25.29

)35.01(5%)13%18(%18

−−+ = 18.56%

(iii) Weighted average cost of capital

Again, this can be computed either from first principles or by using the

MM formula for WACC.

From first principles

WACC = 65.0 x %13 x 25.34

5%56.18 x

25.34

25.29+ = 17.08%

Using the MM formula for WACC

WACCg =

+−

DE

Dt1 Keu

=

−

25.34

35.0 x 51 %18 = 17.08%

The WACC has declined from 18%, reflecting the benefits of tax relief on

interest.

(b) Weaknesses of the traditional and Modigliani-Miller theories

The traditional theory of capital structure is an intuitive theory, which is not

supported by a rigorous model building approach, as is the case with

Modigliani and Miller’s work. It describes how the weighted average cost of

capital declines as gearing increases until a point is reached where WACC is at

its lowest and starts to increase with further increases in gearing. It therefore

suggests that there is an optimal capital structure at which the firm has its

lowest cost of capital and highest value. Unfortunately, because the theory is

purely descriptive, it does not suggest a method of finding that optimal capital

structure, except by trial and error.

The traditional view predicts an optimal WACC position, because it effectively

suggests that the relationship between the cost of equity and gearing is non-

linear. In this respect it is in conflict with the capital asset pricing model and

much of modern financial management theory.

Modigliani and Miller’s theory, used in our discussion of Canalot plc, suggests

that the only advantage of borrowing is the tax relief on debt interest. The

theory results directly from the assumptions that they make. Some of these

are unrealistic, for example:

(i) that individuals and companies can borrow at the same interest rate

(ii) that interest rates do not increase with gearing

(iii) that personal borrowing (which is not covered by limited liability) is no

different from corporate borrowing





(iv) that the capital market is perfect

(v) that (although corporate taxes are considered) personal taxes are

ignored.

Although these assumptions are unrealistic, there is still some logic in MM’s

suggestion that companies should borrow as much as they can in order to

take advantage of tax relief. However, their theory also ignores possible costs

arising at high levels of gearing, such as:

(i) Bankruptcy costs: both direct (sale of assets below going concern

value) and indirect (increased time spent controlling a company which is

near bankruptcy).

(ii) Agency costs: for example, restrictive covenants in loan agreements

which hinder the company’s freedom of operation.

(iii) Tax exhaustion: inability to take advantage of the all tax relief on the

high debt interest because of a lack of taxable profits.

(iv) Debt capacity: inability to offer sufficient security to be able to borrow

to a high level of gearing.

At some level of gearing these costs will start to outweigh the benefits of tax

relief, implying that optimal gearing is achieved at a level just below this

point.

Unfortunately, while the MM theory allows predictions of the effect of

borrowing on the cost of capital, it does not enable this optimal borrowing

level to be established, because it ignores the costs at high gearing.

Miller, in a later paper, argues that when personal taxes are introduced, the

capital structure does not affect the firm’s cost of capital. However, this too

ignores bankruptcy costs and other costs of high gearing.

In summary neither the traditional nor the MM view of capital structure

presents a practical method for identifying a company’s optimal capital

structure. This can only be achieved by intelligent trial and error. However,

Modigliani and Miller do at least identify the various factors which affect the

cost of capital and, at reasonable levels of borrowing, enable the company to

predict the effect of increasing or decreasing gearing on the value of the firm.




Chapter 7

Portfolio theory and the capital asset

pricing model



CHAPTER 7 – PORTFOLIO THEORY AND THE CAPITAL ASSET PRICING MODEL


CHAPTER CONTENTS

PRINCIPLES OF PORTFOLIO THEORY -------------------------------- 149

THE UNDERLYING THEORY OF CAPM --------------------------------- 158

SYSTEMATIC AND UNSYSTEMATIC RISK ----------------------------- 159

THE SECURITY MARKET LINE------------------------------------------ 161

SYSTEMATIC BUSINESS RISK AND SYSTEMATIC FINANCIAL RISK166

ASSUMPTIONS, ADVANTAGES AND LIMITATIONS OF CAPM ------- 172

ARBITRAGE PRICING THEORY AND FAMA & FRENCH THREE FACTOR MODEL ------------------------------------------------------------------- 174

CYGNET PLC ------------------------------------------------------------- 175

FIVE WEALTHY INDIVIDUALS ----------------------------------------- 179

DELL PLC----------------------------------------------------------------- 184

NELSON PLC ------------------------------------------------------------- 186





PRINCIPLES OF PORTFOLIO THEORY

In 1952, Harry Markowitz developed portfolio theory, which is based upon a very

simple principle. Any investment (whether an investment in shares or an

investment in projects), should never be viewed in isolation, but should instead be

considered as part of an overall portfolio of shares or projects.

As everyone’s grandmother might say “Don’t put all of your eggs in one basket!!”

Portfolio theory uses statistical techniques to prove that grandmother is correct!!

The features of portfolio theory are dealt with in detail in the following illustration.

Illustration 1 (Pastel plc)

Pastel plc is considering whether to accept one of two major new investment

opportunities Project 1 and Project 2. Each project would require an immediate

outlay of £10,000 and Pastel plc expects to have available enough resources to

undertake only one of them.

The directors of Pastel plc believe that returns from existing activities and from the

new projects will depend upon which of three economic environments prevails

during the coming year. They estimate returns for the coming year (that is cash

flows to be received at the end of the year plus project value at that time), and the

probabilities of the three possible environments, as follows:

Environment A Environment B Environment C

Probability of environment 0.3 0.4 0.3

£ £ £

Returns from Project 1 12,500 12,500 9,500

Returns from Project 2 10,000 11,750 13,000

Aggregate returns from

existing portfolio of projects

90,000 120,000 130,000

The company has a current market value of £100,000. The directors of Pastel plc

believe that the risk and returns per £ of market value of their existing activities

are similar to those for the stock market as a whole, including their dependence on

whichever economic environment prevails. The current rate of interest on short-

dated government securities and on bank deposit account is 10% per annum.

You are required to prepare calculations for the directors of Pastel plc

showing which, if either, of the two proposed projects should be accepted.

Ignore inflation and taxation





Solution 1 (Pastel plc)

(a) Choice between proposed projects

(i) Conversion of data into period rates of return

Period rate of return = End of year value – Start of year value

Start of year value

Environment PROJECT 1 PROJECT 2 EXISTING

PORTFOLIO

A

10

105.12 −

= 25%

10

1010 −

= 0%

100

10090 −

= -10%

B

10

105.12 −

= 25%

10

1075.11 −

= 17.5%

100

100120 −

= 20%

C

10

105.9 −

= -5%

10

1013 −

= 30%

100

100130 −

= 30%

(ii) Calculation of expected returns (Er) and standard deviations for each

PROJECT w Rates of

Return

Expected return

(Er)

Deviations

(r – Er)

w(r – Er)2 s(σ)

% % %

1 0.3 25 7.5 + 9 24.3

0.4 25 10.0 + 9 32.4

0.3 -5 (1.5) -21 132.3

16.0 √189.0 = 13.75%

2 0.3 0 - -16 76.8

0.4 17.5 7.0 + 1.5 0.9

0.3 30 9.0 +14 58.8

16.0 √136.5 = 11.68%

Existing

Portfolio 0.3 -10 (3.0) -24 172.8

and 0.4 20 8.0 + 6 14.4

Market 0.3 30 9.0 +16 76.8

14.0 √264.0 = 16.25%

(iii) Naive analysis

Provided that investors are generally risk averse, if two mutually exclusive

projects have identical expected returns, the preferred project is that with the

smaller amount of risk (i.e. standard deviation or variance). In this instance:

Er s(σ)

Project 1 16% 13.75%

Project 2 16% 11.68%

Since, they have the same expected returns; it would appear that Project 2 is

preferred as it has the lower standard deviation. Furthermore, given that the

existing projects of Pastel plc provide a lower level of expected return (14%)





for a higher level of risk (a standard deviation of 16.25%) than Project 2, it

appears that Project 2 would be an acceptable investment for Pastel plc to

undertake.

(iv) Portfolio approach

The above approach is considered naive because THE MARGINAL PROJECT

SHOULD NOT BE VIEWED IN ISOLATION, BUT AS PART OF THE OVERALL

PORTFOLIO OF PROJECTS i.e.

(a) Period rates of return

Environment EXISTING PORTFOLIO plus

PROJECT 1

EXISTING PORTFOLIO plus

PROJECT 2

A 110

1105.102 − = - 6.82%

110

110100 − = - 9.09%

B 110

1105.132 − = 20.45%

110

11075.131 − = 19.77%

C 110

1105.139 − = 26.82%

110

110143 − = 30.00%

(b) Calculation of expected returns (Er) and standard deviation for each

PROJECT w Rates of

Return

Expected

return (Er)

Deviations

(r – Er) w(r – Er)2 s(σ)

% % %

Existing +

Proj. 1 0.3 -6.82 -2.046 -21.0 132.30

0.4 20.45 8.18 +6.27 15.73

0.3 26.82 8.046 +12.64 47.93

14.18 √195.96 = 14.00%

Existing +

Proj. 2 0.3 -9.09 -2.727 -23.27 162.45

0.4 19.77 7.908 +5.59 12.50

0.3 30.00 9.000 +15.82 75.08

14.18 √250.03 = 15.81%

CORRELATION CO-EFFICIENTS

Where the two assets behave in an absolutely identical way, there is perfect

positive correlation (+ 1), where they behave in directly opposing ways there is

perfect negative correlation (– 1) and where there is no observable relationship

between the two, there is zero correlation (0). The formula to calculate a

correlation coefficient (which is not provided on the ACCA formula sheet) is:

(r) ρ PROJECT, EXISTING = EXISTINGPROJECT

)EXISTING ,PROJ(

s s

COV





(1) Calculations of covariances

PROJECT 1 and EXISTING PORTFOLIO

w Project 1 Existing Portfolio Covariance

Deviations (r-Er) Deviations (r-Er) Project, Existing

0.3 + 9 - 24 - 64.8

0.4 + 9 + 6 21.6

0.3 - 21 + 16 - 100.8

- 144

PROJECT 2 and EXISTING PORTFOLIO

w Project 2 Existing Portfolio Covariance

Deviations (r-Er) Deviations (r-Er) Project, Existing

0.3 - 16 - 24 115.2

0.4 + 1.5 + 6 3.6

0.3 + 14 + 16 67.2

+ 186

(2) Standard deviations (already calculated)

s PROJ.1 = 13.75% s PROJ.2 = 11.68% s EXISTING = 16.25%

(3) Correlation coefficients

ρ PROJ. 1, EXISTING = 25.16 x 75.13

144− = -0.64

(Fairly high degree of negative correlation!)

ρ PROJ. 2, EXISTING = 25.16 x 68.11

186+ = +0.98

(Extremely high level of positive correlation!)

The above analysis shows that the expanded portfolio (including Project 1) would

be less risky than the expanded portfolio (including Project 2). Whilst Project 1 on

its own is more risky than Project 2. Once more both portfolios show identical

expected returns.

The reason for this decision change is the correlation between each of the proposed

projects and the existing portfolio i.e.

(a) The returns of Project 1 and the existing portfolio are negatively correlated,

whilst

(b) The returns of Project 2 and the existing portfolio show a high degree of

positive correlation.

FORMULAE

Fortunately formulae exist to avoid the necessity for the laborious calculations

shown on page 151 of this solution. These formulae are:

Expected return from portfolio Erp = waEra + wbErb

where wa is the proportion invested in the shares of Company “a”

and, wb is the proportion invested in the shares of Company “b”

Erp is simply a weighted average of the expected returns from each investment.





Risk of portfolio (sp) =

abbaba2

b2

b2

a2

a ρ s s w w 2 + s w + s w

N.B. sa sb ρab = Cov [Era Erb]

NOTE: Provided ρab (correlation coefficient) is less than +1, the risk of the

portfolio (the σ or s of the combined returns) will be less than the weighted average

risk of the portfolios two components.

Relating these formulae to the Pastel problem and treating each new project as “a”

and the existing portfolio as “b”, the expected return and total risk of the existing

portfolio and Project 1 are as follows:

Erp =

+

%14 x

11

10%16 x

11

1 = 14.18%

sp =

−+

+

64.0x 25.16 x 75.13 x

11

10 x

11

1 x 225.16 x

11

1075.13 x

11

122

= 6364.232335.2185625.1 −+ = 14.00%

And the expected return and total risk of the existing portfolio and Project 2 are as

follows:

Erp =

+

%14 x

11

10%16 x

11

1 = 14.18%

sp =

+

+

98.0 x 25.16 x 68.11 x

11

10 x

11

1 x 225.16 x

11

1068.11 x

11

122

= 7445.302335.2181275.1 ++ = 15.81%

Notice how these formulae provide the same results as the calculations performed

on page 151, which thankfully will never have to be repeated thanks to these

formulae.





APPENDIX (To be read after studying the Capital Asset Pricing Model)

The analysis using portfolio theory can be improved upon further by taking into

consideration the Capital Asset Pricing Model. This shows that an investment

project’s risk can be split into two components: Systematic and Unsystematic Risk.

The unsystematic risk of an investment project can be eliminated when it is held as

part of an efficient well diversified investment portfolio.

Therefore, in evaluating the expected return from a project, it should be viewed,

not in relation to the project’s total risk, but just to the systematic portion of that

risk, which cannot be eliminated.

The CAPM gives an expression for the return required from a single investment,

project j:

Erj = Rf + (Erm – Rf) βj

where Erj = required return from investment j

Rf = risk-free return

Erm = expected overall return on the market portfolio

βj = ( )2

m

jm

s

COV

sm2 = variance of the returns from a market portfolio

COV (jm) = covariance of returns of project j with the returns from the market

The data given by this question provides

rf = 10%

Erm = 14%

sm2 = 264

COV (PROJECT 1 & MARKET) = −144

COV (PROJECT 2 & MARKET) = +186

N.B. The question states that the risk and returns on the existing portfolio are

similar to those of the stock market as a whole.

Thus the β in each case is:

β PROJECT 1 = 264

144− = −0.545

β PROJECT 2 = 264

186 = +0.705

Therefore the required return on each project is:

PROJECT 1: ( )264

-144%10%14%10 −+ = 7.8%

PROJECT 2: ( )264

186%10%14%10 −+ = 12.8%

whilst the expected return on both projects = 16%





In conclusion, this analysis shows that, whilst the return expected from both

projects (16%) is above that required (Project 1: 7.8%, Project 2: 12.8%), given

their individual levels of systematic risk, Project 1 is preferred since it provides the

greatest excess return over required return and hence will add most to

shareholders’ wealth. Notice that this conclusion is the complete opposite to that

reached via the naive analysis.

An alternative expression for the calculation of β is:

βj = m

jmj

s

ρs

where sj = standard deviation of the returns of investment j

ρjm = the correlation coefficient between the returns of j and the returns

from the market portfolio

sm = standard deviation of the returns from a market portfolio

Hence the correlation coefficient between the returns of these projects and the

market are:

ρ PROJECT 1, MARKET = ( )

m1 PROJ

MARKET&1P

s s

COV =

25.16 x 75.13

144−

= 4375.223

144− = −0.644

thus β PROJECT 1 = 25.16

644.0x 75.13 − = −0.545

ρ PROJECT 2, MARKET = ( )

m2 PROJ

MARKET&2P

s s

COV =

25.16 x 68.11

186+

= 8.189

186+ = +0.98

thus β PROJECT 2 = 25.16

98.0 x 68.11 = +0.704*

*slight difference from main solution due to rounding





Illustration 2

The following data are available:

Erm = 20% Rf = 8%

sm = 6% sf = 0%

Mr R Atkinson has £100 of his own money and he wishes to invest in Portfolio L

which lies along the Capital Market Line (CML), above the market portfolio (Portfolio

M) where the ratio

Rf , M : M , L = 2 : 1

As a result he must borrow £50 of additional funds (so that the ratio of PERSONAL

FUNDS : BORROWING = 2 : 1) at the risk-free rate. He places the total of £150

in the shares of companies which represent Portfolio M.

Calculate

(a) ErL (i.e. expected return from the total investment), and

(b) sL (i.e. the risk of that portfolio)

Solution 2

(a) Expected return from the total investment

Using basic common sense, this can be calculated as follows:

Amounts

invested

Annual

income

£ £

Own funds (2) 100

Borrowed funds (1) 50

150 x 20% = 30

Interest paid (50) x 8% = (4)

£100 £26

Therefore ErL will obviously be (£26 ÷ £100) = 26% p.a.

Alternatively, ErL can be calculated using the normal formula i.e.

ErL = waEra +wbErb

= (1.5 x 20%) + ([1 −1.5] x 8%) = 26% p.a.

(b) The total risk of the portfolio

If only the personal funds of Mr Atkinson had been invested (i.e. £100), sL would

only be 6%. However, since he borrowed a further £50, sL will clearly increase to

(1.5 x 6%) = 9%

Alternatively, sL can be calculated using the normal formula i.e.

sp = abbaba2

b2

b2

a2


= 0%) x 6% x 1.5] -[1 x 1.5 x (2+0%) x 1.5] -([1+6%) x (1.5 2 = 9%





For Portfolio L

( ) [ ]( )8%1.5120%1.5 ×−+×=Lr =26%

6%1.5 ×=Lσ = 9%

λ

L

M

%26 L

=r

20% =rM

8% =rF

pσ

Capital Market Line

6% 9% 0





THE UNDERLYING THEORY OF CAPM

The CAPM assesses investments from the viewpoint of well-diversified shareholders

and considers that when companies invest in projects they must accept that the

majority of their shareholders are well-diversified institutions (i.e. pension funds,

insurance companies, unit trusts and investment trust companies). In fact only

about 13% of the shares in UK quoted companies are held by individuals and many

of these are so wealthy that they can invest their savings in a number of different

companies in various market sectors.

Obviously an investor can reduce risk by holding a portfolio of shares in companies

in different industries, which will to some degree offer different risk/return profiles

over time. For instance an investor holding shares in both BP and British Airways

should find that if oil prices increase the share price of BP should rise, whereas the

share price of BA would probably fall. Obviously an oil price decrease would cause

an opposite effect on the share prices of the two companies.

Provided that the returns on shares do not demonstrate perfect positive correlation,

any additional investment brought into a shareholders portfolio should (subject to

the point made in the next paragraph) cause the overall risk of the portfolio to

reduce.

Suppose an investor who has built up a small portfolio in the shares of (say) three

companies now decides to add to that portfolio the shares of a few more companies

in different market sectors. He should find a substantial risk reduction as the

additional investments are added to the portfolio. However as the shares of more

and more companies (in different sectors) are added to the portfolio, the risk

reduction will eventually slow down and once the portfolio increases up to about 16

to 20 companies (again in different market sectors) the risk reduction will

eventually cease.

Thus a standard deviation (σ or s) is a measure of total risk, and this can be

analysed between:

● UNSYSTEMATIC (aka SPECIFIC or UNIQUE) RISK i.e. the risk which will

initially disappear as a result of diversification, and

● SYSTEMATIC (aka MARKET) RISK i.e. the risk which can never be

avoided when investing in company shares.

Specific risk reflects factors which are unique to the company or to the industry in

which it operates, whereas systematic risk reflects market wide factors such as the

state of the economy.

Diversification therefore eliminates the unsystematic risk relating to shares held in

a well-diversified portfolio, but sadly the systematic risk of that portfolio will

remain.

Accordingly, CAPM recognises that investors cannot expect to receive a return on

their exposure to unsystematic risk – therefore returns will only be received as a

result of systematic risk, which investors can never avoid.

CAPM uses a β factor, which compares the systematic risk of the shares of a

company with the systematic risk of the market. The higher the β, the greater the

return the investor demands as compensation for the systematic risk borne.

Obviously unsystematic risk (which is diversified away by holding the shares of a

sufficient number of companies) can be ignored.





SYSTEMATIC AND UNSYSTEMATIC RISK

CAPM formulae

CAPM provides the return that would be required by a well-diversified, risk-averse

investor. The formula can be expressed in a variety of ways, e.g.:

E(ri) = Rf + βi (E(rm) – Rf)

Ke = Rf + [Rm – Rf] β

Required return = rf + (Erm – rf) βj

where:

Rf = the risk free rate of interest (e.g. the return on 90 day Treasury bills)

Rm = the average return on a market portfolio (e.g. the return on FTSE 100

constituents)

[Rm – Rf] = the market risk premium or excess market return

β (beta) = an index which compares the systematic risk of the investment with

the systematic risk of the market portfolio

The above CAPM formula appears in one form or another on formulae sheets

provided by the accountancy bodies. However the following formulae for

calculating β are not provided in the examination and must therefore be committed

to memory:

UNSYSTEMATIC RISK

SYSTEMATIC RISK

Total

portfolio risk(s)

Number of different companies in which shares are held

1

Number of different companies in which shares are held

1 5 9 13 17 21 25





Formulae for calculating β

Formula one

βj = m

jjm

s

s ρ

Where ρjm = correlation coefficient between the investment and the market

sj = total risk of the investment

sm = total risk of the market, which is entirely systematic risk since

the market is totally diversified.

Formula two

βj = ( )2

m

jm

s

COV

Where COV(jm) = covariance between the investment and the market

sm2 = variance of the market (i.e. the standard deviation

squared).





THE SECURITY MARKET LINE

The security market line is a graph of the capital asset pricing model i.e.

There are accordingly two benchmarks for β and for the Security market line, i.e.

● The return on a risk free security, which obviously carries no systematic risk

and therefore has a β of 0;

● The return on the market portfolio, which due to its ultimate diversification

carries only systematic risk and will always have a β of 1.

An investment with a:

β of 0 is referred to as a risk free investment;

β of 1 is called a neutral investment (since its risk is equivalent to that of the

market);

β of > 1 is termed an aggressive investment (since it is riskier than average);

β of < 1 is called a defensive investment (since it is less risky than the market

average)

Accordingly if an investor wishes to hold equity shares despite the existence of a

bear market, he would be advised to invest in defensive investments, since their

prices would fall more slowly than the market average. During a bull market an

investor should hold aggressive investments, since their increases in value would

outpace the market average.

Security market line

-0.5 0 0.5 1 1.5 Systematic risk (β)

Rm

Return %

Rf





Illustration 3

In the case that follows, four states-of-the-world are considered with respect to

future prospects for real growth in Gross National Product. State 1 represents a

relatively serious recession, State 2 is a mild recession, State 3 is a mild recovery

and State 4 is a strong recovery. The probabilities of these alternative future

states-of-the-world are set forth in column 2 of the table below. Estimates of

market returns and project rates of return are set forth in the remaining columns.

Summary of information – Morton Company

(1) (2) (3) (4) (5) (6) (7)

State

of

world

Subjective

probability

Market

return Project rates of return

Project 1 Project 2 Project 3 Project 4

w rm

1 0.1 −0.15 −0.30 −0.30 −0.09 −0.05

2 0.3 0.05 0.10 −0.10 0.01 0.05

3 0.4 0.15 0.30 0.30 0.05 0.10

4 0.2 0.20 0.40 0.40 0.08 0.15

The Morton Company is considering four projects in a capital expansion

programme. The economics staff projected the future course of the market

portfolio over the estimated life span of the projects under each of the four states-

of-the-world (first three columns in the table); it is recommended the use of a risk-

free rate of return of 5 per cent. The finance department provided the estimates of

project return conditions on the state-of-the-world (columns 4 to 7 above). Each

project involves an outlay of approximately £50,000.

Assuming that the projects are independent and that the firm can raise sufficient

funds to finance all four projects, which projects would be accepted using the

capital asset pricing model?





Solution 3

In Table 1 the data provided by market relationships are utilised to calculate the

expected return on the market along with its variance. The probabilities of the

future states-of-the-world are multiplied by the associated market returns and their

products are summed to obtain the expected market return (Erm) of 10 per cent.

Table 1: Calculation of Market Parameters

Col.

no. (1) (2) (3) (4) (5) (6) (7)

State of

world

w Rm wRm (Rm –Erm) (Rm – Erm)2 w(Rm – Erm)2

1 0.1 −0.15 − 0.015 − 0.25 0.0625 0.00625

2 0.3 0.05 0.015 − 0.05 0.0025 0.00075

3 0.4 0.15 0.060 0.05 0.0025 0.00100

4 0.2 0.20 0.040 0.10 0.0100 0.00200

Erm = 0.10 Var(Rm) = 0.01

The expected market return (Erm) is used in calculating the variance of the market

returns. This is shown in columns 5 to 7. The expected return is deducted from the

return under each state, and deviations from Erm in column 5 are squared in

column 6. In column 7 the squared deviations are multiplied by the probabilities of

each expected future state (which appear in column 2). The products are summed

to give the variance of the market return. (N.B. The square root of the variance −

which does not have to be calculated in this instance − is its standard deviation).

A similar procedure is followed in Table 2 for calculating the expected return and

the covariance for each of the four individual projects. The expected return is

obtained by multiplying the probability of each state by the associated forecast

return. The deviations of the return under the state from the expected return are

next calculated in column 5. The deviations of the market returns from their mean

are repeated for convenience in column 6. In column 7, the deviations of project

returns are multiplied by the deviations of the market returns. In column 8 the

figures established in column 7 are multiplied by the probability factors to

determine the covariance for each of the four projects.

In Table 3, the beta for each project is calculated as the ratio of its covariance to

the variance of the market return, and they are employed in Table 4 to estimate

the required return on each project in terms of the security market line

relationship. The risk-free rate of return is 5 per cent, with a market risk premium

of (10% − 5%) i.e. 5 per cent.

Required returns as shown in column 2 of Table 4 are deducted from the estimated

returns for each individual project (calculated in column 4 of Table 2) to derive the

‘excess returns’. These relations may be depicted graphically. The CAPM criterion

accepts the projects with positive excess returns, which appear above the security

market line. It rejects those with negative excess returns (plotted below the

security market line).





Table 2: Calculation of Expected Returns and Covariances for Projects

Col

no

(1) (2) (3) (4) (5) (6) (7) (8)

State

of

world

w rj wrj (rj-Erj)(rm-Erm) w(rj-Erj)(rm-Erm)

P1 1 0.1 −0.30 −0.03 (−0.50)(−0.25) = 0.125 0.0125

2 0.3 0.10 0.03 (−0.10)(−0.05) = 0.005 0.0015

3 0.4 0.30 0.12 (+0.10)(+0.05) = 0.005 0.0020

4 0.2 0.40 0.08 (+0.20)(+0.10) = 0.020 0.0040

Er1 = 0.20 Cov(r1,rm) = 0.0200

P2 1 0.1 −0.30 −0.03 (−0.44)(−0.25) = 0.110 0.0110

2 0.3 −0.10 −0.03 (−0.24)(−0.05) = 0.012 0.0036

3 0.4 0.30 0.12 (+0.16)(+0.05) = 0.008 0.0032

4 0.2 0.40 0.08 (+0.26)(+0.10) = 0.026 0.0052

Er2 = 0.14 Cov(r2,rm) = 0.0230

P3 1 0.1 −0.09 −0.009 (−0.12)(−0.25) = 0.030 0.0030

2 0.3 0.01 0.003 (−0.02)(−0.05) = 0.001 0.0003

3 0.4 0.05 0.020 (+0.02)(+0.05) = 0.001 0.0004

4 0.2 0.08 0.016 (+0.05)(+0.10) = 0.005 0.0010

Er3 = 0.030 Cov(r3,rm) = 0.0047

P4 1 0.1 −0.05 −0.005 (−0.13)(−0.25) = 0.0325 0.00325

2 0.3 0.05 0.015 (−0.03)(−0.05) = 0.0015 0.00045

3 0.4 0.10 0.04 (+0.02)(+0.05) = 0.0010 0.00040

4 0.2 0.15 0.03 (+0.07)(+0.10) = 0.0070 0.00140

Er4 = 0.08 Cov(r4,rm) = 0.00550

Table 3: Calculation of the Betas

β1 = 0.0200 ÷ 0.01 = 2.00

β2 = 0.0230 ÷ 0.01 = 2.30

β3 = 0.0047 ÷ 0.01 = 0.47

β4 = 0.0055 ÷ 0.01 = 0.55

Table 4: Calculation of Excess Returns

(1) (2) (3) (4)

Project Measurement of required return Expected

return

Excess return %

(alpha value)

P1 r1 = 0.05 + 0.05(2.0) = 0.150 0.200 + 5.00

P2 r2 = 0.05 + 0.05(2.3) = 0.165 0.140 − 2.50

P3 r3 = 0.05 + 0.05(0.47) = 0.0735 0.030 − 4.35

P4 r4 = 0.05 + 0.05(0.55) = 0.0775 0.080 + 0.25





An all-equity company

Note conflict between dividend valuation model (DVM) & CAPM with projects P2 and

P4.

ke (using DVM) is assumed to be 12%

To construct the SECURITY MARKET LINE

β Return

When 0 5%

At 1 10%

Security Market Line

0

5

10

15

20

25

0.5 1.0 1.5 2.0 2.5 β of

project

• P1

• P2

• P3

P4 ●

Ex

pe

cte

d &

Re

qu

ire

d R

etu

rn o

n P

roje

ct

%

ke





SYSTEMATIC BUSINESS RISK AND SYSTEMATIC

FINANCIAL RISK

At a gearing level of zero, the equity shareholders of a company would have to bear

systematic business risk only. However as a company increases its debt levels and

becomes more and more highly leveraged, its equity shareholders will not only

have to face the same level of systematic business risk as before, but will also have

to accept increasing amounts of systematic financial risk.

Accordingly:

● Equity shareholders in an ungeared company bear systematic

business risk only, whereas

● Equity shareholders in an otherwise identical geared company bear the

same level of systematic business risk as before, but will also have to

face an ever increasing level of systematic financial risk as borrowing

levels become greater and greater,

with a consequence increase in the Ke of the company concerned. This is

illustrated below.

Following the M & M with corporation tax theory of 1963, as gearing levels increase,

Ke behaves as follows:

Now that the issue of leverage has been introduced, there becomes a need to

distinguish:

● β asset (βa), which reflects systematic business risk only, and

● β equity (βe), which reflects both systematic business risk TOGETHER

WITH ANY systematic financial risk which MAY exist.

Gearing % D E

Ke %

SYSTEMATIC BUSINESS RISK

Ke

SYSTEMATIC

FINANCIAL RISK





Therefore:

● In the case of an all equity company, βe = βa, since no systematic financial

risk can possibly exist.

● In the case of a geared company, βe > βa, since βe contains both

systematic business risk and systematic financial risk, whereas βa reflects

systematic business risk only.

The theoretical relationship between βa and βe is commonly expressed by the

following formulae:

βa = ( )( )( )

( )( )

−+

−+

−+ dde

de

de

e βT1VV

T1Vβ

T1VV

V

βa = ( )( )

( )t1DE

t1Dβ

t1DE

Eβ de −+

−+

−+

The latter version will now be used throughout this course.

Illustration 4

Giles plc is an all-equity company whose β coefficient is 0.95. Stiles plc is a levered

company in all other respects has the same risk and operating characteristics as

Giles.

The capital structure of Stiles plc is as follows:

Nominal value Market value

£m £m

Equity 6 15

Debt 4 6

10 21

The debentures of Stiles plc are virtually risk-free and the corporation tax rate is

40%.

What would be the predicted β of the equity of Stiles plc?

Solution 4

Since the debt of Stiles plc may be assumed to be risk free:

βa = ( )t1DE

Eβe −+

Therefore since Giles plc is an all equity company within the same industry as Stiles

plc, the βe of Stiles plc can be calculated as follows:

βe = ( )E

t1DEβa

−+

= ( )15

4.01615 x 95.0

−+

= 1.178





Illustration 5

Hotalot plc produces domestic electric heaters. The company is considering

diversifying into the production of freezers. Data on four listed companies in the

freezer industry and for Hotalot are shown below:

Freezeup Glowcold Shiverall Topice Hotalot

£’000 £’000 £’000 £’000 £’000

Fixed assets 14,800 24,600 28,100 12,500 20,600

Working capital _9,600 _7,200 11,100 _9,600 12,700

24,400 31,800 39,200 22,100 33,300

Financed by:

Bank loans 5,300 12,600 18,200 4,000 17,400

Ordinary shares* 4,000 9,000 3,500 5,300 4,000

Reserves 15,100 10,200 17,500 12,800 11,900

24,400 31,800 39,200 22,100 33,300

Turnover 35,200 42,700 46,300 28,400 45,000

Earnings per share

(in pence)

25 53.3 38.1 32.3 106

Dividend per share

(in pence)

11 20 15 14 40

Price/earnings ratio 12 10 9 14 8

Beta equity 1.1 1.25 1.30 1.05 0.95

*The par value per ordinary share is 25p for Freezeup and Shiverall, 50p for Topice

and £1 for Glowcold and Hotalot.

Corporate debt may be assumed to be almost risk-free, and is available to Hotalot

at 0.5% above the Treasury Bill rate, which is currently 9% per year. Corporate

taxes are payable at a rate of 35%. The market return is estimated to be 16% per

year. Hotalot does not expect its financial gearing to change significantly if the

company diversifies into the production of freezers.

Required:

(a) The equity beta of Hotalot is 0.95 and the alpha value 1.5%. Explain the

meaning and significance of these values to the company.

(b) Estimate what discount rate Hotalot should use in the appraisal of its

proposed diversification into freezer production.

(c) Corporate debt is often assumed to be risk-free. Explain whether this is a

realistic assumption and calculate how important this assumption is likely to

be to Hotalot’s estimate of a discount rate in (b) above. For this purpose

assume that Hotalot and the four freezer companies all have a debt beta of

0.3.

(d) Discuss whether systematic risk is the only risk that Hotalot’s shareholders

should be concerned with.





Solution 5

(a) Alpha and beta values

The equity beta is a measure of the systematic risk of the company’s shares – that

is, the relative volatility of the shares compared with the market as a whole.

Systematic risk, which is caused by general economic and market factors, cannot

be eliminated by diversification. The equity beta can be estimated as

m

m

s

sjρj

where ρjm is the correlation between the returns of the share and the returns of the

market, and sj and sm are the standard deviations of the returns of the share and

the market respectively.

An equity beta of 0.95 for Hotalot plc suggests that if the stock market return

moves up or down by 10%, the return on Hotalot will be expected to move by 0.95

x 10% = 9.5%. In other words, Hotalot’s returns are slightly less volatile than the

market as a whole, because its beta is just less than 1.

The capital asset pricing model shows how the expected returns of a share will

depend on its beta value. If the actual returns of the share are higher or lower

than the CAPM prediction, the share is said to have an abnormal return. The alpha

value is the measure of this abnormal return, that is, the difference between the

actual return and that predicted by the CAPM. In the case of Hotalot the alpha

value is positive, at 1.5%, which should cause investors to buy the shares. This in

turn will increase the price, forcing down the excess return until alpha falls to zero.

Thus alpha values should only be temporary. In a well diversified portfolio the

alpha value is expected to be zero.

(b) Discount rate for the appraisal of the proposed diversification into

freezers

First, estimate the average equity beta in the freezer industry, then degear this

figure. Regear it up to Hotalot’s debt/equity ratio and apply the CAPM to find

Hotalot’s cost of equity. A WACC can then be calculated for Hotalot.

Average equity beta in the freezer industry

Company Value of shares* Equity Beta factor

F 16 million x 0.25 x 12 = £48 million 1.1

G 9 million x 0.533 x 10 = £48 million 1.25

S 14 million x 0.381 x 9 = £48 million 1.30

T 10.6 million x 0.323 x 14 = £48 million 1.05

£192 million

*Value of shares = Number of shares x eps x PE ratio

Since all the companies have the same market value of shares, the average equity

beta is simply:

4

05.130.125.11.1 +++ = 1.175





Total value of debt in the companies is:

£’million

F: 5.3

G: 12.6

S: 18.2

T: 4.0

£40.1 million

The average debt/equity ratio in the freezer industry is therefore

192

1.40

Degearing the equity beta:

βa = ( )t1DE

Eβe −+

= ( )35.011.40192

192 175.1

−+× = 1.035

The market value of Hotalot’s shares is (4 million x £1.06 x 8) = £33.92 million,

the market value of its debt is £17.4 million. Then regearing the beta to Hotalot’s

debt/equity ratio:

βe = E

)t1(DEβa

−+

= ( )

92.33

65.0 x 4.1792.33x035.1

+ = 1.38

The required return on Hotalot’s equity, from the CAPM

= Rf + (Rm − Rf) β

= 9% + (16% − 9%) 1.38 = 18.66%

The weighted average cost of capital for Hotalot’s new diversification is

= ( ) ( ) ( )4.1792.33

4.17 x 35.01%5.9

4.1792.33

92.33 x %66.18

+−+

+= 14.42%

(c) The assumption that corporate debt is risk-free

Corporate debt is not risk-free. There is a risk of default which implies that the

debt has a positive beta. Studies show that corporate debt is likely to have a beta

of between 0.2 and 0.3.

From the information given in this question Hotalot must have a debt beta of

0.0714 since its Kd = 9% + (16% − 9%) 0.0714 = 9.5%. However the

instruction in the question is to assume a debt beta of 0.3, and this must, of

course, be observed.

Assuming that all corporate debt has a beta of 0.3, both the degearing and

regearing calculations in part (b) above will need to be adjusted.





The ‘asset beta’ of an organisation is the weighted average of the beta of equity

and the beta of debt. The asset beta is the same as the degeared beta, so:

βa = ( ) ( )65.0 x 1.40192

65.0 x 1.40 x 3.0

65.0 x 1.40192

192 x 175.1

++

+ =1.07

This is the revised degeared β for the freezer industry.

Regearing to Hotalot’s level of gearing -

1.07 = ( )( )

( )65.0 x 4.1792.33

65.0x4.17 x 3.0

65.0 x 4.1792.33

92.33 x βe

++

+

1.07 = 075.0750.0 x βe +

βe = 1.327

Applying the CAPM gives Hotalot’s cost of equity as

9% + (16% − 9%) 1.327 = 18.29%

Hotalot’s WACC then becomes

32.51

4.17 x 65.0 x %5.9

32.51

92.33 x %29.18 + = 14.18%

compared with the original estimate of 14.42%. The margin of error on these

estimates is, however, quite high – which means that the assumption that

corporate debt is risk-free is unlikely to have a significant effect on the accuracy of

Hotalot’s estimates.

(d) Does systematic risk give the complete picture?

The capital asset pricing model assumes that Hotalot’s shareholders are well

diversified and are only concerned with systematic risk. Undiversified or partly

diversified shareholders should also be concerned with unsystematic risk and

should seek a total return appropriate to the total risk that they face.

Even well diversified shareholders might be concerned with unsystematic risk. The

total risk of a company comprises systematic and unsystematic risk. It is total risk

(the total variability of cash flows) which determines the probability of a company

failing, and the investor experiencing additional bankruptcy costs. The greater the

expected bankruptcy costs and the greater the probability of corporate failure, the

more concerned investors are likely to be with the total risk and not just systematic

risk.





ASSUMPTIONS, ADVANTAGES AND LIMITATIONS OF

CAPM

Assumptions

● All shareholders hold the market portfolio. Although this is questionable in

practice, even a limited spread of shareholdings produces some

diversification, therefore this assumption is appropriate;

● A perfect capital market (e.g. no transaction costs, information about risk and

return is freely available);

● The ability of investors to both borrow and lend at the risk free rate of

interest;

● All forecasts are made for a single time period only;

● All investors share the same uniform expectations concerning future earnings

streams and are only concerned with risk and return.

Advantages

● It demonstrates that unsystematic risk can be diversified away, therefore the

only risk premium required is for systematic risk only;

● Probably the best practical method for establishing the Ke of a publicly traded

company;

● It highlights the relationship between risk and return, based upon stock

market performance and provides a measure of the risk of shares held within

a well-diversified portfolio and measures the required rate of return in view of

that level of risk;

● Helps to provide a risk adjusted discount rate for use in investment appraisal.

Limitations

● It concentrates purely upon systematic risk and is therefore of limited use for

investors who do not hold a well-diversified portfolio;

● Since CAPM only considers the level of return to investors, it ignores the

manner in which that return is received. Therefore, it treats dividends and

capital gains as equally desirable to investors, thus totally ignoring the tax

position of individual investors;

● It is purely a single period model, therefore not ideal for use in projects which

extend for multiple periods;

● The model requires the use of data which can be difficult to obtain i.e.

(i) The risk free rate of interest: It is necessary to take the best proxy

measure of a short-term default free rate e.g. UK 90 day Treasury bills;

(ii) The return on the market portfolio: Should the FT all-share index be

used, or the FTSE 100, or the FTSE 350, or a world composite share

price index?;

(iii) Beta: Clearly this should strictly be based on subjective probabilities of

future events, but since this is impracticable in practice, regression

analysis is often used to compare the historical behaviour of individual





securities with the behaviour of a suitable market index within the same

time period.

● CAPM tends to overstate the required return of high beta securities and to

understate the required return of low beta securities. The returns of small

companies, returns on certain days of the week or months of the year have in

practice been observed to differ from those expected from CAPM.





ARBITRAGE PRICING THEORY AND FAMA & FRENCH

THREE FACTOR MODEL

Arbitrage Pricing Theory (APT), which was first introduced by S A Ross in 1976,

is an alternative theory of risk and return. It states that the risk premium on a

share depends on that share’s exposure to a number of factors, and not simply Erm.

The problem is that APT does not state what these factors are, but researchers

have identified several possibilities, including unanticipated changes in the level of

industrial production; the rate of inflation; the effect of the yield curve; real rates of

interest; levels of personal consumption; money supply in the economy and risk

premiums on bonds.

APT states that the required return from Security A is expressed as follows:

Required return = rf + [ErF1 − rf] βF1 + [ErF2 − rf] βF2 + [ErF3 − rf] βF3

Where:

ErF1 = expected return arising from factor 1

βF1 = 1F

1F,AA

s

ρs

APT has less constraining assumptions than CAPM. For instance, it is not a single

factor model and does not require some of the perfect market assumptions of

CAPM. The major weakness of APT is that it is extremely difficult to identify the

relevant factors and the sensitivity of such factors for individual companies. Hence

APT is difficult to use as a practical decision-making technique.

The Fama and French three factor model was derived in 1993, when two

American academics considered that CAPM could be significantly improved by

introducing two further factors in addition to market risk i.e. Size effect: Investors

find small (less actively traded) companies more risky than larger entities, and

Distress factor: The ratio of book value of equity to market value of equity is

compared. The more market value falls towards book value, the greater the

company’s exposure to financial distress.

Fama and French’s three factor model is as follows:

Required return = rf + [Erm – rf] βjm + [SMB] βjs + [HML] βjd

Where:

βjm is the normal equity beta of the company applied to the excess market return,

βjs is the company’s factor loading for the size effect where [SMB] is the difference

in return between a portfolio of the smallest stocks in the economy and a portfolio

of the largest stocks, and

βjd is the factor loading for the distress effect where [HML] is the difference in

return between a portfolio of the highest book to market value stocks and a

portfolio of the lowest book to market value stocks.

To calculate the SMB and HML premia, Fama and French used stocks quoted on the

New York Stock Exchange, the American Stock Exchange and the NASDAQ.





Cygnet plc

Cygnet plc is a large listed company, which owns a variety of businesses in the

retailing sector. It now wishes to diversify into brewing and has consequently

highlighted two possible target companies in the brewing sector, Parched Ltd and

Fullup Ltd.

The following data has been collected regarding each target company, the existing

activities of Cygnet plc and the market generally.

Parched Ltd Fullup Ltd Cygnet plc Market

Expected return 15% 16% 18% 25%

Risk 10% 12% 15% 20%

Risk is measured as the standard deviation of possible returns around the average

(or expected) return.

Correlation coefficients of targets with:

- existing activities of Cygnet plc; and

- the market generally;

are estimated as follows:

Parched Ltd Fullup Ltd

Cygnet plc 0.85 0.40

Market 0.25 0.95

The risk-free rate is to be taken as 5% and either target will represent 10% of the

now enlarged Cygnet plc (that is the existing operations of Cygnet plc will represent

90% of the expanded company and the new acquisition will form the remaining

10% of Cygnet’s extended business operation).

Required

Appraise each of the target companies using:

(i) portfolio theory; and

(ii) capital asset pricing model

explaining briefly the basis of each method and state which you recommend in this

case.

NOTE: It is thought that for purposes of portfolio theory, the shareholders of

Cygnet plc would accept an increase of 1% in risk to achieve a 0.5% increase in

return or alternatively to accept a 0.5% decrease in return in order to achieve a 1%

decrease in risk.





Cygnet plc solution

(i) Portfolio theory approach

We calculate the expected return and risk of the following combinations:

- Cygnet plc with Parched Ltd

- Cygnet plc with Fullup Ltd

Cygnet plc and Parched Ltd

Expected return is given by

waEra + wbErb

Where wa = proportion represented by Cygnet plc

wb = proportion represented by Parched Ltd

Era = expected return from Cygnet plc

Erb = expected return from Parched Ltd

Return = (0.9 x 18%) + (0.1 x 15%)

= 17.7%

Risk of the combination is given by

sp = abbaba2

b2

b2

a2


where sa = risk of Cygnet plc

sb = risk of Parched Ltd

ρab = correlation coefficient of one with the other.

sp = ( ) ( ) ( )85.0 x 10 x 15 x 1.0 x 9.0 x 210 x 1.015 x 9.022 ++

= ( )95.22125.182 ++

= 14.36%

Cygnet plc and Fullup Ltd

Return = (0.9 x 18%) + (0.1 x 16%)

= 17.8%

sp = ( ) ( ) ( )4.0 x 12 x 15 x 1.0 x 9.0 x 212 x 1.015 x 9.022 ++

= ( )96.1244.125.182 ++

= 14.02%





Summary

Return Risk

Cygnet plc 18% 15%

Cygnet plc and Parched Ltd 17.7% 14.36%

Cygnet plc and Fullup Ltd 17.8% 14.02%

Both takeovers decrease both risk and return. The combination of Cygnet plc and

Fullup Ltd decreases risk by a greater extent and decreases return by a lesser

extent and hence is preferred to the alternative.

In deciding whether the combination is better than Cygnet plc’s existing operations

alone we use the information about shareholders’ attitudes to risk.

The decrease in risk is just under 1%. The acceptable decrease in return

corresponding to this is 0.5%. The actual decrease is 0.2%, and hence the

takeover of Fullup Ltd is worthwhile.

(ii) CAPM approach

We calculate, for each target company, its beta factor and hence the minimum

required return from each company. Comparison of this with the expected return

from each company then determines whether the takeover is worthwhile.

Parched Ltd

βj = m

jjm

s

s ρ

Where ρjm = correlation coefficient between the investment (Parched Ltd)

with the market

sj = risk of the investment

sm = risk of the market.

Hence βj = 20

1025.0 × = 0.125

The CAPM formula now gives

Minimum required return = Rf + (Erm - Rf) βj

= 5 + (25 - 5)0.125

= 7.5%

Fullup Ltd

βj = 20

12 x 95.0 = 0.57

Minimum required return = 5 + (25 - 5)0.57 = 16.4%





Summary

Required return Expected return

Parched Ltd 7.5% 15%

Fullup Ltd 16.4% 16%

Thus, the takeover of Fullup is not worthwhile, since the expected return is less

than that required to compensate shareholders for the systematic risk in the

company. The takeover of Parched should go ahead.

Explanation of the methods and conclusion

Portfolio theory appraises a proposed investment from the point of view of the ‘fit’

that it has with the existing operations of the company. The aim is always to

increase return and decrease risk. Sometimes both these effects are not possible

at the same time, in which case one takes into account the shareholders’ attitudes

to risk (indifference curves). This is, however, difficult in practice.

Unlike portfolio theory, which considers an investment in combination with the

existing portfolio of investments and seeks to obtain satisfactory changes in return

for changes in total risk, CAPM considers an investment in isolation. This is

because the existing portfolio is assumed to be fully diversified and can thus

be ignored. At the point of full diversification only systematic risk remains in a

portfolio. Provided that the new investment being considered makes a sufficient

return to compensate for its level of systematic risk, it is satisfactory. Again this is

in stark contrast to portfolio theory which is concerned with total risk rather

than just systematic risk. A benefit of CAPM is that the conclusion on the

acceptability of an investment would be universally held by all fully diversified

investors.

In this case, since Cygnet plc is large and quoted, it is reasonable to suppose that

its shareholders are well diversified and therefore the CAPM approach would seem

to be the more appropriate. Parched Ltd is thus the preferred takeover target.





Five Wealthy Individuals

Five wealthy individuals have each put £200,000 at your disposal to invest for the

next two years. The funds can be invested in one or more of four specified projects

and in the money market. The projects are not divisible and cannot be postponed.

The investors require a minimum return of 24% over the two years.

Details of these possible investments are:

Initial

cost

Return over

two years

Expected standard deviation of

returns over two years

£’00 (%) (%)

Project 1 600 22 7

Project 2 400 26 9

Project 3 600 28 15

Project 4 600 34 13

Money market (minimum) 100 18 5

Correlation coefficients of returns (over two years)

Between

projects

Between projects and the market

portfolio

Between projects and the

money market

1 and 2: 0.70 1 and market: 0.68 1 and money market: 0.40




2 and 4: 0.57

3 and 4: 0.76 Between the money market and

the market portfolio: 0.40

The risk-free rate is estimated to be 16%, the market return 27% and the variance

of returns on the market 100% (all for the two-year period).

Required:

(a) Evaluate how the £1m should be invested using

(i) portfolio theory,

(ii) the capital asset pricing model (CAPM)

Portfolio risk may be assessed using the formula

sp = abbaba2

b2

b2

a2


(b) Explain why portfolio theory and CAPM might give different solutions as to

how the £1m should be invested.

(c) Discuss the main problems of using CAPM in investment appraisal.





Suggested solution to Five Wealthy Individuals

(a) How the £1 million should be invested

(i) Using portfolio theory

Consider the possible combinations for investing £1 million and the return that

will be made from each combination:

Projects Portfolio return

A: 1 and 2 0.6 x 22% + 0.4 x 26% = 23.6%

*B: 2 and 3 0.4 x 26% + 0.6 x 28% = 27.2%

*C 2 and 4 0.4 x 26% + 0.6 x 34% = 30.8%

D: 1 and money market: 0.6 x 22% + 0.4 x 18% = 20.4%

E: 2 and money market: 0.4 x 26% + 0.6 x 18% = 21.2%

*F: 3 and money market: 0.6 x 28% + 0.4 x 18% = 24.0%

*G: 4 and money market: 0.6 x 34% + 0.4 x 18% = 27.6%

H: Money market only: 18%

The minimum required return is 24%.

* Therefore, only alternatives B, C, F and G are acceptable.

To choose between these we must examine portfolio risk, using the formula

given in the question.

Alternative B: Projects 2 and 3

Portfolio risk: = ( ) ( ) ( )15 x 9 x 65.0 x 6.0 x 4.0 x 215 x 6.09 x 4.0 2222 ++

= 08.136 = 11.67%

Alternative C: Projects 2 and 4


= 81.105 = 10.29%

Alternative F: Project 3 and the money market


= 8.104 = 10.24%

Alternative G: Project 4 and the money market

Portfolio risk = ( ) ( ) ( )5 x 31 x 6.0 x 4.0 x 6.0 x 25 x 4.031 x 6.0 2222 ++

= 56.83 = 9.14%





In order to rank the investment combinations, we need to summarise return

and risk.

Combination Portfolio expected Return Portfolio risk

2 and 3 27.2% 11.67%

2 and 4 30.8% 10.29%

3 and money market 24.0% 10.24%

4 and money market 27.6% 9.14%

In ranking the portfolios, we are looking for high return and low risk

(assuming risk-averse investors). It may therefore be said that:

(1) Combination ‘2 and 4’ is better than ‘2 and 3’ because it has a higher

return and lower risk.

(2) Combination ‘4 and the money market’ is better than both ‘2 and 3’ and

‘3 and the money market’ because it has a higher return and lower risk.

The choice between combinations ‘2 and 4’ and ‘4 and the money market’ is

impossible to make without further data on the investors’ risk/return

preferences.

However, an attempt to make the decision may be possible by calculating the

“coefficient of variation”, which employs the following formula:

Coefficient of Variation = turnRe Expected

Deviation dardtanS

In the case of ‘2 and 4’ this is (10.29% ÷ 30.8%) = 0.334, and in the case of

‘4 and the money market’ this is (9.14% ÷ 27.6%) = 0.331. Clearly the

combination of ‘4 and the money market’ is marginally preferable, since it

offers the lower level of risk per 1% of return. However, this technique is

open to criticism as the decision is “too close for comfort”!!.

(ii) Using the CAPM

First calculate the beta factors of the projects using the formula:

m

jjm

s

s ρ

Project Beta

1 10

7 x 68.0 = 0.476

2 10

9 x 65.0 = 0.585

3 10

51 x 75.0 = 1.125

4 10

31 x 88.0 = 1.144

Money market 10

5 x 4.0 = 0.20





Now calculate the betas of the combinations with returns above 24%. The

beta of a portfolio is the weighted average of the betas of the component

investments.

Combination Portfolio beta

2 and 3 (0.4 x 0.585) + (0.6 x 1.125) = 0.909

2 and 4 (0.4 x 0.585) + (0.6 x 1.144) = 0.920

3 and money market (0.6 x 1.125) + (0.4 x 0.20) = 0.755

4 and money market (0.6 x 1.144) + (0.4 x 0.20) = 0.766

Now find the required return of the portfolio, using the CAPM, and compare it

with its expected return:

Combination CAPM required return Expected return

2 and 3 16% + (27% − 16%) 0.909 = 26% 27.2%

2 and 4 16% + (27% − 16%) 0.920 = 26.12% 30.8%

3 and money

market 16% + (27% − 16%) 0.755 = 24.3% 24.0%

4 and money

market 16% + (27% − 16%) 0.766 = 24.43% 27.6%

Using the CAPM, all combinations except ‘3 and the money market’ are

expected to earn above their minimum required return. If the investors

require the greatest excess return, the choice would be projects ‘2 and 4’,

since its excess return i.e. alpha value, is (30.8% − 26.12%) = 4.68%.

(b) Why portfolio theory and the CAPM might give different solutions

The portfolio theory calculations assume that each portfolio can be viewed in

isolation from any other investments which the wealthy individuals may hold. As

shown in the answer above, the aim is to find the combination of investments with

the most satisfactory trade-off of expected return and risk. Some potential

combinations can be eliminated, but ultimately the final choice is a subjective one

which depends on the investor’s attitude to risk. The portfolio theory approach

recognises that investments must be viewed as part of a portfolio, but it effectively

makes the assumption that the chosen portfolio will account for all the investor’s

funds.

The capital asset pricing model assumes that the investor already holds a widely

diversified portfolio (the market portfolio). New investments are appraised by

considering their effect on the market portfolio in terms of return and risk. In doing

this it becomes apparent that only the systematic risk of the investment is relevant,

that is the proportion of the risk which is dependent on general economic and

market factors. Unsystematic risk is eliminated when the investment is added to

the market portfolio. The result is a simple formula for appraising a new

investment (or combination of new investments) in terms of systematic risk,

measured by the beta factor.





In summary

Portfolio theory

● assumes the new investments are an addition to the investor’s total portfolio;

● considers the total risk of the portfolio of investments.

CAPM

● assumes the new investments are a small addition to the market portfolio;

● considers only systematic risk of the new investments

Investments which have high total risk but low systematic risk will be appraised

more favourably by the CAPM than by portfolio theory.

(c) The main problems of using CAPM in investment appraisal

The problems of using CAPM include

(i) the assumptions behind the model

(ii) the difficulty in obtaining data

(iii) the accuracy of the model in explaining investment and security returns

Many of the assumptions behind the model are unrealistic. The assumptions

include:

(i) Investors can borrow and lend easily at the risk-free rate of return

(ii) No transaction costs or market imperfections exist

(iii) Information about the risk and return of investments is freely available

(iv) Investors measure risk by the standard deviation of expected returns

(v) All investors have the same expectations about future profits and dividends

and are single-period terminal wealth maximisers. This is based only on risk

and return.

Obtaining data for the model is difficult. It is an ‘ex-ante’ model which requires

data for expected returns and risk of the investment and the market. The practical

difficulty of forecasting such risk and returns means that the model is usually

applied using historical ‘ex-post’ data, requiring the beta to be stable over time.

The model requires the risk-free rate, and the market return. What is the

appropriate measure of the risk-free rate and the market return? Over what period

should data be used? At what interval should observations be made? What is the

market – the UK all-share index, or a world composite share price index, or some

other measure e.g. the FTSE 100 index? These are only some of the possible data

problems.

The accuracy of the model has been questioned by many pieces of empirical

research. CAPM requires alpha, the intercept term, not to be significantly different

from zero; many studies suggest that it is significantly different from zero. Low

beta securities earn higher returns than CAPM would predict, and higher beta

securities earn lower returns. Company size, seasonality, day of the week,

dividend yield, and price-earnings ratios are among the factors that are said to

explain observed returns in addition to the systematic risk.

Such problems raise serious questions about the accuracy of using CAPM in

investment appraisal.





Dell plc

You have purchased the following data from a merchant bank.

Company Forecast total

equity return

Standard deviation of

total equity return

Covariance with

market return

Dell plc 17% 6.3% 32%

Baseball plc 12% 4.8% 19%

Burnden plc 14% 4.7% 24%

Roker plc 21% 6.9% 43%

The market return, market standard deviation and market variance are 14.5%, 5%

and 25% respectively, and the risk free rate is 6%. Returns and all other data

relate to a one-year period.

Required:

(a) Estimate the differences between the required returns and the forecast total

equity returns (that is the ‘alpha’ values) for each of these companies’ shares

and explain what use alpha values might be to financial managers.

(b) Briefly discuss reasons for the existence of alpha values, and whether or not

the same alpha values would be expected to exist in one year’s time.

Suggested solution to Dell plc

(a) The alpha value is any abnormal return that exists relative to the required

return from an investment, as estimated by using the capital asset pricing

model (CAPM). The beta of the companies’ shares may be estimated from:

β = m

Jm

Variance

iancevarCo

The beta estimates are:

Dell 25

32 = 1.28

Baseball 25

19 = 0.76

Burnden 25

24 = 0.96

Roker 25

43 = 1.72

Required returns Forecast returns Alpha

Dell 6% + (14.5% - 6%) 1.28 = 16.88% 17% +0.12%

Baseball 6% + (14.5% - 6%) 0.76 = 12.46% 12% -0.46%

Burnden 6% + (14.5% - 6%) 0.96 = 14.16% 14% -0.16%

Roker 6% + (14.5% - 6%) 1.72 = 20.62% 21% +0.38%

A positive alpha value implies that it is possible to make a higher than normal

return, for the systematic risk taken. A negative alpha implies a lower than

normal return.





A financial manager wishing to invest in shares might favour those with a

positive alpha, subject to the shares satisfying other selection criteria such as

the desired level of risk.

If a positive or negative alpha exists for the shares of the company of the

financial manager, and the market is at least semi-strong form efficient, the

alpha would be expected to move to zero as the company’s share price

changes due to arbitrage profit taking. For example in theory a company with

a positive alpha would expect relatively high demand for its shares, increasing

share price and thereby decreasing return until the alpha is zero.

(b) Positive or negative alpha values exist for shares most of the time. If CAPM is

a realistic model alpha values should only be temporary and the same alpha

values would not be expected to exist in a years time.

Alpha may exist due to inaccuracies and/or limitations of the CAPM model

including:

(i) CAPM tends to overstate the required return of high beta securities and

to understate the required return of low beta securities. The returns of

small companies, returns on certain days of the week or months of the

year are observed to differ from those expected from CAPM.

(ii) Data input into the model may be inaccurate. For example it is

impossible to accurately calculate the market risk and return.

(iii) Other factors in addition to systematic risk might influence required

return. The arbitrage pricing theory (APT) suggests that a multi-factor

model is necessary.

(iv) CAPM is based upon a number of unrealistic assumptions.





Nelson plc

The management of Nelson plc wish to estimate their firm’s equity beta. Nelson

has had a stock market listing for only two months and the financial manager feels

that it would be inappropriate to attempt to estimate beta from the actual share

price behaviour over such a short period. Instead, it is proposed to ascertain, and

where necessary adjust, the observed equity betas of other companies operating in

the same industry and with the same operating characteristics as Nelson, as these

should be based on similar levels of systematic risk and be capable of providing an

accurate estimate of Nelson’s beta.

Three companies have been identified as firms having operations in the same

industry as Nelson which utilise identical operating characteristics. However, only

one company, Oak plc, operates exclusively in the same industry as Nelson. The

other two companies have some dissimilar activities or opportunities, in addition to

operating characteristics which are identical to those of Nelson.

Details of the three companies are:

(i) Oak plc. Observed equity beta 1.12. Capital structure at market values is

60% equity, 40% debt.

(ii) Beech plc. Observed equity beta 1.11. It is estimated that 30% of the

current market value of Beech is caused by risky growth opportunities which

have an estimated beta of 1.9. The growth opportunities are reflected in the

observed beta. The current operating activities of Beech are identical to those

of Nelson. Beech is financed entirely by equity.

(iii) Pine plc. Observed equity beta 1.14. Pine has two divisions – East and West.

East’s operating characteristics are considered to be identical to those of

Nelson. The operating characteristics of West are considered to be 50% more

risky than those of East. In terms of financial valuation East is estimated as

being twice as valuable as West. Capital structure of Pine at market values is

75% equity, 25% debt.

Nelson is financed entirely by equity. The tax rate is 40%.

Required:

(a) Assuming all debt is virtually risk-free, determine three estimates of the likely

equity beta of Nelson plc. The three estimates should be based, separately,

on the information provided for Oak, Beech and Pine plc.

(b) Explain why the estimated beta of Nelson, when eventually determined from

observed share price movements, may differ from those derived from the

approach employed in a) above.

(c) Specify the reasons why a company which has a high level of share price

volatility and is generally considered to be extremely risky, can have a lower

beta value, and therefore lower systematic risk, than an equally geared firm

whose share price is much less volatile.





Suggested solution to Nelson plc

(a) Estimates of likely beta

βa = ( )t1DE

Eβe −+

+ ( )

( )t1DE

t1Dβd −+

−

But assumed βd = 0

βa = ( )t1DE

Eβe −+

Therefore βe = ( )E

t1DEβa

−+

(i) The beta of Oak’s equity must be degeared to reflect Nelson’s all equity

status

Hence,

βa = ( )t1DE

Eβe −+

= ( )4.0146

6 x 12.1

−+ = 0.8

(ii) To obtain a beta for Nelson, we must isolate the beta of Beech’s current

operating activities.

Hence 1.11 = (β Current operations x 0.7) + (1.9 x 0.3)

1.11 = (β Current operations x 0.7) + 0.57

0.54 = β Current operations x 0.7

β Current operations = 7.0

54.0 = 0.77

(iii) In this case we must degear Pine’s equity beta to remove the financial

risk carried by Pine and then isolate the beta of Pine’s Eastern Division.

βa = ( )t1DE

Eβe −+

= ( )4.012575

75 x 14.1

−+ = 0.95

β overall = 2/3 βE + 1/3 βW

0.95 = 2/3 βE + 1/3 βW

= 2/3 βE + 1/3 x 1.5 βE

= 2/3 βE + 1/2 βE

= 7/6 βE

Therefore βa = 0.95 x 6/7 = 0.814

Note that this calculation could have been performed by firstly isolating the beta of

the Eastern division and then by degearing to remove the financial risk carried by

Pine.





(b) Reasons for estimated beta differences

The reasons include:

(i) Statistical estimation

Estimates of beta derived from observed share prices are usually the results

of a linear regression. They are, therefore, an estimate of the share beta

rather than a precise determination of that beta. Even if the true underlying

betas are identical, the regression estimates may differ. Normally betas of

portfolios are considered to be more reliable than betas of individual

securities.

(ii) Changes in operations

While the firms may currently have identical operating activities, by the time a

valid estimate of Nelson’s beta can be made from actual share price data

(probably at least three years hence) the operating practices may have

changed.

(iii) Abnormal share price behaviour

The period immediately following a firm’s quotation on a stock exchange may

produce non-typical share price behaviour. The inclusion of such a period in

the observations used to determine beta may distort the calculations.

(iv) Size difference

Difference in size between Nelson and the other companies may cause a

difference in perceived risk which is reflected in the beta estimation.

Generally, smaller companies are perceived as being of greater risk than

larger firms.

(v) Differences in current cost structures

Although firms may appear to have identical operating characteristics,

differences in cost structures (e.g. caused by differences in the ages of

production equipment) can affect beta. Usually, the higher the proportion of

fixed costs the higher will be beta.

(vi) Growth opportunities of Nelson

Investors may perceive Nelson as having opportunities for growth and its

actual share price, share price behaviour and beta may reflect growth

opportunities as well as current activities.

(vii) Degearing process

The approach used to degear betas is derived from the Modigliani and Miller

1963 hypothesis. If any of the assumptions of their theory are violated (e.g.

risk free and permanent debt) then the procedure is invalid. In general terms

any of the criticisms levelled against the Modigliani and Miller 1963 theory

(e.g. bankruptcy costs, tax exhaustion, personal taxes, etc) could be used to

criticise our calculations above.





(c) Share price volatility and systematic risk

The reasons for the lower beta value of a company with high share price volatility

stem from the differences between total risk and systematic risk. Total risk,

represented by measures of total share price (or return) volatility, comprise:

systematic risk + unsystematic risk

The unsystematic element of total risk is not connected with economy-wide factors

but is unique to a particular firm. This unsystematic risk can largely be diversified

away in a widely spread portfolio. The systematic risk results from the connection

between the share and the economy, or stock market, generally and cannot be

diversified away in a portfolio. It is this systematic risk, measured by beta, which is

of relevance.

For example, the success of a mineral prospecting company is unlikely to be a

function of the economy generally and is more likely to be determined by factors

unique to the firm. While the firm’s share price may be very volatile and the share

is extremely risky if held in isolation, the small level of dependence on the economy

means the share is largely risk-free in a portfolio context. Hence, large total risk

but small systematic risk is to be expected from this type of firm.

However, a manufacturing company may have a far greater dependence on the

economy and so its systematic risk is higher, even though its total risk is lower than

that of the prospecting firm.




Chapter 8

Adjusted present value



CHAPTER 8 – ADJUSTED PRESENT VALUE


CHAPTER CONTENTS

ADJUSTED PRESENT VALUE ------------------------------------------- 193

POLYCALC PLC ---------------------------------------------------------- 194

TOVELL PLC ------------------------------------------------------------- 196

ALASTAIR BROWN PLC ------------------------------------------------- 201





ADJUSTED PRESENT VALUE

Traditionally financial management has appraised new investments by discounting

their after-tax operating cash flows to present value at the firm’s weighted average

cost of capital and subtracting the initial investment cost to arrive at an NPV. We

have already noted problems with the use of the WACC and seen that adjustments

are commonly needed to tailor the discount rate to the systematic business risk and

the financial risk of the project under consideration.

M & M based adjustments to the cost of capital form one approach to this problem.

Here we examine another, adjusted present value (APV), which offers significant

advantages.

APV is often described as a “divide and conquer approach”. To do this the project

will first be evaluated as if it were being undertaken by an all-equity company.

“Side effects” like the tax shield on debt and the issue costs being ignored. This

first stage will give us the so-called base NPV or base case NPV. The second stage

is to calculate the present value of the side effects and to add these to the base

NPV. The result is the APV which shows the net effect on shareholder wealth of

adopting the project.

The APV method therefore sees the value of the project to shareholders as being:

Project value if all equity financed + present value of tax + Present value of

(the base case NPV) shield on the loan other side effects

Weaknesses of the APV technique

(a) The process of degearing an equity beta of a levered company in the “new”

industry to obtain a suitable asset beta for an all-equity firm relies upon the M

& M 1963 case. When market imperfections such as bankruptcy costs are

introduced, it is unlikely that the M & M 1963 position is valid.

(b) The discount rates used to evaluate the various side effects can be difficult to

determine. Normally the risk-free rate is used to evaluate the corporation tax

savings on loan interest and issue costs. This is valid if the firm is certain that

it will be earning sufficient profits to take immediate advantage of the tax

relief. If the firm were not certain, then the situation is more risky and a

higher discount rate should be used. The problem is how much higher? This

would largely be a matter of educated guesswork.

(c) In complex investment decisions the calculations can be extremely long.





Polycalc plc

Polycalc plc is an internationally diversified company. It is presently considering

undertaking a capital investment in Australia to manufacture agricultural fertilizers.

The project would require immediate capital expenditure of A$15m, plus A$5m of

working capital which would be recovered at the end of the project’s four year life.

It is estimated that an annual revenue of A$18m would be generated by the

project, with annual operating costs of A$5m. Straight-line depreciation over the

life of the project is an allowable expense against company tax in Australia, which is

charged at a rate of 50%, payable at each year-end without delay. The project can

be assumed to have a zero scrap value.

Polycalc plans to finance the project with a £5m 4-year loan at 10% from the Euro-

sterling market, plus £5m of retained earnings. The proposed financing scheme

reflects the belief that the project would have a debt capacity of two-thirds of

capital cost. Issue costs on the Euro debt will be 2½ % and are tax deductible.

In the UK the fertilizer industry has an equity beta of 1.40 and an average

debt:equity gearing ratio of 1:4. Debt capital can be assumed to be virtually risk-

free. The current return on UK government stock is 9% and the excess market

return is 9.17%.

Corporate tax in the UK is at 35% and can be assumed to be payable at each year-

end without delay. Because of a double-taxation agreement, Polycalc will not have

to pay any UK tax on the project. The company is expected to have a substantial

UK tax liability from other operations for the foreseeable future.

The current A$/£ spot rate is 2.0000 and the A$ is expected to depreciate against

the £ at an annual rate of 10%.

Required

Using the Adjusted Present Value technique, advise the management of Polycalc on

the project’s desirability.





Polycalc solution

Base-case discount rate

β asset = 1.40 x ( )35.0114

4

−+ = 1.20

Base-case discount rate = 9% + (9.17% x 1.20) = 20%

Project tax charge and cash flows in A$m (Years 1 to 4)

Tax Cash flow

Revenue 18 18

Operating costs (5) (5)

Depreciation (15 ÷ 4) (3.75)

Taxable profit 9.25

Tax charge @ 50% 4.625 (4.625)

8.375

Base-case net present value calculation in £m

Year A$m

Exch.

Rate

increasing

at 10% pa £m

20%

Discount

rate

£m PV of

cash flows

0 (15 + 5) = (20) ÷ 2 = (10) x 1 = (10)

1 8.375 ÷ 2.2 = 3.807 x 0.833 = 3.171

2 8.375 ÷ 2.42 = 3.461 x 0.694 = 2.402

3 8.375 ÷ 2.662 = 3.146 x 0.579 = 1.821

4 (8.375 + 5) = 13.375 ÷ 2.9282 = 4.568 x 0.482 = 2.202

Base-case NPV = (£0.404m)

PV of tax shield

Based upon debt capacity created i.e.

3

2 x

2

m15$A = £5m (which happens to be equal to the loan raised)

Annual tax relief on interest = £5m x 0.10 x 0.35 = £175,000

PV of tax relief for 4 years: £175,000 x 3.170 = £554,750

PV of issue costs

£5m x 0.025 x (1 − 0.35) = £81,250


£m

Base case NPV (0.404)

PV of tax shield 0.555

PV of issue costs (0.081)

Adjusted present value £0.07m or +£70,000 approx

Therefore accept project and finance it in the manner indicated.





Tovell plc

The selection of appropriate discount rates for capital investments has frequently

been a problem for the finance director of Tovell plc. The company has adopted a

strategy of diversification into many different industries, in order to reduce risk for

the company’s shareholders. This has resulted in frequent changes in the

company’s gearing level and widely fluctuating risks of individual investments.

The current project under appraisal, an investment in the fast food industry where

Tovell has no other investments, is expected to generate pre-tax operating cash

flows of £420,000 in the first year, rising by 5% per year for the five year expected

life of the project. After five years the land and buildings are expected to have a

realisable value of £1,250,000 (after any tax effects), the same as their original

cost, but in order to continue operations major new investment in equipment would

be required at that time. Other fixed assets would have negligible value after five

years. The total initial outlay of the project (net of issue costs) is £2.3 million, and

all but the land and buildings, attracts a 25% per year capital allowance on a

reducing balance basis.

The project would be financed by a £800,000 fixed rate loan from a regional

development agency at a subsidised interest rate of 6% per year, 3% less than

Tovell could borrow at in the capital market. The remainder of the finance would be

provided by an underwritten rights issue at a 10% discount on current market price

with total underwriting and issue costs of 5% of gross proceeds. The investment is

believed to add £1 million to the company’s debt capacity.

Current financial data for Tovell and the fast food industry includes:

Tovell plc Fast food industry (average)

P/E ratio 12 20

Dividend yield 5% 3%

Equity beta 1.1 1.4

Debt beta 0.2 0.25

Gearing (debt/equity):

Book values 1.1 to 1 1.6 to 1

Market values 0.4 to 1 1 to 1

Share price 470 pence n.a.

Number of ordinary shares 3.5 million n.a.

The corporate tax rate is currently 30% per year, and tax is payable one year in

arrears

Treasury bills are currently yielding 5% per year after tax, and the return required

by well diversified investors is 12.5% per year.

Required:

(a) Provide a reasoned explanation as to whether you would support the

company’s strategy of diversifying into many different industries.

(b) Prepare a report for the finance director of Tovell plc advising on the financial

viability of the proposed fast food investment. Include in the report an

assessment of the limitations of the method of appraisal that you have used.

Supporting calculations should form an appendix to your report.





Tovell plc solution

(a) Candidates are expected to show understanding of the theoretical and

practical arguments relating to corporate diversification into several

industries.

Tovell has a strategy of diversifying into many industries in order to reduce

risk of the company’s shareholders. Rational shareholders should already be

well diversified, in order to eliminate unsystematic risk. If shareholders are

not well diversified this may be achieved quickly and cheaply through the

purchase of such investments as general unit trusts. The expense of the

company undertaking diversification is likely to be much greater than that of

individual investors in the company diversifying themselves, and therefore

sub-optimal strategy from the investors’ viewpoint. As the primary objective

of companies is usually assumed to be the maximisation of shareholder

wealth the strategy would not normally be recommended.

However, diversification might have beneficial effects for shareholders

including:

(i) Less volatile internal cash flows, making servicing existing debt less

risky, and therefore increasing the debt capacity of the company.

Greater use of debt with no extra risk could reduce the overall cost of

capital, and increase shareholder wealth.

(ii) If diversification is into foreign markets where exchange controls or

other barriers prevent or restrict shareholders directly investing (i.e.

segmented markets), it might be possible for shareholders to reduce

their systematic risk through Tovell investing in such markets which

have risk-return combinations which would not otherwise be available to

shareholders.

(iii) If a company fails there are many ‘bankruptcy’ costs including receiver’s

fees and the possibility of assets being sold cheaply in a ‘forced-sale’.

Such costs may significantly reduce wealth of shareholders. A

diversified company may have a lower risk of corporate failure because

of reduced total risk of the company (measured by variance of returns).

Shareholders may be willing to accept the costs of diversification if the

probability of corporate failure is reduced.

(b) Candidates are required to select an appropriate investment evaluation

technique (hopefully APV) in a diversification situation where gearing levels

have changed, to show understanding of its limitations, and to prepare a

report supported by the financial valuation of given data.

Report on the financial viability of the fast food investment

The proposed investment is in an industry where the company has no existing

activities, and differs in risk to the company’s existing activities, as is

evidenced by the equity betas of the company and the industry. The

investment is to be financed £800,000 by debt and £1,578,947 equity, a

gearing level of approximately 0.5 to 1, which is significantly different from

the company’s current market weighted gearing of 0.4 to 1.

As the investment results in a change in capital structure, is not marginal

relative to the size of the company, and does not have the same level of

systematic risk as the company, the current weighted average cost of capital

should not be used as the discount rate.





There is no easy way to adjust the weighted average cost to take into account

these changes. It is recommended that the fast food investment is evaluated

using the adjusted present value (APV) technique. This approach examines

directly the effects of the financing methods that are being used, which, for

this investment relate to tax relief on interest payments, the benefit of a

subsidised loan, and issue costs associated with the rights issue.

The estimated APV of the investment is MINUS £113,620, which suggests that

the investment is not financially viable. However, this ignores the potentially

valuable option to continue operations after the initial five year period by

further investment in equipment. Any final decision should include

consideration of the financial effects of this option, and any other

opportunities that might arise as a result of diversifying into the fast food

industry.

Limitations of APV

APV offers an opportunity to evaluate investments where gearing and risk

differ from the company’s existing operation. However, it has its limitations

including:

(i) The equation for asset betas in a taxed world assumes that cash flows

are perpetuities. The cash flows for this investment are not perpetuities.

(ii) APV requires the identification of all financing side effects and their

discount at a rate reflecting their risk. In a complex investment

situation, especially an overseas investment, it might be difficult to

identify relevant financing side effects, and their appropriate discount

rates.

Appendix

APV = Base NPV plus the present value of financing side effects.

Base case NPV

This may be estimated by discounting net cash flows by the discount rate

applicable to the risk associated with an ungeared investment. As the

investment is in the fast food industry the base case NPV should be estimated

using data from this industry.

β asset = ( )( )

( )t1DE

t1Dβ

t1DE

Eβ de −+

−+

−+

β asset = 1.4 x ( )3.0111

1

−+ + 0.25 x

( )( )3.0111

3.011

−+−

= 0.823 + 0.103 = 0.926

Using CAPM

Ke ungeared = rF + (ErM − rF) β asset

= 5% + (12.5% − 5%) 0.926 = 11.945%





Base case NPV (£000)

Year 0 1 2 3 4 5 6

Operating flows 420 441 463 486 511

Taxation (126) (132) (139) (146) (153)

Tax saved by

Capital allowances* 79 59 44 33 100

Initial outlay (2,300)

Realisable value ______ ___ ___ ___ ____ 1,250 ____

Net flows (2,300) 420 394 390 391 1,648 (53)

Discount factors 1.00 .893 .798 .713 .637 .569 .508

Present values (2,300) 375 314 278 249 938 (27)

Base case NPV = (£173,000)

*Capital allowances

Year Written-down value Allowance Tax saving Available year

1 1,050 262 79 2

2 788 197 59 3

3 591 148 44 4

4 443 111 33 5

5 (Balancing) 332 332 100 6

(It might be argued that the tax saving is a relatively safe cash flow and should be

discounted at a rate lower than the ungeared cost of equity. If so the resultant

base case NPV would be slightly larger).

Financing side effects

(i) Tax relief on interest payments (assumed available years 2 – 6)

The benefit from the investment in terms of increased debt capacity is £1

million. Although only £800,000 is being borrowed, the APV should be based

upon theoretical benefits of the debt capacity as these are available to the

company and may be used through debt issues for other investments (these

too must be evaluated on their own impact on debt capacity).

The tax shield benefit is therefore based upon £1 million of debt, £800,000 at

6% and the remaining £200,000 at the normal market rate of 9%.

Tax relief on annual interest £

£800,000 x 6% = £48,000 x 0.3 = 14,400

£200,000 x 9% = £18,000 x 0.3 = 5,400

£19,800

The discount rate used will be a rate reflecting the risk of the debt, in this

case the pre-tax cost of debt, 9%

PV annuity 9% for five years 3.890 x 19,800 x 09.1

1 = £70,662

The PV of tax relief, commencing year 2, is £70,662





(ii) Subsidised loan

Tovell is receiving £800,000 at 3% less than normal market rates because of

its financing choice.

This produces an after-tax saving (with a one year lag in tax) of:

Years 1 to 5 £800,000 x (0.09 − 0.06) per year = £24,000

Years 2 to 6 tax of £24,000 x 0.3 = (£7,200)

The PV of this saving, discounted at 9% representing the market risk of debt

is:

£

3.890 x £24,000 = 93,360

3.890 x (£7,200) = (25,695)

1.09 _____

£67,665

(iii) Issue costs

The cost of the investment after issue costs (it is assumed that none exist on

the loan) is £2.3 million. Net proceeds of the rights issue are £2.3m − £0.8m

= £1.5m.

With issue costs of 5%, the gross proceeds of the rights issue are 95.0

m5.1£

= £1,578,947.

Issue costs are (£1,578,947 − £1,500,000) = £78,947

The expected APV of the investment is:

£

Base case NPV (173,000)

Tax relief on interest 70,662

Benefit from subsidised loan 67,665

Issue costs (78,947)

APV (113,620)





Alastair Brown plc

Alastair Brown plc is considering diversifying into a ‘new’ industry. The company is

investigating an investment project which would cost £18.8 million. Internally

generated funds would provide £5.8 million of the necessary finance, a further £5.5

million (net of costs) would be raised by means of a rights issue, £2 million would

be provided by a subsidised development loan and the remainder from a clearing

bank term loan at a fixed interest rate of 10%. The subsidised loan offers a 3%

subsidy on normal market rates. Issue costs associated with the loans are 1%.

The rights issue will incur 3% administration costs. This financing package is

thought to fully utilise the project’s debt capacity. Both loans would be for a five

year term.

The project is expected to generate after tax (but, before WDA tax relief) net cash

flows of approximately £4 million per year during the company’s five year planning

period. A residual value of £9 million is expected at the end of the five years.

Corporation tax is at a rate of 40% and is paid 12 months in arrears. Capital

expenditure attracts a 25% Writing Down Allowance (WDA) on the reducing

balance.

Alastair Brown plc has identified a correlation coefficient of +0.7 between the equity

returns from a random sample of companies in the ‘new’ industry and returns from

the market. The standard deviation of market returns is 5%, and the standard

deviation of equity returns of companies in the ‘new’ industry is 8%. The

companies sampled in the ‘new’ industry have an average gearing of 50% equity,

50% debt by book values, and 70% equity, 30% debt by market values.

The yield on Treasury Bills is 10%, and the return on the market is 15.6%.

Corporate debt may be assumed to be approximately risk free.

Required:

(a) Estimate the adjusted present value (APV) of the proposed investment, and

recommend whether it should be undertaken.

(b) Discuss the advantages and disadvantages of the APV relative to alternative

techniques of capital investment appraisal.





Alastair Brown solution

(a) (i) β equity = m

m,industryindustry

σ

ρ x σ

= 5%

70.0 %8 × =1.12

(ii) β asset = ( )t1DE

Eβe −+

= 1.12 x ( )40.0137

7

−+ = 0.89

(iii) Base-case discount rate = rF + [ErM − rF] β asset

= 10% + [15.6% − 10%] x 0.89

= 15% (approx)

Writing-down allowances tax relief (assumes project is bought at start of

company’s accounting year)

£m WDA Tax relief Timing

18.8 x 0.25 = 4.7 x 0.40 = 1.88 Year 2

4.7

14.1 x 0.25 = 3.52 x 0.40 = 1.41 Year 3

3.52

10.58 x 0.25 = 2.65 x 0.40 = 1.06 Year 4

2.65

7.93 x 0.25 = 1.98 x 0.40 = 0.79 Year 5

1.98

5.95 − 9.0 = (3.05) x 0.40 = (1.22) Year 6

(18.8 − 9.0) x 0.40 = 3.92

Base-case net present value (£m)

0 1 2 3 4 5 6

Outlay (18.8)

WDA tax

relief 1.88 1.41 1.06 0.79 (1.22)

After-tax cash

flow 4.0 4.0 4.0 4.0 4.0

Scrap value 9.0

____ ___ ___ ___ ___ ____ ____

Net cash flow (18.8) 4.0 5.88 5.41 5.06 13.79 (1.22)

15% discount

factor _1__ 0.870 0.756 0.658 0.572 0.497 0.432

PV cash flow (18.8) 3.48 4.44 3.56 2.89 6.85 (0.53)

Base-case net present value = +£1.89m





PV of financing side-effects

Financing of project

£m £m

Internal funds 5.8

Rights issue (net receipts) 5.5

Loans (net receipts):

Development 2.0

Bank (balancing figure) 5.5

_7.5

18.8

Funds raised from loans

£m

Total (as above) £7.5m is a net receipt, therefore

The gross amount is (£7.5m ÷ 0.99) = 7.576

Development loan (2.00)

Bank term loan 5.576

PV of the tax shield

(i) Bank term loan

£5.576m x 0.10 = £0.5576m per annum interest

£0.5576m x 0.40 = £0.223m per annum tax relief

£0.223m x a 5 0.10 x (1.10)-1 = £0.223m x 3.791 x 0.909 =

£0.77m

(ii) Development loan

£2m x 0.07 = £0.14m per annum interest

£0.14m x 0.40 = £0.056m per annum tax relief

£0.056m x a 5 0.10 x (1.10)-1 = £0.056m x 3.791 x 0.909 =

£0.19m

PV of cheap loan

(i) PV of interest saved on cheap loan

Interest saved £2m x (0.10 − 0.07) = £60,000 per annum

PV : £60,000 x 3.791 = £0.227m

(ii) Tax relief lost

£2m x 0.03 = £60,000 per annum interest saving

£60,000 x 0.40 = £24,000 per annum tax relief lost

PV : £24,000 x 3.791 x (1.10)-1 = (£0.083m)

PV of the rights issue costs

The rights issue must raise 97.0

m5.5£ = £5.67m

Therefore the rights issue costs are £5.67m − £5.5m = (£0.17m)





PV of the after-tax loan issue cost

Pre-tax loan issue cost ( )

99.0

m2£m5.5£ + x 0.01 = (£0.076m)

Tax relief thereon £0.076m x 0.4 x (1.10)-1 = £0.028m


£m

Base-case net present value 1.89

PV of term loan tax shield 0.77

PV of development loan tax shield 0.19

PV of subsidised development loan: Interest saved 0.227

Tax relief lost (0.083)

PV of rights issue costs (0.17)

PV of loan issue costs: Gross cost (0.076)

Tax relief thereon 0.028

APV +£2.776

(b) Include the following points:

(1) APV is similar to NPV in that both are DCF models. However NPV is only

a project appraisal technique and needs to assume that a company is

maintaining its capital structure. In contrast, APV is a more general

model which can evaluate both a project and its proposed financing

package.

(2) APV is a lengthier analysis than NPV and would only be used for major

projects – especially where there was a complex financing package

involved. The much simpler approach of NPV would be an advantage for

smaller, more routine projects.

(3) APV has similar advantages and disadvantages with respect to the other

main capital investment appraisal techniques (i.e. IRR, payback and

return on investment) it is more complex and so more difficult to use.

On the other hand its ‘divide and conquer’ approach makes it able to

handle much more complex decisions correctly.




Chapter 9

Valuations, acquisitions and

mergers – section 1



CHAPTER 9 – VALUATIONS, ACQUISITIONS AND MERGERS: SECTION 1


CHAPTER CONTENTS

REASONS FOR VALUATIONS ------------------------------------------- 207

METHODS OF SHARE VALUATION ------------------------------------- 208

THE DIVIDEND VALUATION MODEL ---------------------------------- 209

DISCOUNTED CASH FLOW BASIS ------------------------------------- 214

PRICE EARNINGS RATIO BASIS --------------------------------------- 216

NET ASSETS BASIS ----------------------------------------------------- 218

DIVIDEND YIELD BASIS ----------------------------------------------- 220

VALUATION OF DEBT AND PREFERENCE SHARES ------------------- 221

IRREDEEMABLE DEBT 221

REDEEMABLE LOAN STOCK 221

PREFERENCE SHARES 222

CONVERTIBLE DEBT 222

THE THREE ACQUISITION TYPES ------------------------------------- 224

TYPE I ACQUISITIONS 224

TYPE II ACQUISITIONS 224

TYPE III ACQUISITIONS 226

HIGH GROWTH START-UPS -------------------------------------------- 229





REASONS FOR VALUATIONS

Valuations of businesses and financial assets may be needed for several reasons

e.g.

● To establish the terms of takeover bids or mergers;

● To fix a share price for an initial public offering;

● For investors to make buy, hold or sell decisions;

● For capital gains tax or inheritance tax purposes;

● Where a major shareholder or director wishes to dispose of a large block of

shares;

● When the company needs to raise additional finance.





METHODS OF SHARE VALUATION

The main approaches are:

● The dividend valuation model or dividend growth model;

● The discounted cash flow basis;

● The PE ratio (or earnings yield) basis;

● The net assets basis;

● The dividend yield method.





THE DIVIDEND VALUATION MODEL

This method is based upon the fundamental theory of share valuation, whereby a

current share price is taken to reflect the PV of expected future cash flows,

discounted at the required rate of return of the shareholder. In the case of

minority shareholders, this would represent the PV to infinity of the future dividend

stream. In the case of majority shareholders, these amounts will be increased by

the PV of synergies achieved as a result of the acquisition.

Illustration 1

The market expects a rate of return of 20% per annum on ordinary shares in

Winterburn plc, a company which is expected to pay constant annual dividends of

20p per share.

At what price will the market value the shares?

Solution 1

P0 = Ke

D =

2.0

20.0£ = £1.00

Illustration 2

Seaman plc is expected to pay a dividend of 30p per share next year. The market

expects dividends to grow at the rate of 5% per annum and has a required return

of 20%.

Estimate the share price.

Solution 2

P0 = gKe

D1

− =

05.02.0

30.0£

− = £2.00

Illustration 3

Merson plc is just about to pay a dividend of 40p per share. Future dividends are

expected to grow at the rate of 6% per annum. The market’s required return on

shares of this risk level is 25%.

What is the cum-div share valuation?

Solution 3

This year’s dividend, D0 = 40p. Next year’s dividend will be a factor of g higher:

D1 = D0 (1 + g) = 40p (1 + 0.06)

= 42.4p

P0 = 01 D

gKe

D+

− = p40

06.025.0

p4.42+

−

= £2.63





Illustration 4

Wright plc has just paid a dividend of 15p per share. The market is in general

agreement with directors’ forecasts of 30% growth in earnings and dividends for

the next 2 years. Thereafter, a reasonable estimate is 15% growth in year 3

followed by 6% growth to perpetuity.

The market’s required return on investments of this risk level is 25% per annum.

Estimate the share value.

Solution 4

For years1 to 3, compute the expected dividends and discount them.

Dividend computation, Years 1 – 3

Year Dividend 25% factor Present value, p

1 15p x 1.3 = 19.5 0.800 15.60

2 19.5p x 1.3 = 25.35 0.640 16.22

3 25.35p x 1.15 = 29.15 0.512 14.93

46.75p

Then compute the dividend for year 4 and ‘plug’ this into the growth formula with g

= 0.06

Year 4 dividend = 29.15p x 1.06 = 30.90p

Using the growth formula P3 = 06.025.0

p90.30

− = 162.63p

The growth formula for P is based on dividends from year 1 to perpetuity. Since

the dividends in the above calculation go from year 4 to perpetuity, the value for P

above must be at year 3. But we want its present value at year 0. Therefore we

must discount back three further years, using the 3 year factor at 25%, which is

0.512.

Present value at year 0 of dividends from year 4 to perpetuity = 162.63p x 0.512

= 83.27p

Adding the present value of dividends from years 1 to 3 gives:

Share value = 46.75p + 83.27p = £1.30





Illustration 5

Zed plc is considering the immediate purchase of some, or all, of the share capital

of one of two companies – Red Ltd and Yellow Ltd. Both Red and Yellow have 1

million ordinary shares issued and neither company has any debt capital

outstanding.

Both firms are expected to pay a dividend in one year’s time – Red’s expected

dividend amounting to 30p per share and Yellow’s being 27p per share. Dividends

will be paid annually and are expected to increase over time. Red’s dividends are

expected to display perpetual growth at a compound rate of 6% per annum.

Yellow’s dividend will grow at the high annual compound rate of one third until a

dividend of 64p per share is reached in year 4. Thereafter Yellow’s dividend will

remain constant.

If Zed is able to purchase all the equity capital of either company then the reduced

competition would enable Zed to save some advertising and administrative costs

which would amount to £225,000 per annum indefinitely and, in year 2, to sell

some office space for £800,000. These benefits and savings will only occur if a

complete take-over were to be carried out. Zed would change some operations of

any company completely taken over – the details are:

(i) Red – No dividend would be paid until year 3. Year 3 dividend would be 25p

per share and dividends would then grow at 10% per annum indefinitely.

(ii) Yellow – No change in total dividends in years 1 to 4, but after year 4,

dividend growth would be 25% per annum compound until year 7. Thereafter

annual dividends would remain constant at the year 7 amount per share.

An appropriate discount rate for the risk inherent in all the cash flows mentioned is

15%.

Required

(a) Ignoring taxation, calculate:

(i) the valuation per share for a minority investment in each of the firms

Red and Yellow which would provide the investor with a 15% rate of

return.

(ii) the maximum amount per share which Zed should consider paying for

each company in the event of a complete take-over.

(b) Comment on any limitations of the approach used in part (a) and specify the

other major factors which should be important to consider if the proposed

valuations were being undertaken as a practical exercise.





Solution 5

(a) (i) Valuation per share for minority interest

Red Ltd

Employing the dividend growth model:

Ex-div value per share = gKe

D1

−=

%6%15

p30

− = £3.33

Yellow Ltd

PV of future dividend stream:

Year Dividend DF(15%) PV

£ £

1 0.27 0.870 = 0.235

2 0.36 0.756 = 0.272

3 0.48 0.658 = 0.316

4 0.64 0.572 = 0.366

1.189

5 to infinity %15

64.0£ x 0.572 = 2.441

£3.630

Ex-div value per share = £3.63

(ii) Maximum amount per share for take-over

Red Ltd

PV

Total dividends for year 3 £

= 1m @ 25p = £250,000

PV of future dividend stream at Year 2

= %10%15

000,250£

− = £5,000,000

PV at Year 0 = £5,000,000 x 0.756 = 3,780,000

£

Annual savings: %15

000,225£ = 1,500,000

Sale of office space £800,000 x 0.756 = 604,800

PV of savings and benefits 2,104,800

Total value £5,884,800

Maximum amount per share £5.8848





Yellow Ltd

PV

PV of total dividends in Years 1 to 4 £

(see i) above 1m x £1.189 = 1,189,000

Year Dividends DF(15%)

£000

5 (1m x £0.64 x 1.25) 800 0.497 = 397,600

6 1,000 0.432 = 432,000

7 1,250 0.376 = 470,000

2,488,600

8 to infinity %15

250,1£ x

0.376 = 3,133,333

PV at Year 0 5,621,933

PV of savings and benefits (see Red Ltd above) 2,104,800

Total value £7,726,733

Maximum value per share £7.726733

(b) Limitations and practical factors

The approach used in part (a) was to base the equity valuation only on future

dividends alone and no consideration was given to underlying asset values which

may be of importance in a take-over situation. The dividend valuation model is a

valid approach capable of producing accurate results provided the data used are

themselves accurate. The major limitations of the use of the model stem not from

the formula itself, but from the assumptions concerning the input data. The major

limitations include the assumptions of:

(i) Smooth dividend growth. In reality dividends may display some volatility

from year to year.

(ii) Perpetual growth and infinite life. It may be unrealistic to expect an infinite

life for the firm, but due to discounting this assumption may produce a good

working approximation for purposes of the valuation.

(iii) A constant discount rate or expected rate of return.

Other factors which should be considered include:

(i) Are all alternatives equally risky and is risk constant over the whole life?

There may be greater risk during periods of expected high growth (years 1-4

of Yellow) than during periods of low or zero growth. An adjustment to the

required return may be necessary during periods of abnormal risk.

(ii) Asset values may be an important aspect in a take-over and should be

considered. Generally the higher the asset values of the firm taken over, the

greater their marketability, then the lower is the potential risk inherent in that

take-over.

(iii) Management and competition. Will the existing management team continue

and/or will competition increase? The cash flow estimates should consider the

actions of existing management, competition etc.

(iv) Financing of the take-over. The method of financing the take-over (i.e. loans,

own equity etc.) must be considered carefully.

(v) Full consideration of all tax consequences should be taken into account.





DISCOUNTED CASH FLOW BASIS

This method is based upon the present value of the free cash flow to equity of an

enterprise, either for a limited time horizon (fifteen years may be regarded as

typical) or to infinity.

There are a number of variations in the definition of free cash flow to equity, but it

is often described as follows:

Free cash flow to equity is the cash flow available to a company from

operations after interest expenses, tax, repayment of debt and lease

obligations, any changes in working capital and capital spending on assets

needed to continue existing operations (i.e. replacement capital expenditure

equivalent to economic depreciation)

In theory, this is probably the best method by which to value a company. However

it relies on estimates of cash flows, discount rates, tax rates, inflation rates and the

choice of a suitable time horizon. The notion of using a valuation to infinity is

probably unrealistic.

Illustration 6

The predicted free cash flows of Miller Ltd, an all equity company, for its planning

horizon, (which for simplicity is taken to be the next five years) are:

Year Free cash flows

£000

1 150

2 200

3 250

4 375

5 500

A cost of capital of 12% is assumed to represent the systematic risk of the cash

flows of Miller Ltd.

What is the estimated market capitalisation of this company?

Solution 6

Year Free cash flows Discount factor Present values

£000 12% £

1 150 0.893 133,950

2 200 0.797 159,400

3 250 0.712 178,000

4 375 0.636 238,500

5 500 0.567 283,500

Estimated market capitalisation for 5 year planning horizon £993,350





Illustration 7

The following data relating to Morrison Ltd is expected to continue annually for the

foreseeable future:

£m

Turnover 525

Cost of goods sold, excluding depreciation 315

Distribution costs and administrative expenses, excluding depreciation 36

Capital allowances claimed 46.5

Non-current assets purchased in the year 72

Irredeemable bonds (market value £130) 21

Working capital changes are assumed to be insignificant because of the

absence of growth.

Corporation tax rate 30%

Weighted average cost of capital in nominal (i.e. money) terms 13.3%

Predicted inflation rate 3%

Calculate the estimated equity market capitalisation of this company.

Solution 7

Net cash flows

£000

Turnover 525,000

Cost of goods sold (315,000)

Distribution costs and administrative expenses (36,000)

174,000

Tax on operating profits (30% x 174,000) (52,200)

Tax saved on writing down allowances (30% x 46,500) 13,950

Non-current assets purchased (72,000)

Annual net cash flows 63,750

Real discount rate (using Fisher effect)

r = ( )( ) 1

i1

m1−

++

= 103.1

133.1− = 10%

Since the annual net cash flows are perpetuities expressed in terms of real cash

flows, it has been necessary to establish a real discount rate.

£000

Corporate value %10

750,63 637,500

Less market value of irredeemable bonds (21,000 x 1.3) (27,300)

Equity market capitalisation 610,200





PRICE EARNINGS RATIO BASIS

This income based method is popular for the valuation of majority holdings in a

going concern. It requires the prediction of a maintainable EPS for the company

being valued and the use of the PE ratio of a listed company, whose activities are

very similar to those of the business being valued i.e.

Share value = EPS of company being valued x PE of similar listed company

If a similar listed company (pure−play company) is not readily available, it may be

appropriate to use the average PE for the market sector in which the company

operates.

It may be necessary to adjust the PE used or the final calculated price, if the

company being valued is an unlisted company, or where the company in question

has different risk or different growth potential from the similar company or

constituents of the industry average.

Since an earnings yield is simply a reciprocal of the PE ratio, a valuation on an

earnings yield basis would be as follows:

Share value = EPS of company being valued ÷ earnings yield of similar listed

company

Illustration 8

Flycatcher Ltd wishes to make a takeover bid for the shares of an unlisted

company, Mayfly Ltd. The earnings of Mayfly Ltd over the past five years have

been as follows.

2002 £50,000 2005 £71,000

2003 £72,000 2006 £75,000

2004 £68,000

The average P/E ratio of listed companies in the industry in which Mayfly Ltd

operates is 10. Listed companies which are similar in many respects to Mayfly Ltd

are:

Bumblebee plc, which has a P/E ratio of 15, but is a company with very good

growth prospects;

Wasp plc, which has had a poor profit record for several years, and has a

P/E ratio of 7.

What would be a suitable range of valuations for the shares of Mayfly Ltd?





Solution 8

Earnings. Average earnings over the last five years have been £67,200, and over

the last four years £71,500. There might appear to be some growth prospects, but

estimates of future earnings are uncertain.

A low estimate of earnings in 2007 would be, perhaps, £71,500.

A high estimate of earnings might be £75,000 or more. This solution will use the

most recent earnings figure of £75,000 as the high estimate.

P/E ratio. A P/E ratio of 15 (Bumblebee’s) would be much too high for Mayfly Ltd,

because the growth of Mayfly Ltd earnings is not as certain, and Mayfly Ltd is an

unlisted company.

On the other hand, Mayfly Ltd’s expectations of earnings are probably better than

those of Wasp plc.

A suitable P/E ratio might be based on the industry’s average, 10; but since Mayfly

is an unlisted company and therefore more risky, a lower P/E ratio might be more

appropriate: perhaps (60% to 70% of 10) = 6 or 7, or conceivably even as low as

(50% of 10) = 5.

Valuation. The valuation of Mayfly’s shares might therefore range between:

High P/E ratio and high earnings: 7 x £75,000 = £525,000; and

Low P/E ratio and low earnings: 5 x £71,500 = £357,500





NET ASSETS BASIS

Asset-based valuation models include:

● net book value (balance sheet basis) – largely a meaningless figure, since it is

affected by accounting conventions;

● net realisable value basis – again, not particularly relevant. However, where

the break-up value exceeds income-based valuations, it would be advisable

for the proprietor to cease trading and sell the assets as quickly as possible;

● net replacement cost basis – this represents the current cost of setting up the

existing business. Sadly it totally ignores goodwill, which can only be

established by using income-based valuations.

Illustration 9

The current balance sheet of Cactus Ltd is as follows:

£ £

Fixed assets

Land and buildings 160,000

Plant and machinery 80,000

Motor vehicles 20,000

Goodwill 20,000

280,000

Current assets

Stocks 80,000

Debtors 60,000

Short-term investments 15,000

Cash 5,000

160,000

440,000

£ £

Capital and reserves

Ordinary shares of 50p 80,000

Reserves 140,000

220,000

4.9% preference shares of £1 50,000

270,000

12% debentures 60,000

Deferred taxation 10,000

70,000

Creditors: amounts falling due within one year

Creditors 60,000

Taxation 20,000

Proposed ordinary dividend 20,000

100,000

440,000

What is the value of an ordinary share using the net assets basis?





Solution 9

THERE IS INSUFFICIENT INFORMATION TO ANSWER THIS QUESTION, BUT AN

ATTEMPT MUST BE MADE, OTHERWISE NO MARKS WILL BE GAINED, i.e.

£

Total value of net assets 270,000

Less Goodwill (20,000)

Preference shares (50,000)

Net asset value of equity £200,000

Number of ordinary shares (of 50p each) 160,000

Share price £1.25

NOW STATE THAT FAIR VALUE (UNDER IFRS 3 OR FRS 7) DETAILS ARE NEEDED

FOR A DECENT ANSWER! FURTHERMORE, HOW DOES ONE ESTABLISH

GOODWILL?





DIVIDEND YIELD BASIS

This income based method is popular for the valuation of minority holdings in a

going concern. It requires the prediction of a maintainable dividend for the

company being valued and the use of the dividend yield of a listed company, whose

activities are very similar to those of the business being valued i.e.

Share value = company listedsimilar of yield Dividend

valued being company the of Dividend

If a similar listed company (pure−play company) is not readily available, it may be

appropriate to use the average dividend yield for the market sector in which the

company operates.

It may be necessary to adjust the calculated price if the company being valued is

an unlisted company, or where the company in question has different risk or

different growth potential from the similar company or constituents of the industry

average.

Care must be taken to ensure consistency in the treatment of tax credits i.e. look at

the information given in a question very carefully to establish whether the yields

given are net or gross dividend yields and whether the dividends provided include

or exclude related tax credits.

Illustration 10

Taylor Ltd, which has on issue £500,000 ordinary shares of 25p each, intends to

pay a constant dividend of £360,000 (net) for the foreseeable future. Listed

companies within the same industry sector as Taylor Ltd currently provide a gross

dividend yield of 5% p.a. The current rate of tax credit on gross dividends is 10%

(i.e. 1/9th of net dividend).

Estimate a current share price for Taylor Ltd.

Solution 10

Number of ordinary shares on issue = 2,000,000

Expected net dividend per share = 000,000,2

000,360£ = 18p

Expected gross dividend per share = 18p + (1/9 x 18p) = 20p

Net dividend yield for market sector = 5% x 0.9 = 4.5%

Share price = yield Gross

dividend Gross =

%5

p20 = £4.00

or yield Net

dividend Net =

%5.4

p18 = £4.00

Since Taylor Ltd is a private company the calculated share price of £4.00 could be

reduced by between 30% to 50%, i.e. around £2.80 to £2.00, due to lack of

marketability.





VALUATION OF DEBT AND PREFERENCE SHARES

Irredeemable debt

Illustration 11

Koren plc has on issue 7% irredeemable loan stock. The gross return required by

investors is 5% p.a. The corporation tax rate is 30%.

Establish the current market value for this stock.

Solution 11

Market value = yield Gross

payment interest Gross =

5%

100 %7 × = £140

Redeemable loan stock

Illustration 12

Beattie plc has issued £1,000,000 of 6% redeemable bonds. Interest payments will

be made at the end of March, June, September and December of each year until

redemption occurs on 30 June 2010 at £120 per cent. Bondholders require a gross

redemption yield of 1% per quarter.

Calculate the current market value of these bonds at 1 January 2007.

Solution 12

Interest payment for 14 quarters = 4

000,000,1£ %6 × = £15,000

Redemption value = 120% x £1,000,000 = £1,200,000

Market value

Period Cash flow Discount factor 1% per

quarter

Present value

£ £

1-14 15,000 13.00 195,000

14 1,200,000 0.870 1,044,000

Market value of redeemable bonds £1,239,000

Since there are 10,000 bonds on issue each with a £100 par value, an individual

bond has a market value of:

000,10

000,239,1£ = £123.90





Preference shares

Illustration 13

Steele Ltd has on issue some 9% preference shares of £1 nominal value. Investors

require a return of 12.5% p.a. on these shares.

Estimate the current market price per share.

Solution 13

P0 = Kps

D =

0.125

1£ %9 × = 72p

Convertible debt

The value of a convertible cannot fall below its value as debt, but upside potential

exists due to the possibility of an increase in the share price prior to expiry of the

conversion period.

Therefore the theoretical value of a convertible (known as its “formula value”) is

the greater of its value as debt and its value as shares i.e. its conversion value. In

practice the actual price of convertibles will tend to trade at a value in excess of

formula value, reflecting so called “time value” i.e. the possibility that the share

price could rise prior to expiry of the conversion period.

Illustration 14

Kiely plc has 11% convertible loan notes on issue. Each £100 unit may be

converted at any time up to the date of expiry (in seven years time) into 15 fully-

paid ordinary shares in Kiely plc. Any loan notes which remain outstanding at the

end of the seven year period are to be redeemed at £120 per cent.

Loan note holders normally require a yield of 9% p.a. on seven year debt.

Recommend whether investors should convert, if the current share price

is:

(a) £7.00, or

(b) £8.00, or

(c) £9.00.





Solution 14

Value as debt (i.e. if conversion does not take place):

End of year Discount

factor

Present

value

£ 9% £

1 - 7 Gross annual interest 11 5.033 55.36

7 Redemption value 120 0.547 65.64

Value as debt 121.00

Value as equity Value as debt Formula value Convert ?

(a) (15 shares @ £7) = £105 £121 £121 NO

(b) (15 shares @ £8) = £120 £121 £121 NO

(c) (15 shares @ £9) = £135 £121 £135 YES

Notice that there is no need to calculate the present value of the share price, since

under the fundamental theory of share valuation a current share price reflects the

PV of the future cash flow streams associated with holding the share.

The conversion price where the investor would be indifferent between redemption

and conversion is (£121 ÷ 15 shares) i.e. £8.07. The value of the convertible will

never fall below its value as debt (£121). However if the share price rises above

£8.07, the convertible loan notes will then reflect the value of the equity receivable

on conversion.





THE THREE ACQUISITION TYPES

Type I acquisitions

These are acquisitions that do not disturb the acquirer’s exposure to either business

risk or financial risk. In theory, the value of the acquired company, and hence the

maximum amount that should be paid for it, is the Present Value of the future cash

flows of the target business discounted at the WACC of the acquirer. The valuation

techniques already considered would deal adequately with this type of business

combination.

Type II acquisitions

These are acquisitions which do not disturb the exposure to business risk, but do

impact upon the acquirer’s exposure to financial risk e.g. through changing the

gearing levels of the acquirer. Such acquisitions may be valued using the Adjusted

Present Value (APV) technique by discounting the Free Cash Flows of the acquiree

using an ungeared cost of equity and then adjusting for the tax shield.

Illustration 15

The directors of Heincarl plc are considering the acquisition of Newscot Ltd, an

unlisted company. The shareholders of Newscot Ltd are willing to sell the business

on 1st January 2009 for £500 million. From the perspective of the directors of

Heincarl plc, the projections of the performance of Newscot Ltd are as follows:

Current

year Projections during planning horizon (years)

2008 2009 2010 2011 2012 2013 2014

£m £m £m £m £m £m £m

EBITDA 117.00 138.70 162.57 188.83 217.71 249.48 251.48

Depreciation

&

amortisation (40.00) (42.00) (44.00) (46.00) (48.00) (50.00) (52.00)

EBIT 77.00 96.70 118.57 142.83 169.71 199.48 199.48

Interest

charges _ -_ (32.00) (26.88) (20.19) (11.73) (1.28) _ -__

Profit before

tax 77.00 64.70 91.69 122.64 157.98 198.20 199.48

The assumed rate of corporation tax is 35% p.a. The terminal value of the

investment is treated as a constant perpetuity equal to the free cash flows for the

year 2014. The risk free rate of interest is assumed to be 6% p.a., the return on a

market portfolio is taken to be 13.5%, whilst an asset beta of 1.1 is used for

purposes of the appraisal.

Annual capital expenditure from 2008 onwards is estimated at £20 million each

year indefinitely. Newscot Ltd currently has on issue £400 million of 8% debt and it

is intended that all available cash flows should be applied to repaying this debt at

the earliest opportunity.

Advise the directors of Heincarl plc whether to proceed with the

acquisition.





Solution 15

Calculation of Keu

Keu = Rf + (Rm – Rf) βa = 6% + (13.5% – 6%) 1.1 = 14.25%

Calculation of Free Cash Flow of Newscot Ltd

2008 2009 2010 2011 2012 2013 2014

£m £m £m £m £m £m £m

EBIT 77.00 96.70 118.57 142.83 169.71 199.48 199.48

Less CT @

35% (26.95) (33.84) (41.50) (49.99) (59.40) (69.82) (69.82)

50.05 62.86 77.07 92.84 110.31 129.66 129.66

Add back

Depreciation 40.00 42.00 44.00 46.00 48.00 50.00 52.00

Less Capital

expenditure (20.00) (20.00) (20.00) (20.00) (20.00) (20.00) (20.00)

Company

Free Cash

Flow 70.05 84.86 101.07 118.84 138.31 159.66 161.66

Total

£m

Discount

factor

(14.25%) - 0.875 0.766 0.671 0.587 0.514

PV (£m) - 74.25 77.42 79.74 81.19 82.07 394.67

From 2014 to infinity: 514.01425.0

66.161× = 583.11

PV to infinity of Company Free Cash Flow 977.78

Tax Shield (discounted at Kd of 8%)

(32.00 x 35% x 0.926) + (26.88 x 35% x 0.857) + (20.19 x 35% x 0.794)

+ (11.73 x 35% x 0.735) + (1.28 x 35% x 0.681) = 10.37 + 8.06 + 5.61 + 3.02 +

0.31 = 27.37

APV £m

Corporate value (977.78 + 27.37) 1005.15

Less Value of debt (400.00)

Value of equity 605.15

Less Purchase consideration (500.00)

APV 105.15

Therefore, the directors of Heincarl plc should proceed with the acquisition of

Newscot Ltd.





Type III acquisitions

These are acquisitions that impact upon the acquirer’s exposure to both business

risk and financial risk. In order to estimate WACC there is a need to establish the

cost of capital of the combined businesses. However, the Ke of the combination is

dependent upon the price paid for the equity capital of the target, but it is

impossible to establish the price to be paid until the value of the target is

determined.

Illustration 16

Edwards plc is considering the acquisition of a 100% stake in Colman Ltd in order

to achieve backward vertical integration. Considerable savings are anticipated due

to the combination of both the marketing operations and distribution networks of

the two companies. Therefore synergies will arise to create cash flows which are in

excess of the current estimated cash flows of the two separate companies. Upon

the acquisition of Colman Ltd, Edwards plc will immediately sell one of the

warehouses of the target company, providing instant cash inflows of £5 million.

The forecast cash inflows of the merged businesses are as follows:

Year £ millions Year £ millions

2008 (proceeds from warehouse sale) 5.00 2014 92.32

2009 60.00 2015 100.63

2010 65.40 2016 109.68

2011 71.29 2017 119.55

2012 77.70 2018 130.29

2013 84.69 Terminal value 2,396.84

The forecast rate of corporation tax is expected to remain at 30%. The risk free

rate of interest is to be taken at 5% and the expected return on a market portfolio

is 9%.

Information currently relating to the two companies is as follows:

Edwards plc Colman Ltd

£m £m

Market values:

Debt 100 20

Equity 900 280

Total 1,000 300

β asset 0.9 2.4

Cost of debt 7% 7%

Edwards plc plans to make a cash offer of £380 million for the purchase of the

entire share capital of Colman Ltd. This cash offer will be funded by additional

borrowings undertaken by Edwards plc.

Advise the directors of Edwards plc whether to proceed with the

acquisition.





Solution 16

β asset of combined company

β a = 4.2 300000,1

3009.0

300000,1

000,1×

++×

+ = 1.25

β equity of combined company

Revised gearing levels are: £m

E = 900 + 280 = 1,180

D = 100 + 20 + 380 = 500

1,680

βe = ( ) ( )

180,1

3.01 500180,1 25.1

E

t1 DE βa

−+×=

−+× = 1.62

Cost of equity

Ke = 5% + (9% − 5%) 1.62 = 11.48%

Weighted average cost of capital

WACC = ( )3.01 %7 680,1

500%48.11

680,1

180,1−××+× = 9.52%

Present value of combined cash flows

Cash flows of

combined entity

Discount factor

(9.52%)

Present value @

9.52%

£m £m

2008 5.00 1 5.00

2009 60.00 1÷1.0952 54.78

2010 65.40 1÷1.09522 54.52

2011 71.29 1÷1.09523 54.27

2012 77.70 1÷1.09524 54.01

2013 84.69 1÷1.09525 53.75

2014 92.32 1÷1.09526 53.50

2015 100.63 1÷1.09527 53.24

2016 109.68 1÷1.09528 52.99

2017 119.55 1÷1.09529 52.74

2018 130.29 1÷1.095210 52.48

Terminal value 2,396.84 1÷1.095211 881.48

1,422.76

Value of equity

£m

PV of combined entity 1,422.76

Less combined value of debt (500.00)






Therefore the combination is beneficial to the shareholders of Edwards plc, since

the value of their equity shareholding will increase from £900 million to £922.76

million.

However, one further major problem remains! There is an inconsistency! In the

weightings used for the WACC calculation, (1,180 ÷ 1,680) about 70% has been

applied to equity, whilst (500 ÷ 1,680) about 30% has been used for debt. On the

other hand, ultimately the value of equity has been shown to represent (922.76 ÷

1,422.76) about 65% of corporate value and the value of debt (500 ÷ 1,422.76)

about 35% of corporate value.

Where these two sets of weights differ significantly an inconsistent valuation will

occur. There is then a need to adopt an iterative revaluation procedure to achieve

consistency between the WACC and the corporate value. This would involve a

recalculation of βe, using weightings that are closer to those derived from the

valuation. This procedure would be continuously repeated until the assumed

weights and the weightings ultimately derived from the corporate valuation are

reasonably consistent.

Thankfully this iterative process is not performed manually, since it can be

calculated in Excel (shown in Tools > Options > Calculation). The consistent results

of the iterative revaluation procedure apparently work out as follows:

£m

PV of combined entity 1,395.45

Less combined value of debt (500.00)


βe will now become: ( )

895.45

3.01 50045.89525.1

−+× = 1.74

Ke is now revised to become: 5% + (9% − 5%) 1.74 = 11.96%

The weighted average cost of capital is revised to:

WACC = ( )3.01 %7 45.395,1

500%96.11

45.395,1

45.895−××+× = 9.43%

The increased proportion of debt (500 ÷ 1,395.45) i.e. about 36% of corporate

value has caused both βe and Ke to increase, whilst there has been a slight

reduction in WACC due to the larger weighting applied to debt.

Since the value of equity has now fallen to £895.45 million, which is below the

current value of the equity shares in Edwards plc (i.e. £900 million), the acquisition

would cause a reduction in shareholder wealth of £4.55 million. The business

combination should thus be abandoned.





HIGH GROWTH START-UPS

The valuation of Start-ups create additional problems to that of well established

businesses. This may be due to:

● their lack of a proven track record,

● initial on-going losses,

● untested products with little market acceptance,

● little market presence,

● unknown competition,

● high development costs, and

● inexperienced managers with over-ambitious expectations of the future.

The valuation procedures depend upon the reasonableness of financial projections,

the length of the period chosen for long-term projections and the selection of future

growth rates. The growth in earnings may be forecast using Gordon’s growth

approximation i.e. g = br, where normally b = 1, since all profits made are likely to

be reinvested into the business. Therefore the sole determinant of growth is the

measure of “r”.

The decision as to growth expectations is rather critical as shown in the following

illustration:

Illustration 17

Bednar plc anticipates costs of £1,200 million in the coming year, thereafter

growing at a rate of 4% per annum. The anticipated revenues for that year are

expected to be £320 million. The company expects to achieve a return on

reinvested funds of between 16% and 18% per annum. Furthermore the directors

of Bednar plc do not anticipate the payment of any dividends for the foreseeable

future.

Using a cost of equity of 20% p.a., produce a valuation for Bednar plc

based upon both the maximum and the minimum growth rate predictions,

using the Growth Model combined with Gordon’s growth approximation.





Solution 17

Since no dividends are expected to be paid, b = 1

Maximum valuation

Growth prediction: (g = br) g = 1 x 0.18 = 18%

Valuation using the Growth Model:

%4%20

200,1

%18%20

320

−−

− = 16,000 – 7,500 = £8,500 million

Minimum valuation

Growth prediction: (g = br) g = 1 x 0.16 = 16%

Valuation using the Growth Model:

%4%20

200,1

%16%20

320

−−

− = 8,000 – 7,500 = £500 million

Growth rates are affected by changes in technology, management competence,

demand and inflation levels, and are therefore extremely difficult to predict. Notice

the dramatic change in the business valuation that has been caused by a slight

change in the predicted rate of growth.




Chapter 10







CHAPTER CONTENTS

MERGERS AND ACQUISITIONS ---------------------------------------- 233

1. SYNERGY 233

2. HIGH FAILURE RATE OF ACQUISITIONS IN ENHANCING SHAREHOLDER VALUE 234

3. MODE OF OFFER 235

4. DEFENCES 235

5. SIGNIFICANT PERCENTAGE HOLDINGS 236

6. CONDUCT OF TAKEOVER BIDS 236

DARK POOL TRADING -------------------------------------------------- 238

OXCLOSE PLC AND SATAC LTD ---------------------------------------- 239

DEMAST LTD ------------------------------------------------------------- 245

KELLY PLC --------------------------------------------------------------- 250

EICHNER PLC ------------------------------------------------------------ 253





MERGERS AND ACQUISITIONS

1. Synergy

● An expansion policy based on merger or takeover can be justified on the basis

of synergy. (Sometimes stated as 2 + 2 = 5) i.e.

Value of A plc Value of A plc Value of B plc

and B plc combined >>>> operating + operating

independently independently

Acquisitions and mergers are ultimately justified as leading to an increase in

shareholder wealth.

● The potential for synergy is often classified as follows:

Revenue synergy: Sources of which include:

o Economies of vertical integration;

o Market power and the elimination of competition i.e. the desire to earn

monopoly profits (which is good for shareholders but not in the public

interest);

o Complementary resources e.g. a company with marketing strengths

could usefully combine with the company owning excellent research and

development facilities.

Cost synergy: Sources of which include:

o Economies of scale (arising from e.g. larger production volumes and

bulk buying);

o Economies of scope (which may arise from reduced advertising and

distribution costs where combining companies have duplicated

activities);

o Elimination of inefficiency;

o More effective use of existing managerial talent.

Financial synergy: Sources of which include:

o Elimination of inefficient management practices;

o Use of the accumulated tax losses of one company that may be made

available to the other party in the business combination;

o Use of surplus cash to achieve rapid expansion;

o Diversification reduces the variance of operating cash flows giving less

bankruptcy risk and therefore cheaper borrowing;

o Diversification reduces risk (however this is a suspect argument, since it

only reduces total risk not systematic risk for well diversified

shareholders);

o High PE ratio companies can impose their multiples on low PE ratio

companies (however this argument, known as “bootstrapping”, is rather

suspect).





● Conclusions on Synergy

o Synergy is not automatic

o When bid premiums are considered, the consistent winners in mergers

and takeovers are victim company shareholders.

2. High failure rate of acquisitions in enhancing shareholder value

In practice, the shareholders of predator companies seldom enjoy synergistic gains,

whereas the shareholders of victim companies benefit from a takeover. The

acquiring company often pays a significant premium over and above the market

value of the target company prior to acquisition; this problem is particularly acute

for the successful predator following a contested takeover bid.

The reasons advanced for the high failure rate of business combinations from the

perspective of the predator shareholders are as follows:

● Agency theory suggests that takeover bids are primarily motivated by the

self- interest of the managers of bidding companies. Often free cash flow

may be used to increase the size of their company in order to enhance the

status of directors who wish to be seen as heading a large listed plc.

Diversification of the activities of the predator may provide job security for the

directors of such companies;

● Over-optimistic assessment of the economies of scale or economies of scope

that may be achieved as a result of the business combination;

● Inadequate investigation of the victim company prior to the bid being made,

or insufficient appreciation of the problems that may arise after the acquisition

takes place (e.g. the difficulties experienced by Wm. Morrison Supermarkets

following the takeover of Safeway);

● Following a successful bid, the directors and managers of the predator

become too keen to identify their next victim, instead of devoting time to

ensuring that the company that they have already taken over provides the

expected synergies;

● Directors of the predator company become so obsessed with the success of

their bid that they fail to seek alternative target companies. Furthermore,

their valuations of the victim and their justifications for the acquisition

become exaggerated.





3. Mode of offer

Advantages Disadvantages

● Cash - Simple - Liquidity problems

- Price certain - Capital gains tax

● Shares - Saves cash - Value uncertain

- Maintains ownership state - Dilution of EPS

- Avoids capital gains tax

- Vendor placings for sellers

who need cash

● Loan stock - Saves cash - Gearing problems

- Avoids capital gains tax - Changes character of

investment

Sometimes hybrid instruments (e.g convertible loan stock) may be issued.

4. Defences

● Pre-bid

o Strategic shareholdings

o Poison pills

o Fat man strategy

o Golden parachutes

o Crown jewels (or scorched earth) policy

o Pacman strategy (likely target making a reverse takeover bid for a

potential bidder).

o Revaluation of fixed assets

● Post-bid (Note: all defences must be in line with the City Code)

o Appeal to your own shareholders. Argue that victim shares are

undervalued, bidder’s shares are overvalued (contrary to EMH but

directors have inside information).

o White knight defence – encourage a more friendly bid.

o Appeal to the Competition Commission.

o Greenmail – questionable in the UK.

o Crown jewels (or scorched earth) policy, with the approval of

shareholders in general meeting (City Code Rule 21.1 (b)(iv)).





5. Significant percentage holdings

Under CA 2006, the City Code or Listing Rules, the following percentage

acquisitions have a significant impact.

● 3% or more. Disclose your identity to the directors of the company

concerned.

● 15%, but less than 30%. The Substantial Acquisitions Rules once applied to

purchases of shares within this range of shareholding. However, these

Rules were abolished with effect from 20th May 2006.

● 30% or more. A general offer must be made to all remaining shareholders of

the target company

● More than 50%. In normal circumstances control is gained and a

parent/subsidiary undertaking relationship is established.

● 75% or more. A special resolution can be passed once this level of control

has been achieved.

● 90% or more. An offer to minority shareholders can generally be enforced.

6. Conduct of takeover bids

The following information was circulated by the Board of Forte plc as part of its first

Defence document following the takeover offer by Granada plc in November 1995:

Guidance note on the conduct of takeover bids

The purpose of this appendix is to provide some guidance to Forte shareholders

who may be unfamiliar with the detailed provisions contained in the Takeover Code

which govern takeover bids. It is not intended to be a definitive guide and you

should consult your own professional adviser.

Timing

● The offer document was posted to you by the bidder; Granada, on 24th

November, 1995.

● The first closing date for the offer is 15th December, 1995. Typically, in a

contested bid, this date will pass without any action by the vast majority of

shareholders and acceptances at the first closing date will usually be very low.

The bidder has reserved the right to lapse or close its full cash alternative on

the first, or any subsequent closing date.

● The bidder normally extends the offer in 14 day steps. Alternatively, the

bidder may allow the bid to lapse on the first, or any subsequent closing date,

but only if it is not unconditional as to acceptances.

● Forte cannot normally disclose trading results, profit or dividend forecasts,

asset valuations or proposals for dividend payments after the 39th day after

the offer document is posted, currently 2nd January, 1996.

● The bidder cannot normally revise the terms of its bid after the 46th day after

the posting of the offer document, currently 9th January, 1996.

● The bidder must normally declare its bid unconditional as to acceptances (see

below) by 23rd January, 1996, the 60th day after posting, or it will lapse

automatically.





Acceptance condition

● The bidder may declare the bid unconditional as to acceptances at any level

above 50 per cent of the ordinary shares outstanding (assuming that the

bidder is permitted to exclude the Forte trust shares for this purpose).

● Shareholders who have not yet accepted when a bid is declared unconditional

as to acceptances are still able to accept the offer (although not necessarily

any cash alternative) as the bid must be kept open for acceptance for at least

another 14 days after it has been declared unconditional as to acceptances.

Communication with shareholders

● The offer document you have received contains the bidder’s arguments.

● Forte has set out in this defence circular a response to the bidder’s arguments

and why the bid should be rejected.

● Further circulars to shareholders are likely to follow from both Forte and the

bidder.

If another bidder announces an offer, the timetable normally restarts from the date

that its offer document is posted.





DARK POOL TRADING

The recent financial crisis has seen the alleged (see newspaper article below)

growth of a practice, which is sometimes referred to as “Dark pool trading”. It is

also known as “Dark pool liquidity”, the “Upstairs market”, “Dark liquidity” or simply

“Dark pool”.

The term “Dark pool” relates to trades which are concealed from the public – as if

they had been undertaken in “pools of murky water”. Many traders believe that

such activities should be publicised in order to make trading more fair for all parties

involved, so that all such transactions are performed on “a level playing field”.

Dark pool trading refers to the volume of trade created by institutional investors in

financial trading venues or “crossing networks” that are unavailable to the general

public. The bulk of Dark pool liquidity is represented by block trades undertaken

away from the central exchanges. Such transactions are never displayed and are

useful for institutions who wish to deal in large numbers of shares, whilst not

revealing such trades to the open market.

Dark liquidity pools avoid the risk of revealing the actions of such institutions, since

neither the identity of the trader nor the price at which the transactions took place

are displayed. Dark pools are recorded as over-the-counter transactions, but

detailed information is only reported to clients if they so desire and are under a

contractual obligation to do so.

The Upstairs market allows Fund managers to move large blocks of equity shares

without revealing details as to what has actually occurred. The lack of human

intervention within the electronic platforms employed has reduced the time scale

for such trades. The increased responsiveness of equity price movements has

made it extremely difficult to trade large blocks of shares without affecting the

price.

A report in “The Independent” newspaper on 25th May 2010 stated:

“Six big investment banks published trading volumes for their “dark pools” for the

first time yesterday, showing them as a tiny fraction of the market and not the

major hidden rivals to stock exchanges that some argue.

Citi, Credit Suisse, Deutsche Bank, J P Morgan Cazenove, Morgan Stanley and UBS

together executed €596 million (£513 million) of equity trades from 15 countries on

their automated crossing systems on Friday, according to Markit data.

That accounted for about 0.4 per cent of all types of cash equity trades in Europe

and 1.6 per cent of all over-the-counter (OTC) trades reported on the Markit BOAT

service that day, according to Thomson Reuters data.

Dark pools are electronic platforms that allow would-be buyers and sellers of large

orders of shares to avoid revealing pre-trade information and signalling their

intentions to the rest of the market.

Bankers argue that for the bulk of OTC trades they act purely as dealers, using

their own money or share inventories to take one or another side, or they act in a

non-automated way to match buyers and sellers for big blocks of stock.”





Oxclose plc and Satac Ltd

The board of directors of Oxclose plc is considering making an offer to purchase

Satac Ltd, a private limited company in the same industry. If Satac is purchased it

is proposed to continue operating the company as a going concern in the same line

of business.

Summarised details from the most recent financial statements of Oxclose and Satac

are shown below:

Balance sheet at 31 March

Oxclose plc Satac Ltd

£m £m £’000 £’000

Freehold property 33 460

Plant and equipment (net) 58 1,310

Stock 29 330

Debtors 24 290

Cash 3 20

Less: Current liabilities (31) (518)

25 122

116 1,892

Financed by:

Ordinary shares* 35 160

Reserves 43 964

Shareholders’ equity 78 1,124

Medium-term bank loans 38 768

116 1,892

*Oxclose plc 50p ordinary shares; Satac Ltd 25p ordinary shares.

Year # Oxclose plc Satac Ltd

Profit after tax Dividend Profit after tax Dividend

£m £m £’000 £’000

t−5 14.30 9.01 143 85.0

t−4 15.56 9.80 162 93.5

t−3 16.93 10.67 151 93.5

t−2 18.42 11.60 175 102.8

t−1 20.04 12.62 183 113.1

# t−5 is five years ago, t−1 the most recent year, etc.

Satac’s shares are owned by a small number of private individuals. The company is

dominated by its managing director who receives an annual salary of £80,000,

double the average salary received by managing directors of similar companies.

The managing director would be replaced if the company were purchased by

Oxclose.

The freehold property of Satac has not been revalued for several years and is

believed to have a market value of £800,000.

The balance sheet value of plant and equipment is thought to fairly reflect its

replacement cost, but its value if sold is not likely to exceed £800,000.

Approximately £55,000 of stock is obsolete and could only be sold as scrap for

£5,000.





The ordinary shares of Oxclose are currently trading at 430p ex div. It is estimated

that, because of difference in size, risk and other factors, the required return on

equity by shareholders of Satac is approximately 15% higher than the required

return on equity of Oxclose’s shareholders (i.e., 115% of Oxclose’s required

return). Both companies are subject to corporate taxation at a rate of 40%.

You are required:

(a) to prepare estimates of the value of Satac using three different methods of

valuation, and advise the board of Oxclose plc as to the price, or possible

range of prices, that it should be prepared to offer to purchase Satac’s shares;

(b) to briefly discuss the theoretical and practical problems of the valuation

methods that you have chosen;

(c) to discuss the advantages and disadvantages of the various terms that might

be offered to the shareholders of a potential ‘victim’ company in a takeover

situation.





Oxclose plc and Satac Ltd solution

(a) There are various methods by which the value of an unlisted company may be

estimated. These include:

(i) Dividend valuation model

(ii) Price/earnings ratio

(iii) Net assets basis – in this case a going concern

These three are illustrated below. Other methods exist (including the present

value of expected future cash flows for a fixed number of years) but some of

these are of little practical or theoretical relevance.


gKe

DP 1

0 −=

Ke for Oxclose may be estimated from Ke = gP

D

0

1 +

Growth of dividends is approximately 8.8% i.e.

g = 1)01.962.12(4 −÷

= 8.8%

Current dividend per share is 18.03 pence i.e.

D0 = 70

62.12 = 18.03

(N.B. Oxclose has 70m shares on issue of 50p each)

The cost of equity of Oxclose plc is

Ke = ( )

088.0430

088.103.18+

= 13.36%

The cost of equity of Satac Ltd is approximately 15% higher than

Oxclose’s Ke

13.36% x 1.15 = 15.36%

The dividend growth model can now be used to establish the value of

the shares of Satac. Growth in dividends in all years except t−3

(which is assumed to be an extraordinary year) is approximately

10%. The dividend of Satac in the most recent year is £113,100,

thus

P0 = 10.01536.0

1.1 100,113

−

× = approximately £2,321,000





(ii) Price/earnings ratio

The valuation method here is to multiply the current earnings of Satac by

the P/E ratio of a similar company. The only data given relates to

Oxclose plc, a much larger company in the same industry.

EPS of Oxclose = 70

04.20 = 28.63p

P/E ratio of Oxclose = 63.28

430 = 15.02

Satac’s earnings, adjusted for the extra earnings generated if the

managing director is replaced, are: £183,000 + 40,000 (1 – 0.4) =

£207,000

£207,000 x 15.02 = £3,109,140

Some adjustment to the P/E, and therefore to this valuation, is desirable

as:

(1) Satac is not a listed company;

(2) it is much smaller than Oxclose;

(3) the systematic risk of the companies is likely to be different;

(4) earnings growth of Satac has been lower than that of Oxclose and

may be so in the future.

These factors would suggest that a substantially lower P/E ratio and

valuation are appropriate.

(iii) Net assets basis

Replacement cost rather than net realisable value is used, as the

company will continue as a going concern.

£’000 £’000

Freehold property 800

Plant and equipment (net) 1,310

Stock 280

Debtors 290

Cash 20

Less: Current liabilities (518)

72

2,182

Less: Medium term bank loan (768)

1,414

The replacement cost value of net assets is £1,414,000. However, this

does not include any allowance for the goodwill of the business.

On the basis of these estimates a valuation of Satac of well in excess of

£1,414,000, but well below £3,109,140 (say between £2,300,000 and

£2,700,000) would appear to be reasonable. The valuation of unquoted

companies is far from an exact science, and other price ranges are

acceptable. The actual price paid will be a matter for negotiation and

will depend in part upon the current ownership pattern of Satac’s

shares. The highest price suggested might not prove high enough to





purchase Satac if Satac’s managing director or others have majority

control of the shares and do not wish to sell the company.

Other factors of relevance to the buyer might be the impact on future

profits if the managing director is replaced. If he is a ‘key man’ and is

important to the success of the business, profits might fall when he is

replaced. There is also the possibility of a ‘golden handshake’ for the

managing director, which would add to the cost of buying the company.

The question assumes that the taxation rates and regimes for both

Oxclose and Satac are similar. In practice this might not be the case,

and Oxclose might wish to assess the value of Satac based upon pre-tax

rather than post-tax earnings.

On economic grounds the maximum price that Oxclose should be

prepared to offer should depend upon the difference between the

present value of its own expected cash inflows before the acquisition,

and the present value of the combined expected cash flows after the

acquisition which, if synergy occurs, might justify a higher price than

any other valuation methods that have been illustrated.

(b) In theory the present value of the incremental cash flows associated with the

acquisition should form the basis of the valuation. None of the valuation

methods illustrated offers a valuation of this nature (indeed such a valuation,

while theoretically desirable, is in practice very difficult to undertake). The

three valuation methods should only be considered as rough estimates.


The model relies on restrictive assumptions, including a constant

expected growth rate (or a series of different expected growth rates).

How should the growth rates(s) be estimated? If historical data is used

as a guide, over what period of time? Should more recent growth be

more heavily weighted in the estimate?

Any growth rate estimate is likely to involve subjectivity. The valuation

in this question is dependent upon the estimate that Ke for Satac is 15%

higher than for Oxclose. There is no accurate way of estimating such a

relationship.

Dividends can be set at any level that a majority shareholder (or

perhaps dominating managing director) chooses, within the constraints

set by earnings (past and present) and liquidity. It might not, therefore,

be appropriate to value the company by the discounted value of the

future dividend stream.

(ii) P/E ratio

Some of the possible problems of the P/E ratio have been outlined

above. It is difficult to find a ‘comparable’ company from which the P/E

may be taken in order to estimate another company’s value





(iii) Net assets basis

Asset based valuations, even after adjustments, may bear little

relationship to the market value of a company. The market value of

going concern is based upon an expected stream of future earnings,

which will depend upon the quality of management and many other

factors, in addition to the nature of the assets that a company

possesses.

(c) Terms that might be offered in a takeover situation include cash, shares, fixed

interest stock or a combination of these. Occasionally the shareholders of the

‘victim’ company will be offered a choice of terms e.g. all cash or less cash

plus shares or fixed interest stock. Fixed interest stocks might include a

convertible element, or have warrants associated with them.

Advantages and disadvantages may be considered from both the viewpoint of

the bidding company and the shareholders of the potential victim.

The bidding company will wish to offer the terms that result in success at the

minimum expected cost. The use of shares conserves corporate liquidity but

leads to possible dilution in ownership. However, a bid mainly in the form of

shares might be the only possibility when the ‘victim’ company is relatively

large. The use of debt will also conserve corporate liquidity; but it will

increase gearing. A cash bid allows the bidder to know exactly the cost of the

bid.

The victim’s shareholders will similarly only know the exact value of the bid if

it is in the form of cash, as fluctuations in the prices of shares and fixed

interest stocks make their values uncertain. Cash gives shareholders the

freedom to spend the cash or to invest elsewhere (in the bidding company if

they wish!) without incurring the transaction costs of selling the shares.

However, a cash payment might be subject to an immediate tax liability e.g.,

in countries where capital gains tax exists. The use of shares allows the

shareholders to maintain a continued interest in the company, as part of a

larger group. Fixed interest stock also allows a continued interest, but not an

ownership interest, unless the offer is convertible into shares at some future

date (and if market prices are favourable). Fixed interest stock is likely to

alter the nature and risk of the shareholders’ investment portfolios which

might not be well received by the shareholders. Although the stock could be

sold, this would incur additional transaction costs.





Demast Ltd

Demast Ltd has grown during the last five years into one of the UK’s most

successful specialist games manufacturers. The company’s success has been

largely based on its Megaoid series of games and models, for which it holds patents

in many developed countries. The company has attracted the interest of two plcs,

Nadion, a traditional manufacturer of games and toys, and BZO International, a

conglomerate group that has grown rapidly in recent years through the strategy of

acquiring what it perceives to be undervalued companies.

Summarised financial details of the three companies are shown below:

Demast Ltd

Summarised balance sheet as at 31 December 2003

£’000 £’000

Fixed assets (net) 8,400

Current assets

Stock 5,500

Debtors 3,500

Cash 100

9,100

Less: Current liabilities

Trade creditors 4,700

Tax payable 1,300

Overdraft 1,200

7,200

10,300

Medium and long-term loans 3,800

Net assets 6,500

Financed by:

Ordinary shares (25 pence nominal) 1,000

Reserves 5,500

6,500

Summarised profit and loss account for the year ended 31 December 2003

£’000

Turnover 27,000

Profit before tax 4,600

Taxation _1,380

3,220

Dividend 1,500

Retained earnings 1,720

Additional information

(1) The realisable value of stock is believed to be 90% of its book value

(2) Land and buildings, with a book value of £4 million were last revalued in 1989

(3) The directors of the company and their families own 25% of the company’s

shares





Demast Nadion BZO Int

Turnover (£m) 27 112 256

Profit before tax (£m) 4.6 11 24

Fixed assets (£m net) 8.4 26 123

Current assets (£m) 9.1 41 72

Current liabilities(£m) 7.2 33 91

Overdraft (£m) 1.2 6 30

Medium and long-term liabilities (£m) 3.8 18 35

Interest payable (£m) 0.5 3 10

Share price (pence) - 320 780

EPS (pence) 80.5 58 51

Estimated required return on equity 16% 14% 12%

Growth trends per year

Earnings 12% 6% 13%

Dividends 9% 5% 8%

Turnover 15% 10% 23%

Assume that the following events occurred shortly after the above financial

information was produced.

7 September – BZO makes a bid for Demast of two ordinary shares for every

three shares of Demast. The price of BZO’s ordinary shares after the announcement

of the bid is 710 pence. The directors of Demast reject the offer.

2 October – Nadion makes a counter bid of 170 pence cash per share plus one

£100 10% convertible debenture 2018, issued at par, for every £6.25 nominal

value of Demast’s shares. Each convertible debenture may be exchanged for 26

ordinary shares at any time between 1 January 2007 and 31 December 2009.

Nadion’s share price moves to 335 pence. This offer is rejected by the directors of

Demast.

19 October – BZ0 offers cash of 600 pence per share. The cash will be raised by a

term loan from the company’s bank. The board of Demast are all offered seats on

subsidiary boards within the BZO group. BZO’s shares move to 680 pence.

20 October – The directors of Demast recommend acceptance of the revised offer

from BZO.

24 October – BZO announces that 53% of shareholders have accepted its offer

and makes the offer unconditional.

Required

(a) Discuss the advantages and disadvantages of growth by acquisition.

(b) Discuss whether or not the bids by BZO and Nadion are financially prudent

from the point of view of the companies’ shareholders. Relevant supporting

calculations must be shown.

(c) Discuss problems of corporate governance that might arise for the

shareholders of Demast Ltd and BZO plc.





Demast Ltd solution

(a) Growth by acquisition is said to allow companies to expand much more rapidly

than by organic growth. Rapid increases in size may offer:

(i) Economies of scale in production, marketing, R & D and finance

(ii) A reduction in the company’s risk, and cost of capital

(iii) Greater market share and market power. In some markets to operate

effectively requires the achievement of a ‘critical mass’ size.

Additionally acquisitions may allow:

(i) Improvements in gearing

(ii) Purchase of patents, brands or skilled management

(iii) Synergistic effects

(iv) Entry into a new market quickly

(v) Acquisition of undervalued assets or companies, as is the stated strategy

of BZO International. This may encompass the removal of relatively

inefficient management.

However, there is evidence that many acquisitions are financially

unsuccessful. There is often some abnormal return for the shareholders of the

target company (in the form of high prices received for their shares), but very

little for the bidding company’s shareholders. Acquisitions often experience

difficulties in integrating the operations of the companies concerned (unless

asset-stripping is the motive for the acquisition).

(b) Demast is an unlisted company, with no market price. Ideally the valuation of

the company should be based upon the expected net present value of future

cash flows, but accurate estimates of this value will rarely be available in an

acquisition situation. Valuation could in practice be based upon either assets

or earnings. For Nadion, which is likely to be purchasing Demast as a going

concern, an earnings valuation is appropriate. BZO International has a

strategy of acquiring what are perceived to be undervalued companies. If the

intention is to quickly dispose of all or part of the company, the realisable

value of Demast’s assets would provide a useful guide, but if asset stripping is

not to occur an earnings valuation would once again be recommended.

Asset valuations

No precise estimate of the realisable value of assets is possible. Net asset

value, adjusted for a 10% decrease in the value of stock, is £5,950,000 or

149 pence per share. This, however, ignores important factors including:

(i) Land and buildings have not been revalued since 1989. In the light of

the subsequent recession and fall in commercial property prices, the

realisable value could be less than the book value of £4 million.

(ii) No information is provided regarding the difference between book and

realisable values of other fixed assets.

(iii) The patents are not valued in the balance sheet. These could have

substantial value if they have a number of years to run.





Earnings valuations

Two common methods of ‘earnings’ based valuations are the P/E ratio and the

dividend valuation model.

P/E ratio model

As Demast is not listed a P/E valuation must be based upon the P/E of a

similar (pure play) company. The only available information for a company in

the same industry is for Nadion, a much larger company.

The EPS of Demast is 80.5 pence (given in question).

EPS of Nadion is 58 pence.

P/E of Nadion is 320p ÷ 58p = 5.52

If this is used for Demast the estimated value per share is:

5.52 x 80.5p = 444 pence

Although Nadion is listed and much larger than Demast, the much higher

growth rates of Demast might justify the use of the P/E of Nadion, without any

adjustment for lack of marketability.

Dividend valuation model

P0 = gKe

D1

−

Current dividend of Demast is 000,000,4

000,500,1£ = 37.5p per share

At 9% growth the expected net dividend is 37.5 x 1.09 = 40.875p

P0 = 09.016.0

875.40

− = 584 pence per share

All of these estimates are subject to considerable margins of error.

Value of the bids

7 September – BZO bids 710 x 2/3 = 473 pence per share

2 October – Nadion bids 170 pence plus effectively £4 per share (£100

debentures at par for £6.25 nominal value or 25 ordinary shares), amounting

to 570p per share plus the conversion opportunity. The conversion is

currently at an implied price of £100 ÷ 26 = 385 pence per share.

This is only 14.9% above the current share price of Nadion (335p), and the

opportunity for substantial capital gains on conversions exists as there are up

to five years before the final conversion date. A rise in market price could

mean that Nadion issues new shares on conversion at well under market price

to Demast’s old shareholders.

19 October – BZO cash offer of 600 pence per share.





Commentary

Although all offers are significantly above the estimated asset valuation, the

final successful bid is only 16 pence above the dividend valuation model

figure. If this is accurate, the bid would seem to be financially prudent.

However, BZO’s strategy is to acquire undervalued companies. Unless BZO

has knowledge of how to significantly increase the value of Demast e.g. by

disposing of part of the operations, or the land, the acquisition of Demast does

not appear to be in line with this strategy. Additionally financing the 600

pence cash offer with a £24 million term loan increases the book value of

BZO’s gearing (measured by loans and overdraft to shareholders’ funds) from

its already high level of

359172123

3530

−−+

+ =

69

65 = 94%

If the stock market is efficient the significant falls in BZO’s share price on the

occasions of both the company’s bids illustrate that the acquisition is not

regarded as financially beneficial by the company’s shareholders.

(c) Corporate governance is the system by which companies are directed and

controlled. The board of directors should act on behalf of the shareholders,

taking note of other interest groups such as the government, creditors,

customers and employees.

In an acquisition situation the actions of directors are constrained by the City

Code on Takeovers and Mergers, a set of self-regulatory rules administered

and enforced by the Panel on Takeovers and Mergers. The directors of both

the bidding and target companies should disregard their own personal

interests when advising shareholders.

It is questionable whether BZO’s directors’ actions are in the best interests of

the company’s shareholders, given the market reaction to the bid and the

likely adverse effects on the company’s gearing and interest cover. The

company appears short of liquidity (current ratio 0.79:1), and may be trying

to maintain its high growth in turnover through acquisitions.

The directors of Demast advised shareholders to reject the bid of Nadion

worth 570 pence plus a likely capital gain on conversion, and accept the bid

from BZO of 600 pence, which also offered them seats on subsidiary boards

within BZO. It could be argued that the directors were acting in their own

interests to retain well-paid employment, and not in the interests of the

owners of the 75% of the shares not controlled by the directors and their

families, although the value of the conversion option is difficult to quantify.

Acceptance of the bid by BZO might also affect the operations and

employment levels of Demast, if part of the operation or the patents were

sold. Continuity of current operations would be more likely under the

ownership of Nadion, a company in the same industry, though some cost-

saving might occur, with loss of employment.





Kelly plc

On 1st July 2005, Kelly plc had the following three classes of debenture all of which

had been in issue for some years:

Coupon

Rate

Year(s) of

redemption

Date of

redemption

Dates of

interest payments

Market price

at 1 July 2005

14% 2009 31 December 1 July, 31 December £110.43 ex int.

14% 2008-2010 1 July 1 July, 31 December £110.15 ex int.

6% 2010 1 April 1 April, 1 October unlisted

All the company’s debentures will be redeemed at par. Market evidence suggests

that the 6% 2010 debentures should have a six-monthly gross redemption yield (i.e

internal rate of return to maturity) of 6%. The prevailing level of market interest

rates can be assumed to remain unchanged over the next six years.

Requirements

(a) Calculate the six-monthly gross redemption yield of the 14% 2009 debenture

(b) Determine when investors are likely to assume that Kelly plc will redeem the

14% 2008-2010 debentures, and hence calculate their effective annual gross

redemption yield.

(c) Estimate the price on 1st July 2005 that an investor should be prepared to pay

for the 6% 2010 debentures.

NOTE: Ignore taxation





Kelly plc – solution

(a) Six-Monthly Gross Redemption Yield

This is found as the IRR of the following cash flows:

Initial capital cost: market value £110.43

Interest: nine payments of £7 due ½ yearly

Redemption: one payment of £100 in nine ½ years’ time.

Time Cash flows 10% factor PV at 10% 5% factor PV at 5%

£ £ £

0 (110.43) 1 (110.43) 1 (110.43)

1-9 7.00 5.759 40.31 7.108 49.76

9 100.00 0.424 42.40 0.645 64.50

Net present values £(27.72) £3.83

IRR, i.e. 6 monthly yield =

×+ 5

55.31

83.35 = 5.6%

(b) Redemption Date and Effective Annual Gross Redemption Yield

Kelly plc will presumably choose the option which minimises the effective cost

(based on similar IRR calculations) of the loan stock to themselves.

(i) Redeem 2008

PV at 10% PV at 5%

£ £

Market value (110.15) (110.15)

Six interest payments of £7 30.49 35.53

One payment of £100 56.40 74.60

Net present values £(23.26) £(0.02)

IRR = 5%

(ii) Redeem 2010

£ £

Market value (110.15) (110.15)

Ten interest payments of £7 43.02 54.05

One payment of £100 38.60 61.40

£(28.53) £5.30

IRR =

×+ 5

83.33

30.55 = 5.8%

Therefore Kelly will redeem the loan stock in July 2008. The effective annual

gross redemption yield is (1.05)2 − 1 = 10.25%.





(c) Price of Debentures on 1 July 2005

The value at 1 October 2005 is the present value, at 6%, of two cash flows:

(1) Interest: 9 interest payments of £3 plus £3 due on 1 October

(2) Redemption payment: £100 in nine ½ years’ time

PV of interest = [£3.00 x a 9 0.06] + £3.00

= [ ] 00.3£802.600.3£ +×

= £20.41 + £3.00 = £23.41

PV of capital = 592.0100£ × = £59.20

DF @ six monthly yield of 6% for 3 month period

= 06.1 = 1.0296

Value at 1 July = (£23.41 + £59.20) ÷ 1.0296 = £80.24





Eichner plc

At 31 July 2003, Eichner plc and Beck plc both have in issue 5 million ordinary

shares each with a nominal value of 50p. In addition, the companies have in issue

the following actively traded securities.

Eichner plc: 50,000 units of convertible debentures, carrying an annual coupon rate

of 11%. Each unit has a nominal value of £100 and may be converted into 40

ordinary shares at any time up to and including 31 July 2008. At that date any

unconverted debenture will be redeemed at £105 per £100 nominal value.

Beck plc: 800,000 warrants, each of which provides the holder with the option to

subscribe for one ordinary share at a price of £2.50 per share. The warrants can be

exercised at any time up to and including 31 July 2008.

Required:

(a) Calculate the value of each £100 unit of convertible debenture and of each

warrant on 30 July 2008, if the share price for each company on 30 July 2008

is either £2 or £3, and advise holders of the securities whether or not to

exercise their conversion or option rights.

(b) Estimate the market price at 31 July 2003 of each £100 unit of convertible

debenture, if the current share price on the same date is either £2 or £3. The

current pre-tax rate of interest on 11% debentures of companies with similar

risk to Eichner plc is 8% per annum.

(c) Discuss, briefly the factors which would influence the current price of a

warrant.

NOTE: Ignore personal taxation.





Eichner plc – solution

(a) Value of convertibles and warrants

(i) Value of convertibles

Share

price

Value as

debentures Value as shares Market value Convert?

£2 £105 40 x £2 = £80 £105 NO

£3 £105 40 x £3 = £120 £120 YES

(ii) Value of warrants

Share price Exercise price Value of warrant Exercise option?

£2 £2.50 £NIL NO

£3 £2.50 £0.50 YES

(b) Market price of convertible debentures

(i) Value as debt

£

t1−5 £11 x 3.993 = 43.92

t5 £105 x 0.681 = 71.51

£115.43

5 year annuity factor at 8% = 3.993

5 year single discount factor at 8% = 0.681

(ii) Value as equity will be 40 x market price per share

Share price Value as debt

(ex int)

Value as equity

(ex div) Formula value

£2 £115.43 £80 £115.43

£3 £115.43 £120 £120.00

The actual price of the convertibles is likely to display a premium on the

formula value prices, reflecting the time to go before expiry (i.e. time

value). There is no downside risk on the lower share price and only a

limited amount on the higher.

The value of a convertible cannot fall below its value as debt, but upside

potential is available due to the possibility of an increase in share price.

Thus a convertible will trade at a value in excess of formula value, and that

premium will be at its greatest where the value as debt and the value as

equity are fairly close to each other.





(c) Factors influencing the current price of a warrant

Warrants are effectively call options on equity and their value may be

estimated within an option pricing framework.

The major factors determining the market price of a warrant are as follows:

1. The price of the underlying security. Clearly the higher the security

price the more valuable the warrant.

2. The exercise price, i.e. the price at which the underlying security may

be purchased. The lower the exercise price the more valuable the

warrant.

3. The time to expiry. The longer the period to expiry the greater the

probability that the value of the underlying security will rise in value.

4. The volatility of the underlying security. Warrants like options can

give protection from downside risk, but give participation in upside

potential. Accordingly the greater the variability of the underlying

security the greater the probability of the warrant showing high returns.

5. Interest rates. As the exercise of the warrant is at some future date

we must consider the present value of the exercise price in determining

the value of a warrant. As interest rates rise, the present value of the

exercise price will be lower and hence the value of the warrant will

increase.

6. Exercise conditions. Warrants sometimes may only be exercised on

expiry (equivalent to European Call Options) whilst others may be

exercised at any time up to expiry (American Call Options). In most

circumstances it is not sensible to exercise warrants until expiry as

whilst there is still time left to run, the underlying security could

increase in value. In this case both variants should have the same

value. Large dividend payouts effectively transferring equity value to

cash can be detrimental to European type warrants. American type

warrants could exercise early and avoid this problem and therefore may

be more valuable.




Chapter 11







CHAPTER CONTENTS

A QUESTION OF VALUES ----------------------------------------------- 259

MARKET VALUE ADDED 259

ECONOMIC VALUE ADDED (EVA) 261

SHAREHOLDER VALUE ADDED (SVA) 268

INTELLECTUAL CAPITAL ----------------------------------------------- 271

VALUING INTELLECTUAL CAPITAL 271

MARKET-TO-BOOK VALUES 271

TOBIN’S Q 272

CALCULATED INTANGIBLE VALUE 272

ILLUSTRATION – DESTROYING VALUE ------------------------------- 274





A QUESTION OF VALUES

By Steve Jay, BA, M Phil

This is an article, which appeared in the October 2001 edition of Student

Accountant.

Introduction

It is generally accepted that the objective of corporate financial management is to

maximise shareholder wealth in the form of rising share prices and dividends.

Whilst this is obviously in the interest of shareholders it should also benefit society

as a whole. This is because it should lead to the most efficient companies finding it

easiest to raise new share capital and thus ensure that society’s scarce resources

are allocated and managed most efficiently. Unfortunately history shows us that

accounting profit measures often appear to have little correlation with share price

performance. This is particularly true in new-economy companies, many of whom

have poor profit records but who have demonstrated large increases in wealth for

their investors during the 1990s.

Market value added

Before proceeding with a look at economic value added it is important that we

clarify our measure of shareholder wealth. Imagine two quoted companies A plc

and B plc. Both firms are entirely equity financed. Both have a start of year stock

market equity capitalisation of £400 million. A plc raises 20 million via a rights

issue and invests it in a project that adds £100m to the present value of its future

earnings. B plc raises £150 million via a rights issue and invests in a project that

adds £120m to the present value of its future earnings. Table 1 demonstrates the

changes to equity market capitalisation and shareholder wealth.

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Table 1

Changes in stock market value

Company A Company B Opening total value (equity market capitalisation) £400m £400m

Addition to present value of earnings stream £100m £120m

Closing total value (equity market capitalisation) £500m £520m

Changes in shareholder wealth

Increase in total value (equity market capitalisation) £100m £120m

Funds subscribed by shareholders (£20m) (£150m)

Market value added for the period £80m (£30m)

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It is clear that although Company B has the greatest increase in market

capitalisation it has decreased the wealth of its shareholder’s as the present value

of the future income generated by its new project is less than the funds invested.

Company A on the other hand adds £80m to the wealth of its investors.

This is a simple but important point. Shareholder wealth is not simply the increases

in stock market value over the period; rather it is the increase in stock market

value less funds subscribed by shareholders.





This concept can be enlarged to cover the whole life of the business. Over a longer

time period the market value added is the difference between the cash that

investors have put into the business (either by purchase of shares or the

reinvestment of potentially distributable profits) and the present value of the cash

they could now get out of it by selling their shares.

The link with NPV

None of the above is particularly new. NPV is a well-established rule that measures

the impact that new projects will have on shareholder wealth. Table 2 adds some

more detail to the two projects being considered by Companies A and B.

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Table 2

Cash flows Company A

Project

Company B

Project £m £m t0 Initial investment (20) (150)

tl-t4 Net cash flow pa 35.03 46.35

CAPM based required rate of return 15% 20%

Net present value of Project A = (20) + Annuity factor for 4 years @ 15% x 35.03

= (20) + 2.855 x 35.03

= £80m

Net present value of Project B = (150) + Annuity factor for 4 years @ 20% x 46.35

= (150) + 2.589 x 46.35

= £(30m)

Both of these figures correspond with the market value added in the period, thus

the NPV rule should guide managers to select projects that maximise shareholder

wealth.

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Economic value added (EVA)

So far we have established that the prime objective of financial management is to

maximise investor wealth and that this can be achieved by using NPV in decision

making. What is lacking is an operating performance measure for management

that will guide managers to maximise NPV and thus shareholder wealth.

Traditionally operating managers are judged on accounting profit based measures

(controllable profit, return on investment, etc) which we have noted, often lack

correlation with shareholder wealth and largely ignore NPV. It seems very strange

that we expect managers to evaluate new projects on the basis of NPV, but that we

subsequently ignore NPV in appraising managerial performance.

Economic value added attempts to cure this problem.

Economic value can be defined as

Cash earnings before interest but after tax* MINUS An imputed charge for

the capital consumed.

*often referred to as NOPAT (net operating profit after tax)

In this way a manager’s operating performance is judged after charging a £ amount

for capital funds used.

It will be noted that this is very similar to residual income, a performance measure

you will have considered in earlier studies.

Crucially the present value of the economic value added figure equals the NPV of

the project.

Economic value added is sometimes referred to as EVA. EVA is the registered

trademark of Stern Stewart and Co who have done much to popularise and

implement this measure of residual income.

Table 3 shows the calculation of economic value added for our two projects and

demonstrates its equivalence with NPV.

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Table 3

£ million t1 t2 t3 t4

Company A Project

Year beginning capital employed (net) 20 15 10 5

Net of tax operating cash flow 35.03 35.03 35.03 35.03

Economic depreciation* (5) (5) (5) (5)

Imputed capital charge (15% of capital employed) (3)__ (2.25) (1.5) (0.75)

Economic value added 27.03 27.78 28.53 29.28

Company B Project

Year beginning capital employed (net) 150 112.5 75 37.5

Net of tax operating cash flow 46.35 46.35 46.35 46.35

Economic depreciation* (37.5) (37.5) (37.5) (37.5)

Imputed capital charge (20% of capital employed) (30) (22.5) (15)_ (7.5)_

Economic value added (21.15) (13.65) (6.15) 1.35





Equivalence with NPV

Company A economic value added 27.03 27.78 28.53 29.28

PV factors @ 15% 0.870 0.756 0.658 0.572

Present value 23.50 21.00 18.76 16.74

Total present value = £80 million = Project NPV

Company B economic value added (21.15) (13.65) (6.15) 1.35

PV factors @ 20% 0.833 0.694 0.579 0.482

Present value (17.62) (9.47) (3.56) 0.65

Total present value = (£30 million) = Project NPV

*Economic depreciation measures the true fall in the value of assets each year through wear and tear

and obsolescence. Although depreciation would not normally be charged in calculating discounted cash

flow, in this case it must be recovered from a company’s cash flow “to provide investors with a return of

their capital before they can enjoy a return on their capital” G Bennett Stewart. Alternatively it could be

viewed as the capital expenditure the firm would have to make each year to maintain its capital base.

In this example, for simplicity, economic depreciation is assumed to occur on a straight-line basis though

clearly other patterns are possible.

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The Linkages

To recap, the increase in shareholder wealth = Market value added

= Project NPV

= Present value of economic value

added

Therefore if we tell managers that their performance will be judged upon economic

value added, this should result in the maximisation of NPV and thus shareholder

wealth. We now have a performance measure that corresponds exactly with the

NPV based decision-making technique.

Proponents therefore recommend that managers and divisions operating

performance should be measured on an economic value added basis

Some complications

1. Geared companies

Not all companies are financed entirely by equity; many fund substantial parts

of their plant and equipment by using debt finance. The principles of

economic value added still apply.

Cash earnings before interest but after tax are charged for capital at a rate

that blends the after-tax cost of debt and the cost of equity in the target

proportions the firm would plan to employ (rather than the actual mix used in

a particular year).





Imagine that Company A financed its project by 50% equity finance and 50%

risk free debt finance and that this was considered to reflect the target capital

structure. To reflect this higher gearing A’s cost of equity finance increases to

18.5%. Its post-tax cost of debt is 7%. This gives a weighted average cost

of capital for the project of:

18.5% x 50% + 7% x 50% = 12.75%

The capital charge to the project will now be at 12.75% of capital employed at

the start of the year. Note that interest on the loan should not be deducted

from the net of tax operating cash flow as it is allowed for in the imputed

capital charge. The tax relief on interest should not be allowed for in the tax

bill, as once again this is included in the capital charge. Students will note

that this is similar to the approach taken in estimating net cash flow in NPV

calculations.

This approach is illustrated in table 4 together with other adjustments.

2. Economic value added and reported accounting results

Published accounting profit figures are more complicated than operating cash

flow less economic depreciation as featured in Table 3. For reasons of

prudence, losses are often recognised at an early date and accruals

accounting makes many timing adjustments to cash flow in converting it to

accounting profit.

As we are really interested in economic profit rather than accounting profit

these adjustments have to be eliminated or added back in. The consulting

firm Stern-Stewart, have identified 164 performance measurement issues in

its calculation of EVA from published accounts. The adjustments mainly

involve:

(i) Converting accounting profit to cash flow

(ii) Distinguishing between operating cash flows and investment cash flows

They include such issues as treatment of stock valuation, revenue recognition,

bad debts, the treatment of R & D, advertising and promotion, pension

expenses, contingent liabilities etc. Whilst it is unlikely that you would have

to make 164 adjustments in the exam some simple changes may be required!

Some of these are demonstrated in Table 4, which includes a calculation of

EVA from a set of published results.

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Table 4

XYZ plc Profit and Loss Account year ended 31/12/2000 (unadjusted)

£m Sales revenue 50

Cost of sales (28.3)

Depreciation (0.8)

Net operating profit 20.9

Interest paid (1.6)

R & D (2.1)

Advertising (2.3)

Amortisation of goodwill (1.3)


Tax paid (30%) (4.08)

Available to equity 9.52

XYZ plc Balance Sheet as at 31/12/1999 (unadjusted)

£m Fixed assets (net) 40

Current assets 125

Less Current liabilities (98)

Borrowings (27)

Net assets 40

Ordinary shareholders funds 40

XYZ plc Profit and Loss Account year ended 31/12/2000 after

adjustments

£m


Add

Interest paid 1.6 note 1

R & D 2.1 note 2

Advertising 2.3 note 3

Goodwill 1.3 note 4

Net operating profit 20.9

Less adjusted tax bill (4.56) note 5

Adjusted profit 16.34 note 7

XYZ plc Balance Sheet as at 31/12/1999 after adjustments

£m

Ordinary shareholders funds 40

Add

Borrowings 27 note 1

R & D 13.4 note 2

Advertising 15 note 3

Goodwill 8.9 note 4

Adjusted capital employed 104.3

Adjusted return 16.34

Required return (15% x £104.3m) = (15.645) note 6

EVA £0.695m

Conclusion: this company has added value for its shareholders





Notes

1 Interest paid is added back as this will be charged in the imputed capital

charge. Borrowings are added to the capital base as profits must cover

the cost of borrowings (see geared companies above).

2 R & D is considered an investment in the future in the same way as

expenditure on capital equipment. £2.1m is therefore removed from the

P & L account. At the same time the last (say) 5 years R & D expense

(assumed £13.4m) is added back to the balance sheet. This will

increase the capital base and thus the imputed capital charge. A small

charge for R & D may remain in the P & L a/c to reflect the economic

depreciation of the capitalised value.

3 Advertising is a market building investment and is removed from the P &

L a/c. The last (say) 5 years advertising expense is added to the capital

base (assumed £15m).

A small charge for advertising may remain in the P & L a/c to reflect the

economic depreciation of the capitalised value.

4 Goodwill represents the premium paid for a business on acquisition.

Again this is an investment in the future and similar adjustments as for

R & D and advertising apply. The cumulative goodwill write off of

(assumed £8.9m) is added to the capital base.

5 The tax figure will include tax relief on debt interest. As this will be

allowed for in the weighted average cost of capital it should be adjusted

out. The tax bill will rise to 4.08 + (30% x £1.6m) = £4.56m.

6 This is an assumed 15% WACC applied to the adjusted capital

employed. Note that WACC would be calculated following the approach

outlined in geared companies above.

7 No adjustment is made for depreciation as this is assumed to

approximate economic depreciation on physical assets as discussed

above.

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Arguments for and against Economic Value Added

FOR

1. It makes the cost of capital visible to managers. Under conventional

management accounting performance measures the only profit and loss

charge for capital is depreciation on the asset. Under the economic value

added approach managers will also be charged the financing cost of capital

employed. This should cause managers to be more careful in investing new

funds and to control working capital investment. It can also lead to under-

utilised assets being disposed of. To improve their performance managers will

have to:

● Invest in positive NPV projects, OR

● Eliminate negative NPV operations, OR

● Reduce the firms weighted average cost of capital, OR

● Hopefully all three

2. It supports the NPV approach to decision making. If managers pursue

negative NPV projects they will eventually find that the imputed capital charge

outweighs earnings and will lead to a deterioration in their reported

performance.

AGAINST

1. Economic value added does not measure NPV in the short term. Some

projects have poor cash flows at the beginning, but much better ones at the

end (and vice versa). Projects with good NPVs may show poor economic

value added in earlier years and thus be rejected by managers with an eye on

their performance measure. Managers who have a short term time horizon

(possibly due to impending promotion or retirement) could still make

decisions that conflict with NPV and thus the maximisation of shareholder

wealth.

If we return to projects being considered by Companies A and B, but this time

alter the pattern of cash flows (but not the NPVs) the point will be clearer.

Table 5 illustrates this point.

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Table 5

Cash flows £m

Company A Project Company B Project

£m

DF 15%

PV £m

£m

DF 20%

PV £m

t0 Investment (20) 1 (20) (150) 1 (150)

t1 Net cash flow 5 0.870 4.35 133.52 0.833 111.22

t2 Net cash flow 5 0.756 3.78 5 0.694 3.47

t3 Net cash flow 5 0.658 3.29 5 0.579 2.90

t4 Net cash flow 154.87 0.572 88.58 5 0.482 2.41

NPV £80m £(30m)

NPVs are unchanged and should therefore have the same effect on market

value added as before.





Economic value added computations

Company A Project

Year beginning capital employed

(net)

20 15 10 5

Net of tax operating cash flow 5 5 5 154.87

Economic depreciation (5) (5) (5) (5)

Imputed capital charge (15% of

capital employed) (3) (2.25) (1.5) (0.75)

Economic value added (3) (2.25) (1.5) 149.12

DF(15%) 0.870 0.756 0.658 0.572

PV NPV = £80m (2.61) (1.70) (0.99) 85.30

Company B Project

Year beginning capital employed

(net)

150 112.5 75 37.5

Net of tax operating cash flow 133.52 5 5 5

Economic depreciation (37.5) (37.5) (37.5) (37.5)

Imputed capital charge (20% of

capital employed) (30) (22.5) (15) (7.5)

Economic value added 66.02 (55.0) (47.5) (40.0)

DF(20%) 0.833 0.694 0.579 0.482

PV NPV = −−−−£30m 54.99 (38.20) (27.50) (19.29)

Conclusion

The present value of the economic value added figures is still equal to the

projects NPV, but the year-by-year distribution of economic value added has

changed. Managers with a short term time horizon may well accept Company

B’s project but reject Company A’s project.

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2. Validity of EVA adjustments

Part of the problem with economic value added in the short term lies in the

accounting measurement of profit. In table 5, Company A’s project might

show poor cash flows earlier on due to large investments in R & D. To a

certain extent this problem can be removed by using the adjustments

proposed by Stern Stewart covered above. However Brealey and Myers

question if these adjustments to accounting profit are sufficient. They cite the

case of Microsoft and question whether its capital base has been understated

in published Stern Stewart figures. “The value of its intellectual property - the

fruits of its investment in software and operating systems is not shown in the

balance sheet”. This would undervalue its capital base and result in its

imputed capital charge being too small and thus overstate its EVA.





Shareholder value added (SVA)

Shareholder value is a much-discussed concept and many companies now express

a commitment to it. It should be noted however that economic value added is

simply one way of measuring the increase in shareholder wealth achieved by the

company. Kevin Mayes gave a useful overview of the various shareholder value

metrics in a Student Newsletter article in the November/December 2000 edition.

Of these competitors to EVA, shareholder value added is also included in the Paper

P4 syllabus.

Shareholder value added involves calculating the present value of the projected

future free cash flow to equity of the business. Any increase in this present value

should result in an equivalent increase in market value added and thus increase

shareholder wealth.

Free cash flow to equity is the cash flow available to a company from operations

after interest expenses, tax, repayment of debt and lease obligations, any changes

in working capital and capital spending on assets needed to continue existing

operations (i.e. replacement capital expenditure equivalent to economic

depreciation).

Although different definitions of free cash flow exist they all relate to cash flow after

replacement capital expenditure. Free cash flow in our definition represents the

cash available to shareholders, which in principle could be used to invest in new

positive NPV projects, paid out as dividend or used for share repurchase. The

present value of this free cash flow should equal the current equity market

capitalisation of the business, and any changes in this present value (less

shareholder funds subscribed) represent the market value added.

Table 6 gives an example of the types of calculation involved.

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Table 6

A company prepares a forecast of future free cash flow at the end of each year. A

period of 15 years is used as this is thought to represent the typical time horizon of

investors in this industry. The company’s CAPM derived cost of equity is 10%.

During 2000, a rights issue of £5m is made which is invested in a project that will

increase future earnings.

Note that present values are calculated at a cost of equity, as free cash flow is

measured after debt servicing costs (i.e. it represents a return to equity holders).

If debt interest and principal payments had been excluded from the free cash flow

calculation then the present value would have been calculated at the WACC as this

version of free cash flow represents a return to both equity and debt holders. The

resultant present values would then represent the value of debt plus equity in the

company. The value of equity could be calculated by subtracting the stock market

value of debt.





Free cash flow forecast as at 31/12/1999

£m t1 t2 t3-t15

Sales 10,000 12,000 14,000

Operating costs (4,000) (5,000) (6,000)

Interest (1,000) (1,000) (500)

Debt repayments - (4,000) -

Working capital (500) (500) (500)

Replacement capital expenditure - (3,000) -

Tax (1,000) (1,000) (1,000)

Free cash flow to equity 3,500 (2,500) 6,000

PV factors @ 10% (the company’s cost of equity) 0.909 0.826 5.870*

Present value of free cash flow to equity 3,182 (2,065) 35,220

Total present value 36,337

Free cash flow forecast as at 31/12/2000

£m t1 t2 t3-t15 Sales 12,000 14,000 15,000

Operating costs (5,000) (6,000) (6,000)

Interest (1,000) (500) (500)

Debt repayments (4,000) - -

Working capital (500) (500) (500)

Replacement capital expenditure (3,000) - -

Tax (1,000) (1,000) (1,000)

Free cash flow to equity (2,500) 6,000 7,000

PV factors @ 10% (the company’s cost of equity) 0.909 0.826 5.870*

Present value of free cash flow to equity (2,273) 4,956 41,090

Total present value 43,773

£m

PV of free cash flow to equity as at 31/12/2000 43,773

PV of free cash flow to equity as at 31/12/1999 36,337

Increase in present value 7,436

Funds subscribed by shareholders in the year (5,000)

Market value added 2,436

Conclusion This company has increased the wealth of its shareholders

* The annuity factor for t3-t15 is calculated as follows:

t Annuity factor

1 to 15 7.606

1 & 2 (1.736)

5.870

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Arguments for and against the shareholder value added approach

For

It takes a multi-period view and should therefore overcome some of the “short

termism” of EVA

Against

1. The estimates of future free cash flow are very subjective and are very

difficult to verify. This technique would be almost impossible for outsiders to

the business to use.

2. The time horizon over which free cash flow is forecast is difficult to determine.

If you use a short period you lose the present value earned in later years, but

if a long period is used the forecasting of cash flows becomes very subjective.

Conclusions

Shareholder value is high on the agenda of many companies as shareholders

increasingly look for competitive rates of return on their investments. The two

metrics discussed here draw heavily on traditional financial management and

management accounting theory. EVA, SVA and free cash flow are all included in

the Paper P4 syllabus and are “fair game” for future exam questions.

References and Acknowledgements

G Bennett Stewart: The EVA Fact or Fantasy-Journal of Applied Corporate Finance

1994.

R Brealey & S Myers: Principles of Corporate Finance-McGraw Hill 6th Edition 2000

K Mayes: Shareholder Value-ACCA Student Newsletter November/December 2000

Thanks to Scott Goddard for his valuable comment on the drafts of this article.





INTELLECTUAL CAPITAL

Patents, trademarks and copyrights are the only form of intellectual capital that are

regularly recognised in financial reporting. However, accounting conventions based

upon historical cost often understate their value, since market values and value in

use would be more appropriate.

The “the Value Platform” is an intellectual capital management model which

recognises its three main components:

● Human capital – this refers to the know-how, capabilities, skills and expertise

of the human members of the organisation;

● Organisational (structural) capital – this refers to the organisational

capabilities developed to meet market requirements e.g. patents, design

rights, trade secrets, corporate culture, information systems and financial

relations;

● Customer (relational) capital – this refers to the connections outside the

organisation e.g. customer loyalty, brands, distribution channels, supplier

relations and franchising agreements.

Valuing intellectual capital

Intellectual capital is influenced by the unique culture of the organisation and the

distinct processes and relationships evolving therein. In view of its complexity the

measurement of intellectual capital would require a number of evaluation

measures.

Three broad indicators have been developed to facilitate comparisons of intellectual

capital stocks between organisations:

● market-to-book values;

● Tobin’s q;

● Calculated intangible value

Market-to-book values

This is the most widely known indicator of intellectual capital. The contention is

that the value of an entity’s intellectual capital will be represented by the difference

between the book value of the enterprise and its market value. If a company’s

market value is £10m and its book value £5m, then the residual £5m represents

the value of the firm’s intangible (or intellectual) assets. The principal benefit of

this method is its simplicity. However, as with most other measures, the more

simple the calculation, the less likely it is to capture the complexities of the real

world. In this case, simply subtracting book value from market value tends to

ignore external factors that can influence market value, such as deregulation,

supply conditions and general market nervousness, as well as the various other

types of information that determine investors’ perception of the income-generating

potential of the business, such as industrial policies in foreign markets, media,

political influences, rumour, etc.

In addition, the current accounting model does not attempt to value a company in

its entirety. Instead it records each of its separate net assets at an amount

appropriate to the relevant financial reporting standard, under which the accounts





have been prepared (e.g. historical cost, modified historical cost, replacement cost,

etc.). The market, however, values a business in its entirety as a going concern

with strategic intent. It may be argued that the differences between these two

forms of valuation can be defined as the value of intellectual capital. This value will

then be subject to variations arising from the book value of the separable net

assets, their current market price, and various imperfections that may exist in the

market valuations.

Calculations of intellectual capital that use the difference between market and book

values can also suffer from inaccuracy because book values can be affected if

businesses choose, or are required, to adopt tax depreciation rates for accounting

purposes, and the tax rates reflect factors other than an approximation of the

diminution in value of an asset.

Tobin’s q

Another way of getting around the depreciation rate problem when comparing the

intellectual capital between entities is to use Tobin’s q. This was developed initially

by James Tobin as a method of predicting investment behaviour. It uses the value

of the replacement costs of a company’s assets to predict the investment decisions

of a business, independent of interest rates. The q is the ratio of the market value

of the enterprise (i.e. number of shares on issue multiplied by mid-market price) to

the replacement cost of its assets. If the replacement cost of a company’s assets is

lower than its market value, then a company is obtaining monopolistic benefits, or

higher-than-normal returns on its investments. A high value of q indicates that the

company will likely purchase more of those assets. Technology and human capital

assets are typically associated with high q-values. As a measure of intellectual

capital, Tobin’s q identifies a company’s ability to get unusually high profits because

it has something that no other business has.

However, Tobin’s q is subject to the same external variables that influence market

price as the market-to-book value approach. Both methods are best suited to

making comparisons of the value of intangible assets of businesses within the same

industry, serving the same markets, and having similar types of tangible assets. In

addition, these ratios are useful for comparing the changes in the value of

intellectual capital over a number of years. When both the Tobin’s q and the

market-to-book value ratio of a company are falling over time, it is a good indicator

that the intangible assets of the firm are depreciating. This may provide a signal to

investors that a particular company is not managing its intangible assets effectively

and may cause them to adjust their investment portfolios towards companies with

increasing or stable values of q.

By making intra-industry comparisons between a company’s primary competitors,

these indicators can act as performance benchmarks and can be used to improve

the internal management or corporate strategy of the entity.

Calculated intangible value

A third measure, calculated intangible value (CIV) has been developed by NCI

Research to calculate the fair market value of the intangible assets of the entity.

The CIV involves taking the excess return on tangible assets, using this figure as a

basis for determining the proportion of return attributable to intangible assets.

Merck & Co, a pharmaceutical company, can be used as an example in illustrating

how the CIV works:





1. Calculate average pre-tax earnings for three years. For Merck: $3.694bn.

2. Go to the balance sheet and calculate the average year-end tangible assets

over three years: US$12.952bn.

3. Divide earnings by assets to get the return on assets (ROA): 29 per cent.

4. For the same 3 years, find the industry’s return on assets. For

pharmaceuticals, the number in this example was 10 per cent. If a company’s

ROA is below average, then stop. NCI’s method will not work.

5. Calculate the ‘excess return’. Multiply the industry-average ROA by the

company’s average tangible assets; this shows what the average drug

company would earn from that amount of tangible assets. Now subtract that

from the company’s pre-tax earnings. For Merck, excess earnings are:

3.694bn – (0.10 x 12.952bn) = $2.39bn

This figure shows how much more Merck earns from its assets than the

average drug-maker would!

6. Calculate the 3-year average income tax rate and multiply this by the excess

return. Subtract the result from the excess return to show the after-tax

premium attributable to intangible assets. For Merck (average tax rate 31 per

cent) the figure was $1.65bn.

7. Calculate the net present value (NPV) of the premium. This is done by

dividing the premium by an appropriate discount factor such as the company’s

cost of capital. Using an arbitrarily chosen 15 per cent yields, for Merck,

$11bn. This is the CIV of Merck’s intangible assets – the one that does not

appear on the balance sheet.

While the CIV offers the potential to make inter- and intra-industry comparisons on

the basis of audited financial results, two problems remain. First, the CIV uses

average industry ROA as a basis for determining excess returns. By nature,

average values suffer from certain problems and could result in excessively high or

low ROA. Second, the company’s cost of capital will dictate the NPV of intangible

assets. However, in order for the CIV to be comparable within and between

industries, the industry average cost of capital should be used as a proxy for the

discount rate in the NPV calculation. Again, the problem of averages emerges, and

one must be careful in choosing an average that has been adjusted for excessively

high or low values.

Conclusion

It is recognised that the intellectual capital of a business plays a significant role in

creating competitive advantage, and thus managers and other stakeholders in

organisations are asking, with increasing frequency, that its value be measured and

reported for planning, control, reporting and evaluation purposes. However, at this

point, there is still a great deal of room for experimentation in quantifying and

reporting on the intellectual capital of the entity. Given the potential for both

complexity and diversity, developing intellectual capital measures and reporting

practices that are comparable between enterprises remains one of the key

challenges to the accountancy profession.





Illustration – Destroying value

The most recent published results for V plc are shown below.

£m

20XX profit before tax 13.6

Summary consolidated balance sheet at 31 December 20XX

£m

Fixed assets 35.9

Current assets 137.2

Less: current liabilities (95.7)

Net current assets 41.5

Total assets less current liabilities 77.4

Borrowings (15.0)

Deferred tax provisions (7.6)

Net assets 54.8

Capital and reserves 54.8

An analyst working for a stockbroker has taken these published results, made the

adjustments shown below, and has reported his conclusion that ‘the management

of V plc is destroying value’.

Analyst’s adjustments to profit before tax

£m


Adjustments

Add: Interest paid (net) 1.6

R & D (research and development) 2.1

Advertising 2.3

Amortisation of goodwill 1.3

Less: Taxation paid (4.8)

Adjusted profit 16.1

Analyst’s adjustments to summary consolidated balance sheet at 31 December

20XX

£m

Capital and reserves 54.8

Adjustments

Add: Borrowings 15.0

Deferred tax provisions 7.6

R & D 17.4 Last 7 years’ expenditure

Advertising 10.5 Last 5 years’ expenditure

Goodwill 40.7 Written off against

reserves on acquisitions in

previous years

_____

Adjusted capital employed 146.0

£m

Required return (12% x £146.0m) 17.5 (weighted average cost of capital = 12%)

Adjusted profit 16.1

Value destroyed 1.4





The chairman of V plc has obtained a copy of the analyst’s report.

Required

(a) Explain, as management accountant of V plc, in a report to your chairman,

the principles of the approach taken by the analyst. Comment on the

treatment of the specific adjustments to R & D, advertising, interest and

borrowings and goodwill.

(b) Having read your report, the chairman wishes to know which division or

divisions are ‘destroying value’, when the current internal statements show

satisfactory returns on investment (ROIs). The following summary statement

is available.

Divisional performance, 20XX

Division A

(Retail)

Division B

(Manufacturing)

Division C

(Services)

Head

Office Total

£m £m £m £m £m

Turnover 81.7 63.2 231.8 - 376.7

Profit before

interest and tax 5.7 5.6 5.8 (1.9) 15.2

Total assets less

current liabilities 27.1 23.9 23.2 3.2 77.4

ROI 21.0% 23.4% 25.0%

Some of the adjustments made by the analyst can be related to specific

divisions:

● Advertising relates entirely to Division A (retail)

● R & D relates entirely to Division B (manufacturing)

● Goodwill write-offs relate to

Division B (Manufacturing) £10.3m

Division C (Services) £30.4m

● The deferred tax relates to

Division B (Manufacturing) £1.4m

Division C (Services) £6.2m

● Borrowings and interest, per divisional accounts, are as follows:

Division A

(Retail)

Division B

(Manufacturing)

Division C

(Services)

Head

Office Total

£m £m £m £m £m

Borrowings - 6.6 6.9 1.5 15.0

Interest

paid/(received) (0.4) 0.7 0.9 0.4 1.6

Required

Explain, with appropriate comment, in a report to the chairman, where ‘value

is being destroyed’. Your report should include:

● A statement of divisional performance

● An explanation of any adjustments you make

● A statement and explanation of the assumptions made

● comment on the limitations of the answers reached





Solution to ‘Destroying value’

(a)

REPORT

To: Chairman

From: Management accountant Date: XX.XX.XX

Subject: Destroying value in V plc

This report considers the recent observations by the analyst of X Stockbrokers

on our 20XX results. It will explain the principles of the approach taken by

the analyst and will provide a commentary on the treatment of the specific

adjustments made to our reported profit figure and balance sheet.

I Principles of the approach taken: economic value added

1. A management team is required by an organisation’s shareholders

to maximise the value of their investment in the organisation and

several performance indicators are used to assess whether or not

the management team is fulfilling this function.

2. The majority of these performance measures are based on the

information contained in the organisation’s published accounts.

These indicators can be easily manipulated and often provide

misleading information. Earnings per share, for example, are

increased by deferring expenditure in research and development

and in marketing.

3. The financial statements themselves do not provide a clear picture

of whether or not shareholder value is being created or destroyed:

(a) The profit and loss account, for example, indicates the

quantity but not quality of earnings

(b) It ignores the cost of equity financing and only takes into

account the costs of debt financing, thereby penalising

organisations such as ourselves which choose a mix of debt

and equity finance.

(c) Neither does the Cash flow statement provide particularly

appropriate information. Cash-flows can be large and

positive if an organisation reduces expenditure on

maintenance and undertakes little capital investment in an

attempt to increase short-term profits at the expense of long-

term success.

4. The analyst has therefore adopted an approach known as economic

value added to evaluate our performance.

● This approach hinges on the calculation of economic profit,

which requires several adjustments to be made to

traditionally reported accounting profits.

● These adjustments are made to avoid the immediate write-

off of value-enhancing expenditure such as research and

development or the purchase of goodwill. They are intended

to produce a figure for capital employed, which is a more

accurate reflection of the base upon which shareholders





expect their returns to accrue. They also provide a profit-

after-tax figure, which is a more realistic measure of the

actual cash yield generated for shareholders from recurring

business activities.

It is not very surprising that if management are assessed using

performance measures calculated using traditional accounting

policies, they are unwilling to invest in activities which immediately

reduce current year’s profit.

II The Treatment of specific items

1. Research and development

The analyst has added back expenditure of £2.1 million to the

20XX profit figure on the grounds that the expenditure is providing

a base for future activities. Similarly the research and

development expenditure over the last seven years of £17.4million

has been added back to the capital employed figure on the basis

that we are continuing to benefit from the expenditure. A

depreciation charge should probably be made against this

capitalised value, however, to reflect any fall in its value.

2. Advertising

The analyst has added back advertising expenditure of £2.3 million

to the 20XX profit figure on the assumption that the expenditure

has supported sales, raised customer awareness and/or increased

brand image/loyalty, all of which could produce significant

cashflows in the future and hence are for the long-term benefit of

the organisation. The advertising expenditure over the last five

years of £10.5 million has been added back to the capital

employed figure (in much the same way as the research and

development expenditure) to reflect the fact that the costs will

provide for future growth. Again, an amortisation charge should

be made if brand values are being eroded, possibly by competition.

3. Interest and borrowings

Because our profits are being earned using both debt and equity

finance, the published profit figure is overstated since it takes no

account of the cost of the equity finance. The analyst has

therefore added back the cost of the debt finance to the 20XX

profit figure and the borrowings figure to the capital employed.

This produces a profit figure before the cost of borrowing, which

can be compared with a figure representing the total long-term

finance in our organisation.

4. Goodwill

The analyst has added back goodwill amortisation of £1.3 million to

the 20XX profit figure. Goodwill is the difference between the price

paid for a business acquisition and the current cost valuation of

that acquisition’s net assets. On the assumption that a realistic

price was paid, the goodwill purchased should provide benefits in

the future, not just in the year of purchase. And the goodwill of





£40.7 million, which has been written off against reserves on

acquisitions in previous years has been added back to the capital

employed figure so as to provide a more realistic base upon which

we must earn a return. Again, the goodwill capitalised should be

regularly reviewed and amortised to reflect any reductions in its

value.

I hope this information has been of use. If I can be of any further assistance

please do not hesitate to contact me.

Signed: Management Accountant

(b)

REPORT

To: Chairman

From: Management accountant Date: XX.XX.XX

Subject: Where is value being destroyed?

An analyst working for X Stockbrokers has recently commented that ‘the

management of V plc is destroying value’. In an attempt to establish where

value is being destroyed in our organisation, a revised statement of divisional

performance has been prepared, adopting an approach similar to that used by

the analyst. The statement, plus supporting explanations, is set out in

Appendix 1.

The analysis shows that value of £0.1 million was destroyed in Division B,

while value of £2.3 million was destroyed in Division C. Division A, on the

other hand, created value of £1 million.

This is in marked contrast to the performance indicated in the conventional

divisional performance report prepared for 20XX. This shows all three

divisions earning a return on investment in excess of 20%, with Divisions B

and C, the destroyers of value, making higher returns on investment than

Division A, the creator of value.

The analyst’s approach is similar to performance evaluation using residual

income in that a charge is made for the capital employed within the division.

Further adjustments are also made to both profit and capital employed to

provide more realistic measures for performance analysis (as explained in my

earlier report and in Appendix 1). The results of the analysis are dependent

upon the following factors:

1. Head office expenses are assumed to have been incurred in relation to

divisional turnover. Any one of a number of other bases might be

equally valid.

2. Tax paid is assumed to be related to divisional profit after interest and

head office expenses. Deferred tax liabilities have not been incorporated

into the analysis.

3. Each division’s share of head office assets has been assumed to be in

proportion to the division’s share of total turnover. Other bases could be

equally valid.

4. It has been assumed that each division has the same cost of capital.

This takes no account of the individual characteristics of each division,

its risk profile and its mix of financing.





Despite the limitations set out above, the analyst’s approach provides an

alternative insight into how our divisions are performing and could well prove

useful in enabling us to create value for our shareholders in the future.

Signed: Management Accountant

APPENDIX 1

Statement of profitability

Divisions

A B C Head office Total

£m £m £m £m £m

20XX PBIT 5.7 5.6 5.8 (1.9) 15.2

Add back

Advertising 2.3 - - - 2.3

R & D - 2.1 - - 2.1

Goodwill (1) - 0.3 1.0 - 1.3

Head office expenses (2) (0.4) (0.3) (1.2) 1.9 -

Less: tax paid (2.0) (1.6) (1.2) - (4.8)

Revised profit 5.6 6.1 4.4 - 16.1

Statement of capital employed

Divisions


£m £m £m £m £m

Total assets less current

liabilities

27.1 23.9 23.2 3.2 77.4

Adjustments

Advertising 10.5 - - - 10.5

R & D - 17.4 - - 17.4

Goodwill - 10.3 30.4 - 40.7

Head office assets (4) 0.7 0.5 2.0 (3.2) -

Revised capital 38.3 52.1 55.6 - 146.0

Economic value added

Divisions


£m £m £m £m £m

Revised profit 5.6 6.1 4.4 - 16.1

Required return (5) 4.6 6.2 6.7 - 17.5

Value added/(destroyed) 1.0 (0.1) (2.3) - (1.4)





Explanation of adjustments made

1. Goodwill

Goodwill amortised has been apportioned to Divisions B and C in

proportion to the value of goodwill written off to capital and reserves.

Division Goodwill

write-off Goodwill amortised

£m % £m

B 10.3 25.3 x £1.3m 0.3289

C 30.4 74.7 x £1.3m 0.9711

40.7 100.0 1.3000

2. Head office expenses

No direction is provided as to the way in which head office expenses

should be apportioned to the three divisions. An activity-based

approach could be the most suitable but, in the absence of appropriate

data, allocation based on turnover has been adopted.

3. Tax paid

The tax liability of £4.8 million for V plc has to be apportioned over the

three trading divisions. Given that the divisions’ taxable profits will be

affected by the allocation of head office expenses and the interest paid,

the overall tax liability has been apportioned on the basis of divisional

profit after interest paid and allocated head office costs.

Division PBIT Interest

paid

Head office

expenses

Apportionme

nt figures Charge

£m £m £m % £m

A 5.7 − (0.4) − 0.4 = 5.7 41 2.0

B 5.6 − 0.7 − 0.3 = 4.6 33 1.6

C 5.8 − 0.9 − 1.2 = 3.7 26 1.2

14.0 100 4.8

4. Head office assets

Head office assets have been apportioned to the three trading divisions

on the basis of divisional turnover so as to be consistent with the basis

used to apportion head office expenses

5. Required return

The required return is based on a weighted average cost of capital of

12%.




Chapter 12

Corporate reconstruction and

reorganisation



CHAPTER 12 – CORPORATE RECONSTRUCTION AND REORGANISATION


CHAPTER CONTENTS

FINANCIAL RECONSTRUCTION ---------------------------------------- 283

ILLUSTRATION – JENKINS PLC --------------------------------------- 285

MANAGEMENT BUYOUTS (MBO)--------------------------------------- 290





FINANCIAL RECONSTRUCTION

● The Companies Act (CA) 2006 provides for the reduction of the share capital

of a company, subject to:

o The passing of a special resolution;

o Confirmation by the High Court*; and

o The articles of the company not specifically restricting or prohibiting a

reduction of capital (N.B. Under CA 1985, the articles of the company

had to actually give authority for the reduction).

● *Under CA 2006, where a private company limited by shares undertakes a

capital reduction scheme, confirmation of the court is not necessary if the

directors make a “Solvency statement”. This is a statement, made before the

date of the proposed resolution, that each of the directors has the view that

there are no grounds on which the company could then be found unable to

pay its debts and are of the opinion that any winding up made within the next

year would be a solvent liquidation.

● The Court will usually sanction such a scheme, provided that the rights of all

creditors are protected and that losses are fairly divided among all interested

parties.

● Under a scheme of capital reduction, a company may:

1. Extinguish or reduce the liability on any of its shares, which are not paid

up; or

2. Cancel any paid-up share capital that is lost or unrepresented by

available assets; or

3. Repay any paid-up share capital in excess of the company’s wants.

● The Court must settle a list of creditors entitled to object and hear objections.

However the Court may choose to dispense with the consent of any creditor

provided the company secures payment of that claim.

● The Court may order the company to publish the reasons for the reduction in

capital. It may also order the company to add the words “and reduced” to the

end of its name.

● Under Situation 2. above, the objective of a capital reduction scheme is

normally to:

o Write-off any debit balances on the profit and loss reserve;

o Write-off or write-down any asset values, which are considered to be

excessive;

o Revalue all assets on a “going concern” basis; and

o Reorganise the capital structure of the company in line with the assets

employed.

● Guidelines for implementation of the scheme are as follows:

o Ordinary shareholders (i.e. the risk-takers) must bear the majority of

the losses;

o Preference shareholders may be asked to bear a small part of such

losses. However, they may be issued with new equity shares in the





company as compensation for their waiver of any arrears of unpaid

preference dividends;

o In exceptional circumstances, bondholders and other creditors may be

persuaded to participate in part of the losses;

o Amounts made available under the terms of the scheme would then be

used to write-off any overstated values and to adjust the values of all

assets on a “going concern” basis;

o It would also be necessary to ensure the provision of adequate working

capital to meet foreseeable future needs. A rights issue is likely to be

necessary, with the directors expected to take up any such shares which

are rejected by other shareholders.





Illustration – Jenkins plc

Jenkins plc has been suffering from adverse trading conditions largely due to the

effect of obsolescence on its products. This has resulted in losses in each of the

last five years. The company’s bankers have refused to extend the present

overdraft facility and creditors are pressing for payment.

The directors feel that a new product recently developed by the company will make

the company profitable in the future, but they are worried that a winding-up order

may be made before this can be achieved.

They have therefore asked you to suggest a scheme of capital reduction that would

be acceptable to both the court and creditors and to advise them as to what action

should be taken to enable the company to continue trading.

The following is the present balance sheet of the company:

Book

values

Present

“going

concern”

values

£ £ £ £

Non-current assets

Intangible

Goodwill 30,000 -

Patents, trade marks etc 11,000 2,000

41,000

Tangible

Freehold land and buildings 120,000 150,000

Plant and vehicles _50,000 36,000

170,000

Current assets

Stocks and debtors 64,000 58,000

Listed shares at cost 15,000 14,000

79,000

Creditors falling due within

one year

Trade 118,000

Overdraft _31,000

(149,000)

Net current liabilities (70,000)

Total assets less current liabilities 141,000

Creditors falling due after one year

12% mortgage loan secured on freehold (60,000)

£81,000


Called up share capital

7% cumulative preference shares (£1)

fully paid (dividends are three years in

arrears)

50,000

Ordinary shares of 50p each – fully paid 200,000

250,000

Share premium account 60,000

Profit and loss account reserve (229,000)

£81,000





You ascertain the following:

1. Scheme costs are estimated at £4,800.

2. Preference shares rank in priority to ordinary shares in the event of winding-

up.

3. The bank has indicated that it would advance a loan of up to £50,000

provided that the overdraft is cleared and a second mortgage on the freehold

is given.

4. To ensure speedy manufacture of the new product it would be necessary to

expend £20,000 on new plant and £15,000 on increasing stocks.

5. The creditors’ figure of £118,000 includes £19,000 that would be preferential

in a liquidation.

Requirements:

(a) Suggest a scheme of capital reduction and write up the capital reduction

account.

(b) Outline your suggestions as to the action that should be taken by the

directors.

(c) Show the balance sheet after implementing your suggestions.

Ignore taxation.





Solution to Jenkins plc

Explanation

The first step is to estimate the losses to be suffered by preference shareholders on

a liquidation.

For example, on liquidation the following position may arise

Proceeds

£

Freehold 150,000

Plant (say 2/3 of £36,000) 24,000

Stocks and debtors (say ½ of £58,000) 29,000

Listed shares _14,000

£217,000

These proceeds will be used to repay the liabilities:

£

Secured mortgage 60,000

Overdraft 31,000

Trade creditors 118,000

£209,000

This leaves £8,000 for the shareholders. This will go to the preference

shareholders in priority to the ordinary shareholders. Therefore, the loss suffered

by the preference shareholders is £(50,000 – 8,000), i.e. £42,000. The loss

allocated to them under the scheme must be less than this.

Memorandum to the board

(a) Scheme of capital reduction

The objective of such a scheme is to write down the capital of the company so that

it realistically reflects the present values of the assets (on a going concern basis).

The major part of the loss should be borne by the ordinary shareholders although

the preference shareholders should bear a part of the loss where it is unlikely that

they would receive all their capital in a winding-up. A corresponding increase in the

rate of preference dividend is sometimes given as compensation. The reduced

capital of the company will ensure that it is possible to pay dividends when the

company achieves profitability.

Where arrears of cumulative preference dividends have accrued, it is usual to

compensate preference shareholders by issuing reduced ordinary shares in part

satisfaction of such arrears.

Explanation

Draw up a pro forma balance sheet after the scheme, and capital reduction

account; post through the opening position (writing off all goodwill and

accumulated losses); then adjust the assets to going concern values posting the

double entry as you work through.

Remember to post through the scheme costs and compensation in new shares to

the preference shareholders; then write down the ordinary and preference shares

to a round sum amount to cover the overall loss. The loss written off to the

preference shareholders may not exceed £42,000 and ideally should be less than

that.





Capital reduction account

£ £

Write offs Surplus on freehold 30,000

Profit & loss reserve 229,000

Plant & vehicles 14,000

Goodwill, patents etc 39,000

Investments 1,000

Current assets 6,000 Losses c/d 259,000

£289,000 £289,000

Losses b/d 259,000 Share premium account 60,000

Costs of scheme 4,800 Amounts written off

Ordinary share capital Ordinary shares (49p) 196,000

Issue re arrears of preference Preference shares (30p) 15,000

dividend (50%) 5,250

Balance c/d __1,950 ______

£271,000 £271,000

Explanation

Use notes c) to e) in the question; list total costs, compare to money coming in

(always sell any non-trade investments). Issue enough new shares to leave a

positive cash balance. Complete double entries as you work. Finally complete the

balance sheet.

(b) Suggested action (outline)

(i) The preferential creditors to be paid off in full immediately to prevent them

“blocking” the scheme.

(ii) The investments to be sold to produce part of the funds necessary to continue

trading.

(iii) Accept the bank’s offer of a maximum loan of £50,000 (subject to a second

mortgage charge being created)

(iv) The balance of the funds necessary to be provided by an issue of shares (on a

10 for 1 basis) at par for cash to the directors and shareholders. The

following cash is required:

£

Preferential creditors 19,000

Purchase of new plant 20,000

Additional stock 15,000

Pay costs of scheme 4,800

Clear existing overdraft 31,000

£89,800

£

Produced by

Sale of investments (ignoring costs) 14,000

Bank loan 50,000

Issue of shares to directors and existing shareholders

(10 x 400,000 x 1p) _40,000

£104,000

Leaving a balance at bank of £14,200





(c) Balance sheet if scheme adopted

£ £

Non-current assets

Intangible

Patents £(11,000 – 9,000) 2,000

Tangible

Freehold £(120,000 + 30,000) 150,000

Plant and vehicles £(50,000 – 14,000 + 20,000) 56,000

206,000

208,000

Current assets

Stock/debtors £(64,000 – 6,000 + 15,000) 73,000

Bank balance (per b) iv) above) 14,200

87,200

Creditors – Amounts falling due within one year

Trade £(118,000 – 19,000) (99,000)

Net current liabilities (11,800)

Total assets less current liabilities 196,200

Creditors falling due after one year

Loan (secured on the freehold) (60,000)

Bank loan (50,000)

(110,000)

£86,200


Called up share capital

1p ordinary shares fully paid

£(200,000 – 196,000 + 5,250 + 40,000) 49,250

70p 10% preference shares fully paid

£(£50,000 – 15,000) 35,000

84,250

Reserve arising on scheme (capital reduction account) 1,950

£86,200

Explanation

It could be argued that Jenkins plc is still not in a sufficiently strong liquidity

position.





MANAGEMENT BUYOUTS (MBO)

Distinguishing features

● Group of managers acquire effective control and substantial ownership of an

operation and form an independent business.

● Also employee buyouts, buy-ins, spinouts.

Motivations

● For sale - Parent company disposals due to losses, lack of fit, or

size

- Private business owners wishing to sell out

● For purchase - Potential high returns

- Relatively low risk as compared to “green field” starts

- Elimination of managerial slack

Financing

● Commonly highly geared to leave managers with controlling interest in equity.

● Support from institutions normally required

o Examples include clearing banks, 3i group

o Institutions normally require business plans, details of exit routes,

sometimes board representation

o Commonly instruments include debt, preference shares, equity (limited),

mezzanine finance (e.g. convertible loan stock, junk bonds)

Potential problems

● Loss of head office support services

● Quality and resources of management team

● Third party bids at buyout stage

● Problems of high gearing




Chapter 13

Corporate dividend policy



CHAPTER 13 – CORPORATE DIVIDEND POLICY


CHAPTER CONTENTS

DIVIDEND IRRELEVANCE HYPOTHESIS ------------------------------ 293

DIVIDENDS IN AN IMPERFECT MARKET ----------------------------- 294

POSSIBLE APPROACHES TO DIVIDEND POLICY --------------------- 295

ALTERNATIVES TO A CASH DIVIDEND ------------------------------- 296

PARABAT PLC ----------------------------------------------------------- 297





DIVIDEND IRRELEVANCE HYPOTHESIS

Theory

The proponents of the dividend irrelevance hypothesis (Miller & Modigliani) claim

that the value of a firm is determined by its future earnings stream. The way this

stream is split between dividends and retentions has no impact upon shareholder

wealth.

Given a set investment policy, a dividend cut now to finance new projects will be

compensated by higher dividends at a later stage.

The shareholder will be indifferent to the dividend policy provided the PRESENT

VALUE of dividend payments remains unchanged.

Assumptions

● A set investment policy so that shareholders know the reason for withholding

dividends

● No transactions costs

● No distorting taxes

● Share prices move in the manner predicted by the model

In the case of a withheld dividend, the shareholder can maintain his level of income

by selling shares to generate ‘home made’ dividends, with no consequent decrease

in wealth.





DIVIDENDS IN AN IMPERFECT MARKET

Information content (dividend signalling)

● Dividends are an important current source of information

● Share price will increase if the dividend is greater than expected and vice

versa. Tendency to over-react

Transactions costs

● Shareholder can no longer replace a withheld dividend by selling shares

without incurring dealing commissions

● Company will benefit by financing investments from retained earnings to

avoid the high costs associated with raising new finance

Preference for current income

It is sometimes argued that shareholders prefer high dividend payouts as they see

these as more secure than capital gains (the “bird in the hand” theory)

This argument is sometimes thought to be weak. Current dividends are safe, but

so are current capital gains. Future dividends are just as uncertain as future capital

gains.

Distorting taxes

● Individuals will generally prefer dividends to capital gains whether a basic-rate

or higher-rate tax payer, subject to certain complications:

● exemption limit for capital gains tax

● non-tax-paying individuals

● tax-exempt institutions.





POSSIBLE APPROACHES TO DIVIDEND POLICY

Stable policy with moderate payout

● Stable level of dividends with occasional increases (where justified). This

would avoid sharp movements in share price.

● Moderate payout policy in order to sustain the level of dividends in the face of

fluctuating earnings.

● Very common approach for listed companies.

Constant payout ratio

● Constant proportion of earnings paid out as a dividend.

● Not particularly suitable as dividends will fluctuate, causing erratic share price

movements.

Residual dividend policy

● Remaining earnings, after funding all profitable projects, are paid out as

dividend.

● Tends to lead to fluctuating dividends and therefore not particularly suitable.

Clientele theory

● Consistent dividend policy is maintained which will attract a group of

shareholders to whom the policy is suited in terms of tax, need for current

income, etc.

Other considerations

● Legality, re distributable profits.

● Existence of inflation and consideration of real profitability.

● Growth and requirements for retained earnings.

● Liquidity position.

● Limited sources of funds (particularly for small companies).

● Stability of earnings.





ALTERNATIVES TO A CASH DIVIDEND

During the last twenty years or so, a number of companies have established ways

of rewarding shareholders other than by traditional dividend payments. These

methods include:

Shareholder perks

Several UK companies (notably hotel operators) offer discounts to shareholders on

room bookings and restaurant meals. A number of transport companies offer

reductions in fares. Some retailers provide discount vouchers, which are sent to

shareholders at the same time as the annual report and accounts.

Scrip dividends

When the directors of a company consider that they must pay a certain level of

dividend, but would really prefer to retain funds within the business, they can

introduce a scrip dividend scheme.

This involves giving ordinary shareholders the choice of a cash dividend or newly

created shares in the company of a similar monetary value. Scrip dividend plans

were very popular in the 1990s since they enabled companies to use share

premium accounts to create the new shares (instead of reducing retained profits)

and there were certain tax advantages for the company.

However a change in the accounting regulations subsequently forced companies to

charge the profit and loss account with the scrip dividend, and a later change in UK

legislation removed the tax advantages, which companies had enjoyed. Therefore

UK companies abandoned scrip dividend schemes at the turn of the century,

although there is now evidence of a few companies re-introducing this method (e.g.

Millennium and Copthorne Hotels plc and Whitbread plc).

Dividend reinvestment plans (DRIPs)

Since many companies had spent the 1990s persuading shareholders to take more

shares in the company (rather than receive a cash dividend) shareholders were

keen for an alternative to be offered when scrip dividend schemes were abandoned.

In the early years of the 21st century DRIPs were created. Shareholders opting for

these schemes choose to have their dividends used to purchase existing shares in

the company on the open market, through a special arrangement involving very

low dealing charges and the payment of stamp duty.

Share repurchases

Companies with cash surpluses, but having no positive NPV projects, may choose to

introduce a share buy-back scheme, whereby the company’s shares are purchased

at the company’s instructions on the open market.

This will have the effect of using up the surplus cash, increasing future EPS

(because of the reduction in the number of shares in issue), changing the gearing

level of the company and (hopefully) reducing the likelihood of a takeover.

However share repurchases are often seen as an admission that the company

cannot make better use of shareholders’ funds.





Parabat plc

Parabat plc has an issued capital of 2 million ordinary shares of 50p each and no

fixed interest securities. It has paid a dividend of 70p per share for several years,

and the stock market generally expects that level to continue. The market price is

£4.20 per share, cum div.

The firm is now considering the acceptance of a major new investment which would

require an outlay of £500,000 and generate net cash receipts of £120,000 per

annum for an indefinite period. The additional receipts would be used to increase

dividends.

Parabat is appraising three alternative sources of finance for the new project:

(i) Retained earnings. The usual annual dividend could be reduced. Parabat

currently holds £1.4 million for payment of the dividend which is due in the

near future.

(ii) A rights issue of ordinary shares. One new share would be offered for every

ten shares held at present at a price of £2.50 per share; the new shares

would rank for dividend one year after issue, when cash receipts from the new

project would first be available.

(iii) An issue of ordinary shares to the general public. The new shares would rank

for dividend one year after issue.

Assume that, if the project were accepted, the firm’s expectations of future results

would be discovered and believed by the stock market, and that the market would

perceive the risk of the firm to be unaltered.

You are required to:

(a) Estimate the price ex div of Parabat’s ordinary shares, following acceptance of

the new project, if finance is obtained from (i) retained earnings or (ii) a

rights issue.

(b) Calculate the price at which the new shares should be issued under option (iii)

assuming the objective of maximising the gain of existing shareholders.

(c) Calculate the gain made by present shareholders under each of the three

finance options.

Ignore taxation and issue costs of new shares





Parabat plc solution

(a) This is a company financed entirely by equity, hence the dividend valuation

model can be used to find the cost of capital i.e.

Ke = )divex( P

D

0 −

Ke = ( )p70p420

p70

− =

p350

p70 = 20%

(i) Financed by retained earnings

Here the valuation model incorporating a new project can be used i.e.

New Price = capital equity of tcos

increase futuredividend existing +

Future increase per share = 000,000,2

000,120£ = 6p

Hence new price = 20.0

p6p70 + = £3.80

(ii) Financed by rights issue

First the new dividend per share must be calculated, and then the new

ex div price

Future expected earnings £1,400,000 + £120,000 = £1,520,000

Future number of shares 2,000,000 + 200,000 = 2,200,000

Future dividend per share = 000,200,2

000,520,1£ = 69p approx

New price = 20.0

p69 = £3.45

(b) Issue of ordinary shares to the public

The issue price can be calculated by reference to the change in wealth of the

shareholders i.e.

New market value = old market value + NPV of new project

Old market value = 2m shares x £3.50 = £7m

NPV of new project = 000,500£20.0

000,120£− = £100,000

Therefore new market value = £7,100,000

Issue price per new share should be 000,00,0,2

000,100,7£ = £3.55p

As £500,000 is required, this would result in the issue of (£500,000 ÷ £3.55)

= 140,845 new 50p shares.





This can be checked as follows:

Total number of shares x Market Price = Market Value of company

2,140,845 shares x £3.55 per share = £7,600,000

Expected dividend now equals £1,520,000.

Hence the return of 00,600,7

000,520,1£ = 20% to the shareholders has been

maintained.

(c) Gain made by present shareholders under each option:

Retained

Earnings

Rights

Issue

New

Issue

£ £ £

Expected future value 3.80 3.80* 3.55

Current value per share 3.50 3.50 3.50

Gain 0.30 0.30 0.05

Less: Dividend foregone 000,000,2

000,500£ 0.25

Paid for rights issue 10

50.2£

0.25

___ ___ ___

Net gain per share £0.05 £0.05 £0.05

* This represents 1.1 shares @ £3.45 each (i.e. allowing for the 1 for 10

rights issue).

Hence the gain to the original shareholders is 5p per share in each case,

whatever the method of financing. The NPV of the project (i.e. £100,000) has

been allocated over the 2,000,000 shares already on issue, irrespective of

whether the project has been financed by retentions, a rights issue or a

correctly priced issue of shares to the general public.

Hence the dividend decision was “irrelevant”.




Chapter 14

Management of international trade

and finance



CHAPTER 14 – MANAGEMENT OF INTERNATIONAL TRADE AND FINANCE


CHAPTER CONTENTS

INTERNATIONAL TRADE ----------------------------------------------- 303

FREE TRADE AND PROTECTIONISM 303

TRADE BLOCKS 303

GATT AND THE WORLD TRADE ORGANISATION (WTO) 304

MULTINATIONAL COMPANIES (MNCS) 304

THE BALANCE OF PAYMENTS 304

THE INTERNATIONAL FINANCIAL INSTITUTIONS 305

THE EUROMARKETS 305

THE GLOBAL DEBT PROBLEM 306

RISKS OF FOREIGN TRADE 306

SOURCES OF FINANCE FOR FOREIGN TRADE 307

COUNTERTRADE 308

ARTICLE FROM STUDENTS’ NEWSLETTER ---------------------------- 309





INTERNATIONAL TRADE

International trade occurs to allow companies to enjoy economies of scale, increase

their turnover and profits, use up spare capacity and to promote division of labour.

In economics, theoretical justifications of the benefits of international trade were

put forward by:

● Adam Smith – the theory of absolute advantage

● David Ricardo – the theory of comparative advantage

Sources of advantage may include close proximity to raw materials or markets,

access to capital or an available labour force with the necessary skills.

Free trade and protectionism

Free trade is the unhindered movement of goods and services throughout world

markets.

Protectionism aims to boost the economic wealth of the country concerned through

government measures which prevent free trade. However retaliatory measures

may defeat such government action. Protectionist measures may include:

● Tariffs

● Import quotas

● Bureaucratic regulations (red tape)

● Exchange controls

● Government subsidies to domestic industries

● Imposition of import licenses

● Devaluation of the currency – making imports more expensive

● Subsidies to exporters

Trade blocks

Trade blocs arise where a group of countries conspire to promote trade between

themselves. Trade blocs include:

● Free trade area – free movement of goods and services (no internal tariffs)

between member countries, with external tariffs set individually e.g. North

American Free Trade Area (NAFTA)

● Customs union – no internal tariffs between member countries and with

common external tariffs against non-member countries e.g. the former

European Economic Community

● Common market – no internal tariffs, common external tariffs, as well as the

free movement of labour and capital between member countries e.g.

European Union





GATT and the World Trade Organisation (WTO)

The General Agreement on Tariffs and Trade was set up in 1947 with the aim of

achieving agreements between trading nations to reduce protectionism and to free

international trade by the progressive removal of artificial barriers. Several rounds

of agreement were achieved - notably the Kennedy Round in the mid 1960s, the

Tokyo Round in the late 1970s and the Uruguay Round which ended in 1994.

The treaty at the conclusion of the Uruguay Round created the WTO as a

replacement body to continue the work of GATT into the future. GATT ceased to

exist in 1994.

The WTO will press for future reductions on trade barriers in areas such as

agriculture, textiles, intellectual property rights and services. The WTO, based in

Geneva, currently has a membership of about 150 countries. Membership obliges

countries to sign up to an extensive range of agreements, rather than be selective,

as was the case with GATT.

Multinational companies (MNCs)

A MNC owns or controls production or service facilities based in a number of

overseas countries. MNCs may engage in “foreign direct investment” (FDI) in order

to seek markets, raw materials, knowledge, production efficiency, or safety from

political interference. Horizontal or vertical integration and product specialisation

have fuelled the growth of companies such as General Motors, Royal Dutch Shell,

BP Amoco, Nissan and Hitachi and many MNCs now have annual turnovers

exceeding the GNPs of several large countries.

The balance of payments

The balance of payments is a statistical record of a country’s international trade

transactions (current account) and capital transactions with the rest of the world

over a period of time e.g.

UK balance of payments 2010

£bn

Current account

Exports 200

Imports (215)

Visible balance (15)

Invisibles balance 5

(10)

UK external assets and liabilities: net transactions 2

Balancing item 8

10

N.B. The statistics that are gathered are not wholly perfect and some transactions

will be omitted. Thus the balancing item is unavoidable.

Temporary deficits can be financed by short term borrowing, but persistent balance

of payments deficits usually require government intervention, such as:

● Devaluation of the currency or government intervention on the foreign

exchange markets





● Raising interest rates

● Restricting the money supply

● Imposing tariffs or import quotas

The international financial institutions

International Monetary Fund (IMF)

Founded in Bretton Woods, New Hampshire in 1944 with the aim of promoting

world trade and maintaining global monetary stability. Assists countries with

balance of payments problems by making loans in the form of Special Drawing

Rights.

Such loans are normally dependent upon the country concerned making strict

internal financial adjustments to solve their economic problems.

The International Bank for Reconstruction and Development

(IBRD)

Popularly known as the World Bank, it was also created at Bretton Woods in 1944,

with the aim of financing the reconstruction of Europe after the Second World War.

The World Bank is now an important source of long-term low interest funds for

developing countries.

The Bank for International Settlements (BIS)

Established in Basle, Switzerland in 1930, it acts as a supervisory body for central

banks assisting them in the investment of monetary assets. It acts as a trustee for

the IMF in loans to developing countries and provides bridging finance for members

pending their securing longer term finance for balance of payments deficits.

The Euromarkets

The Euromarkets refer to transactions between banks and depositors/borrowers of

Eurocurrency.

● Eurocurrency refers to a currency held on deposit outside the country of its

origin e.g. Eurodollars are $US held in a bank account outside the USA

● Eurocurrency loans are bank loans made to a company, denominated in a

currency of a country other than that in which they are based. The term of

these loans can vary from overnight to the medium term.

● Eurobonds are bonds issued (for 3 to 20 years) simultaneously in more than

one country. They usually involve a syndicate of international banks and are

denominated in a currency other than the national currency of the issuer.

Interest is paid gross.

● Euronotes are issued by companies on the Eurobond market. Companies

issue short-term unsecured notes promising to pay the holder of the Euronote

a fixed sum of money on a specified date or range of dates in the future.

● Euroequity market refers to the international equity market where shares in

US or Japanese companies are placed on as overseas stock exchange (e.g

London or Paris). These have had only limited success, probably due to the

absence of a effective secondary market reducing their liquidity.





The global debt problem

This problem arose following the oil price increases in the 1970s, when the OPEC

countries invested their large surpluses with banks in the western world. The

banks then lent substantial sums to the less developed countries (LDCs) believing

the default risk to be low. The oil price rises fuelled inflation and interest rates

increased, forcing the developed countries into recession.

High interest rates and reduced exports placed LDCs in a situation where they could

no longer pay interest or repay loans. These problems made economic conditions

in many LDCs extremely difficult, affecting the position of multinationals and

making international banks less willing to lend.

Methods of dealing with such excessive debt burdens have been:

● A programme of debt write-offs by banks and other lenders

● Rescheduling existing debt repayments

● Re-selling debt at a discount to recoup capital

● Provision of additional loans where the debt problem is regarded as temporary

● Drastic changes in the economic policies of the LDC imposed and monitored

by the IMF

Risks of foreign trade

Importing from and exporting to foreign countries includes the following categories

of risk:

● Currency risk – sometimes referred to as “exchange rate risk”. It involves the

possibility of financial gains or losses arising out of unpredictable changes in

exchange rates. It can be classified into

o Translation risk – the gains or losses to be reported when overseas

operations are consolidated into group accounts in accordance with

SSAP 20/UITF 9, or IAS 21 and 29,or FRS 23 and 24 .

o Economic risk – the possibility that the value of the overseas entity

(based upon the PV of all future cash flows) will change due to

unexpected exchange rate movements arising at sometime in the future.

o Transaction risk – the gains or losses that are made when ultimate

settlement occurs at a date when the exchange rate differs from the rate

prevailing at the date of the original transaction. This is seen as the

short-term manifestation of economic risk. It is this category of foreign

currency risk, which is particularly relevant to this syllabus.

● Political risk – the possibility of the financial success of a venture being

affected by the actions of an overseas government or population.

Government agencies can advise on potential risks.

● Physical risk – the likelihood of damage or theft arising from the physical

distances involved and the length of time between despatch and receipt of the

goods by the customer. Normal commercial insurance is, of course, available.

● Credit risk – this is the risk of non-payment for the goods/services involved in

an export transaction. Insurance cover for up to 180 days can be provided by

NCM UK; for longer periods the ECGD may provide this service. Private sector

companies such as Trade Indemnity plc provide similar services.





● Trade risk – the overseas customer may refuse to accept the goods and be

uncooperative in returning them, thus taking advantage of the long physical

distances involved.

● Liquidity risk – this is caused by the duration of the delivery period and the

lengthy periods of credit expected by some overseas customers.

● Cultural risk – there may be misunderstandings caused by differences in trade

practice, religious and moral attitudes, legal systems and language barriers.

Sources of finance for foreign trade

● Bank overdrafts – either in sterling or in the overseas currency

● Bills of exchange – a negotiable instrument drafted by the exporter (the

drawer), accepted by the importer (the drawee) who thereby agrees to pay

for the goods/services either immediately or more commonly after a specified

period of credit. If the importer accepts the bill it is known as a “trade bill”,

whereas if the importer arranges for its bank to accept the bill, it becomes a

less risky “bank bill”.

Where payment will be made after the specified period of credit, the exporter

can sell the bill at a discount to its face value and receive the cash

immediately. If the bill is dishonoured the exporter can seek legal remedies

in the country of the importer.

● Promissory notes – similar, but less common than bills of exchange, since

they cannot usually be discounted prior to maturity.

● Documentary letters of credit – the importer obtains a Letter of Credit from its

bank, which guarantees payment to the exporter via a trade bill. Though slow

to arrange, this method is virtually risk free provided the exporter presents

specified error free documents (e.g shipping documents, certificates of origin

and a fully detailed invoice) within a specified time period. The high bank fees

for this procedure are normally borne by the importer, and the DLC is

normally reserved for expensive goods only.

● Factoring – the factoring company (often the subsidiary of a bank) assumes

the responsibility for collecting the trade debts of another – in this case an

exporter. The factor may provide a range of services e.g. providing advances,

administering the sales ledger, credit insurance etc for an additional fee.

Widely regarded as a useful means of obtaining trade finance and collecting of

debts for small or medium sized exporters. However the exporter must

always bear in mind the eventual consequences of dispensing with the

services of the factor and undertaking the running of the sales ledger and

cash collection activities itself.

● Forfaiting – a medium term source of finance whereby a domestic bank will

discount a series of medium term bills of exchange, which have normally been

guaranteed by the importers bank. The forfaiting bank normally forgoes the

right of recourse to the exporter if the bill is dishonoured. The exporter

obtains the benefit of immediate funds, but the bank charges are expensive.

Forfaiting is normally used for the export of capital goods, where the importer

pays in a series of instalments over a period of years.





● Leasing and hire purchase – the exporter sells capital goods to a lessor, which

in turn enters into a leasing agreement with the exporter’s overseas

customer. Alternatively the equipment can be sold to a hire purchase

company which resells to the importer under a HP agreement.

● Acceptance credits – a large reputable exporter can arrange for its bank to

accept bills of exchange (which are related to its export activities) on a

continuing basis. These bills can then be discounted at an effective cost,

which is lower than the bank overdraft interest rate.

● Produce loans – where an importer acquires commodities for the purpose of

immediate resale, it can raise a loan from its bank, which takes custody of the

goods until the importer is able to sell them. Thereafter the principal sum,

interest and storage costs are repaid to the bank out of the proceeds of the

sale.

● Requesting payment in advance from the importer – if this were possible it

would avoid all of the above complications.

Countertrade

This is an agreement in which the export of goods to a country is matched by a

commitment to import goods from that country. This usually occurs because the

foreign importing country either lacks foreign currency, has exchange controls in

place or where there are barriers to imports which can be circumvented by means

of countertrade.

The volume of countertrade is now reported at about 30% of total international

trade. In the case of some Eastern European and Third World countries it is the

only way of organising international trade because of their shortage of foreign

currency. Many countertrade deals can be highly complex involving many parties.





ARTICLE FROM STUDENTS’ NEWSLETTER

This is a slightly updated version of an article, which appeared in the November

1999 edition of Students’ Newsletter. The article was not originally intended for

Paper 3.7 or Paper P4 students, but it provides a useful insight into the introduction

of the Euro. You are therefore asked not to learn the contents of this article in

detail, but to gain an overall insight into the features of the single European

currency and the arguments in favour and against the entry of the UK into the

European Monetary Union. The author, John O’Toole, is a lecturer at Griffith

College, Dublin.

EUROPEAN MONETARY UNION AND THE SINGLE EUROPEAN CURRENCY

In 1998, the Heads of State or Government of the European Union (EU) Member

States confirmed that 12 Member States qualified to form Economic and Monetary

Union (EMU) and adopt the single currency, the euro, from 1 January 1999. The

twelve original member states of the “Eurozone” were Austria, Belgium, Finland,

France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal and

Spain. On 31 December 1998 the Council of Economic and Finance Ministers

irrevocably fixed the conversion rates to apply between the currencies of these

Member States and the euro, and on 1 January 1999 the euro came into being.

The United Kingdom and Denmark exercised their Treaty opt-outs from EMU and

Sweden deliberately failed to fulfil all the criteria for entry and was therefore

rejected by the Commission.

Slovenia also joined the Eurozone on 1 January 2007, followed by Malta and Cyprus

on 1 January 2008. In addition, three European microstates (Vatican City, Monaco,

and San Marino), although not EU members, have adopted the euro via currency

unions with member states. Andorra, Montenegro, Kosovo, and Akrotiri and

Dhekelia have adopted the euro unilaterally despite not being EU members.

Nine relatively new EU member states are required by their Accession Treaties to

join the Eurozone, on 1 January of the following years:

Slovakia in 2009, Lithuania in 2010, Estonia in 2011, Bulgaria, Czech

Republic, Hungary, Latvia and Poland in 2012 and finally Romania in 2014.

The formation of EMU and the creation of the euro were the culmination of a

process of preparation which had been going on since the signing in 1992 of the

Treaty on European Union (the Maastricht Treaty). EMU is one of the most far-

reaching steps in the history of the European enterprise.

Internally, the single currency was intended contribute to a greater sense of

common purpose and common endeavour among the peoples of the European

Union; externally it is intended to strengthen the Union’s ability to play a role in the

world commensurate with its economic and political importance.

The European Monetary System (EMS)

To understand why this single currency was set up it is necessary to look at the

previous arrangements.

The idea of a single currency in Europe is not new. It goes back at least to 1970.

While its fortunes have varied since, the then European Community never lost sight

of it as a goal. The European Monetary System (EMS) and its Exchange Rate

Mechanism (ERM), which were set up in 1979, were intended to move towards

monetary union. The Single Market programme of the late 1980s gave fresh

impetus to it.





In April 1978 at a meeting of the European Heads of State the German Chancellor

Schmidt and the French President, Giscard d’Estaing, proposed the creation of a

European Monetary System (EMS) with the purpose of creating a zone of monetary

stability in Europe. In March 1979 the EMS commenced operations in the hope that

closer monetary co-operation between member states would lead to monetary

stability and economic growth. The EMS utilised a system of quasi-fixed exchange

rates, known as the Exchange Rate Mechanism (ERM), and had as its unit of

account the European Currency Unit (ECU). The value of the ECU was the weighted

average of a basket of national currencies with the weight allocated to each

currency being determined by that country’s GNP and intra-EC trade.

Those countries which were members of the ERM declared a central exchange value

for their currency and the majority of currencies agreed to fluctuate within a band ±

2.25% of this central value. This meant that the Central Bank of each participating

currency was committed to intervening, when necessary, in order to maintain their

exchange rate within the specified band. This was done by buying their own

currency when it was weak and selling their currency when it was strong. The UK,

although a member of the EMS since its inception, did not join the ERM until

October 1990.

The rules of the EMS allowed governments to realign the central value of their

exchange rate if changing circumstances showed it to be no longer appropriate. In

the early part of the EMS from 1979 to 1983 there were a number of realignments.

However, from 1987 the system became very rigid and there was only one

realignment from 1987 – the lira was realigned in January 1990 – until the currency

crisis in 1992.

The currency crisis

Speculators interpreted a number of developments in the world economy during

1992 as being attributable to fundamental weaknesses within currency markets.

This perception stimulated a period of intense speculative pressure which caused a

currency crisis.

German unification was a principal cause of the currency crisis. It is difficult to

imagine a bigger shock to the fixed parities of the ERM than the absorption of the

then East Germany into the European economy. Demand for consumer goods

soared, pushing up inflation. The government’s budget expanded adding to the

Bundesbank’s (German Central Bank) alarm. Very low, short-term American

interest rates caused huge surges of money from the US into Germany, further

fuelling German inflation rates. The Bundesbank reacted by pushing up German

interest rates. These high German interest rates occurred just when the rest of

Europe needed the rates to be low. The German mark was the anchor currency of

the ERM, so no European country could hold its interest rates below those in

Germany. When interest rates in Germany were increased all other EMS countries

followed suit.

Other causes of the currency crisis were the lack of realignments with the EMS, so

that its exchange rates had become increasingly rigid and out of touch with

international developments. Furthermore, the necessary behind the scenes macro-

economic co-ordination was not taking place as EU Member States publicly bickered

over interest rate policy. The existence of widespread unemployment as economic

recession threw millions out of work intensified these tensions.

The straw that broke the camel’s back was 2 June 1992 when the Danish people

rejected the Maastricht Treaty in a referendum. The Danish rejection by 50.7% to

49.3% cast immediate doubt over the whole process of economic and monetary





union. Under EU law, the Danish failure to ratify the Maastricht Treaty made the

treaty null and void. As there had been no realignments within the ERM since

January 1987, the money markets had assumed that the European Union’s political

commitment to EMU meant that the parties were virtually fixed. Doubts over

Maastricht destroyed this assumption. Almost immediately the weaker currencies

came under selling pressure.

The pressure resulted in the devaluation of the Finnish mark, the Spanish peseta,

the Irish punt, the Portuguese escudo and the Swedish krona, in addition to forcing

the UK and Italy to leave the ERM in September 1992. In August 1993, further

speculative pressure against the French franc and the Danish krone led to a

decision to widen fluctuation bands within the ERM to ± 15%. This action

effectively ended the currency crisis.

These events strengthened the political resolve in Europe to introduce Economic

and Monetary Union and the single currency.

The Maastricht Treaty

The Treaty on European Union was signed at the Dutch town of Maastricht in

February 1992. This Treaty became known as the Maastricht Treaty. The

centrepiece of the Maastricht Treaty was the decision to set up a single European

currency.

A single European currency meant that all the participating countries would use the

same currency. The new currency was called the “euro”. It is divided into one

hundred cents.

An essential aspect of a single European currency is the close co-ordination of

economic policies between Member States of the European Union. Economic and

Monetary Union means that the currencies of the member states are locked

irrevocably to one another at the same exchange rate. (Irrevocably means that

these exchange rates cannot be changed afterwards). The EMU depends on a

similar level of development of the economies of the countries which are members.

In order to ensure that the economies of the countries concerned are at similar

levels of development five convergence criteria were developed. These

convergence criteria are economic indicators of the strength of each economy.

Economic and Monetary Union involves:

● an internal market with free movement of persons, goods, services and

capital;

● the irreversible locking of exchange rates;

● a single currency among participating Member States;

● EU management of macro-economic policy with intensified co-ordination of

the economic and budgetary policies of participating countries;

● EU management of market-regulating policies, for example, competition

policy, to ensure every country plays by the same rules;

● a European Central Bank in Frankfurt deciding European monetary policy.

The Stability and Growth Pact is part of the arrangements agreed by those

countries which are part of the EMU. The pact requires Member States in the EMU

to commit themselves to aim for a medium-term budgetary position of close to

balance or in surplus. As part of the process of ensuring that the euro is as stable

as possible, the Stability and Growth Pact is aimed at minimising internal fiscal

imbalances in the short term. The rationale underlying the pact is that in





favourable economic times, Member States should so manage their budgets as to

ensure that they can, over the course of a normal economic cycle, reliably keep

under the 3% ceiling on budget deficits set out in the Treaty. The pact allows for

exceptional circumstances when deficits can exceed 3% of GDP. It provides for

penalties and fines of up to 0.5% of GDP if deficits persist.

The five Maastricht criteria

These criteria are measures of the economy of each country across a number of

headings:

Inflation

The level of inflation must be within 1.5% of the average of the three lowest

inflation countries in the system.

Government borrowing

The amount of Government borrowing is an important measure of the strength of

the economy. The amount of this borrowing as a percentage of the Gross Domestic

Product must be below 60% or making progress towards 60%.

Interest rates

States are permitted a maximum of 2% points above the average of the three

lowest inflation countries.

Budget deficit

This is the toughest and politically most sensitive criterion involving tax policy and

overall debt. Member states must keep their government budget deficit within 3%

of Gross Domestic Product.

Exchange rates

The fifth and final criterion for joining the EMU covers exchange rates. Countries

must carefully manage their exchange rate and must not have unilaterally devalued

their currency within two years.

The timetable to EMU

The timetable to Economic and Monetary Union was decided by European leaders.

On 1 January 1999 the new European currency, the euro, came into being. From

this date there was be no change in the exchange rates of the member countries.

Euro notes and coins were introduced into circulation on 1 January 2002. Dual

circulation of the euro and the legacy currencies of each country continued for a

short period of time. Thereafter participating countries have only used euro notes

and coins.

The arguments in favour of EMU

Transparency

The strongest argument in favour of a single European currency is transparency –

prices of goods in the shops will be in the same currency and this will allow people

to compare prices between euro countries.

Foreign exchange costs

Another advantage is that bank commission charges will no longer be levied on

transactions between the currencies of member states. Economists call these

transaction costs. The EU Commission has estimated that there will be savings of

0.25% of GDP on transaction costs which will improve conditions for trade within





the EU and make EU industry more competitive on world markets. The elimination

of these transaction costs will help also tourism and investment among participating

Member States.

Stability in global trade

The introduction of a single currency will help eliminate exchange rate uncertainty

and currency fluctuations within Europe and with other countries. This will increase

trade among members of the Union and globally. This is because currency

movements can inhibit business people from expanding their sales in other

countries.

Political union

Economic and monetary union is an important step towards closer European

integration.

Interest rates

Interest rates will be lower and fairly uniform in participating countries within the

EMU, and this will reduce costs for government and business.

Price stability

With prices, margins and profits coming under competitive pressure as a result of

the introduction of the single currency, inflation rates will tend to move towards

lower levels under the EMU.

Economic growth and stability

Economic growth will be increased by entering the EMU and there will be increased

attractiveness of participating Member States to foreign investment.

The EMU makes it necessary that Governments act very responsibly as regards tax

and spending.

Fragmentation of Europe

If a country refuses to join, it may be isolated and risk becoming excluded from

important decisions that will apply to it in any event.

Global currency

The euro is emerging as a significant international reserve currency.

The level playing field

The discipline of a single currency prevents individual countries depreciating their

currency to steal competitive advantages over each other. Without a single

currency, there would always be a temptation for some countries to devalue, which

undermines a single market.

The arguments against EMU

Loss of control over economic policy

The most important argument against the EMU is the loss of economic sovereignty.

Countries are no longer able to pursue their own independent economic policies.

This is particularly important in the area of exchange rates. With independent

monetary policies the countries with weaker economies were able to devalue their

currencies. With the EMU, devaluation will not be possible for any reason.

European monetary policy will now be decided by the European Central Bank in

Frankfurt, Germany.

Less flexibility





A disadvantage of joining the EMU would be that countries would have less

flexibility in their economic policies. Under the Stability and Growth Pact countries

will have less economic flexibility.

Loss of national pride

Many countries, like Britain are proud of their currencies as a symbol of economic

success and national cohesion.

Price increases

Some firms might use the transition to the euro to disguise price increases.

The weak currencies

Those in favour of the EMU make much of the benefits of being tied to Europe’s

stronger currencies. There would be powerful pressures on members to bail out

economies that borrow too much. This could be very costly.

Regional disparities

Another disadvantage of the EMU is that it may contribute to greater regional

disparities, especially for more peripheral regions. There may be a tendency for

economic activity to move towards the core of Europe, the golden triangle between

Paris, Hamburg and Rome.

Loss of foreign exchange earnings

A disadvantage of the EMU is the loss of money to the banks for the purchase and

sale of foreign exchange.

One way Street

The EMU sets EU member states on an inevitable track to a federal Europe.

Effectively, once a country signs up it loses control of economic policy. As a result,

national parliaments would be no more than regional town halls within Europe, with

effectively little more power than local government.

Changeover costs

The changeover to the euro involves transition costs for business, public

administrations and financial institutions.

The position of the UK

In a speech in July 1997, the UK Chancellor of the Exchequer specified five

economic tests of the UK’s suitability for EMU membership. The five economic tests

are:

1 Are business cycles and economic structures compatible, so that the UK and

others could live comfortably with euro interest rates on a permanent basis?

2 If problems emerge, is there sufficient flexibility to deal with them?

3 Would joining the EMU create better conditions for firms making long-term

decisions to invest in Britain?

4 What impact would entry into the EMU have on the competitive position of the

UK’s financial services industry, particularly the City’s wholesale markets?

5 Will joining the EMU promote higher growth, stability and a lasting increase in

jobs?

In his statement on the EMU to the House of Commons on 27 October 1997, the

Chancellor assessed these five economic tests. His analysis was based on a UK





Treasury paper published on that date. This concluded that a successful EMU would

bring benefits for the UK economy by securing macro-economic stability and

underpinning a well-functioning single market. This in turn would be good for

investment, growth and employment in the UK economy.

However, reflecting the cyclical divergences between the UK and continental

European economies at this time, the Chancellor concluded it would not be right for

the UK to join the EMU from the outset.

On 23 February 1999 the UK Prime Minister, in a statement to the House of

Commons, launched an Outline National Changeover Plan. In his statement he

indicated that Britain’s intention is that it should join a successful single currency

provided that the five conditions are met. The plan indicated that making a

decision to join the single currency at that time was not realistic but that, should

the economic tests be met, this could be decided at some future time.

Conclusion

The global economic environment is changing fast. This process will continue, and

would continue if the EMU had never been thought of. It involves greater

globalisation of activity, increasing intensification of competition among all the

countries of the world and increasing technological change.

The formation of the EMU marked a substantial change in the economic

environment of the European Union as a whole. This is true for all Member States,

and it is true whether or not they have joined the EMU. Continuation of the status

quo is not an option for any Member State, whether it has joined the EMU or not.

Appendix One: International Financial Institutions

The European Central Bank

A European Central Bank (ECB) to operate the single monetary policy of the euro

was set up on 1 June, 1998. The European System of Central Banks (ESCB) is

comprised of the ECB and the central banks of the Member States. The primary

objective of the ESCB is to maintain price stability. Without prejudice to this

objective, the ESCB supports the general economic policies of the EU with a view to

contributing to the achievement of EU objectives. Briefly, these are to promote

sustainable and non-inflationary growth, a high level of employment and social

protection, economic and social cohesion and solidarity among the Member States.

The basic tasks of the ESCB are to:

● decide and implement the monetary policy of the EU;

● conduct foreign exchange operations;

● hold and manage the official external reserves of the Member States; and

● promote the smooth operation of payment systems

The Maastricht Treaty provides for the strict independence and accountability of the

ECB.





The International Monetary Fund – the IMF

The IMF is a specialised agency within the UN system. It had its origins in the

desire of members of the international community to avoid unemployment and

economic recession. It is the central institution in the international monetary

system and its aims are:

● to promote international monetary co-operation and to allow the expansion of

international trade

● to provide financial support to countries with temporary balance of payments

deficits

● to provide for the orderly growth of international liquidity.

The World Bank

The World Bank (the International Bank for Reconstruction and Development i.e.

the IBRD) assists the economic development of countries by making loans

available. These loans are used to build up the educational system, through new

schools, and the health system, through new hospitals. This helps to reduce

poverty in the developing countries. In recent years the World Bank has

increasingly emphasised environmental protection in its work.




Chapter 15

Hedging foreign exchange risk



CHAPTER 15 – HEDGING FOREIGN EXCHANGE RISK


CHAPTER CONTENTS

HEDGING TECHNIQUES FOR FOREIGN CURRENCY RISK ----------- 319

TRADE IN THE DOMESTIC CURRENCY ONLY 319

MATCHING 319

NETTING 319

LEADING AND LAGGING 320

FORWARD EXCHANGE CONTRACTS 320

SYNTHETIC FOREIGN EXCHANGE AGREEMENTS (SAFE’S) 320

MONEY MARKET HEDGING 321

FOREIGN CURRENCY OPTIONS 321

FINANCIAL FUTURES MARKET 321

CURRENCY SWAPS 321

FINANCIAL TIMES CURRENCY TABLES ------------------------------- 322

THE FOREX MODIFIED BLACK-SCHOLES OPTION PRICING MODEL334

MULTILATERAL NETTING ---------------------------------------------- 343





HEDGING TECHNIQUES FOR FOREIGN CURRENCY RISK

When an enterprise decides to trade internationally, it will become exposed to

exchange rate risk. Indeed, where a company has a long-term overseas

investment (e.g. in a foreign subsidiary), it may wish to hedge its foreign currency

assets by raising a long-term loan in the same foreign currency – whereby

exchange losses or gains on the assets are offset by matching currency gains or

losses on the liability. Sometimes management may consider it appropriate not to

hedge exchange rate risk in order to avoid transaction costs – this must be

carefully considered and not be an outright gamble, which could of course, be

dangerous!!

The main methods of currency risk management are:

Trade in the domestic currency only

If an exporter always invoices in his domestic currency or an importer insists on

paying in his own domestic currency, there is no foreign exchange risk for that

company. However, the risk shifts to the other party in the transaction, which may

not be welcomed by an exporter’s overseas customers.

Matching

When an enterprise has both receipts and payments expected on the same date for

the same amount in the same foreign currency, no formal hedge is really

necessary, since they can be matched against each other.

Netting

When an enterprise has both receipts and payments expected on the same date in

the same foreign currency, but the amounts are different, netting may be

employed. For instance, if a UK company expects to receive €5,000,000 from an

Italian customer and expects to pay €3,700,000 to a Spanish supplier on the same

future date, it would only be necessary to use a formal hedging technique (with the

associated transaction costs) for the net receipt of €1,300,000.

In instances where two group members wish to settle their inter-company

indebtedness using the same currency, the transaction costs associated with

foreign exchange receipts and payments that are payable to banks can be reduced

considerably by employing bilateral netting. In cases where several group

members wish to settle their inter-company indebtedness, large savings in

transaction costs can also be achieved by the use of multilateral netting. These

procedures are illustrated starting on page 343.





Leading and lagging

If an importer believes that the currency that it is shortly expecting to pay will

appreciate against its home currency, it may decide to settle the liability as soon as

possible. This is referred to as leading (and, of course, it may also be possible to

take advantage of an early settlement discount). However, if an importer believes

that the currency it is shortly expecting to pay will depreciate against its home

currency, it may choose to delay payment beyond the due date. This course of

action is known as lagging.

These approaches are not really hedging techniques, they are simply based upon

belief and this will only succeed if the direction of rate movement is correctly

estimated.

Forward exchange contracts

A forward market hedge offers protection against foreign exchange risk through a

company entering into a binding contract with a bank to purchase or sell a specified

quantity of foreign currency at a rate of exchange that is fixed when the contract is

made. The purchase or sale is fixed for a specified date when a company expects

foreign currency payments or receipts, or between two specified dates (an option

forward contract). Most forward contracts are for periods of up to one year, but

longer contracts may be arranged in major currencies.

Synthetic foreign exchange agreements (SAFE’s)

In order to reduce the volatility of their exchange rates, some countries (e.g. China,

Russia, India, Brazil, Philippines and Korea) have attempted to ban forward foreign

exchange trading. In these markets, non-deliverable forwards (NDF’s) have been

developed. Although they resemble forward contracts, no physical currency

delivery actually takes place. Instead, the difference between the actual spot rate

and the NDF rate is calculated. This will result in a profit or loss on the transaction

between the two counterparties, who merely settle with each other for this net

amount.

When this profit or loss is combined with the actual currency exchanged at the

prevailing spot rate, this will effectively fix the ultimate exchange rate in a manner

which resembles a forward exchange contract.

The underlying principles of a SAFE are similar to the procedures employed for a

forward rate agreement (FRA), which is offered by banks for clients who wish to

hedge their interest rate risk. These procedures are dealt with in detail in Chapter

17 “Hedging Interest Rate Risk” starting on page 375





Money market hedging

This involves the company borrowing funds in one currency and exchanging the

proceeds for another currency, often with reinvestment in the second currency. For

example a UK company due to pay a dollar debt in three months time might borrow

pounds now, convert these pounds to dollars at the present spot rate (this fixes the

exchange rate) and invest the dollars in the USA for three months at the end of

which the total proceeds of the investment may be used to pay the dollar debt.

The cost of the money market hedge is directly determined by the interest rate

differential between the two countries concerned. This is in contrast to the cost of

a forward market hedge, which depends upon the forward rates quoted by the bank

(NB these are, of course, indirectly influenced by that interest rate differential, as

explained below under the interest rate parity theory).

Foreign currency options

These offer the right to buy or sell a given amount of foreign exchange at a fixed

price (the exercise price) usually at any time during a specified period. There is

normally a choice of exercise price and maturity date, the price of the option

varying according to the combination of exercise price and maturity date selected.

The price of the option is determined by the difference between the exercise price

and spot rate, maturity, relative interest rates in the countries concerned, currency

volatility and the supply and demand for specific options. The option need only be

exercised if exchange rates move in favour of the option holder; this limits the

“downside risk” of the holder.

Options may be purchased in “standard” sizes and maturities on certain Futures

Exchanges or over-the-counter in major banks to the clients’ particular size and

maturity requirements.

Financial futures market

Several financial futures markets offer foreign currency futures. These offer

purchase or sale of a standard amount of a limited number of foreign currencies at

a specified time and price.

They may be considered as an alternative to the forward foreign exchange market,

but are less flexible and require initial margin and thereafter variation margin may

have to be paid dependent upon subsequent movements in exchange rates.

Currency swaps

These are dealt with in Chapter 18 “Swaps” starting on page 407.





FINANCIAL TIMES CURRENCY TABLES





Illustration 1

(a) Structure of Exchange Rates

The following information on exchange rates was extracted from the Financial

Times several years ago

Pound spot - forward against the pound:

Days spread Close Three months

United States 1.7545 – 1.7710 1.7680 – 1.7690 1.56 – 1.51 cpm

Switzerland 2.2669 – 2.2770 2.2693 – 2.2714 3.39 – 3.73 cdis

Required:

(i) Identify the bank’s buying and selling rates.

(ii) Calculate the three months rates for the US dollar and the Swiss franc.

(b) Determinants of Forward Rates

The spot rate for the $/£ exchange is $1.77. Interest rates in London are

14% p.a. and in New York 12% p.a.

Required:

Ignoring transaction costs calculate the best rate (for the customer) at which

a bank will sell the US $ twelve months forward.

(c) Hedging ‘Forex’ Risk

The following information is available with respect to the $/£ exchange rate

and interest rates in London and New York.

$/£

Spot 1.7680 − 1.7690

Three months 1.56 − 1.51 cpm

Interest rates:

Borrow Lend

London 15% p.a 13% p.a.

New York 10.5% p.a. 8.5% p.a.

Required:

(i) An American customer will pay $3m in three months’ time. Show how

foreign exchange risk can be eliminated using:

(1) forward market cover, and

(2) money market cover.

(ii) You must pay an American supplier $3m in three months’ time. Show

how foreign exchange risk can be eliminated using:

(1) forward market cover, and

(2) money market cover.





Solution 1

(a) The spot and the three month forward rates are:

US Dollars Swiss Francs

(i) Spot 1.7680 – 1.7690 2.2693 – 2.2714

(Prem)/dis (0.0156) – (0.0151) cpm 0.0339 – 0.0373 cdis

(ii) 3 month rates 1.7524 – 1.7539 2.3032 – 2.3087

BANK Sell $ Buy $ Sell SF Buy SF

WE Buy $ Sell $ Buy SF Sell SF

(b) This exchange rate can be calculated from first principles as follows:

Bank borrows at 14% (say) £1,000

Buys $ spot at $1.77 = $1,770

Invests $ at 12% for twelve

months

In one year, the bank has:

$ asset $1,770 x 1.12 = $1,982.4

£ liability £1,000 x 1.14 = £1,140.0

Therefore the bank cannot sell $ forward for more than $1.7389 (i.e. $1,982.4

÷ £1,140).

However the interest rate parity theory can alternatively be used i.e.

Interest rate parity theory (IRPT)

Proponents of this theory claim that the difference between current spot rates and

forward rates is based upon interest rate differentials between the two countries

concerned. Therefore the principle of interest rate parity links the international

money markets with the foreign exchange markets.

Forward rate (Fo) = Current Spot rate rate erestint ome

rate erestint oreignx

h1

f1

+

+ =

+

+×

b

c0

i1

i1 S

Forward rate = $1.77 14.1

12.1× = $1.7389

In this instance the current spot rate is $1.77 = £1, whereas the one year forward

rate is $1.7389 = £1. Thus there is a premium of $0.0311!!

Accordingly, provided this theory holds, where:

Foreign interest rates < UK interest rates, the forward rate is quoted at a

premium,

and where:

Foreign interest rates > UK interest rates, the forward rate is quoted at a

discount.





(c) (i) (1) Forward market hedge

The selling rate in the 3 month forward market (i.e. the banks buying

rate) is $1.7539 (see part a))

By selling forward you will receive $3,000,000 ÷ 1.7539 =

£1,710,474 in three months time.

(2) Money market hedge : exporter case

Has a $ asset therefore must create $ liability

(1) Borrow in USA $3,000,000 ÷ 1.02625* = $2,923,264

(2) Sell $ spot $2,923,264 ÷ 1.7690 = £1,652,495

(3) Invest in UK £1,652,495 x 1.0325# = £1,706,201 proceeds

(4) Repay $ loan with receipts from customer = $3,000,000

*

4

%5.10 = 2.625%

#

4

%13 = 3.25%

It is more effective to hedge in the forward market.

(ii) (1) Forward market hedge

Buy $ forward : $3,000,000 ÷ 1.7524 = £1,711,938

(2) Money market hedge : importer case

Has $ liability therefore must create $ asset

(3) Borrow in UK = £1,661,525

(2) Convert to $ £1,661,525 x 1.7680 = $2,937,577

(1) Invest in USA $2,937,577 x 1.02125* = $3,000,000

(4) Repay £ loan £1,661,525 x 1.0375# = £1,723,832 cost

*

4

%5.8 = 2.125%

#

4

%15 = 3.75%

The forward market cover is cheaper.





Illustration 2 (Oxlake plc)

Oxlake plc has export orders from a company in Singapore for 250,000 china cups,

and from a company in Indonesia for 100,000 china cups. The unit variable cost to

Oxlake of producing china cups is 55 pence, and unit sales price to Singapore

$2.862 and to Indonesia, 2,246 Rupiahs. Both orders are subject to credit terms of

60 days, and are payable in the currency of the importers. Past experience

suggests that there is 50% chance of the customer in Singapore paying 30 days

late. The Indonesian customer has offered to Oxlake the alternative of being paid

US $125,000 in 3 months time instead of payment in the Indonesian currency. The

Rupiah is forecast by Oxlake’s bank to depreciate in value during the next year by

30% (from an Indonesian viewpoint) relative to the $US.

Whenever appropriate, Oxlake uses option forward foreign exchange contracts.

Foreign Exchange Rates (mid rates)

$Singapore/$US $US/£ Rupiahs/£

Spot 2.1378 1.4875 2,481

1 month forward 2.1132 1.4963 No forward

2 months forward 2.0964 1.5047 market exists

3 months forward 2.0915 1.5105

Assume that in the United Kingdom any foreign currency holding must be

immediately converted into pounds sterling.

Money Market Rates (% per year)

Deposit Borrowing

UK clearing bank 6 11

Singapore bank 4 7

Euro-dollars 7½ 12

Indonesian bank 15 Not available

Euro-sterling 6½ 10½

US domestic bank 8 12½

These interest rates are fixed rates for either immediate deposits or borrowing over

a period of two or three months, but the rates are subject to future movement

according to economic pressures.

Required

(a) Using what you consider to be the most suitable way of protecting against

foreign exchange risk, evaluate the sterling receipts that Oxlake can expect

from its sales to Singapore and to Indonesia, without taking any risks.

All contracts, including foreign exchange and money market contracts, may

be assumed to be free from the risk of default. Transactions costs may be

ignored

(b) If the Indonesian customer offered another form of payment to Oxlake,

immediate payment in $US of the full amount owed in return for a 5%

discount on the Rupiah unit sales price, calculate whether Oxlake is likely to

benefit from this form of payment.

(c) Discuss the advantages and disadvantages to a company of invoicing an

export sale in a foreign currency.





Solution 2 (Oxlake plc)

(a) Sales to Singapore

Cross rates S$ to £

Spot 2.1378 x 1.4875 = 3.1800

1 month forward 2.1132 x 1.4963 = 3.1620

2 months forward 2.0964 x 1.5047 = 3.1545

3 months forward 2.0915 x 1.5105 = 3.1592

The management of Oxlake plc may cover the foreign exchange risk in one of

two ways:

1. In the forward currency market

Since the payment date is uncertain the appropriate device is an option

forward contract (sometimes called an option date contract).

(Note: an ordinary forward contract specifies the date of the exchange

and the exchange rates). Option forward contracts specify a period over

which the contract may be completed, at Oxlake’s option. The forward

rate for an option forward contract is the worst rate prevailing during the

period of the option. Oxlake could take out an option forward contract

to sell S$ to be fulfilled between two and three months hence. The rate

will be the worse of the 2 month and 3 month rates (for the seller) i.e.

3.1592.

Sterling received

(3 months hence) =

1592.3

862.2000,250 × =

1592.3$S

500,715$S = £226,481

This is worse than the two month rate:

1545.3$S

500,715$S = £226,819

2. In the money market

Oxlake expects to receive 250,000 x 2.862 = S$715,500 in 3 months’

time. Therefore:

1) Borrow in Singapore S$715,500 ÷ 1.0175* = S$703,194

2) Sell S$ spot S$703,194 ÷ 3.18 = £221,130

3) Invest in Eurosterling £221,130 x 1.01625# = £224,723

(better than UK rate of 6% p.a.) proceeds

4) Repay S$ loan in 3 months time with receipts = S$715,500

*

4

%7 = 1.75%

#

4

%6 21

= 1.625%

Oxlake is best advised to deal in the forward exchange market





Sales to Indonesia

Oxlake will receive 100,000 x 2,246 = 224,600,000 Rupiahs in two months’

time. No forward rate exists so Oxlake cannot cover its position in the

forward market. Furthermore a money market hedge cannot be achieved

since a Rupiah liability cannot be created. However, the management still has

two options using the US$ alternative.

1. Forward currency market

Oxlake may accept the alternative payment of $125,000. It can sell the

$ forward, thus guaranteeing a sterling receipt in 3 months’ time of

125,000 ÷ 1.5105 = £82,754.

2. Money market

1) Borrow in Eurodollar market $125,000 ÷ 1.03* = $121,359

(better than US rate of 12½% p.a.)

2) Sell $ spot $121,359 ÷ 1.4875 = £81,586

3) Invest in Eurosterling £81,586 x 1.01625#= £82,912

(better than UK rate of 6% p.a.) proceeds

4) Repay Eurodollar loan in 3 months with receipts = $125,000

*

4

%12 = 3%

#

4

%6 21

= 1.625%

Oxlake should cover its position in the money market.

(b) Alternative form of payment

Sales value in Rupiahs = 100,000 cups x 2,246 = 224,600,000

Less 5% discount (11,230,000)

Discounted sales value 213,370,000

Using cross rates: 2,481 ÷ 1.4875 = 1,667.90

Proceeds of sale = 90.667,1

000,370,213 = $127,927

The best US$ deposit rate of interest is 8% p.a. in a US domestic bank. The

yield after three months is $127,927 x 1.02* = $130,486. Converted into

sterling, using the three month forward market, this is 5105.1

486,130$

= £86,386.

*

4

%8 = 2%





Alternatively, the US dollar proceeds could be converted immediately into

sterling and then invested for three months in the Eurosterling market. The

calculation is as follows:

(i) Conversion of US$127,927 into sterling yields

4875.1

927,127 = £86,001 i.e.

481,2

000,370,213 = £86,001

(ii) Yield of Eurosterling 3 month deposit

= £86,001 x 1.01625 # = £87,399

#

4

%6 21

= 1.625%

Conclusion: The best yield without the offer of immediate payment was

£82,912. With the alternative form of payment, both the forward market and

the money market yield better returns, with the money market’s £87,399 as

the better form of hedging.

(c) When a company invoices sales in a currency other than its own, the amount

of ‘home’ currency it will eventually receive is uncertain. This may be an

advantage or a disadvantage, depending on changes in the exchange rate

over the period between invoicing and receiving payment. With this in mind,

invoicing in a foreign currency has the following advantages.

● The foreign customer will find the deal more attractive than a similar

one in the exporter’s currency, since the customer will bear no foreign

exchange risk. Making a sale will therefore be that much easier.

● The exporter can take advantage of favourable foreign exchange rate

movements by selling the exchange receipts forward (for more of the

home currency than would be obtained by conversion at the spot rate).

● In some countries, the importer may find it difficult or even impossible

to obtain the foreign exchange necessary to pay in the exporter’s

currency. The willingness of the exporter to sell in the importer’s

currency may therefore prevent the sale falling through.

The disadvantages of making export sales in foreign currency are the reverse

of the advantages.

● The exporter (rather than the foreign customer) bears the foreign

exchange risk

● If the exchange rate movement is unfavourable, the exporter’s profit will

be reduced.





Illustration 3 (Fidden Ltd)

Fidden Ltd is a medium-sized UK company with export and import trade with the

USA. The following transactions are due within the next six months. Transactions

are in the currency specified.

Purchases of components, cash payment due in three months: £116,000

Sale of finished goods, cash receipt due in three months: $197,000

Purchase of finished goods for resale, cash payment due in six months: $447,000

Sale of finished goods, cash receipt due in six months: $154,000

Exchange rates (London market)

$/£

Spot 1.7106 – 1.7140

Three months forward 0.82 – 0.77 cents premium

Six months forward 1.39 – 1.34 cents premium

Interest rates

Three months or six months Borrowing Lending

Sterling 12.5% 9.5%

Dollars 9% 6%

Foreign currency option prices (New York market)

Prices are cents per £, contract size £12,500

Calls Puts

Exercise price ($) March June Sept March June Sept

1.60 − 15.20 − − − 2.75

1.70 5.65 7.75 − − 3.45 6.40

1.80 1.70 3.60 9.90 − 9.32 15.35

Assume that it is now December with three months to expiry of the March contract

and that the option price is not payable until the end of the option period, or when

the option is exercised.

Requirements:

(a) Calculate the net sterling receipts/payments that Fidden Ltd might expect for

both its three and six month transactions if the company hedges foreign

exchange risk on:

(i) the forward foreign exchange market;

(ii) the money market.

(b) If the actual spot rate in six months’ time was with hindsight exactly the

present six months forward rate, calculate whether Fidden Ltd would have

been better to hedge through foreign currency options rather than the forward

market or money market.

(c) Explain briefly what you consider to be the main advantage of foreign

currency options.





Solution 3 (Fidden Ltd)

(a)

Fidden Ltd Buys Sells

$ $

Spot 1.7106 1.7140

3 months 1.7024 1.7063

6 months 1.6967 1.7006

THREE MONTH TRANSACTIONS

1. Forward Cover

Sell $ $197,000 ÷ 1.7063 = £115,454

2. Money Market Cover (Exporter)

1. Borrow in USA at 9% p.a. for 3 months

0225.1

000,197$ = $192,665

2. Convert to £ (sell $ spot) 7140.1

665,192$ = £112,407

3. Invest in UK at 9½% for 3 months

£112,407 x 1.02375 = £115,076

4. Repay loan with $197,000 proceeds

FORWARD MARKET IS MORE LUCRATIVE!

THEREFORE, NET STERLING PAYMENT IS:

(£116,000 − £115,454) = £546

SIX MONTH TRANSACTIONS

1. Forward Cover

Buy $ ( )

6967.1

000,154$000,447$ − =

6967.1

000,293$ = £172,688

2. Money Market Cover (Importer)

3. Borrow in UK at 12½% for 6 months = £166,296

2. Convert to $ (buy $ spot)

£166,296 x 1.7106 = $284,466

1. Invest in USA at6% for 6 months

$284,466 x 1.03 = $293,000

4. Repay £ loan £166,296 x 1.0625 = £176,690

FORWARD MARKET IS CHEAPER!





(b)

We want a right to sell £ in New York, therefore buy put options!

A) $1.70 put costs 3.45 c per £

$1.70 puts require 70.1$

000,293$ = £172,353

500,12£

353,172£ = 14 contracts (approx)

Premium is: 14 x £12,500 x 3.45 c per £ = $6,037.50

In six months:

$ $

14 contracts x £12,500 x $1.70 297,500

Payment to supplier 293,000

Payment of premium 6,037.50

299,037.50

Short by $1,537.50

Total cost

£

14 contracts @ £12,500 175,000

Extra $ 6967.1$

50.537,1$ 906

_______

Total cost of exercising option £175,906

N.B. If the currency option were not exercised, the sterling cost would

be:

6967.1$

50.037,6$000,293$ + = £176,247

B) $1.80 put costs 9.32 c per £

$1.80 puts require 80.1$

000,293$ = £162,778

500,12£

778,162£ = 14 contracts (approx)

Premium is: 14 x £12,500 x 9.32 c per £ = $16,310





In six months:

$ $

14 contracts x £12,500 x $1.80 315,000

Payment to supplier 293,000

Payment of premium 16,310

309,310

Over by $5,690

Total cost

£

14 contracts @ £12,500 175,000

less $ sold 7006.1$

690,5$ (3,346)

_______

Total cost of exercising option £171,654

N.B. If the currency option were abandoned, the sterling cost would be:

6967.1$

310,16$000,293$ + = £182,301

Therefore the purchase of $1.80 put options is the cheapest strategy of

all.

(c) Advantages of foreign currency options

The main advantage of foreign currency options is that they offer a right,

which need not be exercised, to buy or sell foreign currency. If exchange

rates move such that exercising the option is favourable, then the option will

be sold or exercised. If exchange rates move in an unfavourable manner for

the option holder, the option will be allowed to lapse unexercised and the only

cost will be the option premium. Options therefore offer a way of limiting

“downside risk” while offering potentially unlimited returns.





The FOREX modified Black-Scholes option pricing model

Currency options can be priced using an adapted version of the Black-Scholes

model, known as the “Grabbe variant”. The risk free rate of interest is one of the

five components used in the Black-Scholes formula, however the problem that

arises with currency options is that there are two risk free rates to consider – one

for each of the countries whose currencies are involved.

These two interest rates are incorporated into the formula by predicting the forward

rate using the interest rate parity theory. For the more familiar indirect currency

quotes, this is expressed as follows:

Forward rate (Fo) = Current Spot rate rate erestint ome

rate erestint oreign

h1

f1

+

+× =

+

+×

b

c0

i1

i1 S

However, since the Grabbe variant employs direct quotes, the basic formula must

be rearranged as follows:

Forward rate (Fo) = Current Spot rate rate erestint oreign

rate erestint ome

f1

h1

+

+× =

+

+×

c

b0

i1

i1 S

Formulae, which were provided in the 2007 version of the ACCA Formulae sheet for

the FOREX modified Black-Scholes option pricing model are shown below in bold

print:

Value of a currency call option (c) c = e -rt

[ F0N(d1 ) – XN(d2)]

Value of a currency put option (p) p = e -rt

[ XN(–d2 ) – F0N(–d1)]

The values for d1 and d2 in the specification are:

d1 = ( )

Ts

T/2s/XFln 20 +

d2 = Tsd1 −

Where:

F0 = the forward rate, calculated using the interest rate parity formula (as

above)

X = the current spot rate employing direct quotes

r = the continuous compound domestic (home) risk-free interest rate

The remaining symbols have already been introduced in the basic Black-Scholes

option pricing model. Notice that the ACCA have used both T and t to represent the

remaining life of the option, expressed in years and percentages thereof.

The 2011 version of the ACCA Formulae sheet has omitted this FOREX modified

formulae. However this topic has not yet been officially removed from the revised

P4 syllabus. Accordingly, this subject is retained within these Class Notes pending

formal clarification.





Illustration 4

Sophie plc (a British company) is planning to undertake a construction project in

Belgium and in three months time expects to learn whether its tender has

succeeded. In that event, an immediate euro (€) payment will have to be made.

The corporate treasurer intends to hedge this payment using € currency options.

Relevant information is as follows:

£/€ direct spot rate £0.80 = €1

€/£ indirect spot rate €1.25 = £1

Three month £ LIBOR 4.5% p.a.

Three month € EURIBOR 3% p.a.

Volatility (σ) of the € against £ 20% p.a.

Required

Calculate the premium on a three month € “at the money” call option with an

exercise price of £0.80 = €1.

Solution 4

Forward rate (F0) = Current Spot rate f1

h1

++

×

= £0.8 ( )

( )%312/31

%5.412/31

×+×+

× = £0.8 0075.1

01125.1× = £0.803

X = 0.8

F0 = 0.803

r = 0.045

T/t = 0.25

s = 0.2

d1 = ( ) ( )

25.02.0

225.02.08.0803.0ln 2 ÷×+÷ =

1.0

005.000374.0 + = 0.0874

d2 = 0.0874 – 0.2 25.0 =–0.0126

Using the standard normal distribution tables:

d1 = 0.0874 (i.e. 0.09) gives 0.0359

d2 = –0.0126 (i.e. – 0.01) gives –0.004

N(d1) = 0.5 + 0.0359 = 0.5359

N(d2) = 0.5 – 0.004 = 0.496

c = e-(0.045 x 0.25) [0.803 x 0.5359 – 0.8 x 0.496]

= 0.9888 x [0.43033 – 0.3968]

= £0.03315 i.e. 3.315p per €





Illustration 5 Marion Inc

Marion Inc., a company based in the USA, is taking legal action for breach of

copyright against an Italian competitor. The matter will be resolved in nine months

time and, if successful, Marion Inc. will benefit from an immediate euro (€) receipt.

The corporate treasurer intends to hedge this receipt using € currency options.

Relevant information is as follows:

$/€ direct spot rate $1.3249 = €1

€/$ indirect spot rate €0.7548 = $1

Three month $ Federal Reserve rate 5% p.a.

Three month € EURIBOR 3% p.a.

Volatility (σ) of the € against $ 25% p.a.

Required:

Calculate the premium on a nine month € “at the money” put option with an

exercise price of $1.3249 = €1.

Solution 5

Forward rate (F0) = Current Spot rate x f1

h1

++

= $1.3249 x ( )( )%3 1291

%5 1291

×+

×+

= $1.3249 x 0225.1

0375.1 = $1.3443

X = 1.3249

F0 = 1.3443

r = 0.05

T/t = 0.75

s = 0.25

d1 = ( ) ( )

75.025.0

275.025.03249.13443.1ln 2 ÷×+÷

= 2165.0

02344.001454.0 + = 0.1754

d2 = 75.025.01754.0 − = -0.0411


d1 = 0.1754 (i.e. 0.18) gives +0.0714

d2 = – 0.0411 (i.e. – 0.04) gives –0.0160

N(–d1) = 0.5 – 0.0714 = 0.4286

N(–d2) = 0.5 + 0.0160 = 0.5160

p = e-(0.05 x 0.75) [1.3249 x 0.5160 – 1.3443 x 0.4286]

= 0.9632 x [0.68365 – 0.57617]

= $0.10353 i.e. 10.353 cents per €





Illustration 6 (currency futures)

A UK company imports from the USA and is invoiced for $297,500 payable in

October.

$/£ spot rate 1.7500 – 1.7520

October forward 1.7000 – 1.7015

Required

(a) Show how a forward market hedge would be carried out.

(b) Show how a futures market hedge would be carried out (one £ futures

contract represents £12,500 and December £ futures are priced at $1.70).

What would be the result in October of the futures market hedge in each of

the following independent circumstances?

(i) The $/£ spot turned out to be $1.5000 – $1.5020 and December £

futures were then priced at $1.50?, and

(ii) The $/£ spot turned out to be $1.7800 – $1.7820 and December £

futures were then priced at $1.78?





Solution 6

IMPORTER SITUATION

(a) Forward market hedge

7000.1$

500,297$ = £175,000

(b) Futures market hedge

70.1$

500,297$ = £175,000

500,12£

000,175£ = 14 contracts

Situation (i)

The UK importer requires protection against a weakening £. As the $

strengthened to $1.5000 = £1 by October, he would have to pay ($297,500

÷ 1.5000) £198,333 to clear his obligation.

Obviously he could protect his exposure to foreign exchange risk by SELLING

14 December £ futures contracts NOW at $1.70, and then closing his position

by BUYING a similar number of December £ futures when the price has moved

to $1.50. Clearly the ($0.20 x £12,500) $2,500 gain on each of the 14

futures contracts i.e. $35,000 would be converted at the then spot rate

$1.5000 to provide £23,333 which would compensate for the adverse

movement on the foreign exchange market i.e.

CASH MARKET £

Payment to supplier ($297,500 ÷ 1.5000) = 198,333

FUTURES MARKET $

Now: SELL 14 contracts 1.70

In October: BUY 14 contracts 1.50

Gain per £ $0.20

Total Gain 000,35$1£

20.0$500,12£contracts 14 =

××

In £: ($35,000 ÷ 1.5000) = (23,333)

TOTAL COST £175,000





Situation (ii)

CASH MARKET £

Payment to supplier ($297,500 ÷ 1.7800) = 167,135

FUTURES MARKET $

Now: SELL 14 contracts 1.70

In October: BUY 14 contracts 1.78

Loss per £ $(0.08)

Total loss 000,14$1£

08.0$500,12£contracts 14 =

××

In £: ($14,000 ÷ 1.7800) = 7,865

TOTAL COST £175,000

As can be seen from the above calculations, hedging with a futures contract

means that any profit or loss on the underlying will be offset by any loss or

profit made on the futures contract. In practice, a perfect hedge is unlikely

because of:

● The “round sum” nature of futures contracts, which can only be bought

or sold in whole numbers, and

● Basis risk i.e. the possibility of variability in the prices of the two related

securities in the hedging arrangement. For example, if changes in the

price of the currency future do no perfectly match the change in the

price of the underlying security then a profit or loss may occur on the

hedge position. This potential variability in the outcome of a hedge is

referred to as “basis risk”.

Since this example had a precise round number of contracts and there was no

basis risk, the total cost is the same whatever the actual exchange rate.





Illustration 7 currency options

(a) Explain briefly what is meant by foreign currency options and give examples

of the advantages and disadvantages of exchange traded foreign currency

options to the financial manager.

(b) Exchange traded foreign currency option prices in Philadelphia for

dollar/sterling contracts are shown below:

Sterling (£12,500) contracts

Calls Puts

Exercise price

($)

September December September December

1.90 5.55 7.95 0.42 1.95

1.95 2.75 3.85 4.15 3.80

2.00 0.25 1.00 9.40 -

2.05 - 0.20 - -

Option prices are in cents per £. The current spot exchange rate is $1.9405 -

$1.9425/£.

Required:

Assume that you work for a US company that has exported goods to the UK

and is due to receive a payment of £1,625,000 in three months time. It is

now the end of June.

Calculate and explain whether your company should hedge its sterling

exposure on the foreign currency option market if the company’s treasurer

believes the spot rate in three months time will be:

1. $1.8950 − $1.8970/£.

2. $2.0240 − $2.0260/£.





Solution 7

(a) A foreign currency option is a financial instrument, which gives the buyer of

the option the right, but not the obligation, to buy or sell a currency at a

specified rate of exchange (normally) at any time up to a specified date.

Advantages include:

● They limit downside risk whilst allowing companies to take advantage of

favourable foreign exchange rate movements.

● They are a useful hedge against exchange risk when a company is

unsure whether a future foreign exchange risk will occur, for example,

when tendering for a contract which it might not obtain, or issuing a

price list in foreign currencies.

● They provide an effective currency hedge, especially when foreign

exchange markets are volatile.

Disadvantages include:

● Cost. A premium is payable when the option is arranged, whether or

not the option is exercised.

● Exchange traded options are only available in a small number of

currencies with specific expiry dates (OTC options are much more

flexible).

(b) Any belief about future spot exchange rates by the company’s treasurer is a

personal viewpoint and, if acted upon, could leave the company exposed to

foreign exchange risk. If the company is worried about foreign exposure it

should hedge the risk using options, forward contracts or other techniques no

matter what the treasurer personally believes the future spot rate will be.

If the company acts upon the treasurer’s forecasts it will need to sell sterling

for dollars, i.e. buy put options on sterling. £1,625,000 will require

(£1,625,000 ÷ £12,500) 130 contracts.

1. $1.8950 - $1.8970/£.

The relevant future spot rate for selling £ for $ is $1.8950/£, since a

bank would obviously hand over the lower number of $ for each £ sold.

If the future spot rate is $1.8950, the company would receive (£1.625m

x $1.8950) i.e. $3,079,375 using the spot market. The £ is expected to

weaken relative to the dollar. September options are available at

exercise prices of $1.90, $1.95 and $2.00. At all of these prices the

option will be exercised.

At $1.90 $

Receipts are £1.625m x $1.90 3,087,500

Option cost of £1.625m x $0.0042 (6,825)

Net $3,080,675

At $1.95 $

Receipts are £1.625m x $1.95 3,168,750

Option cost of £1.625m x $0.0415 (67,438)

Net $3,101,312





At $2.00 $

Receipts are £1.625m x $2.00 3,250,000

Option cost of £1.625m x $0.0940 (152,750)

Net $3,097,250

All three options result in higher expected dollar receipts than using the

spot market in three months (excluding any further transactions costs).

Selection of the $1.95 exercise price would give the highest expected

receipts.

2. $2.0240 - $2.0260/£.

If the spot rate for buying dollars in three months time is $2.0240/£

then, if purchased, the options would not be exercised as using the spot

rate in three months would give higher dollar receipts (i.e. £1.625m x

$2.0240 = $3,289,000) than any of the available option exercise prices.

Therefore, the company would not purchase currency options.

It must be stressed that this would leave the company exposed to

foreign exchange risk, as the spot rate in three months time could be

very different to the rate forecast by the treasurer.





Multilateral netting

This is a procedure whereby the debts of the different group companies

denominated in a given currency are netted off against each other. The principal

benefit is that foreign exchange purchase costs, including commission, the buy/sell

spread and money transmission costs are reduced. Additionally, it will reduce the

loss of interest earned. This is because funds spend less time in transit.

Illustration 8

Forun plc, a UK registered company, operates with four subsidiaries in different

foreign countries. It has a number of intra-group transactions with its four foreign

subsidiaries in six months time. These are summarised below denominated in US

dollars:

Paying company

Receiving company UK Sub 1 Sub 2 Sub 3 Sub 4

$US’000

UK - 300 450 210 270

Subsidiary 1 700 - 420 - 180

Subsidiary 2 140 340 - 410 700

Subsidiary 3 300 140 230 - 350

Subsidiary 4 560 300 110 510 -

Required

Explain and demonstrate how multilateral netting might be of benefit to Forun plc.





Solution 8

Multilateral netting is an effective means of reducing the transaction costs

associated with foreign exchange receipts and payments that are payable to banks.

The netting of Forun’s intra-company US dollar exposures gives the following net

payments and receipts:

Paying company

Receiving

company UK Sub 1 Sub 2 Sub 3 Sub 4

Total

receipts

Net

receipts

(payments)

$US’000

UK - 300 450 210 270 1,230 (470)

Subsidiary 1 700 - 420 - 180 1,300 220

Subsidiary 2 140 340 - 410 700 1,590 380

Subsidiary 3 300 140 230 - 350 1,020 (110)

Subsidiary 4 560 300 110 510 - 1,480 (20)

Total payments 1,700 1,080 1,210 1,130 1,500 6,620 NIL

US dollar payments will still need to be made by the UK parent, Subsidiary 3 and

Subsidiary 4 to Subsidiary 1 and Subsidiary 2. However these payments/receipts

only amount to a total of $600,000. These amounts are insignificant when

compared to the total value of transactions amounting to $6,620,000, which would

have been involved if multilateral netting had not taken place.

Therefore, this technique will reduce transaction and other costs that would

otherwise have been payable on the net difference of $6,020,000.

Where only two group members are involved in attempting to settle their intra-

company indebtedness, the much simpler technique called bilateral netting may be

employed.




Chapter 16

Futures and options



CHAPTER 16 – FUTURES AND OPTIONS


CHAPTER CONTENTS

FUTURES ----------------------------------------------------------------- 347

OPTIONS ----------------------------------------------------------------- 348

THE BLACK-SCHOLES OPTION PRICING MODEL --------------------- 350

PUT-CALL PARITY ------------------------------------------------------ 360

THE GREEKS ------------------------------------------------------------- 361

1. DELTA 361

2. GAMMA 361

3. VEGA 362

4. THETA 362

5. RHO 362

SUMMARY OF THE GREEKS 362

REAL OPTIONS ---------------------------------------------------------- 363

APPLYING THE BLACK SCHOLES MODEL TO ESTIMATE THE VALUE OF EQUITY ------------------------------------------------------------------ 368

LIFFE EQUITY OPTIONS TABLE --------------------------------------- 374





FUTURES

Financial futures contracts

A financial futures contract is a legally binding agreement between two parties to

buy or to sell a standardised quantity of a specific financial instrument at a future

date, but at a price agreed today, through the medium of an organised exchange.

The Clearing House

Each futures exchange has a Clearing House. When a futures deal has been made

the Clearing House assumes the role of counterparty to both the buyer and the

seller. Thus the buyer has effectively bought from the Clearing House whilst the

seller is treated as having sold to the Clearing House, thus removing the risk of

default on the futures contract. The Clearing House imposes upon its members the

requirement to pay “margin”, which effectively acts as a security deposit.

Margin

When a deal has been made both buyer and seller are required to pay margin to

the Clearing House. This sum of money must be deposited (and maintained) in

order to provide protection to both parties.

Initial margin is the sum deposited when the contract is first made. Variation

margin is payable or receivable to reflect the day-to-day profits or losses made on

the futures contract. If the futures price moves adversely a payment must be

made to the Clearing House, whilst if the futures price moves favourably variation

margin will be received from the Clearing House. This process of realising profits or

losses on a daily basis is known as “marking to market”.

Ticks

A tick is the minimum price movement permitted by the exchange on which the

futures contract is traded. Price movements are then stated in numbers of ticks.

Thus if a three month interest rate futures contract has a contract size of £500,000

and a tick size of 0.01%, the tick value is (0.0001 x 3/12 x £500,000) £12.50.

If you bought 15 Contracts at 93.20 and the contract price rose to 94.50, each

contract will have risen in price by (1.30 x 100) 130 ticks. Thus your total profit is

(15 contracts x 130 ticks x £12.50 per tick) £24,375, which will wholly or partly

cancel any losses made on the cash market due to adverse movements in market

interest rates.

Hedging

Hedging with a futures contract means that any profit or loss on the underlying

instrument will be offset by any loss or profit made on the futures contract. A

perfect hedge is unlikely because of:

(a) Basis risk i.e. the possibility that the futures price will move slightly differently

to the cash (or spot) market price, and

(b) The “round sum” nature of futures contracts, which can only be bought or sold

in whole numbers.





OPTIONS

A number of types of option may be created, for example:

● Companies can create call options on their own shares for purposes of share

option schemes for directors and employees, and

● Over-the-counter (OTC) or negotiated options are often created by e.g. banks

to suit the needs of the buyer.

However a large volume of trading occurs in options created by dealers on

specialised exchanges. In the UK, the London International Financial Futures and

Options Exchange (LIFFE) oversees the creation of options on various financial

assets. In 2002, LIFFE was taken over by Euronext and is now known as

Euronext.liffe. The paragraphs which follow are mainly concerned with these

exchange traded options.

Option

An option confers on the buyer the right, but not the obligation to buy from or sell

to the writer, a fixed amount of a financial asset (or instrument) on or before a

future maturity date, at a specific exercise price which is fixed today.

Call option

The buyer of a call option has the right to buy the asset, whilst the writer (or seller)

of a call option will be obliged to sell the asset should the buyer so elect.

Put option

The buyer of a put option has the right to sell the asset, whilst the writer (or seller)

of a put option will be obliged to buy the asset should the buyer so elect.

Exercise price

This is the price, which is fixed in the contract at which the underlying instrument

can be bought or sold. Sometimes referred to as the strike price. These strike

prices are fixed by the Exchange in accordance with a predetermined scale.

Expiry date

Also known as maturity date. Options are traded for delivery either on (or at any

time up to) the maturity date.

American style options

The majority of options are “American style”, in that they can be exercised, should

the buyer so decide, at any time between entering into the contract and expiry

date.

European style options

The comparatively rare “European style” options can only be exercised on the

maturity date.





Bermudan style options

These are options where early exercise is restricted to certain specified dates over

the life of the option.

Premium

The premium is the price that the buyer of the option pays for his right to trade the

instrument and is the maximum he can lose on the deal. The writer receives the

premium for having taken on the obligation to go through with the deal should the

buyer so elect. The writer of an option risks potentially unlimited losses.

In-the-money options

A call option is in-the-money if the current market price exceeds the exercise price.

A put option is in-the-money if the current market price is below the exercise price.

Out-of-the money options

A call option is out-of-the money if the current market price is below the strike

price. A put option is out-of-the money if the current market price exceeds the

strike price.

At-the-money options

Put and call options are at-the-money if the current market price happens to be

equal to the exercise price.

Intrinsic value of an option

The profit that the buyer of an “in-the-money” option could make if the option were

to be exercised immediately.

Time value of an option

If there is still a period of time to go before an option expires the option premium

will exceed the intrinsic value. Thus the value of the option premium will be equal

to intrinsic value plus time value. The greater the time to expiry, the greater the

time value.

The determinants of the value of a call option premium

1. The higher the price of the underlying instrument, the higher the value of

the call option premium.

2. The longer the time to expiry of the option, the higher the value of the call

option premium.

3. The greater the price volatility of the underlying instrument, the higher the

value of the call option premium.

4. The higher the risk free rate of interest, the higher the value of the call

option premium.

5. The higher the exercise price of the option, the lower the value of the call

option premium.





THE BLACK-SCHOLES OPTION PRICING MODEL

In 1973, Fischer Black and Myron Scholes developed a model to value particular

types of options. This model, commonly called the Black-Scholes option pricing

model, and its many derivations have been used extensively in establishing the

value of a call option. Such sophisticated models are used to determine the

appropriate relationship between the price of an option trading on an organised

exchange and the cash market price of the underlying financial claim.

The Black-Scholes model includes the following five factors in its specification:

1. The price of the underlying security

2. The length of time to expiry of the option period

3. A measure of price volatility

4. The risk-free rate of interest

5. The exercise price

In its basic form, the model cannot be used to incorporate income (i.e. dividends or

interest) received on the financial claim.

The model originally developed by Black-Scholes was designed for European call

options. The model assumes no return on the underlying financial claim and that

the options are marketable, that is, they can be bought and sold. This is a very

important assumption, since many forms of option that are created cannot be

transferred (i.e. are not traded options). This means that the value of options,

without transferability, will be less than would be calculated using the Black-Scholes

formula. The original model also ignored transaction costs and taxes, but a later

improved version introduced the assumption that transaction costs are minimal and

that all parties to the transaction have the same marginal tax rate.

Given these limitations the model has been successfully used to value many types

of options. The objective of the model is to estimate the market value of a call

option, c. The model specification is:

c = Pa N(d1) −−−− Pe N(d2) e-rt

where:

c = Call price for a European option

Pa = Current market price of the related security

Pe = The exercise price at the option’s maturity

e = The exponential constant i.e. 2.7183

r = Continuous compound risk-free interest rate

t = Remaining life of the option, expressed in years and percentages

thereof

N(d1) = The cumulative probability distribution from a normal distribution

for the value of d1. N(d1) provides an estimate of delta (refer to

page 361).

N(d2) = The cumulative probability distribution from a normal distribution

for the value d2





The values for d1 and d2 in the specification are

d1 = ts

)t0.5s + (r + )/Pln(P 2ea or ts 5.0

ts

rt + )/Pln(P ea ++++

N.B. The left hand version is given on the ACCA Formulae sheet, whilst

the right hand version was used (with different symbols) in the old

syllabus Paper 3.7

d2 = d1 – ts

where:

ln(Pa/Pe) = the natural logarithm of (Pa ÷ Pe )

s = the standard deviation (σ) of the continuously compounded rate of

return on the underlying financial claim

The assumptions for the Black-Scholes model appear to be numerous i.e.

● Returns on the underlying stock are normally distributed;

● The standard deviation of returns must be estimated and be constant over the

life of the option;

● Transaction costs and taxes are zero;

● The share pays no dividends;

● The option has European exercise terms;

● The market is efficient and operates continuously;

● The short-term (risk-free) interest rate is known and constant.

Although these assumptions are necessary for the Black-Scholes model to be

correct - if they do not hold, a variation is often available. Many financial scholars

have expanded upon the original work. For example, in 1973, Robert Merton

relaxed the assumption of no dividends by simply reducing the current share price

by the present value of all dividends expected to be paid before expiry of the

option. These dividends must be discounted at the risk free rate. Therefore, if a

current share price is 520p and a dividend of 21p is expected to be paid shortly

before expiry of a call option in one years time and the risk-free rate of interest is

5%, Pa will become: 520p – (21p ÷ 1.05) = 500p.

In 1976, Jonathan Ingerson relaxed the assumption of no taxes or transaction

costs, whilst Merton responded by removing the restriction of constant interest

rates.

The values of the options given by the Black-Scholes model vary considerably. The

impact of changes in s (i.e. the σ) and time to expiry have a particularly large

impact on value. A number of computer programs have been developed to permit

analysts to calculate quickly the option values using this model and variations of it.

This clearly simplifies the complex and laborious calculations.





Illustrations of the Black-Scholes model

1. The following details relate to an option to buy one share in Hoult plc:

Strike price = 45p

Time remaining to expiration = 183 days

Current share price = 47p

Expected price volatility = standard deviation = 25%

Short-term risk-free rate = 10%

Calculate the price of a European call option premium using the Black Scholes

option pricing model.

2. The following details concern the shares and related call options of Lyttle plc:

Current share price = 165p

Exercise price = 150p

Risk-free interest rate = 6%

Time to the option’s expiry = 2 years

Volatility (standard deviation) of share price = 15%



3. Consider an option to purchase an ordinary share in Clement plc at 65p when

the price of the share is 62.5p. The option will expire in four months or 120

days. The risk-free interest rate is 5 per cent. The volatility of Clement plc

shares as measured by the standard deviation of the return on the shares for

the 120-day period to expiry is estimated to be 40%.



4. A call option on an ordinary share in Gilchrist plc has a strike price of £1.20.

The current share price is £1.50 and the risk free rate of interest is 7.5%.

The standard deviation of the share is measured at 25% for the 6 month

period to maturity.

Calculate the price of a European call option using the Black Scholes option

pricing model.

5. The current share price of McInnes plc is £2.90. Estimate the value of a

European call option on the shares of the company (with an exercise price of

£2.60) which has 6 months to run before it expires. The risk free rate of

interest is 6% and the variance of the rate of return on the share has been

15%.

6. The price per ordinary share of Balis plc is 36p, whilst the exercise price is

40p. The risk-free interest rate is 10%, whilst the standard deviation of the

rate of return is 40% and the time to expiry is 90 days.







7. From the following data, calculate the call premium on an ordinary share of

Butler plc.

The share price is £1, whilst the related strike price is 90p. The risk free

interest rate is 10%. The volatility (measured by standard deviation) is 30%,

whilst the remaining time to expiry is 90 days.

Suggested solutions to illustrations

1. Pe = 45

t = 0.5 (183/365, rounded)

Pa = 47

s = 0.25

r = 0.1

d1 = ( ) ( )

5.025.0

5.025.05.01.04547ln 2×++÷

= 1768.0

015625.005.00435.0 ++

= 1768.0

109125.0

= 0.6172

d2 = 0.6172 − 0.25 x 5.0 = 0.4404


d1 = 0.6172 gives 0.2324

d2 = 0.4404 gives 0.1700

N(d1) = 0.5 + 0.2324 = 0.7324

N(d2) = 0.5 + 0.17 = 0.67

c = (47 x 0.7324) − (45 x 0.67 x e-0.1 x 0.5)

= 34.423 − (45 x 0.67 x 2.7183-0.05)

= 34.423 − (45 x 0.67 x 0.9512)

= 34.423 −28.68

= 5.74p





2. Pa = 165

Pe = 150

r = 0.06

t = 2

s = 0.15

d1 = ( ) ( )

215.0

215.05.006.0150165ln 2×++÷

= 2121.0

0225.012.00953.0 ++

= 2121.0

2378.0

= 1.121

d2 = 1.121 − 0.15 2 = 0.91


d1 = 1.121 gives 0.3686

d2 = 0.91 gives 0.3186

N(d1) = 0.5 + 0.3686 = 0.8686

N(d2) = 0.5 + 0.3186 = 0.8186

c = (165 x 0.8686) − (150 x 0.8186 x e-0.06 x 2)

= 143.319 − (150 x 0.8186 x 2.7183-0.12)

= 143.319 − (150 x 0.8186 x 0.8869)

= 143.319 − 108.905

= 34.41p





3. Pe = 65

Pa = 62.5

t = 0.33 (about four months)

r = 0.05

s = 0.4

d1 = ( ) ( )

33.04.0

33.0045.005.0655.62ln 2×++÷

= 2298.0

0264.00165.00392.0 ++−

= 2298.0

0037.0

= 0.016

d2 = 0.016 − 0.4 33.0 = −0.2138


d1 = 0.016 gives 0.0080

d2 = −0.2138 gives −0.0832

N(d1) = 0.5 + 0.008 = 0.508

N(d2) = 0.5 − 0.0832 = 0.4168

c = (62.5 x 0.508) − (65 x 0.4168 x 2.7183-0.05 x 0.33)

= 31.75 − (65 x 0.4168 x 2.7183-0.0165)

= 31.75 − (65 x 0.4168 x 0.9836)

= 31.75 − 26.65

= 5.1p





4. Pe = 120

Pa = 150

t = 0.5

r = 0.075

s = 0.25

d1 = ( ) ( )

5.025.0

5.025.05.0075.0120150ln 2×++÷

= 1768.0

015625.00375.02231.0 ++

= 1768.0

27622.0

= 1.5624

d2 = 1.5624 − 0.25 5.0 = 1.386


d1 = 1.5624 gives 0.4406

d2 = 1.386 gives 0.4177

N(d1) = 0.5 + 0.4406 = 0.9406

N(d2) = 0.5 + 0.4177 = 0.9177

c = (150 x 0.9406) − (120 x 0.9177 x e-0.075 x 0.5)

= 141.09 − (120 x 0.9177 x 2.7183-0.0375)

= 141.09 − (120 x 0.9177 x 0.9632)

= 141.09 − 106.07

= 35.02p





5. Pa = 290

Pe = 260

t = 0.5

r = 0.06

s2 = 0.15

d1 = ( ) ( )

5.015.0

5.015.05.006.0260290ln

×

×++÷

= 075.0

0375.003.01092.0 ++

= 2739.0

1767.0

= 0.6451

d2 = 0.6451 5.015.0 ×− = 0.3712


d1 = 0.6451 gives 0.2422

d2 = 0.3712 gives 0.1443

N(d1) = 0.5 + 0.2422 = 0.7422

N(d2) = 0.5 + 0.1443 = 0.6443

c = (290 x 0.7422) − (260 x 0.6443 x e-0.06 x 0.5)

= 215.24 − (260 x 0.6443 x 2.7183-0.03)

= 215.24 − (260 x 0.6443 x 0.9704)

= 215.24 − 162.57

= 52.67p





6. Pa = 36

Pe = 40

r = 0.1

s = 0.4

t = 0.25 (90/365, rounded)

d1 = ( ) ( )

25.04.0

25.04.05.01.04036ln 2×++÷

= 5.04.0

02.0025.01054.0

×

++−

= 2.0

604.0−

= −0.302

d2 = −0.302 25.04.0− = −0.502


d1 = −0.302 gives −0.1179

d2 = −0.502 gives −0.1915

N(d1) = 0.5 − 0.1179 = 0.3821

N(d2) = 0.5 − 0.1915 = 0.3085

c = (36 x 0.3821) − (40 x 0.3085 x e-0.1 x 0.25)

= 13.76 − (40 x 0.3085 x 2.7183-0.025)

= 13.76 − (40 x 0.3085 x 0.9753)

= 13.76 − 12.04

= 1.72p





7. Pa = 100

Pe = 90

r = 0.1

s = 0.3

t = 0.25 (90/365, rounded)

d1 = ( ) ( )

25.03.0

25.0 3.05.01.090100ln 2×++÷

= 15.0

01125.0025.01054.0 ++

= 15.0

14165.0

= 0.9443

d2 = 0.9443 25.03.0− = 0.7943


d1 = 0.9443 gives 0.3264

d2 = 0.7943 gives 0.2852

N(d1) = 0.5 + 0.3264 = 0.8264

N(d2) = 0.5 + 0.2852 = 0.7852

c = (100 x 0.8264) − (90 x 0.7852 x e-0.1 x 0.25)

= 82.64 − (90 x 0.7852 x 2.7183-0.025)

= 82.64 − (90 x 0.7852 x 0.9753)

= 82.64 − 68.92

= 13.72p





PUT-CALL PARITY

Once a value has been established for call options, the following equation can be

used to establish the value of a put option with the same exercise price and expiry

date as the related call:

Price of a

put = Price of a call −

Current value of

underlying

security

+ Present value of

the exercise price

p = c −−−− Pa + Pe e

-rt

Referring to the earlier illustrations, the related put premium in each case is:

Example

1. 5.74 − 47 + (45 x e-0.1 x 0.5)

= 5.74 – 47 + (45 x 2.7183-0.05)

= 5.74 – 47 + 42.81 = 1.55p

2. 34.41 – 165 + (150 x e-0.06 x 2)

= 34.41 – 165 + (150 x 2.7183-0.12

)

= 34.41 – 165 + 133.04 = 2.45p

3. 5.1 – 62.5 + (65 x e-0.05 x 0.33)

= 5.1 – 62.5 + (65 x 2.7183-0.0165)

= 5.1 – 62.5 + 63.94 = 6.54p

4. 35.02 – 150 + (120 x e-0.075 x 0.5)

= 35.02 – 150 + (120 x 2.7183-0.0375)

= 35.02 – 150 + 115.58 = 0.6p

5. 52.67 – 290 + (260 x e-0.06 x 0.5)

= 52.67 – 290 + (260 x 2.7183-0.03)

= 52.67− 290 + 252.32p = 14.99p

6. 1.72 – 36 + (40 x e-0.1 x 0.25)

= 1.72 – 36 + (40 x 2.7183-0.025)

= 1.72 – 36 + 39.01 = 4.73p

7. 13.72 −100 + (90 x e-0.1 x 0.25)

= 13.72 – 100 + (90 x 2.7183-0.025)

= 13.72 – 100 + 87.78 = 1.5p





THE GREEKS

In principle, an option writer could sell options without hedging his position. If the

premiums received accurately reflect the expected payouts at expiry, there is

theoretically no profit or loss on average. This is analogous to an insurance

company not reinsuring its business. In practice, however, the risk that any one

option may move sharply in-the-money makes this too dangerous. In order to

manage a portfolio of options, the dealer must know how the value of the options

he has sold and bought will vary with changes in the various factors affecting their

price. Such assessments of sensitivity are measured by the “Greeks”, which can be

used by options traders in evaluating their hedge positions.

1. Delta

For each option held, the delta value can be established i.e.

Delta = security underlying of price in Change

price option in Change

Delta is a measure of how much an option premium changes in response to a

change in the security price. For instance, if a change in share price of 5p results

in a change in the option premium of 1p, then the delta has a value of (1p/5p) 0.2.

Therefore, the writer of options needs to hold five times the number of options than

shares to achieve a delta hedge. The delta value is likely to change during the

period of the option, and so the option writer may need to change his holdings to

maintain his delta hedge position.

Accordingly a writer can hedge a holding of 300,000 shares using options with a

delta value estimated by N(d1) of 0.6, by holding the following number of LIFFE

contracts (each on 1,000 shares).

size Contractvalue Delta

shares ofNumber

× =

000,16.0

000,300

× = 500 contracts.

A delta value ranges between 0 and +1 for call options, and between 0 and -1 for

put options. The actual delta value depends on how far it is in-the-money or out-

of-the-money.

The absolute value of the delta moves towards 1 (or -1) as the option goes further

in-the-money and shifts towards 0 as the option goes out-of-the-money. At-the-

money calls have a delta value of 0.5, and at-the-money puts have a delta value of

-0.5.

2. Gamma

Gamma measures the amount by which the delta value changes as underlying

security prices change. This is calculated as the:

security underlying the of price the in Change

value delta the in Change





3. Vega

Vega measures the sensitivity of the option premium to a change in volatility. As

indicated above higher volatility increases the price of an option. Therefore any

change in volatility can affect the option premium. Thus:

Vega = volatility in Change

price option the in Change

N.B. Vega is the name of a star, not a letter of the Greek alphabet!!

4. Theta

Theta measures how much the option premium changes with the passage of time.

The passage of time affects the price of any derivative instrument because

derivatives eventually expire. An option will have a lower value as it approaches

maturity. Thus:

Theta = expiry to time in Change

value) in changes to (due price option the in Change

5. Rho

Rho measures how much the option premium responds to changes in interest rates.

Interest rates affect the price of an option because today’s price will be a

discounted value of future cash flows with interest rates determining the rate at

which this discounting takes place. Thus:

Rho = interest of rate the in Change

price option the in Change

Summary of the Greeks

Changes in In response to changes in

DELTA Option premium Value of underlying security

GAMMA Delta value Value of underlying security

VEGA Option premium Volatility

THETA Time value in option premium Time to expiry

RHO Option premium Risk free rate of interest





REAL OPTIONS

Flexibility increases the value of an investment and financial options theory

provides a guide as to how this flexibility can be incorporated into project appraisal.

Conventional project appraisal techniques do not adequately recognise the value of

flexibility. However, real options theory attempts to apply the principles used in the

evaluation of financial options and develop them for use in capital investment

appraisal.

In some project evaluation situations, a company may have one or more options to

make strategic changes to the project during its life e.g. the:

● Option to delay (i.e. defer investment without loss of the opportunity for

further investment, effectively creating a call option);

● Option to expand (i.e. to increase the scale of investment if market conditions

change). Thus the right to expand is effectively a call option;

● Option to abandon (i.e. where a project consists of clearly identifiable stages,

an abandonment option can be considered at the end of each stage, if this is

preferable to continuation). The right to generate some salvage value if

abandonment occurs is effectively a put option;

● Option to redeploy (i.e. switch to another use). This could result in the

creation of a put option if there is salvage value from the work already

performed, together with a call option arising on the right to commence the

new investment at a later stage.

There may even be options to downsize, options to change inputs or outputs,

options to shut down and then subsequently restart or, perhaps, options to invest

in stages (as opposed to one single major investment).

The building of the East Stand at West Bromwich Albion FC is cited as an example

of real options in investment appraisal.

This stand, which contains extensive corporate facilities, was built between 1999

and 2001 as a single tier stand. However, due to the stronger foundations which

were laid and the design of exits and walkways etc., it would be relatively

straightforward to add a second tier at some future stage without having to

demolish the existing first tier. Obviously, this single tier stand was more

expensive to build than a conventional one tier stand, but the additional

expenditure was the premium that was paid as a call option to expand, if or when

attendances grow to justify the additional ground capacity.

The Black-Scholes option pricing model can be applied to real options (sometimes

referred to as “embedded options”), where there is a single source of uncertainty

and a single expiry date (i.e. a European style option). Obviously this model

employs the usual five features i.e.

● Pa : The value of the underlying asset is no longer a share price, but

the PV of the future cash flows arising from the project;

● Pe : The exercise price is the capital expenditure (or receipts) arising

from the option;

● s : This will represent the volatility (in the form of the σ) of the

operating cash flows related to projects of the type under

consideration;





● r : This is the risk free rate of interest, however some writers believe

that additional project risk should be reflected with the use of a

higher interest rate;

● t : This is, as usual, the time to expiry for exercising a European style

option.

Illustration of an option to expand

Winter plc has investigated the opening of a new restaurant in the Isle of Man. The

initial capital expenditure is estimated at £12 million, whilst the present value of the

net cash inflows is expected to be £12.005 million. Since the resulting NPV of

£0.005 million is a very small positive amount, this appraisal suggests that the

project is extremely marginal.

However, if this first restaurant is opened, Winter plc would gain the right, but not

the obligation to open a second restaurant in five years time at a capital cost of £20

million. The present value of the associated future net cash inflows is estimated at

£15 million, with a standard deviation of 28.3%.

If the risk free rate of interest is 6%, determine whether to proceed with the

restaurant projects.






t = 5; Pe = 20; Pa = 15; s = 0.283; r = 0.06

d1 = ( ) ( )

5283.0

5283.05.006.02015ln 2×++÷

= 6328.0

2002.03.02877.0 ++− =

6328.0

2125.0 = 0.3358

d2 = 5283.03358.0 ×− = –0.297


d1 = 0.3358 gives 0.1331; thus N(d1) = 0.5 + 0.1331 = 0.6331

d2 = –0.297 gives –0.1179; thus N(d2) = 0.5 – 0.1179 = 0.3821

c = (15 x 0.6331) – (20 x 0.3821 x e-0.06 x 5)

= 9.4965 – (20 x 0.3821 x 0.7408)

= 9.4965 – 5.6613

= £3.8352m

Conclusion:

£m

NPV of first restaurant 0.005

Value of call option (to expand) on second restaurant 3.8352

Value of combined projects +3.8402

Therefore the project should be accepted, since the additional value (which

incorporates the option to expand), allows Winter plc to avoid the downside

element of risk.

Illustration of an option to abandon

Summer plc is undertaking a brewing joint venture with Autumn Inc. This project

requires an initial outlay by Summer plc of £250 million. The present value of the

net cash inflows is expected to be £254 million, with a variance of 9%. The

arrangement thus provides an extremely small positive NPV of £4 million. Summer

plc, however, has the right but not the obligation to sell its share of the joint

venture to Autumn Inc for £150 million at the end of the first five years of the

venture.

If the risk free rate of interest is 7%, calculate the value of this abandonment

option.






Pa = 254; Pe = 150; s2 = 0.09; t = 5; r = 0.07

Firstly, calculate the value of the call option:

d1 = ( ) ( )

509.0

509.05.007.0150254ln

×

×++÷

= 6708.0

225.035.05267.0 ++ = 1.6423

d2 = 1.6423 − 0.6708 = 0.9715


d1 = 1.6423 gives 0.4495; thus N(d1) = 0.5 + 0.4495 = 0.9495

d2 = 0.9715 gives 0.3340; thus N(d2) = 0.5 + 0.3340 = 0.8340

c = (254 x 0.9495) – (150 x 0.8340 x e-0.07 x 5)

= 241.173 – (150 x 0.8340 x 0.7047)

= 241.173 – 88.156 = 153.017

Secondly, using the put call parity relationship, calculate the value of the put option

p = c - Pa + Pe e-rt

= 153.017 – 254 + (150 x 2.7183-0.07 x 5)

= 153.017 – 254 + 105.703

= £4.72m

Alternatively, it is possible to directly calculate the value of the put option using the

following modified Black-Scholes formula, but this is not provided on the ACCA

formula sheet:

p = Pe N(−−−−d2)e-rt – Pa N(−−−−d1)

where:

N(−−−−d1) = 0.5 – 0.4495 = 0.0505

N(−−−−d2) = 0.5 − 0.3340 = 0.166

p = (150 x 0.166 x 2.7183-0.35) – (254 x 0.0505)

= (150 x 0.166 x 0.7047) – 12.827

= 17.547 – 12.827

= £4.72m





Conclusion:

£m

NPV of joint venture project 4

Value of put option (to abandon joint

venture)

4.72

Total NPV with the abandonment option +8.72

Therefore Summer plc should go ahead with the joint venture, since the additional

value, which incorporates the option to abandon allows Summer plc to avoid the

downside element of risk.





APPLYING THE BLACK SCHOLES MODEL TO ESTIMATE

THE VALUE OF EQUITY

A major aspect of the P4 syllabus is the emphasis on corporate valuation. There

may, of course, be some companies that cannot realistically be valued by

conventional techniques.

The Black Scholes Option Pricing (BSOP) model provides a basis for corporate

valuation in cases where traditional methods are either inappropriate, or where

they fail to fully reflect the risks involved. Some authors refer to the Black Scholes

Merton model to reflect the work performed by Robert Merton (a key member of

the research team which developed the model).

The usual determinants in the valuation of options need to be redefined, when the

valuation of equity is treated as a call option:

Determinants Possible appropriate measures

Valuation of the underlying The fair value of the assets of the company

Exercise price Settlement values of outstanding liabilities

Volatility of the underlying Standard deviation of underlying assets

Risk-free rate of interest Current yield on company debt

Time to expiry Average period to settlement of company liabilities

Where the assets of the company are actively traded and easily liquidated, their

current market value would be appropriate. In the case of most companies, fair

value will normally be based upon the present value of the future cash flows that

the company’s assets are expected to generate over their useful lives.

The volatility of the underlying assets is likely to be the most difficult measure to

estimate accurately. One approach is to estimate the probabilities of the likely

future cash flows of the company and generate a distribution of their present values

from which a standard deviation could be established.

A possible approach to the determination of an exercise price is to assume that the

company’s liabilities consist entirely of debt in the form of a zero coupon bond. If

the company’s debt includes other types of bond, adjustments are necessary as

shown in the following illustration.

Illustration 1

A company has on issue a 5% bond with five years to redemption with a gross yield

to maturity of 8%.

Required:

Estimate the market value of that bond and that of an equivalent zero coupon

bond.





Solution 1

The market value of the debt is estimated as follows:

Year 1 2 3 4 5

Annual interest and redemption payments (£) 5 5 5 5 105

Discount factors @ 8% 0.926 0.857 0.794 0.735 0.681

Present values (£) 4.63 4.29 3.97 3.67 71.50

Present value of debt = £88.06

The redemption value of a zero coupon bond of the same market value is calculated

by establishing the unknown future value which (when discounted at 8% p.a. for a

five year period) provides a present value of £88.06 i.e.

Future value = £88.06 x 1.085 = £129.39

Therefore £129.39 is treated as the exercise price (i.e. the redemption value of a

zero coupon bond with the same features as the debt currently in issue, which has

a yield to maturity of 8%).

Assuming that acceptable estimates of the input variables have been established,

the next step is to incorporate them into the BSOP model. The model does have a

number of restricting assumptions, but it can be used to produce an acceptable

valuation of a company.

Illustration 2

In March 2007, Northern Rock (a UK bank) reported assets and liabilities at fair

values of £113.2 billion and £110.7 billion respectively. The average term to

maturity on the liabilities of the bank (which consisted of short-term money market

borrowing and deposits) was 100 trading days, whilst the annual number of trading

days was 250 approximately. At that time the risk-free rate of interest was 3.5%

and the company had 495.6 million equity shares in issue.

Required:

(a) Using the BSOP (sometimes referred to as the Black Scholes Merton) model,

estimate the share price of Northern Rock in each of the following situations:

(i) Assuming that the standard deviation of the bank’s assets was 5%; and

(ii) Assuming that the volatility of the bank’s assets was 10%.

(b) Using the Black Scholes Merton model, recalculate an estimate of the share

price of Northern Rock if the fair value of the company’s assets fell to £110.7

billion and their volatility was 5%.

(c) Comment upon the results and consequences of the calculations performed in

parts (a) and (b) above.





Solution 2

This entire procedure is based on the notion that if equity shareholders pay off the

liabilities at “expiry date”, they are effectively paying the “exercise price” of a call

option and thus “exercising their right to buy” the underlying assets of the company

at their fair value.

Taking the data provided and converting to the ACCA symbols:

(a)

Pa = 113.20; Pe = 110.70; r = 0.035; t = (100 ÷ 250) = 0.4 (since

the annual number of trading days is 250); s is initially taken as 0.05 and,

subsequently as 0.1

(i) If volatility (s or σ) = 0.05:

d1 = ( ) ( )

4.005.0

4.005.05.0035.070.11020.113ln 2×++÷

= 0316227.0

0005.0014.00223323.0 ++

= 0316227.0

0368323.0 = 1.16474

d2 = 1.16474 - 0.0316227 = 1.13312

From Normal Distribution tables:

d1 = 1.16474, by interpolation:

1.16 gives 0.3770

1.17 gives 0.3790

1.16 gives 0.3770

(474 ÷ 1000) x 0.0020 = 0.00095

0.37795


1.13 gives 0.3708

1.14 gives 0.3729

1.13 gives 0.3708

(312 ÷ 1000) x 0.0021 = 0.00065

0.37145

Of course, in an exam it is quicker to round up or down to the two decimal

places provided by the ACCA tables. In this case, 1.16 (giving 0.3770) and

1.13 (giving 0.3708) would be used!

N(d1) = 0.5 + 0.37795 = 0.87795

N(d2) = 0.5 + 0.37145 = 0.87145

c = (113.20 x 0.87795) – (110.70 x 0.87145 x e -0.035 x 0.4)

= 99.384 – (110.70 x 0.87145 x 0.98610)

= 99.384 – 95.128 = £4.258 bn

Price = (£4.258 bn ÷ 495.6 m shares) = £8.59 per share





(ii) If volatility (s or σ) = 0.1:

d1 = ( ) ( )

4.01.0

4.01.05.0035.070.11020.113ln 2×++÷

= 0632455.0

002.0014.00223323.0 ++

= 0632455.0

0383323.0 = 0.60609

d2 = 0.60609 – 0.0632455 = 0.54284



0.60 gives 0.2257

0.61 gives 0.2291

0.60 gives 0.2257

(609 ÷ 1000) x 0.0034 = 0.00207

0.22777


0.54 gives 0.2054

0.55 gives 0.2088

0.54 gives 0.2054

(284 ÷ 1000) x 0.0034 = 0.00097

0.20637

Again, in an exam it is quicker to round up or down to the two decimal places

provided by the ACCA tables. In this case, 0.61 (giving 0.2291) and 0.54

(giving 0.2054) would be used!

N(d1) = 0.5 + 0.22777 = 0.72777

N(d2) = 0.5 + 0.20637 = 0.70637

c = (113.20 x 0.72777) – (110.70 x 0.70637 x e -0.035 x 0.4)

= 82.3836 – (110.70 x 0.70637 x 0.98610)

= 82.3836 – 77.1082 = £5.2754 bn


(b)

In this instance, the asset value (Pa) falls and is now equal to the liability value (at

a volatility of 0.05), so that both Pa and Pe become 110.70. All other facts are

unchanged.

The calculations are:

d1 = ( ) ( )

4.005.0

4.005.05.0035.070.11070.110ln 2×++÷

= 0316227.0

0005.0014.00 ++





= 0316227.0

0145.0 = 0.45853

d2 = 0.45853 – 0.0316227 = 0.42691



0.45 gives 0.1736

0.46 gives 0.1772

0.45 gives 0.1736

(853 ÷ 1000) x 0.0036 = 0.0031

0.1767


0.42 gives 0.1628

0.43 gives 0.1664

0.42 gives 0.1628

(691 ÷ 1000) x 0.0036 = 0.0025

0.1653

Once more, in an exam it is quicker to round up or down to the two decimal places

provided by the ACCA tables. In this case, 0.46 (giving 0.1772) and 0.43 (giving

0.1664) would be used!

N(d1) = 0.5 + 0.1767 = 0.6767

N(d2) = 0.5 + 0.1653 = 0.6653

c = (110.70 x 0.6767) – (110.70 x 0.6653 x e -0.035 x 0.4)

= 74.9107 – (110.70 x 0.6653 x 0.98610)

= 74.9107 – 72.6250 = £2.29 bn


(c) Comments

As can be seen from the calculations in part (a), the value of an option increases as

the level of risk rises. At a standard deviation of 5%, the share price is £8.59,

whilst at a volatility of 10%, the share price rises to £10.64. The actual share price

of Northern Rock in March 2007 fluctuated around £9.50 per share.

In part (b) of this illustration, the fair value of the bank’s assets fell to £110.7

billion to be equal to the fair value of its liabilities. Accordingly, the Statement of

financial position would show an equity value of zero. However, the BSOP model

shows a quite different result, at a volatility of 5% the total value of the equity is

still worth £2.29 billion, that is £4.62 per share – almost precisely its value in

September 2007!

At this date, the information being released from the company suggested that its

assets had fallen in value as the bank’s mortgage receivables were written down in

line with falling house prices and potential defaults.

It was only when the threat of nationalisation became a real possibility (during the

final months of 2007) that the equity value began to collapse - and this can be

explained within the framework of the BSOP model. Nationalisation eliminates the

possibility of asset recovery for the shareholders. This deprives them of the “time

value” on their call option on the underlying assets of the business.





The rationale for this rather strange result is that the equity of a business can still

have a substantial positive value (despite the Statement of financial position

showing a zero equity value) because of the presence of limited liability!

Limited liability protects shareholders from a loss - and in fact they have everything

to gain if the fair value of the assets should recover! When the equity of a

company is “at or near the money”, ie when its gearing levels approach 100%, the

equity investors will become increasingly risk aggressive (i.e. risk-seeking). Agency

theory suggests they will provide management with incentives to increase risk,

rather than reduce it. Hence, the very high levels of reward offered to bank

employees, particularly those employed in the risk-taking departments of the

business.

The work of Black, Scholes and Merton provides a framework to value those

companies that are financed, in part, by borrowing. Where shareholders are

protected by limited liability, they have a call option on the underlying business

assets. Employing the BSOP model, an estimate can be made of the value of a

company’s equity on the basis of the value of its assets and their volatility.

For companies that are deep “in-the-money”, time value is small and the intrinsic

value of the business (i.e. the present value of the net assets) will dominate the

value of the equity. In this case, normal risk aversion can be expected to apply as

that intrinsic value will be exposed to equal positive and negative movements in the

value of the company’s assets.

This situation dramatically changes when companies are “near-the-money”. This

occurs with high growth start-ups financed by debt, leveraged buyouts and

companies that are in risk of default.

One class of company (banks) always operate “near-the-money”, and in valuing

such businesses, time value would be more significant than intrinsic value in equity

valuation.

When time value dominates, shareholders become risk-seekers and they will grant

management incentives to take greater risk, which will cause the company to be

pushed closer and closer “to-the-money”, by expanding assets and liabilities

without increasing the equity capital.





LIFFE EQUITY OPTIONS TABLE




Chapter 17

Hedging interest rate risk



CHAPTER 17 – HEDGING INTEREST RATE RISK


CHAPTER CONTENTS

METHODS OF HEDGING INTEREST RATE RISK ---------------------- 377

FORWARD RATE AGREEMENTS (FRA) 377

INTEREST RATE GUARANTEES (IRG) 377

INTEREST RATE FUTURES 378

OPTIONS ON INTEREST RATE FUTURES 379

THE MACAULAY DURATION METHOD --------------------------------- 401

TERM STRUCTURE OF INTEREST RATES ------------------------------ 404

THE NORMAL YIELD CURVE 404

THE INVERSE YIELD CURVE 405





METHODS OF HEDGING INTEREST RATE RISK

There are a number of methods that may be used by a company to reduce its

exposure to possible adverse fluctuations in interest rates, in either a borrowing or

lending arrangement.

The main methods are as follows:

Forward rate agreements (FRA)

A forward rate agreement allows a company to effectively agree with a banker a

fixed interest rate for a specified level of borrowing or lending for a given future

period.

An FRA is commonly quoted so as to specify the number of months hence when the

borrowing or lending starts and the number of months hence when it finishes. For

instance, where a company wishes to borrow for a five month period starting in two

months time, this would require a “2 v.7 FRA”, i.e. the borrowing will start in two

months time and end in seven months time.

Accordingly, a company which has borrowed at a floating rate of interest may enter

into an FRA, which effectively locks the company into a fixed rate of interest.

Whatever happens, the company will continue to pay its original lender the

appropriate amount of interest based upon the agreed floating rate.

However, if actual interest rates rise higher than the percentage agreed under the

FRA, the bank will pay the amount of the difference as compensation to the

company. If rates fall lower than agreed, the company must pay the difference as

compensation to the bank.

Conversely a lender (i.e. investor) may enter into a similar agreement. If actual

floating interest rates fall below the agreed fixed percentage, the bank will pay the

difference to the company. If rates rise above that specified in the FRA, the

company must pay the difference to the bank.

FRAs involve no borrowing or lending of the principal sum. They are usually for at

least £500,000 (or the equivalent in major currencies) and for periods of less than

one year.

Interest rate guarantees (IRG)

An interest rate guarantee is an interest rate option specifically arranged with a

bank, i.e. it is an over-the-counter (OTC) product. An IRG provides the right, but

not the obligation, to pay or receive a fixed specified rate of interest for a defined

period of time. Accordingly, it would provide a borrower with the assurance of

never paying more than a maximum interest rate (a cap) or give an investor the

peace of mind of never earning less than a minimum interest rate (a floor).

However, an IRG, like all options will allow the buying company to take advantage

of favourable movements in interest rates.

An interest rate guarantee therefore gives ‘the best of both worlds’, in that if a

borrower purchases such an option, it will be exercised if rates rise above the

guaranteed percentage, but will be abandoned if rates fall below that percentage,

so that the borrower will be able to take advantage of the lower market interest

rates.





Equally, if an investor buys an interest rate guarantee, it will be exercised if rates

fall below the guaranteed percentage, but will be allowed to lapse if rates rise

above that percentage, so that the investor can take advantage of the higher

market interest rates.

The opportunity to abandon the arrangement is not available with FRAs or the

futures market. However this advantage must be weighted against the price of the

option (the ‘premium’) which must be paid up-front to the bank. Many companies

consider that they are too expensive since a significant premium is payable.

Interest rate futures

An interest rate future is a binding contract between a buyer and a seller for

delivery of an agreed interest rate commitment on an agreed date and at an agreed

price. It can be used to protect against unwanted interest rate movements.

For example, if a borrower is worried about interest rates rising, it may sell interest

rate futures, knowing that if interest rates do rise, the price of the futures will fall,

allowing the borrower to buy them back at a lower price. The gain on the futures

market can be offset against the additional interest suffered. The reverse happens

if interest rates fall. This will have the effect of more or less fixing the effective

interest rate paid by the borrower.

Equally, if an investor is concerned about interest rates falling, it may buy interest

rate futures, knowing that if interest rates do fall, the price of the futures will rise,

allowing the investor to sell them at a higher price. The gain on the futures market

can be added to the smaller amount of interest actually earned. The reverse

happens if interest rates rise. This again has the effect of more or less fixing the

effective interest rate received by the investor.

Each futures exchange has a Clearing House. When a futures deal has been made

the Clearing House assumes the role of counterparty to both the buyer and the

seller. Thus the buyer has effectively bought from the Clearing House, whilst the

seller is treated as having sold to the Clearing House, thus removing the risk of

default on the futures contract.

When a deal has been made, both buyer and seller are required to pay margin to

the Clearing House. This sum of money must be deposited (and maintained) in

order to provide protection to both parties.

Initial margin (of between 5% and 10% of contract value) is the sum deposited

when the contract is first made. Variation margin is payable or receivable to

reflect the day-to-day profits or losses made on the futures contract. If the futures

price moves adversely a cash payment must be made to the Clearing House, whilst

if the futures price moves favourably the party concerned can elect to receive a

cash refund from the Clearing House. This process of realising profits or losses on

a daily basis is known as “marking to market”.

Contract sizes are for fixed sums, e.g. £500,000 for short sterling contracts, which

means that a perfect hedge is difficult to achieve.

A further reason why a perfect hedge is unlikely is basis risk i.e. the possibility of

variability in the prices of the two related securities in the hedging arrangement.

For example, if changes in the price of the interest rate future do not perfectly

match the changes in the rate of interest, a profit or loss may occur on the hedge

position.





Futures contracts are available from LIFFE (London International Financial Futures

and Options Exchange). In 2002, LIFFE was taken over by Euronext and is now

known as Euronext.liffe.

Options on interest rate futures

These exchange traded instruments provide the buyer with the right, but not the

obligation to buy or sell the related interest rate futures contract. Once more, the

objective is to protect the buyer of the instrument against unwanted interest rate

movements.

LIFFE deals in option contracts in standard amounts (e.g. £500,000 for short

sterling contracts), at standard exercise prices and expiry dates. These traded

options are of two kinds:

o put options carry the right to sell the related interest rate futures

contract, and

o call options carry the right to buy the related interest rate futures

contact.

LIFFE offers these option contracts at a limited number of different exercise (strike)

prices. The buyer of the option is required to pay a non-refundable option

premium for the flexibility of being allowed to exercise or abandon the option.

This premium is the maximum that the buyer can lose on the deal. A writer

receives the premium for having taken on the obligation to go through with the deal

should the buyer so elect. The writer of an option risks potentially unlimited losses.

Borrowers

If a borrower is worried about interest rates rising, but is not totally convinced that

they will in fact do so, he may decide to buy put options.

If interest rates do subsequently increase, the borrower can exercise the put option

and thus sell the related interest rate futures contract, then immediately buy it

back at a profit. This gain will obviously offset the additional interest payment

suffered on the amount of the borrowing.

Should interest rates subsequently remain steady or indeed fall, the borrower would

then allow the put option contracts to lapse.

Investors

If an investor is fearful that interest rates will fall, but is not totally convinced that

they will in fact do so, he may decide to buy call options.

If interest rates do subsequently decline, the investor will exercise the call option

and thus buy the interest rate futures contract, then immediately sell it at a profit.

This gain will of course compensate for the smaller amount of interest received on

the investment.

Should interest rates subsequently remain steady or actually increase, the investor

would then abandon the call option contracts.





Illustration 1

It is now 31 December 2006. The corporate treasurer of Tripod plc is concerned

about the level of cash flows of the company during the next six months, and how

the company might be protected from the adverse effects of changing interest

rates. Interest rates are widely expected to change in late April when a General

Election is due, but the size and direction of the change is dependent upon the

result of the election which is forecast by opinion polls to be very close. Current

interest rates for Tripod are 11% per year for short-term borrowing, and 8% per

year for short-term investment.

Apart from an overdraft facility to finance short-term cash shortages, the company

has no other form of floating rate debt.

Cash forecasts reveal that the company expects to have a fairly consistent

overdraft level of approximately £2,420,000 between the end of April and the end

of June 2007.

June sterling three months deposit futures are currently priced at 90.25. The

standard contract size is £500,000 and the minimum price movement is one tick

(the value of one tick is 0.01% per year of the contract size).

Interest rate guarantees at 11.5% per year for a two month period from May are

available to Tripod for a premium of 0.2% of the size of the loan to be guaranteed.

Forward rate agreements are available for period of up to four months from May at

11.88-11.83%.

Required:

If at the end of April, interest rates have moved as follows:

Scenario (1)

Borrowing rate for Tripod 13% per year

Investment rate for Tripod 10% per year

June sterling three month time deposit futures 88.05

Scenario (2)

Borrowing rate for Tripod 9.5% per year

Investment rate for Tripod 6.8% per year

June sterling three month time deposit futures 91.75,

evaluate with hindsight, separately for each of scenarios (1) and (2) above, the

results of four alternative strategies that the company might have adopted towards

its interest rate risk.

Taxation, margin requirements and the time value of money may be ignored.





Solution 1

Four strategies that the company could adopt are as follows:

1. Adopt no protective strategy on the basis that the company’s exposure to

adverse rate movements may be negligible;

2. Enter into forward rate agreements (FRAs) with bank;

3. Use interest rate guarantees; or

4. Use sterling three month interest rate futures.

Each of these strategies is considered in turn.

Tutorial note: since the question only gives data for the prices of FRAs, interest rate

guarantees and futures we have no choice but to select these strategies. There is

no further information on the fourth strategy, so it must be to do nothing. The risk

exposure from interest rates is sometimes very small. Given that rates can move

favourably as well as unfavourably, it may be appropriate for no complex hedging

strategy to be adopted. The cost of a hedging strategy might be avoided if the risk

of adverse movements were minimal.

1. No hedge

Scenario I

May and June interest = £2.42m x 13% x 2/12 = £52,433

Scenario II

May and June interest = £2.42m x 9.5% x 2/12 = £38,317

2. Use an FRA

(A 4 v. 6 FRA is needed i.e. one starting 4 months hence and ending in 6 months

time)

Scenario I

£

Cost in cash market = £2.42m x 13% x 2/12 = 52,433

Less compensation

paid by the bank to

Tripod

£2.42m x (11.88% − 13%) x 2/12 = (4,517)


Scenario II

£

Cost in cash market = £2.42m x 9.5% x 2/12 = 38,317

Plus compensation

paid by Tripod to the

bank

£2.42m x (11.88% − 9.5%) x 2/12 = 9,599


(Tutorial note: once the FRA has been entered into, the interest paid by the

company for the two months will be £47,916, whatever the prevailing level of

interest rates).





3. Interest rate guarantee

Scenario I

Premium payable = 0.2% x £2.42m = £4,840

Interest payable = £2.42m x 11.5% x 2/12 = £46,383

Total cost of strategy = £4,840 + £46,383 = £51,223

Scenario II

Premium payable = £4,840 (as above)

This time the option will be abandoned, so the company can enjoy the lower

prevailing interest rate.

Interest payable = £2.42m x 9.5% x 2/12 = £38,317

Total cost of strategy = £4,840 + £38,317 = £43,157

4. Use futures

Scenario I

Cash market: May and June interest, as i) above = £52,433

In December, the company wants to hedge for two months an amount of £2.42m

using three month futures contracts each of £500,000.

Therefore need to sell m5.0£

m42.2£3

2 × = 3.22 contracts

We may choose to round down to 3 contracts – see result in the Summary shown

below. However, rounding up, the company must sell 4 contracts to be fully

hedged.

Profit on the futures contracts = 4 x (90.25 – 88.05)

= 4 x 220 ticks

= 4 x 220 x £12.50*

= £11,000

The net interest payable is £52,433 − £11,000 = £41,433

*Note: one tick is valued at 0.0001 x £500,000 x 3/12 = £12.50

Scenario II

Cash market: May and June interest, as i) above = £38,317

Loss on the futures contracts = 4 x (91.75 – 90.25)

= 4 x 150 ticks

= 4 x 150 x £12.50

= £7,500

The net interest payable is £38,317 + £7,500 = £45,817





SUMMARY

Scenario I Scenario II

£ £

No hedge 52,433 38,317

FRA 47,916 47,916

Interest rate guarantee 51,223 43,157

Futures

Using 3 contracts 44,183 43,942

Using 4 contracts 41,433 45,817





Illustration 2

The corporate treasury team of Murwald plc are debating what strategy to adopt

towards interest rate risk management. The company’s financial projections show

an expected cash deficit in three months time of £12 million, which will last for a

period of approximately six months. Base rate is currently 6% per year, and

Murwald can borrow at 1.5% over base, or invest at 1% below base. The treasury

team believe that economic pressures will soon force the European Central Bank to

raise interest rates by 2% per year, which could lead to a similar rise in UK interest

rates. The European Central Bank move is not certain, as there has recently been

significant pressure from certain European Union countries not to raise interest

rates.

In the UK, the economy is still recovering from a recession and representatives of

industry are calling for interest rates to be cut by 1%. Opposing representations

are being made by pensioners, who do not wish their investment income to fall

further due to an interest rate cut.

The corporate treasury team believes that interest rates are more likely to rise than

to fall, and does not want interest payments during the six month period to

increase by more than £10,000 from the amounts that would be paid at current

interest rates. It is now 1 December.

Liffe prices (1 December)

Futures: LIFFE £500,000 three month sterling interest rate (points of 100%)

December 93.75

March 93.45

June 93.10

Options: LIFFE £500,000 short sterling options (points of 100%)

Calls Puts

Exercise price June June

9200 3.33 -

9250 2.93 -

9300 2.55 0.92

9350 2.20 1.25

9400 1.74 1.84

9450 1.32 2.90

9500 0.87 3.46

Required:

(a) Illustrate the results of futures and options hedges if, by 1 March:

(i) Interest rates rise by 2%. Futures prices move by 1.8%

(ii) Interest rates fall by 1%. Futures prices move by 0.9%

Recommend with reasons, how Murwald plc should hedge its interest rate

exposure. All relevant calculations must be shown. Taxation, transactions

costs and margin requirements may be ignored. State clearly any

assumptions that you make.

(b) Discuss the advantages and disadvantages of other derivative products that

Murwald might have used to hedge the risk.





Solution 2

(a) The treasury team believe that interest rates are more likely to increase than

to decrease, and any hedging strategy will be based upon this assumption.

There is also a requirement that interest payments do no increase by more

than £10,000 from current interest payments.

Current expectations

£12m deficit: interest payments £12m x (6% + 1.5%) x 6/12 = £450,000

Using futures hedges (Either March or June contracts may be used – or

both).

The suggested solution uses June contracts.

(i) If interest rates rise

With an expected £12m deficit – using June contracts

As a six month hedge is required the number of contracts sold will be:

months3

months6

000,500£

m12£× = 48 contracts

The tick value is 12

3000,500£0001.0 ×× = £12.50

Cash market Futures market

Current cost = £450,000 Dec 1: Sell 48 three month

sterling futures at 93.10

With 2% increase

£12m x 9.5% x 6/12 = £570,000 After interest rate increase:

Buy 48 three month sterling

futures at (93.10 – 1.80) =

91.30

Extra cash market cost = £120,000 Futures gain: 48 x 180# x

£12.50 = £108,000

#(100 x 1.80) = 180 ticks

Net additional cost after hedging = £12,000

If Murwald expects basis risk to exist (i.e., the futures price moves by a

different amount to the cash market interest rates), the number of

contracts could be modified to reflect such risk:

i.e. %8.1

%248 × = 53.3 contracts

then 53.3 x 180 x £12.50 = £120,000.

However, basis risk is difficult to predict.





(ii) If interest rates fall

With an expected £12m deficit

Cash market Futures market

Current cost = £450,000 Dec 1: Sell 48 contracts at

93.10

With 1% decrease After interest rate decrease:

£12m x 6.5% x 6/12 = £390,000 Buy 48 three month sterling

futures at (93.10 + 0.90) =

94.00

Cash market saving = £60,000 Futures loss 48 x 90* x

£12. 50= £54,000

*(100 x 0.90) = 90 ticks

Overall net extra saving = £6,000

Based upon these futures prices, hedging in the futures market does not

allow the company to guarantee that interest costs (in the case of a

deficit) do not increase by more than £10,000.

Using option hedges

The expectation is for interest rates to rise, therefore put options on futures

will be purchased.

N.B. Since Murwald may want the right to sell futures, put options must be

bought. (If interest rates rise the value of the put options will also increase)

For example, using the 9400 exercise price:

(i) If interest rates rise


Cash market Options market

Current cost = £450,000 Dec 1: Buy 48 9400 puts at 1.84

With 2% increase After interest rate increase:

Cost (see above) = £570,000 The option may be exercised to sell

June futures at 94.00

Extra cash market

cost

= £120,000 June futures may be purchased on

LIFFE at (93.10 – 1.80) = 91.30

Profit from options is:

94.00 – (91.30 + 1.84) = 0.86

(0.86 x 100) = 86 ticks

48 x 86 x £12.50 = £51,600

Overall net extra cost = £68,400

In reality the options are likely to be sold rather than exercised, as being

June contracts they will still have time value which will be reflected in the

option price. The gain from the options sale is therefore likely to be

higher than the gain from exercising the options. However, no data is

provided on option prices on 1 March.





(ii) If interest rates fall



Current cost = £450,000 Dec 1: Sell 48 contracts at

93.10

With 1% decrease After interest rate decrease:

Cost (see above) = £390,000 The futures price moves to

(93.10+ 0.90) = 94.00 and

the option would not be

exercised

Cash market saving = £60,000 The loss on options is the

premium paid 48 x 184# x

£12.50 = £110,400

#(100 x 1.84) = 184 ticks

Overall net extra cost = £50,400

Summary

Futures Options

£ £

2% interest rate increase

on £12m deficit (12,000) (68,400)

1% interest rate decrease

on £12m deficit 6,000 (50,400)

Different option outcomes will exist if different put option exercise prices are

selected. The best exercise price to select if the put options are used

will be the 9350 option:

This will give a gain if exercised of:

93.50 – (91.30 + 1.25) = 0.95 or 95 ticks

i.e. 48 contracts x 95 ticks x £12.50 = £57,000

If the futures price moves to 94.00, the option will not be exercised, and the

loss will be the premium paid of:

(1.25 x 100) i.e. 125 ticks x 48 contracts x £12.50 = £75,000

Outcomes using 9350 options:


£ £ £

2% increase (120,000) + 57,000 = (63,000)

1% decrease 60,000 + (75,000) = (15,000)

Neither futures nor options hedges can satisfy, with certainty, the requirement

that the interest payment should not increase by more than £10,000.

However, one way to achieve this would be to use a collar option, whereby

downside risk is protected, but potential gains are also restricted. A collar

effectively fixes both a maximum and a minimum interest rate.





If a company expects to be borrowing and is worried about interest rate

increases, a suitable collar can be achieved by buying put options and selling

(or writing) call options, to reduce the cost of protection.

For example, a collar could be achieved by buying 48 9400 put options at

1.84 and selling 48 9400 call options at 1.74, a net premium cost of 0.10

(N.B. other alternatives are possible).

Murwald does not want interest to move adversely by more than £10,000 for

a six month period on a £12 million loan.

In annual terms this is months 6

months 12

m12£

000,10£× = 0.167% p.a.

A put option at the current interest rate (6%) and a total premium cost of less

than 0.167% will satisfy the company’s requirement. In the above example,

the total premium cost is 0.10%, and no matter what happens to interest

rates Murwald can fix its borrowing cost at 7.6% p.a. that is:

Interest rate implied by 9400 exercise price %

(100 – 94.00) 6.0

Risk premium 1.5

Net option premium paid (1.84 – 1.74) 0.1

Borrowing cost p.a. 7.6%

This satisfies the requirement. Interest payments would be £12m x 7.6% x

6/12 = £456,000, which is only £6,000 higher than the current interest

payment.

The use of a collar is thus the recommended hedging strategy.

(b) Alternative interest rate hedges include:

● Forward rate agreements (FRAs)

● Over-the-counter (OTC) interest rate options – including interest rate

guarantees

● Interest rate swaps.

1. A forward rate agreement is a contract to agree to pay a fixed

interest rate that is effective at a future date. As such Murwald could

fix now a rate of interest of 6.1% (for example) to be effective in three

months time for a period of six months.

If interest rates were to rise above 6.1%, the counter-party (usually a

bank) would compensate Murwald for the difference between the actual

rates and 6.1%. If interest rates were to fall below 6.1%, Murwald

would compensate the counter-party for the difference between 6.1%

and the actual rate.

2. OTC options. Instead of market traded interest rate options such as

those that are available on LIFFE, Murwald might use OTC options

through a major bank. This would allow options to be tailored to the

company’s exact size and maturity requirements. An OTC collar would

be possible, and the cost of this should be compared with the cost of

using LIFFE options. Interest rate options for periods of less than one

year are sometimes known as interest rate guarantees.





3. Interest rate swaps. Murwald expects to borrow at a floating rate of

interest. It might be possible for Murwald to swap its floating rate

interest stream for a fixed rate stream, pegging interest rates to

approximately current levels (the terms of the swap would have to be

negotiated). Interest rate swaps are normally for longer periods than

six months.

Solutions could also have made reference to Swaptions. A Swaption is a option to

enter into an interest rate swap. Murwald could purchase such an instrument,

which gives the right but not the obligation to enter into a swap within a

predetermined period. The premium would be relatively high in cases where there

was a general expectation of interest rate rises and furthermore the arrangement

may not satisfy the financial objectives set by Murwald.





Illustration 3

It is now 31 October. Barney plc wishes to borrow £20 million on 1 March next

year for a period of six months, but wishes to protect itself against market interest

rates rising above the current LIBOR (London Inter Bank Offered Rate) of 6%.

Barney plc can borrow at LIBOR +2%.

LIFFE three month Sterling futures: £500,000 contract size, £12.50 tick size

December 93.95

March 93.90

June 93.85

LIFFE option price on the appropriate three months Sterling futures: £500,000

contract size, £12.50 tick size

Calls Puts

Strike price Dec Mar June Dec Mar June

9375 0.18 0.35 0.46 0.14 0.25 0.42

9400 0.07 0.22 0.33 0.28 0.37 0.54

9425 0.02 0.13 0.23 0.48 0.53 0.69

Required:

Using interest rate options, calculate the outcome of the hedge if interest rates and

futures prices were to move on 1 March next under each of the following scenarios:

SCENARIO ONE: LIBOR falls by 2% and the relevant futures price rises to 95.90

SCENARIO TWO: LIBOR rises to 9% and the relevant futures price falls to 91.20

SCENARIO THREE: LIBOR rises by 100 basis points and the change in the futures

price reflects no basis risk.

Note:

Assume that interest rates charged by the bank remain constant following the

interest rate change.

Ignore margin requirements

Do NOT employ collars or similar option combinations.





Solution 3

To protect against interest rates rising above current LIBOR, Barney plc (a

borrower) will need to buy put option contracts at a (100 − 6) 9400 exercise price.

December contracts will expire before the borrowing starts, therefore March or June

contracts are suitable. March contracts are preferred due to their cheaper

premium.

No. of contracts needed months 3

months 6

000,500£

m20£× = 80 contracts

The premium payable on exercise or expiry for March 9400 puts is (0.37 x 100) =

37 ticks. Thus, the total premium is 80 contracts x 37 ticks x £12.50 = £37,000.

Scenario one

£

Cash market saving (2% x 6/12 x £20m) 200,000

Options market

NOW: Buy 80 March put option contracts at 9400

exercise price

AFTER THE INTEREST RATE CHANGE:

Abandon the option (since Barney would not

wish to sell at 94.00, then buy at 95.90)

Loss is the premium paid - as above (37,000)

NET GAIN £163,000

Scenario two

£

Cash market loss (3% x 6/12 x £20m) (300,000)

Options market


exercise price


1. Exercise and sell at 94.00

2. Then buy at (91.20)

2.80

less premium (0.37)

2.43 x 100

= 243 ticks

Profit (80 contracts x 243 ticks x £12.50) 243,000

NET LOSS £(57,000)





Scenario three (100 BASIS POINTS = 1%)

£

Cash market loss (1% x 6/12 x £20m) (100,000)

Options market


exercise price


1. Exercise and sell at 94.00

2. Then buy at (93.90 − 1.00) (92.20)

1.10

less premium (0.37)

0.73 x 100

= 73 ticks

Profit (80 contracts x 73 ticks x £12.50) 73,000

NET LOSS £(27,000)





Illustration 4

It is now 31 December 2006 and the corporate treasurer of Omniown plc is

concerned about the volatility of interest rates. His company needs to immediately

borrow £5,000,000 for a six month period. Current interest rates are 14% per year

for the type of loan Omniown would use, and the treasurer does no wish to pay

more than this. He is considering using either:

(i) A forward rate agreement (FRA), or

(ii) Interest rate futures, or

(iii) An interest rate guarantee

(a) Explain briefly how each of these three alternatives might be useful to

Omniown plc.

(b) The corporate treasurer of Omniown plc expects interest rates to increase

by 2% almost immediately and has decided to hedge the interest rate risk

using interest rate futures.

June sterling three months time deposit futures are currently priced at 86.25.

The standard contract size is £500,000 and the minimum price movement is

one tick (the value of one tick is 0.01% per year of the contract size).

Required:

Illustrate the results of using a futures hedge under each of the following

three scenarios, if for the entire six month period:

(i) Interest rates increase by 2% and the futures market price also moves

by 2%.

(ii) Interest rates increase by 2% and the futures market price moves by

1.5%.

(iii) Interest rates fall by 1% and the futures market price moves by 0.75%

Ignore taxation, margin requirements, and the time value of money.

(c) As an alternative to interest rate futures, the corporate treasurer has been

able to purchase interest rate guarantees at a rate of 14% per annum for a

premium of 0.2% of the size of the loan to be guaranteed.

Required:

Calculate whether the total cost of the loan after hedging in each of the three

scenarios in (b) above would have been cheaper or more expensive with the

futures hedge than with the interest rate guarantee. The guarantee would be

effective for the entire six month period of the loan.

Ignore taxation, margin requirements, and the time value of money.





Solution 4

(a) Explanation of the three alternative hedging strategies

(i) Forward rate agreements

A forward rate agreement is a contract between a company and a bank

which sets the interest rate on future borrowings (or deposits). A

company can make a FRA with a bank that fixes the rate of interest to

be paid at a certain time in the future. If the actual interest rate at the

time is higher than that agreed, the bank pays the difference; if it is

lower than the rate agreed then the company pays the difference. A

FRA does not affect the principal sum. The actual borrowing itself must

be arranged separately either with the same bank as the FRA is

organised or with a different bank.

A FRA could be useful to Omniown since the treasurer will know in

advance what the loan is going to cost. The minimum amount is usually

£500,000 so would not be a problem in this case. However, if it is

expected that interest rates are going to rise, the treasurer might have

difficulty in negotiating a FRA at the current rate of 14%.

(ii) Interest rate futures

Interest rate futures are contracts of standard amounts and for standard

periods of time running from a limited number of dates. They are

therefore less flexible than a FRA. They take the form of a contract

between buyer and seller on an interest rate at an agreed price on an

agreed date. The contract will require a small initial margin payment

and thereafter variation margin will apply. Interest rate futures are

similar in effect to forward rate agreements, except that the terms,

amounts and periods are standardised. They are traded on the

Euronext.liffe.

For Omniown protection against interest rate increases could be

achieved by selling futures contracts now. As interest rates rise the

value of futures contracts will fall. Hence Omniown can buy back the

contracts at a lower price and make a profit. This profit should

compensate the company for the increase in market interest rates,

though (due to basis risk) this profit is unlikely to match perfectly the

additional interest costs incurred.

(iii) Interest rate guarantees

An interest rate guarantee is an option which enables the treasurer to fix

a maximum interest rate for a period in the future. If the market rate

falls the treasurer would choose not to exercise the option and take

advantage of the lower rate. Because of the additional benefit of taking

advantage of lower interest rates, options tend to be rather expensive.

They involve payment of a non-refundable premium in advance at the

time the contract is entered into.

In this case, since the option would be to guarantee rates at their

existing level and because it is a short-term option, the premium is

likely to be fairly high unless the market expects rates to fall.

N.B. The premium would be lower if the guaranteed rate were higher

than existing rates e.g. 16%.





(b) Interest rate futures

Number of contracts sold = months 3

months 6

000,500£

000,000,5£× = 20 contracts

The value of one tick is 0.0001 x £500,000 x 3/12 = £12.50

(i) Interest rates increase by 2% and the futures market price falls by

2%

CASH MARKET

£

Extra interest paid (2% x6/12 x £5,000,000) (50,000)

FUTURES MARKET

On 31 December 2006:

Sell 20 £500,000 June sterling time deposit

contracts at (effectively 13.75% per year

interest)

86.25

After interest rate increase:

Buy 20 £500,00 June sterling time deposit


interest)

84.25

2.00 x 100

= 200 ticks

Gain on futures contracts

= 20 contracts x 200 ticks x £12.50 = 50,000

OVERALL NET PROFIT/(LOSS) ON STRATEGY NIL

This is a perfect hedge with 100% hedge efficiency.

(ii) Interest rates increase by 2% and the futures market price falls by

1.5%

CASH MARKET

£

Extra interest paid (as above) (50,000)

FUTURES MARKET




interest)

86.25

After interest rate increase:


contracts at effectively 15.75% per year

interest)

84.25

1.50 x 100

= 150 ticks

Gain on futures contracts

= 20 contracts x 150 ticks x £12.50 = 37,500

OVERALL NET (LOSS) ON STRATEGY £(12,500)

This is a hedge efficiency of 000,50£

500,37£ = 75%





(iii) Interest rates fall by 1% and the futures market price increases by

0.75%

CASH MARKET

£

Saving of interest (1% x 6/12 x £5,000,000) 25,000

FUTURES MARKET




interest)

86.25

After interest rate reduction:


contracts at effectively 13% per year interest)

87.00

(0.75) x 100

= 75 ticks

Loss on futures contracts

= 20 contracts x 75 ticks x £12.50 = (18,750)

OVERALL NET GAIN ON STRATEGY £6,250

This is a hedge efficiency of 750,18£

000,25£ = 133 %

SUMMARY:

Scenario (i) (ii) (iii)

£ £ £

Cash market interest paid:

(16% x 6/12 x £5,000,000) 400,000 400,000

(13% x 6/12 x £5,000,000) 325,000

(Gain)/Loss on futures contracts (50,000) (37,500) 18,750

OVERALL COST £350,000 £362,500 £343,750

(c) Interest rate guarantees

The cost (premium) of the guarantee is £5,000,000 x 0.2% = £10,000, payable

whether or not the guarantee is ‘exercised’.

(i) & (ii) Interest rates increase by 2%

As interest rates have risen to 16%, the guarantee at 14% will be used

i.e.

£

Cash market cost (14% x 6/12 x £5,000,000) 350,000

Premium 10,000

£360,000

This is more expensive than the futures hedge for (i) and cheaper than

for (ii)





(iii) Interest rates fall by 1%

As interest rates have fallen to 13%, the guarantee at 14% will not be used

i.e.

£

Cash market cost (13% x 6/12 x £5,000,000) 325,000

Premium 10,000

£335,000

This is cheaper than the futures hedge as the guarantee has allowed the

company to take advantage of lower cash market interest rates.





Illustration 5

The directors of Tayquer plc are considering the use of options to protect the

current interest yield from their company’s £9.75 million short-term money market

investments. Having made initial enquiries they have been discouraged by the cost

of the option premium. A member of the treasury staff has suggested the use of a

collar as this would be cheaper.

Protection is required for the next eight months. Assume that it is now 1st June.

LIFFE interest rate options on three month money market futures

Contract size is £500,000; premium cost is in annual %

Calls Puts

Dec March Dec March

9100 0.90 1.90 - 0.02

9150 0.56 1.45 0.05 0.06

9200 0.27 1.04 0.17 0.13

9250 0.09 0.68 0.45 0.24

9300 0.01 0.20 0.83 0.32

9350 - 0.05 1.13 0.54

Tick size is 0.01%, and tick value £12.50.

The current interest rate received on Tayquer’s short-term money market

investments is 7.5% per annum.

Assume that Tayquer can buy or sell options at the above prices. Commission,

taxation and margins may be ignored.

Required:

Discuss how, and estimate at what cost, collars may be used to protect against the

interest yield risk. Recommend at which exercise price(s) the collar should be

arranged.





Solution 5

A collar will involve Tayquer arranging both a floor and a ceiling (lower and upper

limits) on its interest yield. This may be achieved by buying a call option on futures

and selling (or writing) a put option on the same futures contract, but with a

different exercise price.

As protection is required for the next eight months, to cover the full period, March

contracts will be used.

If Tayquer wishes to protect its current interest yield, the company is likely to fix

the floor at the current yield, i.e. it will buy call options at 9250, which implies an

interest rate of 7.5%.

The option would be exercised if interest rates fall below 7.5% and the futures price

rises above 9250. In order to reduce the net premium cost, the potential gain on

the interest from short-term investments (if interest rates were to rise) may be

reduced by selling March put contracts at a lower exercise price than 9250.

For example, if the interest rate rose to 9% and the put option had been sold at the

9150 exercise price, the buyer of the put option would exercise the option at any

futures price lower than 9150. A 9% interest rate implies a futures price of 9100.

The 1.5% gain in interest rate rises would be split 1% to Tayquer and 0.5% to the

buyer of the put option. Any further interest rate rises will result in the extra

interest earned by Tayquer being equal to the increased loss on the puts.

Hence Tayquer will only benefit from the first 1% of interest rate increases, but will

be protected from any reduction in interest rates. Tayquer, in this example, has

fixed the minimum interest received at 7.5%, and the maximum at 8.5%.

To protect £9.75 million for eight months, the following number of contracts are

required:

£500,000

million 75.9£ x

months 3

months 8 = 52 contracts

The net percentage premium payable at various combinations of collar are:

Buy call Premium

paid

Write put Premium

received

Net premium

cost (%)

Net premium

cost (£)

1) 9250 0.68 9200 0.13 0.55 35,750

2) 9250 0.68 9150 0.06 0.62 40,300

3) 9250 0.68 9100 0.02 0.66 42,900

The net premium cost is calculated as follows:

1) 0.55 x 100 = 55 ticks

52 contracts x 55 ticks x £12.50 = £35,750

2) 0.62 x 100 = 62 ticks


3) 0.66 x 100 = 66 ticks






The choice of exercise price at which to sell the put option will depend upon

Tayquer’s views on how far interest rates could rise, and the potential gains if rates

do rise.

Interest

rate

Put

exercise

price

Net

premium

cost %

Interest

gain %

Net gain or

loss %

Net gain or

loss £

8% 9200 (0.55) 0.50 (0.05) (3,250)

8½% 9150 (0.62) 1.00 0.38 24,700

9% 9100 (0.66) 1.50 0.84 54,600

The net sterling gains and losses are calculated as follows:

52 contracts x (0.05) x 100 x £12.50 = £(3,250)

52 contracts x 0.38 x 100 x £12.50 = £24,700

52 contracts x 0.84 x 100 x £12.50 = £54,600

The best potential gains are from a put option exercise price of 9100, but Tayquer

may not be willing to lose the £7,150 premium income relative to 9200 put option

exercise price.

The £7,150 premium income that would be lost is calculated as follows:

9200 premium income = 52 x 0.13 x 100 x £12.50 = 8,450

9100 premium income = 52 x 0.02 x 100 x £12.50 = 1,300

£7,150

Alternatively, compare the net premium cost in 3) above of £42,900 with the net

premium cost in 1) above of £35,750. The difference between these two amounts

is £7,150.

In reality trading costs may make any option strategies more expensive than they

appear to be from the figures presented.





THE MACAULAY DURATION METHOD

In 1938, Frederick R. Macaulay defined “Duration” as the total weighted average

time for recovery of the payments and principal in relation to the current market

price of a bond.

The maturity of a bond is not a particularly good indication of the timing of the cash

flows associated with that bond, since a significant proportion of those cash flows

will occur prior to maturity – normally in the form of interest payments.

One could calculate an average of the timings of each cash flow, weighted by the

size of those cash flows. Duration is very similar to such an average, but instead of

taking each cash flow as a weighting, duration uses the present value of each cash

flow.

Steps required to calculate bond duration

1. Establish the cash flows arising at each future time period;

2. Calculate the present value of these future cash flows, discounted at the IRR

(i.e. the gross yield to maturity) of the security. Incidentally, the sum of

these figures must be the current price of the bond;

3. Calculate each year’s discounted cash flow as a proportion of the current

value of the bond;



Illustration 6

Seven years prior to the maturity of a bond with a 10% coupon, it is trading at a

price of £95.01 per cent and has a gross yield to maturity of 11.063%. Using the

Macaulay duration method, you are required to calculate the bond duration.

Solution 6

Yr 1 2 3 4 5 6 7

1 Annual cash

flows (£) 10.00 10.00 10.00 10.00 10.00 10.00 110.00

2 Discounted

@11.063%

(£)

9.00 8.11 7.30 6.57 5.92 5.33 52.78

3 Proportion of

price (£95.01) 0.095 0.085 0.077 0.069 0.062 0.056 0.556

4 Proportion

multiplied by

year number.

0.095 0.170 0.231 0.276 0.310 0.336 3.892

Finally, find the totals of row 4, since these provide the bond duration of 5.31

years, ie the weighted average time to full recovery of an investment in this bond.

Remember that if the monetary amounts in row 2 (above) are cross-cast, the result

must obviously be the current price of the bond, since the gross yield to maturity is

the internal rate of return of all cash flows associated with the bond.

Furthermore, the above calculation is almost identical to the approach used for

calculating the duration taken to recover an original investment in project appraisal

(as described earlier on page 78 and page 79).





Significance of the calculation of Duration

Duration is an important measure for fixed-income investors and their advisers,

since bonds with higher durations may have greater price volatility than similar

bonds with lower durations. In general:

● Changes in the value of a bond are inversely related to changes in the rate of

return i.e. the lower the yield to maturity, the higher the value of the bond;

● Long-term bonds have higher interest rate risk than shorter term bonds, due

to the greater probability (over the longer time period) of market interest rate

increases; and

● High coupon bonds have less interest rate sensitivity than low coupon bonds,

since the greater the amounts of the cash flows received in the short-term,

the earlier the purchase price of the bond will be recouped.

The Macaulay duration method measures the number of years required to recover

the cost of the bond (taking account of the present value of all interest and capital

cash flows within the future time period). The result is expressed in years.

A measure referred to as Modified Duration (or Volatility) expands on the basic

method, but the ACCA P4 Syllabus only requires a knowledge of the “simple”

Macaulay duration method, as a means of assessing exposure to interest rate

changes.

The basic lessons of “duration” are:

● As maturity increases, the measure of duration will also increase and the

market value of the bond will become more sensitive to changes in the level

of interest rates;

● As the coupon rate of a bond increases, duration will decrease and the value

of the bond will be less sensitive to changes in the level of interest rates; and

● As interest rates rise, duration will decrease and the value of the bond will be

less sensitive to subsequent rate changes.

Illustration 7

In each of the following cases, you are required to use the Macaulay duration

method to calculate the duration for each of the following securities:

(a) A bond with a five year maturity has a current value of £92.41 per cent, a

coupon rate of 8% and a market yield of 10%.

(b) On the 1 February 2011, a 5.5% Treasury Bond (which is redeemable on 1

February 2015), has a market value of £110.28 per cent and a yield to

maturity of 2.75%.

(c) A 6% bond has three years to redemption. It has a current market price of

£89.85 per cent. Interest is paid half-yearly and its market yield is 10% per

annum (i.e. 5% every six months).





Solution 7

(a)

Year 1 2 3 4 5

1 Annual cash flows (£) 8.00 8.00 8.00 8.00 108.00

2 Discounted @ 10% (£) 7.27 6.61 6.01 5.46 67.06

3 Proportion of bond value

(£92.41) 0.079 0.072 0.065 0.059 0.726

4 Proportion multiplied by year

number 0.079 0.144 0.195 0.236 3.630

Finally, establish the totals of row 4, since these provide the bond duration of 4.284

years i.e. the weighted average time to full recovery of an investment in this bond.

(b)

Year 1 2 3 4

1 Annual cash flows (£) 5.50 5.50 5.50 105.50

2 Discounted @ 2.75% (£) 5.35 5.21 5.07 94.65


(£110.28) 0.049 0.047 0.046 0.858

4 Proportion multiplied by year

number 0.049 0.094 0.138 3.432

Finally, establish the totals of row 4., since these provide the bond duration of

3.713 years i.e. the weighted average time to full recovery of an investment in this

bond.

(c)

Period ½ 1 1½ 2 2½ 3

1 Half-yearly cash flows (£) 3 3 3 3 3 103

2 Discounted @ 5% per

half year (£) 2.86 2.72 2.59 2.47 2.35 76.86


(£89.85) 0.032 0.030 0.029 0.028 0.026 0.855

4 Proportion multiplied by

period number 0.016 0.030 0.044 0.056 0.065 2.565

Finally, establish the totals of row 4., since these provide the bond duration of

2.776 years i.e. the weighted average time to full recovery of an investment in this

bond.

General observations

Note that Macaulay duration will always be lower than the term to maturity

(assuming that the coupon rate exceeds zero - you may think that this is a stupid

comment, but the world of finance is going through some amazing times!!).

Nowadays, the value of Macaulay duration is less evident, due to wide availability of

computer programs with Monte Carlo simulation. Obviously, bonds are subject to

risk, but duration is not intended to reflect risk; it measures interest rate

sensitivity.





TERM STRUCTURE OF INTEREST RATES

The “term structure of interest rates” reflects the manner in which the gross

redemption yield on government bonds varies with the term to maturity i.e. the

period of time before the stock is to be redeemed. For example, government bonds

may be short-dated (e.g. repayment within 5 years), medium-dated (repayment

between 5 and 20 years) or long-dated (redemption in excess of 20 years). Of

course, some government bonds e.g. 2½% Consols are undated (i.e.

irredeemable).

This data is often presented in the form of a graph to illustrate the “bond yield

curve”, which is created by plotting the gross redemption yield of the bond against

the term to maturity. In normal circumstances the yield curve is upward sloping.

The gross redemption yield reflects the internal rate of return on the cash flows

associated with the bond i.e. it incorporates the effect of the current market value

of the bond, the gross interest payments and the redemption value of the bond – in

other words it measures not only the gross interest yield but also the capital gain or

loss to maturity. The calculation of the gross redemption yield is very similar to the

calculation of the cost of redeemable debt for the company – the notable difference

is that interest payments are included gross (as opposed to net of corporation tax

as is used in arriving at Kd).

The normal yield curve

The general shape of the normal upward sloping yield curve appears as follows:

0 5 10 15 20 25 30

Term to maturity (years)

A normal yield curve slopes upwards because the yield on longer dated bonds is

normally higher than the yield on shorter dated bonds. If you are confused by this

point, remember that your mortgage is only cheaper than your overdraft because

the mortgage is secured on the property, whereas the overdraft is unsecured. The

Gross

Redemption

Yield

%

Bond

Yield Curve





reason for the upward sloping shape of the yield curve is thought to be based on

the following theories:

● liquidity preference theory

● expectations theory

● market segmentation theory

Liquidity preference theory

Lenders have a natural preference for holding cash rather than securities − even

low risk government securities. They therefore need to be compensated for being

deprived of their cash for a longer period of time – hence the higher yield on long-

dated securities and the lower yield on short-dated securities. There is a greater

risk in lending long-term than in lending short-term. To compensate lenders for

this risk they would require a higher return on longer dated investments.

Expectations theory

This theory states that the shape of the yield curve will vary dependent upon a

lender’s expectations of future interest rates (and therefore inflation levels). A

curve that rises from left to right indicates that rates of interest are expected to

increase in the future to reflect the investors fear of rising inflation rates.

Market segmentation theory

The slope of the yield curve is thought to reflect conditions in different segments of

the market. In other words lenders and borrowers tend to confine themselves to a

particular segment of the market and thus it is probably futile to compare short-

term with long-term lending and borrowing. Thus, companies typically finance

working capital with short-term funds and non-current assets with long-term funds.

This leads to different factors affecting short-term and long-term interest rates

leading to irregularities which cause humps, dips or wiggles in the shape of the

yield curve.

The inverse yield curve

A yield curve may occasionally slope downwards, since short-term yields may be

higher than long-term yields for the following reasons:

● Expectations i.e. if interest rates are currently high, but the market

anticipates a steep fall in the near future, the resultant yield curve will be

downward sloping.

● Government intervention i.e. a policy of keeping interest rates relatively high

might have the effect of forcing short-term yields higher than long-term

yields.

An inverse yield curve is downwards sloping and its general shape is as follows:





0 5 10 15 20 25 30

Term to maturity (years)

Gross

Redemption

Yield

%

Bond

Yield Curve




Chapter 18

Swaps



CHAPTER 18 – SWAPS


CHAPTER CONTENTS

INTEREST RATE SWAPS, CURRENCY SWAPS AND SWAPTIONS --- 409

INTEREST RATE SWAPS 409

CURRENCY SWAPS 409

SWAPTIONS 410

ILLUSTRATION 1 – INTEREST RATE SWAPS ------------------------- 410

ILLUSTRATION 2 – CURRENCY SWAPS ------------------------------- 414

ILLUSTRATION 3 – SWAPTIONS -------------------------------------- 420





INTEREST RATE SWAPS, CURRENCY SWAPS AND

SWAPTIONS

Interest rate swaps

These are transactions which allow a company to exploit different interest rates in

different markets for borrowing, and thereby reduce or alter the timing of interest

payments. The parties to a swap may either be two companies, or a company and

a bank. In the former case the companies may arrange the agreement themselves

or a bank may act as intermediary.

The parties to a swap exchange their interest rate commitments with each other.

That is, the company with a fixed rate commitment (which believes that interest

rates are about to fall) effectively swaps with a counterparty with a floating rate

commitment (which believes that interest rates are about to increase). In doing

this they simulate each others’ borrowings, but retain their obligations to the

original lenders. Thus they must accept a degree of counterparty risk since if the

other party defaults on the interest payments, the original borrower remains liable

to the lender.

The benefits are that the company can obtain interest rates which are lower than it

could get directly from a bank or from other investors, and may be able to structure

the timing of payments so as to improve the matching of cash outflows with

revenues. Swaps are easy to organise and are flexible since they can be arranged

in any size. They may also be reversible by negotiation, but this may involve the

payment of a substantial termination premium by the party seeking release from

the swap commitment.

Currency swaps

Two parties agree to swap equivalent amounts of currency for a given period. This

effectively involves the exchange of debt from one currency to another. Again,

liability on the principal is retained and the parties are liable to counterparty risk.

One benefit to a company is that it can gain access to debt finance in another

country and currency where it is little known (and consequently has a poorer credit

rating) than in its home country. It can therefore take advantage of lower interest

rates than it could obtain if it arranged the loan itself.

A further purpose of currency swaps is to restructure the currency base of the

company’s liabilities. This may be important where the company is trading

overseas and receiving revenues in foreign currencies, but its borrowings are

denominated in its home currency. Currency swaps therefore provide a means of

reducing exchange rate risk exposure.

A third benefit of currency swaps is that at the same time as exchanging currency,

the company may also be able to convert fixed rate debt to floating rate or vice

versa. Thus it may obtain some of the benefits of an interest rate swap in addition

to achieving the other advantages of a currency swap.





Swaptions

These are an option to enter into an interest rate swap or currency swap. A

company could purchase such an instrument, which gives the right, but not the

obligation to enter into a swap arrangement within a predetermined period. The

premium paid to the bank would be relatively high in cases where there was a

general expectation of volatile interest rate or exchange rate movements.

Illustration 1 – Interest rate swaps

Manling plc has £14 million of fixed rate loans at an interest rate of 12% per year

which are due to mature in one year. The company’s treasurer believes that

interest rates are going to fall, but does not wish to redeem the loans because large

penalties exist for early redemption. Manling’s bank has offered to arrange an

interest rate swap for one year with a company that has obtained floating rate

finance at London Interbank Offered Rate (LIBOR) plus 1.125%. The bank will

charge each of the companies an arrangement fee of £20,000 and the proposed

terms of the swap are that Manling will pay LIBOR plus 1.5% to the other company

and receive from the company 11.625%.

Corporation tax is at 35% per year and the arrangement fee is a tax allowable

expense. Manling could issue floating rate debt at LIBOR plus 2% and the other

company could issue fixed rate debt at 11.75%. Assume that any tax relief is

immediately available.

Required:

(a) Evaluate whether Manling plc would benefit from the interest rate swap

1. If LIBOR remains at 10% for the whole year

2. If LIBOR falls to 9% after 6 months

(b) If LIBOR remains at 10% evaluate whether both companies could benefit from

the interest rate swap if the terms of the swap were altered. Any benefit

would be equally shared.





Solution 1

(a) Evaluation of interest rate swap

1. If LIBOR remains at 10% for whole year

Manling Other company

% %

Existing commitment (12) (10% + 1.125%) (11.125)

Manling pays (10% + 1.5%) (11.5) 11.5

Manling receives 11.625 (11.625)

Revised commitment (11.875) (11.25)

The current cost of fixed rate debt is:

£14m x 12% less tax relief at 35% = £1,092,000

The cost under the swap is:

£14m x 11.875% less tax relief at 35% = 1,080,625

Plus the arrangement fee £20,000

less tax relief at 35% 13,000

Total cost £1,093,625

The swap would not be beneficial, as the final cost, after tax, is

increased by (£1,093,625 less £1,092,000) = £1,625

2. If LIBOR falls to 9% after six months


% %


Manling pays (9% + 1.5%) (10.5) 10.5

Manling receives 11.625 (11.625)


If LIBOR falls to 9% after six months the cost is

£14m x 11.875% x 6/12 x 0.65 = 540,312

£14m x 10.875% x 6/12 x 0.65 = 494,813

1,035,125

Plus arrangement fee (net of tax) = 13,000


The swap would then be beneficial since Manling benefits by

(£1,092,000 less £1,048,125) = £43,875





(b) Whether both parties would benefit from the swap if LIBOR remains

at 10%

Ignoring the arrangement fee, both companies are benefiting from the swap

i.e.

For a floating rate arrangement:

%

Manling would normally pay LIBOR plus 2%

but is actually paying LIBOR plus 1.875%

Thus saving 0.125

For a fixed interest rate arrangement:

The other company would normally pay 11.75%

but is actually paying fixed interest of 11.25%

Thus saving 0.5

Total saving 0.625%

If this saving were divided equally, each company would save 0.3125% i.e.


% %

Normal floating rate

LIBOR of 10% + 2% = (12) Normal fixed rate (11.75)

Saving 0.625% ÷ 2 = 0.3125 0.3125


Accordingly if the terms of the swap were varied so that Manling paid the

other company LIBOR plus 1.3125%, which is calculated as follows:

%

Present arrangement of LIBOR plus 1.5

add back original saving 0.125

less revised saving (0.3125)

Revised arrangement of LIBOR plus 1.3125

and the remaining terms of the swap were unchanged, the effect would be:


% %


Manling pays LIBOR

+ 1.3125% (11.3125) 11.3125

Manling receives 11.625_ (11.625)_


Thus Manling is paying interest at 0.3125% below its normal floating rate of

LIBOR + 2% and the other company is paying at 0.3125% below its normal

fixed rate of 11.75%.





The total cost to Manling of using these new terms is:

£

£14m x 11.6875% x 0.65 1,063,562

Plus arrangement fee (net of tax) 13,000


This is a saving of (£1,092,000 − £1,076,562) = £15,438 relative to not

undertaking the swap.





Illustration 2 – Currency swaps

(a) Discuss how interest rate swaps and currency swaps might be of value to the

corporate financial manager.

(b) Calvold plc has a one year contract to construct factories in a South American

country. At the end of the year the factories will be paid for by the local

government. The price has been fixed at 2,000 million pesos, payable in the

South American currency.

In order to fulfil the contract Calvold will need to invest 1,000 million pesos in

the project immediately, and a fixed additional sum of 500 million pesos in six

months time.

The government of the South American country has offered Calvold a fixed

rate-fixed rate currency swap for one year for the full 1,500 million pesos at a

swap rate of 20 pesos/£. Net interest of 10% per year would be payable in

pesos by Calvold to the government.

There is no forward foreign exchange market for the peso against the pound.

Forecasts of inflation rates for the next year are:

Probability UK South American country

0.25 4% and 40%

0.50 5% and 60%

0.25 7% and 100%

The peso is a freely floating currency which has not recently been subject to

major government intervention.

The current spot rate is 25 pesos/£. Calvold’s opportunity cost of funds is

12% per year in the UK. The company has no access to funds in the South

American country.

Taxation, the risk of default, and discounting to allow for the timing of

payments may be ignored.

Required:

Evaluate whether it is likely to be beneficial for Calvold plc to agree to the

currency swap.





Solution 2

(a) Interest rate swaps

An interest rate swap is a transaction which allows a company to exploit

different interest rates in different markets for borrowing, and thereby reduce

or alter the timing of interest payments. The parties to a swap may be either

two companies, or a company and a bank. In the former case the companies

may arrange the agreement themselves or a bank may act as intermediary.

The parties to a swap, exchange their interest rate commitments with each

other. In doing this they simulate each others’ borrowings but retain their

obligations to the original lenders. Thus they must accept a degree of

counterparty risk since if the other party defaults on the interest payments,

the original borrower remains liable to the lender.

The benefits are that the company can obtain interest rates which are lower

than it could get directly from a bank or from other investors, and may be

able to structure the timing of payments so as to improve the matching of

cash outflows with revenues. Swaps are easy to arrange and are flexible since

they can be arranged in any size. They may also be reversible by

negotiation, but this may involve the payment of a substantial termination

premium by the party seeking release from the swap commitment.

Interest rate swaps also provide a means of financial speculation, but your

course is more concerned with the hedging of risk as opposed to the seeking

of risk.

Currency swaps

In a currency swap, two parties agree to swap equivalent amounts of currency

for a given period. This effectively involves the exchange of debt from one

currency to another. As with interest rate swaps, liability on the principal is

not transferred and the parties are liable to counterparty risk.

One benefit to the company is that it can gain access to debt finance in

another country and currency where it is little known, and consequently has a

poorer credit rating, than in its home country. It can therefore take

advantage of lower interest rates than it could obtain if it arranged the loan

itself.

A further purpose of currency swaps is to restructure the currency base of the

company’s liabilities. This may be important where the company is trading

overseas and receiving revenues in foreign currencies, but its borrowings are

denominated in the currency of its home country. Currency swaps therefore

provide a means of reducing exchange rate exposure.

A third benefit of currency swaps is that at the same time as exchanging

currency, the company may also be able to convert fixed rate debt to floating

rate or vice versa. Thus it may obtain some of the benefits of an interest rate

swap in addition to achieving the other purposes of a currency swap.





b) Currency swap by Calvold plc

The expected level of inflation in the UK is 5.25%, and in the South American

country 65%. The purchasing power parity theory may be used to estimate

an expected exchange rate at the end of the year, but it is likely to be more

useful to Calvold to see the range of exchange rates that might occur under

each of the different inflation scenarios, and evaluate their effects on sterling

cash flows.

Rate after one year = current spot rate x h1

f1

++

Rate after six months = current spot rate x h1

f1

++

where f = the foreign inflation rate; and h = the home inflation rate

Illustration

With 40% SA inflation and 4% UK inflation:

Rate after one year = 25 x 04.1

4.1 = 33.65

Rate after six months = 25 x 04.1

4.1 = 29.00

However a six month exchange rate of 29.325 pesos/£ would be acceptable,

being the simple average of the current spot rate (25 pesos) and the predicted

one year spot rate (33.65 pesos).

Forecast exchange rates are:

Inflation Forecast exchange rate

Month SA UK

% %

0 25.00

6 40 4 29.00

12 40 4 33.65

0 25.00

6 60 5 30.86

12 60 5 38.10

0 25.00

6 100 7 34.18

12 100 7 46.73





The effect of the swap will be compared with the use of currency markets for

each of the three scenarios. It is assumed that Calvold will have to borrow

funds in the UK to finance the deal and interest is therefore calculated at the

opportunity cost of funds i.e.

For one year 12%

For six months: use 12% x 6/12 = 6%

or 112.1 − = 5.8%

this will depend upon the method of calculating interest charges. In the

following solution a six-monthly rate of 6% is used.

(i) Using the currency markets

1. Inflation rates 4% and 40%

Exchange

rate

Interest

@12%

p.a.

Pesos (m) £m £m

Investment –

month 0 (1,000.00) 25.00 (40.00) (4.80)

Investment –

month 6 (500.00) 29.00 (17.24) (1.03)

(57.24) (5.83)

Interest (5.83)

Total cost (63.07)

Received –

month 12 2,000.00 33.65 59.44

Net (loss) (3.63)


Investment –

month 0 (1,000.00) 25.00 (40.00) (4.80)

Investment –

month 6 (500.00) 30.86 (16.20) (0.97)

(56.20) (5.77)

Interest (5.77)

Total cost (61.97)

Received –

month 12 2,000.00 38.10 52.49

Net (loss) (9.48)


Investment –

month 0 (1,000.00) 25.00 (40.00) (4.80)

Investment –

month 6 (500.00) 34.18 (14.63) (0.88)

(54.63) (5.68)

Interest (5.68)

Total cost (60.31)

Received –

month 12 2,000.00 46.73 42.80

Net (loss) (17.51)





(ii) Using the currency swap

The currency swap will provide some protection against the likely

depreciation in the value of the peso. 1,500 million pesos will be

swapped, with the swap reversed at the year end at the same swap

rate of 20 pesos/£. Calvold will have to borrow sterling in the UK to

finance the swap, which will cost (1,500 million pesos ÷ 20) i.e. £75

million.

Since the cost of funds in the UK is 12% p.a., the interest charge for the

year will be (12% x £75 million) = £9million.

However swaps involve the transfer of interest rate liabilities as well as

of principal, therefore the interest cost to Calvold will be the rate given

in the swap agreement of 10% p.a. i.e. (10% x 1,500 million pesos) 150

million pesos.

It is assumed that no interest will be earned on the 500 million pesos

which will be lying idle until month 6.

Accordingly, Calvold will only remain exposed to exchange risk on the

balance of the purchase price (500 million pesos) which will be

converted at whatever the prevailing end of year rate happens to be. If

it is assumed that no interest will be paid to the South American

government until the end of the year, the sterling value of interest

payments (based on 150 million pesos) will also be dependent on the

then prevailing exchange rate.


£m

Receipts (500 million pesos ÷ 33.65) 14.86

Interest paid (150 million pesos ÷ 33.65) (4.46)

Net receipt 350 ____

Net profit with swap 10.40

Net loss without swap (£m) (3.63)


£m







£m










The above calculations show that since Calvold’s receipts, denominated

in pesos, will not be received until year end, the profitability of the deal

is eroded by inflation if the currency is traded on the markets. However

a swap arrangement should be entered into, whereby Calvold borrows

£75 million in the UK and immediately exchanges this for 1,500 million

pesos from the South American government (whilst similarly swapping

interest payment obligations). The effect will be that only the balance of

the receipts (500 million pesos) will be subject to exchange fluctuations

and therefore the effects of inflation diminished. Thus it appears that it

would be beneficial for Calvold to use the currency swap.





Illustration 3 – Swaptions

Noswis plc borrowed two million Euros (€) in four year floating rate notes funds

nine months ago at an interest rate EURIBOR plus 1%, in an attempt to reduce the

level of interest paid on its loans. At that time EURIBOR was 6%. Unfortunately

EURIBOR interest rates have increased since that time to 7.2%. The company

wishes to protect itself from further interest rate volatility, but does not wish to lose

the benefit of possible interest rate reductions that might occur in a few months

time. An adviser has suggested the use of a six month American style Euro

swaption at 8.5% with a premium of €50,000, commencing in three months time

and with a maturity date the same as the floating rate Euro loan.

Required:

Briefly explain what is meant by a swaption, and illustrate under what

circumstances this proposed swaption would benefit Noswis. The time value of

money may be ignored.





Solution 3

Swaptions are hybrid derivative products that integrate the benefits of swaps and

options. The buyer of a swaption has the right, but not the obligation, to enter into

an interest rate or currency swap during a limited period of time and at a specified

rate.

Swaptions are available on the over-the-counter market and involve the payment of

a premium, normally in advance. They may be ‘European style’, exercisable only

on the maturity date, or ‘American style’, exercisable on any business day during

the exercise period.

Noswis is interested in protection against interest rate volatility, but wishes to

maintain the flexibility to benefit from falls in interest rates. A swaption would offer

the opportunity to do this.

Noswis is currently paying 8.2% on its Euro loan. The swaption offers a swap from

floating rate to fixed rate finance for the remaining three year period of the Euro

loan. (N.B. the four year loan was raised nine months ago and the swaption will

not commence until another three months have elapsed).

The fixed rate is 0.3% per annum above the current floating rate payable by

Noswis.

The premium payable of €50,000 is 2.5% of the total value of the loan, or, ignoring

the time value of money, 0.833% per year over the remaining three year period of

the loan.

If Euro interest rates rise during the next nine months by more than 0.3% the

swaption is likely to be exercised. For the swaption to be beneficial to Noswis, the

average floating rate payable by Noswis without the swap over the three year

period would have to exceed:

8.2% + 0.3% + 0.833% = 9.333%

This is a 13.8% increase on the current EURIBOR payable rate (i.e. over 8.2%)

If interest rates fall then the swaption would not be exercised and Noswis would

benefit from borrowing at the lower floating rates. If the swaption is not exercised

the premium is still payable, and Noswis would be worse off by the amount of the

premium than if no swaption had been agreed.

However, this premium is the price that must be paid for the flexibility of being able

to take advantage of any lower interest rates in the future.

Furthermore it should be noted that once the swaption is exercised this action

cannot be reversed. Therefore if interest rates subsequently fall, Noswis will

continue to pay the fixed rate of interest set out in the agreement.




Chapter 19

International investment

appraisal



CHAPTER 19 – INTERNATIONAL INVESTMENT APPRAISAL


CHAPTER CONTENTS

INTERNATIONAL INVESTMENT AND FINANCING DECISIONS ----- 425

INTRODUCTION 425

PARENT OR PROJECT VIEWPOINT? 425

PURCHASING POWER PARITY THEORY (PPPT) 426

FOUR-WAY EQUIVALENCE 427

REMISSION OF FUNDS 428

EXCHANGE RATE RISK 428

POLITICAL RISK 428

PROJECT DISCOUNT RATES 429

FINANCING OVERSEAS PROJECTS 429

REPATRIATION OF CASH FROM OVERSEAS INVESTMENTS 430

TRANSFER PRICING ---------------------------------------------------- 435

ARTICLE FROM A USA PUBLICATION 435

BROOKDAY PLC --------------------------------------------------------- 439

ZEDLAND POSTAL SERVICE -------------------------------------------- 443

AXMINE PLC ------------------------------------------------------------- 448





INTERNATIONAL INVESTMENT AND FINANCING

DECISIONS

Introduction

In essence capital budgeting for overseas investments is similar to domestic

investment appraisal. The normal procedure of determining the relevant cash flows

and discounting at the rate of return commensurate with the project’s risk should

be followed to determine project NPV’s. In practice, however, several complexities

may be encountered. These are examined below.

Parent or project viewpoint?

Any overseas capital project can be assessed from the point of view of the parent

company or the local subsidiary. Relevant cash flows may vary between the two

viewpoints due to the following factors:

● Timing of the receipt of funds;

● Impact of exchange rate changes on the value of the funds;

● Impact of local and home country tax on the value of funds received;

● Effect on other parts of the organisation (e.g. sales by the subsidiary reducing

the parent’s export market sales).

As the objective of financial management is to maximise shareholder wealth, and

the vast majority of the shareholders are likely to be located in the parent country,

it is essential that projects are evaluated from a parent currency viewpoint. After

all, in the UK only sterling receipts can be used to pay sterling dividends.

Accordingly, the following three-step procedure is recommended for calculating

project cash flows:

1. Compute local currency cash flows from a subsidiary viewpoint as if it were an

independent entity;

2. Calculate the amount and timing of transfers to the parent company in

sterling terms;

3. Allow for the indirect costs and benefits of the project in sterling terms (e.g.

the contribution lost due to the turnover of other members of the group being

affected by this overseas project).





Purchasing power parity theory (PPPT)

This theory is based upon the “law of one price” i.e. in equilibrium identical

products must have the same relative cost irrespective of the currency used. PPPT

claims that the rate of exchange between two currencies depends upon the inflation

levels in the countries concerned. The formula is designed to estimate a predicted

spot rate between two currencies at some future time.

Formula (assuming use of indirect currency quotes)

Predicted Spot rate (S1) = ratelationinfome

ratelationinforeign

h1

f1rate Spot Current

+

+×

=

+

+×

b

c0

h1

h1S

Illustration 1

Startall plc wishes to estimate future exchange rates based upon the following

projections of inflation.

UK USA Bargonia

Year 1 5% 5% 20%

2 5% 5% 30%

3 5% 7% 30%

4 5% 7% 30%

5 5% 7% 30%

If current spot rates are US$1.60 = £1 and Bargonian Dowl 250 = £1, using the

PPPT, what are the predicted spot rates for the currencies concerned at the end of

each of the next five years?

Solution 1

Exchange rates

Year 0 1 2 3 4 5

Dowl/£ 250.0 285.7 353.7 438.0 542.2 671.3

05.1

2.1×

05.1

3.1×

05.1

3.1×

05.1

3.1×

05.1

3.1×

US$/£ 1.60 1.60 1.60 1.630 1.662 1.693

05.1

05.1×

05.1

05.1×

05.1

07.1×

05.1

07.1×

05.1

07.1×





Four-way equivalence

Where Fo = forward rate

So = current spot rate

S1 = predicted spot rate

ic = interest rate in country c (the foreign country)

ib = interest rate in country b (the home country)

hc = expected inflation rate in country c (the foreign

country)

hb = expected inflation rate in country b (the home country)

i (or m) = money (or nominal) interest rate (i.e. including the

effect of inflation)

r = real interest rate (i.e. excluding the effect of inflation)

h (or i) = expected inflation rate

INTEREST RATE PARITY THEORY

Forward rate (F0) =

+

+×=

++

×b

c0

i1

i1S

rate nteresti ome

rate nteresti oreign

h1

f1rate Spot Current

PURCHASING POWER PARITY THEORY

Predicted Spot rate (S1) =

+

+×=

++

×b

c0

h1

h1S

rate nflationi ome

rate nflationi oreign

h1

f1rate Spot Current

INTERNATIONAL FISHER EFFECT

( ) ( )( )h1r1i1 ++=+

or

( ) ( )( )i1r1m1 ++=+

EXPECTATIONS THEORY





Remission of funds

Certain costs to the subsidiary may in reality be revenues to the parent company.

For example, royalties, supervisory fees and purchases of components from the

parent company are costs to the project, but result in revenues to the parent. Care

should be exercised in identifying exactly how and when funds are repatriated. The

normal methods of returning funds to the parent company are:

● Dividends

● Royalties

● Transfer prices; and

● Loan interest and principal

It is important to note that some of these items may be locally tax-deductible for

the subsidiary but taxable in the hands of the parent.

Exchange rate risk

Changes in exchange rates can cause considerable variation in the amount of funds

received by the parent company. In theory this risk could be taken into account in

calculating the project’s NPV, either by altering the discount rate or by altering the

cash flows in line with forecast exchange rates. Virtually all authorities recommend

the latter course, as no reliable method is available for adjusting discount rates to

allow for exchange risk.

Political risk

This relates to the possibility that the NPV of the project may be affected by host

country government actions. These actions can include:

● Expropriation of assets (with or without compensation!);

● Blockage of the repatriation of profits;

● Suspension of local currency convertibility;

● Requirements to employ minimum levels of local workers or gradually to

pass ownership to local investors.

The effect of these actions is almost impossible to quantify in NPV terms, but their

possible occurrence must be considered when evaluating new investments. High

levels of political risk will usually discourage investment altogether, but in the past

certain multinational enterprises have used various techniques to limit their risk

exposure and proceed to invest. These techniques include the following

(a) Structuring the investment in such a way that it becomes an

unattractive target for government action. For example, overseas

investors might ensure that manufacturing plants in risk-prone countries

are reliant on imports of components from other parts of the group, or

that the majority of the technical “know-how” is retained by the parent

company. These actions would make expropriation of the plant far less

attractive.

(b) Borrowing locally so that in the event of expropriation without

compensation, the enterprise can offset its losses by defaulting on local

loans.





(c) Prior negotiations with host governments over details of profit

repatriation, taxation, etc, to ensure no problems will arise. Changes in

government, however, can invalidate these agreements.

(d) Attempting to be “good citizens” of the host country so as to reduce the

benefits of expropriation for the host government. These actions might

include employing large numbers of local workers, using local suppliers,

and reinvesting profits earned in the host country.

Project discount rates

In the same way as for domestic capital budgeting, project cash flows should be

discounted at a rate that reflects their systematic risk. Many firms assume that

overseas investment must carry more risk than comparable domestic investment

and therefore increase discount rates accordingly.

This assumption, however, is not necessarily valid. Although the total risk of an

overseas investment may be high, in the context of a well-diversified parent

company portfolio much of the risk may be diversified away. Because of the lack of

correlation between the performance of some national economies, the systematic

risk of overseas investment projects may in fact be lower than that of comparable

domestic projects.

It must therefore be realised that the automatic addition of a risk premium simply

because a project is located overseas does not always make sense, and any

increase in the discount rates used for foreign projects should be viewed with

caution.

Financing overseas projects

The chief sources of long-term finance are the following:

(a) Equity

The subsidiary is likely to be 100% owned by the parent company. However,

in some countries it is necessary for nationals to hold a stake, sometimes

even a majority of the ordinary shares on issue.

(b) Loans

These could be in sterling, or in the currency of the country of operation, or in

another currency (e.g. US dollars) particularly if funds are raised through the

Euromarkets.

The usual approach taken is to match the assets of the subsidiary as far as

possible with a loan in the local currency. This has the advantage of reducing

exposure to currency risk. However, this reduced risk must be weighed

against the interest rate paid on the loan. A loan in the local currency may

carry a higher interest rate, and it may be preferable, for example, to arrange

a Eurocurrency loan in a major currency which is highly correlated with the

currency of the overseas operations.

(c) Government grants

Finance may be available from the UK, the overseas government, or an

international body, such as the World Bank.

(d) Intercompany accounts

Financing by intercompany account is useful in a situation where it is difficult

to get funds out of the foreign country by way of dividends. This is further

discussed below.





Repatriation of cash from overseas investments

If it is difficult to repatriate the cash as dividends, various other alternatives are

possible, for example

● Reasonably high management charges

● Moderately excessive royalties

● Slightly inflated transfer prices; and

● Fairly high interest rates on inter-company loans.

Comprehensive example

The directors of Eibl plc are considering whether to set up a subsidiary in Heina, a

country whose currency is the Croll. The Heina subsidiary would assemble and

market a sophisticated tractor. Survey data indicates that the Heina subsidiary

could expect to sell 500 tractors in the first year of operations, increasing by 10

tractors in each of the next four years.

In the first year, the unit selling price of a tractor would be three million Crolls,

increasing at an annual rate of 10% (rounded to the nearest 100,000 Crolls) and

each tractor would require components costing £5,000. The cost of the

components would increase by 6% per annum in subsequent years. Eibl plc would

provide the components to be assembled and would invoice its Heina subsidiary for

these with no profit mark-up. The unit cost would be calculated to the nearest

£100.

Annual production, administration and selling costs in Heina are expected to be

45% of the sales value of tractors sold in that year.

At the start of its operations, the Heina subsidiary would require working capital of

160 million Crolls. At the end of each year of production, the required level of

working capital would be approximately equal to 10% of that year’s sales.

Assembly equipment costing 1,200 million Crolls would be installed and paid for

immediately. Annual profits of companies in Heina are subject to a business tax of

40%. Working capital movements are excluded from the computation of taxable

profit, but companies are entitled to include a deduction, representing 20% of the

cost of equipment for each of the first five years of the equipment’s life. Business

tax is paid at the end of the year to which the assessment relates.

Eibl plc would usually evaluate this type of investment over a five-year period. At

the end of the fifth year, a notional market value of the subsidiary would be

calculated by applying a price-earnings ratio of six to the profit after tax arising in

the fifth year (as pre-tax accounting profit equals taxable profit, no deferred tax

liabilities can arise). If Eibl plc were to sell its subsidiary after five years, the sale

proceeds would be taxed in Heina at a rate of 30%

The initial finance of 1,360 million Crolls would be provided in the form of equity

capital from the existing cash resources of Eibl plc. The cost of capital used by Eibl

plc for this type of venture is 25%, but investors based in Heina would require a

return of only 20%, when investing in an equivalent venture. At present, the

Croll/£ exchange rate is 150 Croll/£ although predictions of the relative interest and

inflation rates of the UK and Heina suggest that the Croll will depreciate against the

£ by 4% per annum. In the project appraisals of Eibl plc, the exchange rate is

rounded to the nearest whole number.





Apart from the initial investment, revenues costs and working capital changes can

be assumed to arise at the end of the year in which they occur.

Required

(a) Prepare a statement showing to the nearest 100,000 Crolls the net cash flow

that would arise in each year of the venture and hence determine whether the

investment would be acceptable to investors based in Heina (assuming details

of the venture remain as outlined).

(b) Calculate whether Eibl plc should set up the Heina subsidiary, assuming cash

surpluses are remitted to the UK at the end of each year.

(c) Discuss what improvement could be made by Eibl plc to the proposed financial

arrangements with the Heina subsidiary.

Note: Ignore UK taxation

Use the following discount factors:

End of year 1 2 3 4 5

20% 0.83 0.69 0.58 0.48 0.40

25% 0.80 0.64 0.51 0.41 0.33





Solution

(a) Net cashflow for each year of the venture and appraisal from

viewpoint of investors in Heina

Crolls (millions)

Year 0 1 2 3 4 5

Sales revenue (W1) 1,500.0 1,683.0 1,872.0 2,120.0 2,376.0

Components (W2) (390.0) (437.9) (492.1) (556.5) (619.1)

Overhead cost

(45% x sales) (675.0) (757.3) (842.4) (954.0) (1,069.2)

435.0 487.8 537.5 609.5 687.7

Business tax @

40%

(excluding capital

allowances)

(174.0) (195.1) (215.0) (243.8) (275.1)

Assembly

equipment

(1,200)

Tax relief @ 40%

(over 5 years) 96.0 96.0 96.0 96.0 96.0


Working capital

(W3)

(160) 10.0 (18.3) (18.9) (24.8) (25.6)

Net cash flow in

first 5 years* (1,360) 367.0 370.4 399.6 436.9 483.0

20% factor 1 0.83 0.69 0.58 0.48 0.40

PV (1,360) 305 256 232 210 193

NPV = −164 million Crolls

(*ignoring any final value of investment or return of working capital)

This NPV figure ignores the value of the investment at the end of the five-year

period because the question asks for the net cashflow in each year. However, the

computations are not complete without including this factor. There are various

possibilities:

1. The business winds up after five years, returning only working capital. This

has a value of 238m Crolls, if recovered in its entirety, which has a present

value of 238m x 0.40 = 95m Crolls.

The NPV of the project is then –69m Crolls (not worthwhile).

2. The business continues as a going concern with a value of 6 x profit after tax

in fifth year: i.e. 6 x 509 (approx) = 3,054m Crolls.

PV of this = 3,054 x 0.40 = 1,222m Crolls

NPV of project = 1,058m Crolls which is obviously worthwhile.





Workings

1. Sales revenue

Year 0 1 2 3 4 5

Sales price per

tractor (Cr

millions)

3 3.3 3.6 4.0 4.4

Sales volume

(units)

500 510 520 530 540

Sales revenue

(Cr millions)

1,500 1,683 1,872 2,120 2,376

2. Component cost

per tractor £5,000 £5,300 £5,600 £6,000 £6,300

Total

component

Cost (£m)

2.500 2.703 2.912 3.180 3.402

Exchange rate 150 156 162 169 175 182

Component

cost (Cr

millions)

390 437.9 492.1 556.5 619.1

3. Working capital

WC at end of

each year

(10% x sales) 160 150 168.3 187.2 212.0 237.6

Increase/

(decrease) in

year (10) 18.3 18.9 24.8 25.6

(b) Appraisal from viewpoint of Eibl plc

Year 0 1 2 3 4 5

Net

cashflow

remitted (Cr

millions) (1,360) 367 370.4 399.6 436.9 483

Exchange

rate 150 156 162 169 175 182

Net

cashflow

(£m) (9.07) 2.35 2.29 2.36 2.50 2.65

25% factor 1 0.80 0.64 0.51 0.41 0.33

PV (9.07) 1.88 1.47 1.20 1.03 0.87

NPV = −£2.62m.





However this excludes the cashflow from sale of the subsidiary at its notional

market value of 3,054m Crolls. Net of tax this produces:

3,054 x (1 – 0.3) = 2,138m Crolls

182

m138,2 = £11.75m

which has a present value of £11.75m x 0.33 = £3.88m

The project is therefore worthwhile, with an NPV of 3.88 – 2.62 = £1.26m.

(c) Improvement to the proposed financial arrangements with the Heina

subsidiary

Investments in foreign countries involve significant additional risks. Chief amongst

these are the problems caused by currency movements. There are several ways in

which currency fluctuations can be handled, but the most important point to

concern Eibl is that the currency risk attached to a foreign subsidiary can be

reduced by matching the subsidiary’s assets with liabilities in the same currency.

This implies that the subsidiary should be financed to a large extent by borrowing in

Crolls. This particularly applies if it is estimated that the Croll will be depreciating

against the £, because the annual interest suffered becomes lower each year when

converted to £. However, it is said that there are no free gifts in foreign exchange

and it is likely that the interest rate suffered on a Heina loan is higher than on a

sterling loan.

A further risk of investments in some countries is the problem of remitting the

subsidiary’s cash surpluses back to the UK. Usually, dividends are the most difficult

to get past exchange control regulations. It may be that Eibl would do better to

invoice for the components which it supplies at a mark-up on cost rather than at

straight cost. Tax considerations are also of prime importance in transfer pricing

policy.

The following amendments to the financial arrangements could also be considered:

● Eibl could charge the subsidiary with a royalty per tractor produced or sold;

● Eibl could invoice the subsidiary for management charges for advice given;

● Eibl could lend money to the subsidiary and charge interest on those loans.

However these revenues would cause a UK corporation tax liability to be incurred.





TRANSFER PRICING

Article from a USA publication

A particularly sensitive problem for multinational firms is establishing a rational

method for pricing of goods, services, and technology between related affiliates in

different countries. Even purely domestic firms find it difficult to reach agreement

on the best method for setting prices on transactions between affiliates. In the

multinational case, managers must balance conflicting considerations. These

include fund positioning, income taxes, managerial incentives and evaluation, tariffs

and quotas, and joint-venture partners.

Fund positioning effect

Transfer price setting is a technique by which funds may be positioned within a

multinational enterprise. A parent wishing to remove funds from a particular

foreign country can charge higher prices on goods sold to its affiliate in that

country. A foreign affiliate can be financed by the reverse technique, a lowering of

transfer prices. Payment by the affiliate for imports from its parent transfers funds

out of the affiliate. A higher transfer (sales) price permits funds to be accumulated

within the selling country.

Transfer pricing may also be used to transfer funds between sister affiliates.

Multiple sourcing of component parts on a worldwide basis allows changes in

suppliers from within the corporate family to function as a device to transfer funds.

Income tax effect

A major consideration in setting transfer price is the income tax effect. Worldwide

corporate profits may be influenced by setting transfer prices to minimise taxable

income in a country with a high income tax rate and maximise income in a country

with a low income tax rate.

Needless to say, government tax authorities are aware of the potential income

distortion from transfer price manipulation. A variety of regulations and court cases

exist on the reasonableness of transfer prices, including fees and royalties as well

as prices set for merchandise. If a government taxing authority does not accept a

transfer price, taxable income will be deemed larger than was calculated by the firm

and taxes will be increased. An even greater danger, from the corporate point of

view, is that two or more governments will try to protect their respective tax bases

by contradictory policies that subject the business to double taxation on the same

income.

Typical of laws circumscribing freedom to set transfer prices is Section 482 of the

US Internal Revenue Code. Under this authority the Internal Revenue Service

(IRS) can reallocate gross income, deductions, credits, or allowances between

related corporations in order to prevent tax evasion or to reflect more clearly a

proper allocation of income. Under the IRS guidelines and subsequent judicial

interpretation, the burden of proof is on the taxpayer to show that the IRS has

been arbitrary or unreasonable in reallocating income. The “correct price”

according to the guidelines is the one that reflects an arm’s length price, that is,

a sale of the same goods or service to an unrelated customer.





IRS regulations provide three methods to establish arm’s length prices: comparable

uncontrolled prices, resale prices, and cost-plus. A comparable uncontrolled price is

regarded as the best evidence of arm’s length pricing. Such prices arise when

transactions in the same goods or services occur between the multinational firm

and unrelated customers, or between two unrelated firms. The second-best

approach to arm’s length pricing starts with the final selling price to customers and

subtracts an appropriate profit for the distribution affiliate to determine the

allowable selling price for the manufacturing affiliate. The third method is to add an

appropriate markup for profit to total costs of the manufacturing affiliate. The

same three methods are recommended for use in member countries by the

Organisation for Economic Cooperation and Development (OECD) Committee on

Fiscal Affairs.

Although all governments have an interest in monitoring transfer pricing by

multinational firms, not all governments use these powers to regulate transfer

prices to the detriment of multinational firms. In particular, transfer pricing has

some political advantages over other techniques of transferring funds. Although

the recorded transfer price is known to the governments of both the exporting and

importing countries, the underlying cost data are not available to the importing

country. Thus the importing country finds it difficult to judge how reasonable the

transfer price is, especially for non-standard items such as manufactured

components. Additionally, even if cost data could be obtained, some of the more

sophisticated governments might continue to ignore the transfer pricing leak. They

recognise that foreign investors must be able to repatriate a reasonable profit by

their own standards, even if this profit seems unreasonable locally. An unknown or

unproven transfer price leak makes it more difficult for local critics to blame their

government for allowing the country to be “exploited” by foreign investors. On the

other hand, if the host government has soured on foreign investment, transfer price

leaks are less likely to be overlooked. Thus within the potential and actual

constraints established by governments, opportunities may exist for multinational

firms to alter transfer prices away from an arm’s length market price.

Managerial incentives and evaluation

When a firm is organised with decentralised profit centres, transfer pricing between

centres can disrupt evaluations of managerial performance. This problem is not

unique to multinational firms, but has been a controversial issue in the

“centralisation versus decentralisation” debate in domestic circles. In the domestic

case, however, a modicum of coordination at the corporate level can alleviate some

of the distortion that occurs when any profit centre sub-optimises its profit for the

corporate good. This statement might also be true in the multinational case, but

coordination is often hindered by longer and less efficient channels of

communication and the need to consider the unique variables that influence

international pricing. Even with the best intent, a manager in one country finds it

difficult to know what is best for the firm as a whole when buying at a negotiated

price from an affiliate in another country. If corporate headquarters establishes

transfer prices and sourcing alternatives, managerial disincentives arise if the prices

seem arbitrary or unreasonable. Furthermore, if corporate headquarters makes

more decisions, one of the main advantages of a decentralised profit centre system

disappears. Local management loses the incentive to act for its own benefit.





Tariff and quota effect

Transfer pricing may have an influence on the amount of import duties paid. If the

importing affiliate pays ad valorem import duties, and if those duties are levied on

the invoice (transfer) price, duties will arise under the high-markup policy.

The incidence of import duties is usually opposite to the incidence of income taxes

in transfer pricing, but income taxes are usually a heavier burden than import

duties. Therefore transfer prices are more often viewed from an income tax

perspective. In some instances, however, import duties are actually levied against

internationally posted prices, if such exist, rather than against the stated invoice

price. If so, duties will not be influenced by the transfer price policy. Income taxes

will still be affected by both the residual location of operating profit and the

deductibility of the assessed import duties.

Related to the tariff effect is the ability to lower transfer prices to offset the volume

effect of foreign exchange quotas. Should a host government allocate a limited

amount of foreign exchange for importing a particular type of good, a lower transfer

price on the import allows the firm to bring in a greater quantity? If, for example,

the imported item is a component for a locally manufactured product, a lower

transfer price may allow production volume to be sustained or expanded, albeit at

the expense of profits in the supply affiliate.

Effect on joint-venture partners

Joint ventures pose a special problem in transfer pricing, because serving the

interest of local stockholders by maximising local profit may be suboptimal from the

overall viewpoint of the multinational firm. Often the conflicting interests are

irreconcilable. When Ford Motor Company decided to rationalise production on a

worldwide basis so that each division could specialise in certain products or

components, it was forced to abandon its policy of working with joint ventures

partly because of the transfer pricing problem. It had to purchase the large British

minority interest in Ford some years ago, despite the well publicised and ill-timed

drain on the US balance of payments. For identical reasons, General Motors has

seldom worked with joint ventures despite its arrangement with Toyota.

Transfer pricing in practice

Given the potential for conflicting objectives, what transfer pricing policies do

multinational firms utilise in practice? An empirical study of 164 US multinational

firms sheds considerable light on this question.

Although Section 482 of the US Internal Revenue Code requires use of “arms

length” pricing, only 35% of the responding firms indicated that they used “market

based” methods to set the “arms length” transfer price. Almost all of the other

firms used either some version of a “cost plus” price or a “negotiated” price. This

split presumably reflects the relative proportion of products which had a recognised

external market price compared to products or components that had no external

market price.

The authors of the study used the response data to test various hypotheses about

the determinants motivating a firm’s choice of a particular transfer pricing policy.

They found that “legal” and “size” variables were statistically significant

determinants of market-based transfer pricing. Legal considerations include

compliance with tax rules (Section 482), customs regulations, antidumping laws,

antitrust laws, and the accounting norms of host countries. Large-size firms with





multiple products and locations were also likely to use market-based transfer

pricing whenever possible. This was probably because they are highly visible and it

would be difficult to customise transfer pricing given the complexities of their sales

networks.

Another interesting finding of the study was that “economic restrictions (such as

exchange controls, price controls, and restrictions on imports), political-social

conditions, and the extent of economic development in host countries are either

unimportant or are secondary determinants of market-based transfer pricing

strategy”. Furthermore, they found no statistical support for assuming that these

variables influenced non market-based transfer pricing policies. These findings

suggest that transfer pricing policies are not very sensitive to the positioning of

funds considerations which were described earlier in this article.

The study also found that internal considerations, such as performance evaluation

of subsidiaries and their management, were not statistically significant

determinants of transfer pricing policies. Presumably multinational firms prefer to

maintain separate sets of books for that purpose.

A much earlier study of 60 non-US multinational firms and their US affiliates found

distinct national differences with respect to the weight accorded host country

environmental variable and internal company parameters. Canadian, French,

Italian, and US parent firms judged that the tax effect of transfer pricing was the

most important consideration. British parent firms emphasised the strong financial

appearance of their US affiliates. Inflation was an important consideration by all

parent firms, except those in Scandinavia; these firms considered acceptability to

the host government to be the most important determinant of their transfer pricing

policies. German firms appeared to be least concerned about transfer pricing

policies. Non-US firms, in contrast to US firms, did not consider the evaluation of

managerial performance to be important because, contrary to the practice of many

US firms, they did not usually operate their foreign affiliates on a profit centre

basis.





Brookday plc

Brookday plc is considering whether to establish a subsidiary in the USA. The

subsidiary would cost a total of $20 million, including $4 million for working capital.

A suitable existing factory and machinery have been located and production could

commence quickly. A payment of $19 million would be required immediately, with

the remainder required at the end of year one.

Production and sales are forecast at 50,000 units in the first year and 100,000 units

per year thereafter.

The unit price, unit variable cost and total fixed costs in year one are expected to

be $100, $40 and $1 million respectively. After year one prices and costs are

expected to rise at the same rate as the previous year’s level of inflation in the

USA; this is forecast to be 5% per year for the next 5 years. In addition a fixed

royalty of £5 per unit will be payable to the parent company, payment to be made

at the end of each year.

Brookday has a 4 year planning horizon and estimates that the realisable value of

the fixed assets in 4 years time will be $20 million.

It is the company’s policy to remit the maximum funds possible to the parent

company at the end of each year. Assume that there are no legal complications to

prevent this.

Brookday currently exports to the USA yielding an after tax net cash flow of

£100,000. No production will be exported to the USA if the subsidiary is

established. It is expected that new export markets of a similar worth in Southern

Europe could replace exports to the USA. United Kingdom production is at full

capacity and there are no plans for further expansion in capacity.

Tax on the company’s profits is at a rate of 50% in both countries, payable one

year in arrears. A double taxation treaty exists between the UK and the USA and

no double tax is expected to arise. No withholding tax is levied on royalties payable

from the USA to the UK.

Tax allowable ‘depreciation’ is at a rate of 25% on a straight line basis on all fixed

assets.

Brookday believes that the appropriate beta for this investment is 1.2 The after-

tax market rate of return is 12%, and the risk free rate of interest 7% after tax.

The current spot exchange rate is US $1.300/£1, and the pound is expected to fall

in value by approximately 5% per year relative to the US dollar.

Required:

(a) Evaluate the proposed investment from the viewpoint of Brookday plc. State

clearly any assumptions that you make.

(b) What further information and analysis might be useful in the evaluation of this

project?





Brookday plc – solution

(a) Brookday’s stated policy is to remit the maximum funds possible to the parent

company. The net present value of relevant cash flows to the parent

company will be the appropriate decision criterion, and should lead to

maximisation of parent shareholder wealth.

The dollar profit and relevant cash flow from the subsidiary must be

determined first:

Projected earnings data of the US subsidiary


$’000 $’000 $’000 $’000 $’000

Sales (note 1) 5,000 10,500 11,025 11,580

Variable cost 2,000 4,200 4,410 4,630

Fixed costs 1,000 1,050 1,102 1,158

Royalty (note

2)

309 586 557 529

Depreciation 4,000 4,000 4,000 4,000

7,309 9,836 10,069 10,317

Taxable profit (2,309) 664 956 1,263

US tax payable

(note 3)

0 0 0 0 (287)

Profit after tax (2,309) 664 956 1,263 (287)

Projected cash flow data of the US subsidiary

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

$’000 $’000 $’000 $’000 $’000 $’000

Profit after tax (2,309) 664 956 1,263 (287)

Depreciation 4,000 4,000 4,000 4,000

Initial

investment (19,000)

Additional

capital (1,000)

Realisable

value of fixed

assets (note 4) 20,000

Tax on

realisable value (10,000)

Working capital

available ______ _____ _____ _____ 4,000 ______

Cash flow

available to

parent (19,000) 691 4,664 4,956 29,263 (10,287)





Projected cash flow data for the parent company

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

£’000 £’000 £’000 £’000 £’000 £’000

Available from

US subsidiary (14,615) 559 3,976 4,445 27,633 (10,226)

Royalty

payment

250 500 500 500

UK tax on

royalty (note

5) _____ ___ (125) (250) (250) (250)

Net cash flow (14,615) 809 4,351 4,695 27,883 (10,476)

Discount

factors @ 13%

(note 6) 1 0.885 0.783 0.693 0.613 0.543

Present values (14,615) 716 3,407 3,254 17,092 (5,688)

Net present value = +£4,166,000

The loss of exports to the USA if the project is undertaken is not a relevant

cash flow.

Notes:

1. Sales price increases by 5% per year

Year 1 Year 2 Year 3 Year 4

Price ($) 100.00 105.00 110.25 115.80

Units (000) 50 100 100 100

Sales revenue ($’000) 5,000 10,500 11,025 11,580

Similar calculations are necessary for variable costs and price

adjustments for fixed costs.

2. The royalty is payable in £’s and will depend upon the $/£ exchange

rate. The £ is expected to fall in value by 5% per year relative to the $.


Expected exchange rates $/£ 1.235 1.173 1.115 1.059 1.006

Royalty (£’000) 250 500 500 500

Royalty ($’000) 309 586 557 529

3. Losses are assumed to be carried forward and allowed against future

profits for taxation purposes.

4. Although the subsidiary will exist for more than four years, the

company’s planning horizon is only four years. A value must be placed

upon the subsidiary at this time. The only information available is an

estimate of realisable value of fixed assets. Tax on this realisable value

will be payable as the assets are fully depreciated. Potential working

capital available must also be considered.

5. There will be no double taxation on cash flows from the USA. However,

the royalty has not been subject to US tax, and will be liable to UK

taxation.





6. Using the capital asset pricing model to determine the discount rate:

ke = rf + (Erm – rf) β project

ke = 7% + (12% − 7%) 1.2 = 13%

(b) Further information and analysis might include:

(i) How accurate are the cash flow forecasts? How have they been

established?

(ii) Why has a four year planning horizon been chosen? The valuation of the

fixed assets at year 4 is highly significant to the NPV solution. How has

this valuation been established? Is this valuation based upon future

earnings as a going concern? It would be more desirable to evaluate the

project over the whole of its projected life.

(iii) Risk is taken into account by using a CAPM derived discount rate. How

has this rate been derived for a situation involving two countries? Does

this fully reflect the risk of the project? Is the use of CAPM appropriate

as it is a single period model? Other, theoretically weaker, measures of

risk might be useful as an aid to decision-making e.g., sensitivity

analysis of the key variables or simulation.

(iv) Cash flow is usually assumed to occur at the end of each year. Greater

accuracy would result if consideration were given to when during the

year cash flow arises and these cash flows discounted at the appropriate

rate.

(v) Political and economic factors should be considered. How stable is the

US government policy? Will a change in government lead to changes in

taxation policy, exchange controls, restrictions on the remittance of

funds or attitudes towards foreign investment?

(vi) Are there any intangible benefits of establishing a manufacturing plant in

the USA e.g. making the American public more aware of Brookday’s

product?





Zedland Postal Service

The general manager of the nationalised postal service of a small country, Zedland,

wishes to introduce a new service. This service would offer the same-day delivery

of letters and parcels posted before 10am, within a distance of 150 km. The

service would require 100 new vans costing $8,000 each and 20 trucks costing

$18,000 each. 180 new workers would be employed at an average annual wage of

$13,000 and five managers at average annual salaries of $20,000 would be moved

from their existing duties, where they would not be replaced.

Two postal rates are proposed. In the first year of operation, letters will cost

$0.525 and parcels $5.25. Market research undertaken at a cost of $50,000

forecasts that demand will average 15,000 letters each working day and 500

parcels each working day during the first year, and 20,000 letters a day and 750

parcels a day thereafter. There is a five-day working week. Annual running and

maintenance costs on similar new vans and trucks are estimated in the first year of

operation to be $2,000 a van and $1,000 a truck. These costs will increase by 20%

a year compound (excluding the effects of inflation). Vehicles are depreciated over

a five-year period on a straight line basis. Depreciation is tax-allowable and the

vehicles will have negligible scrap value at the end of the five years. Advertising in

year one will cost $1,300,000 and in year two $250,000. There will be no

advertising after year two. Existing premises will be used for the new service, but

additional costs of $150,000 a year will be incurred.

All the above data are based on price levels in the first year and exclude any

inflation effects. Wage and salary costs and all other costs are expected to rise

(because of inflation) by approximately 5% a year during the five-year planning

horizon of the postal service. The government of Zedland will not permit annual

price increases within nationalised industries to exceed the level of inflation.

Nationalised industries are normally required by the government to earn at least an

annual after-tax return of 5% on average investment and to achieve, on average,

at least zero net present value on their investments.

The new service would be financed half with internally generated funds and half by

borrowing on the capital market at an interest rate of 12% a year. The opportunity

cost of capital for the postal service is estimated to be 14% a year. Corporate

taxes in Zedland, to which the postal service is subject, are at the rate of 30% for

annual profits of up to $500,000 and 40% for the balance in excess of $500,000.

Tax is payable one year in arrears. The postal service’s taxable profits from

existing activities exceed $10,000,000 a year. All transactions may be assumed to

be on a cash basis and to occur at the end of the year, with the exception of the

initial investment which would be required almost immediately.

Required:

Acting as an independent consultant, prepare a report advising whether the new

postal service should be introduced. Include in your report a discussion of other

factors that might need to be taken into account before a final decision is made on

the introduction of the new postal service.

State any assumptions that you make.





Zedland Postal Service – solution

Report on proposed same-day delivery service

To: The Governing Board, National Postal Service, Zedland.

From: International Management Consultants Ltd

1. Terms of reference

This report considers whether the proposed new same-day delivery service

will earn sufficient to meet the twin targets of a 5% after-tax return on

average investment and a net present value of at least zero. Other factors

affecting the decision are also considered.

2. Conclusion and recommendation

Our calculations on target returns are shown in the appendix. The return on

investment, as calculated by us, is 12%, which is acceptable, but the net

present value is negative. We therefore recommend that the service is not

run under the existing proposals, but this recommendation is subject to the

factors considered in the next section.

3. Other factors affecting the decision

(a) The project could possibly be made more profitable by increasing prices

or reducing costs. These possibilities should be investigated. It is good

practice to carry out a sensitivity analysis on the estimates made to

discover which are the key factors in determining the success or failure

of the project. Furthermore analysis can be undertaken on these factors

with the objective of making more accurate estimates. For example, our

initial reaction is that the price/demand relationship and the staffing

levels required should both be subject to further analysis.

(b) The proposed service might be of great benefit to the public and to the

economy as a whole. The government may consider that it is worth

subsidising this service from the profits of the Postal Service’s other

operations.

(c) The effect of the new service on existing services does not appear to

have been specifically investigated. There will possibly be a reduction in

revenue from existing services which should be included in the

calculations.





Appendix

1. Incremental profit figures for the five-year planning horizon

Year 1 2 3 4 5

$’000 $’000 $’000 $’000 $’000

Revenue:

Letters (W1) 2,048 2,867 3,010 3,160 3,318

Parcels (W2) _682 1,075 1,129 1,185 1,244

2,730 3,942 4,139 4,345 4,562

$’000 $’000 $’000 $’000 $’000

Expenses:

Additional staff (W3) 2,340 2,457 2,580 2,709 2,844

Vehicle depreciation (W4) 232 232 232 232 232

Vehicle running costs (W5) 220 277 349 440 554

Advertising 1,300 263

Premises costs 150 158 165 174 182

4,242 3,387 3,326 3,555 3,812

Profit before tax (1,512) 555 813 790 750

Taxation @ 40% 605 (222) (325) (316) (300)

Profit after tax (907) 333 488 474 450

2. Average annual after-tax return on average investment

$

Total investment 800,000

Vans 360,000

Advertising 1,563,000

2,723,000

Average investment = $2,723,000 ÷ 2 = $1,361,500

Average profit = (-907 + 333 + 488 + 474 + 450) ÷ 5

= $167,600

Average annual after-tax return on average investment

= 5.361,1

6.167 = 12.3%

3. Net present value (in $’000)

Year 0 1 2 3 4 5 6

Profit before tax (1,512) 555 813 790 750

Add depreciation 232 232 232 232 232

Taxation (one

year delay)

605 (222) (325) (316) (300)

Cost of vehicles (1,160) ____ ____ ___ ___ ___ ___

(1,160) (1,280) 1,392 823 697 666 (300)

14% factor 1 0.877 0.769 0.675 0.592 0.519 0.456

Present value (1,160) (1,123) 1,070 556 413 346 (137)

Net present value = $35,000 negative





4. Assumptions

(i) The rate of inflation for revenue and costs (excluding depreciation) is

assumed to be 5% p.a. over the five-year planning horizon.

(ii) The cost of market research already undertaken is ignored (sunk cost).

(iii) The cost of the five managers used for the project is already contracted

for and therefore ignored in these calculations, which assume that they

would not be made redundant if the project did not go ahead.

(iv) Return on investment has been computed including advertising costs as

part of the investment but, ignoring financing costs.

(v) The cost of borrowings is assumed to be already included in the

opportunity cost of capital of 14%.

Workings

1. Revenue from letters:

Year 1: 15,000 letters x 5 x 52 x $0.525 = $2,047,500

Year 2: 20,000 letters x 5 x 52 x $0.525 x 1.05 = $2,866,500,

increasing at 5%

p.a. thereafter.

2. Revenue from parcels:

Year 2: 500 parcels x 5 x 52 x $5.25 = $682,500

Year 2: 750 parcels x 5 x 52 x $5.25 x 1.05 = $1,074,937,

increasing at 5%

p.a. thereafter.

3. Additional staff cost:

180 x $13,000 in year 1 = $2,340,000, rising at 5% p.a. thereafter.

The cost of managers is not relevant, as they would have been paid anyway,

and it is assumed that they will not be made redundant if the new project is

not undertaken.

4. Depreciation:

$

Cost of vans: 100 x $8,000 = 800,000

Cost of trucks: 20 x $18,000 = 360,000

$1,160,000

Annual depreciation = $1,160,000 ÷ 5 = $232,000

(Note: No inflation increase!)

5. Vehicle running costs:

$

Year 1: Vans 100 x $2,000 = 200,000

Year 1: Trucks 20 x $1,000 = 20,000

$220,000

These running costs in subsequent years are found by multiplying by 1.26

each year.





6. Taxation

Because the other operations of the postal service make high profits, not only

will all marginal tax calculations be at 40%, but it is assumed that the losses

made in year 1 will result in a reduction in the total tax charge of 40% of the

loss made. This is therefore shown as a notional receipt.





Axmine plc

(a) The managers of Axmine plc, a major international copper processor are

considering a joint venture with Traces, a company owning significant copper

reserves in a South American country. If the joint venture were not to

proceed Axmine would still need to import copper from the South American

country. Axmine’s managing director is concerned that the government of the

South American country might impose some form of barriers to free trade

which puts Axmine at a competitive disadvantage in importing copper. A

further director considers that this is unlikely due to the existence of the

World Trade Organisation (WTO).

You are required to briefly discuss possible forms of non-tariff barrier that

might affect Axmine’s ability to import copper, and how the existence of the

WTO might influence such barriers. (8 marks)

(b) The proposed joint venture with Traces would be for an initial period of four

years. Copper would be mined using a new technique developed by Axmine.

Axmine would supply machinery at an immediate cost of 800 million pesos

and 10 supervisors at an annual salary of £40,000 each at current prices.

Additionally Axmine would pay half of the 1,000 million pesos per year (at

current prices) local labour costs and other expenses in the South American

country. The supervisors’ salaries and local labour and other expenses will be

increased in line with inflation in the United Kingdom and the South American

country respectively.

Inflation in the South American country is currently 100% per year, and in the

UK it is expected to remain stable at around 8% per year. The government of

the South American country is attempting to control inflation, and hopes to

reduce it each year by 20% of the previous year’s rate.

The joint venture would give Axmine a 50% share of Trace’s copper

production, with current market prices at £1,500 per 1,000 kilogrammes.

Trace’s production is expected to be 10 million kilogrammes per year, and

copper prices are expected to rise by 10% per year (in pounds sterling) for

the foreseeable future. At the end of four years Axmine would be given the

choice to pull out of the venture or to negotiate another four year joint

venture, on different terms.

The current exchange rate is 140 pesos/£. Future exchange rates may be

estimated using the purchasing power parity theory.

Axmine has no foreign operations. The cost of capital of the company’s UK

mining operations is 16% per year. As this joint venture involves diversifying

into foreign operations the company considers that a 2% reduction in the cost

of capital would be appropriate for this projct.

Corporate tax is at the rate of 20% per year in the South American country

and 35% per year in the UK. A tax treaty exists between the two countries

and all foreign tax paid is allowable against any UK tax liability. Taxation is

payable one year in arrears and a 25% straight-line writing-down allowance is

available on the machinery in both countries.

Cash flows may be assumed to occur at the year end, except for the

immediate cost of machinery. The machinery is expected to have negligible

terminal value at the end of four years.





You are required to prepare a report discussing whether Axmine plc should

agree to the proposed joint venture. Relevant calculations must form part of

your report or an appendix to it.

State clearly any assumptions that you make. (18 marks)

(c) If the South American government were to fail to control inflation, and

inflation were to increase rapidly during the period of the joint venture,

discuss the likely effect of very high inflation on the joint venture. (4 marks)

Total: 30 marks





Axmine plc – solution

(a) Forms of non-tariff barrier and the WTO

Axmine’s ability to import copper from the South American country might be

affected by the following forms of non-tariff barrier:

(i) Deliberately obstructive customs procedures. The authorities might

require time-consuming documentation to be completed before exports

of copper are permitted, or might carry out detailed quality assurance

inspections. Such inspections would be justified in the name of safety or

quality control, but in reality the purpose is to reduce the volume of

exports.

(ii) Export quotas. The country might set maximum limits of copper that it

is prepared to export. The purpose would be to reduce supply and

therefore hope to increase the price of copper provided.

(iii) Artificial exchange rates. The country might insist that an artificially

high exchange rate is used to pay for goods exported. Perhaps a range

of different rates could be set by the country for different forms of

exports (copper, electrical goods, timber etc) so that control can be

exercised over each category.

(iv) Selective embargo. The country might totally refuse to permit exports

to a certain country, either on human rights grounds or to retaliate

against alleged unfair trading practices from that other country.

Essentially this is a special case of export quotas, with the quota to

particular countries set at zero.

(v) Withdrawal of government assistance. Governments commonly offer

their exporters a range of export credit guarantees to encourage foreign

trade, perhaps taking on the risk of other countries not honouring their

debts. Where these guarantees are reduced or withdrawn altogether,

exports will be discouraged. Similar points apply to other forms of

government assistance e.g., grants or subsidised loans.

The General Agreement on Tariffs and Trade (GATT) was signed in 1947 by 23

countries in an attempt to encourage world-wide trade after the Second World

War. The aims of GATT were to reduce existing barriers to free trade, to

reduce discrimination in world-wide trade and to prevent protectionism by

encouraging member countries to consult with others before taking

protectionist measures.

GATT eventually had more than one hundred signatory member countries,

including many less developed countries, and the last round of negotiations

undertaken (the ‘Uruguay Round’) was concluded in 1994.

A new body, the World Trade Organisation (WTO) was set up in 1995 as a

successor body to GATT, which itself officially ceased to exist at the end of

1995.

The WTO, with a membership of about 150 countries, has to try to map out

the road ahead for global trade policy. The Uruguay Round bequeathed the

WTO a substantial agenda. It included further negotiations or reviews in

areas including agriculture, textiles, intellectual property rights and services.





The implications of the WTO on Axmine plc depend on a number of factors:

(i) If the South American country is not a member of the WTO, then the

WTO is irrelevant.

(ii) GATT was generally successful in driving tariff barriers out of the world

trade scene, but has been much less successful in non-tariff barriers.

Many countries continue to impose non-tariff barriers, especially against

imports rather than exports, since they see doing this as in their best

domestic interests.

(iii) GATT allowed a number of facilities to favour less developed countries at

the expense of developed countries, so the South American country

might not contravene GATT/WTO terms by its actions of imposing

barriers. GATT also allowed preferential rates to exist within trade blocs

(e.g. the European Union) and these continue to exist under the WTO.

(b) Report on the proposed joint venture with Traces

To: The Board of Directors of Axmine plc

From: L Hughes, Financial Analyst

Terms of reference

The board of directors has requested an evaluation of the financial

implications of the proposed joint venture with Traces and of the risks and

other factors, which are relevant to making a decision.

Recommendation

An examination of the expected cash flows from this project shows that it is

financially sound, having an expected net present value of £4.7 million from

an initial outlay of (800m pesos ÷140) £5.7 million. There would need to be

large adverse movements in some of the estimates before the project became

unattractive.

On this basis, it is recommended that the joint venture negotiations proceed

whilst gathering as much additional information as possible.

The calculations are included in the appendix to this report, but before making

a decision, members of the board should weigh up the risks and other

considerations, which are listed in the next section.

Risks and other considerations

Some of the cash flow estimates used in the calculations are subject to wide

margins of error. For example, both copper prices and exchange rates are

extremely volatile. Calculations of exchange rates are based on ‘purchasing

power parity’ a theory, which does not fully explain exchange rate

movements.

A sensitivity analysis will be undertaken on the key estimates in the

calculations. This analysis will be available before the next board meeting.





Other risk factors to consider include the following:

(i) The joint venture is based on our confidence that Traces is a sound

company and that the management is both competent and trustworthy.

(ii) Political risk has not been considered in sufficient detail. In addition to

trade barriers, the risk of expropriation of assets or severe exchange

control regulations must be assessed in a country, which is known to be

politically unstable.

(iii) An estimate must be made of the speed at which skills will be

transferred to the local workforce, as this will be a factor in determining

the length of the involvement.

On the positive side the calculations have ignored the option to withdraw from

the venture or negotiate a new agreement at the end of the initial period of

four years. This option will itself have a value, which will increase the net

present value of the project.

On a technical note, further consideration must be given to the discount rate,

which was agreed for use in the calculations. Further thought must be given

to obtain a more accurate estimate of the systematic risk of South American

mining operations, which will help set up a more suitable discount rate.

Reducing the discount rate by 2% simply because of diversification overseas

is somewhat questionable. However the change in the net present value is

not expected to be significant.

Appendix

Forecast of future exchange rates

Current exchange rate is 140 pesos/£. Using purchasing power parity:

South American

inflation*

Exchange rate

(Peso/£)

Year

0 100% : = 140

1 80% : 140 x 08.1

80.1 = 233.3

2 64% : 233.3 x 08.1

64.1 = 354.3

3 51.2% : 354.3 x 08.1

512.1 = 496.0

4 41.0% : 496.0 x 08.1

41.1 = 647.6

5 32.8% : 647.6 x 08.1

328.1 = 796.3

*At 80% of previous year’s rate





Forecast copper prices

Axmine’s share of output is (50% x 10m kg x £1.5) = £7.5m. Prices increase

at 10% p.a., then convert to local currency.

Year Sales (£000) Exchange rate Sales peso(m)

1 8,250 x 233.3 = 1,925

2 9,075 x 354.3 = 3,215

3 9,983 x 496.0 = 4,952

4 10,981 x 647.6 = 7,111

Supervisory labour costs

Currently (10 x £40,000) = £400,000, increasing at the 8% p.a. inflation rate

and convert to pesos.

Year Cost (£000) Exchange rate Cost peso(m)

1 432 x 233.3 = 101

2 467 x 354.3 = 165

3 504 x 496.0 = 250

4 544 x 647.6 = 352

Local labour costs

Axmine’s share currently (50% x 1,000m) = 500m pesos increasing by

local inflation prices.

Year Inflation Labour costs

% peso(m)

1 80 900

2 64 1,476

3 51.2 2,232

4 41.0 3,147

UK taxation

UK tax 35% (20% paid abroad) 15% of foreign taxable income to be paid in

UK.

Year £000

1 3.233

724 x 15% 465

2 3.354

374,1 x 15% = 582

3 496

270,2 x 15% = 686

4 6.647

412,3 x 15% = 790





Net present value calculation

Year: 0 1 2 3 4 5

Peso (m)

Investment (800)

Sales 1,925 3,215 4,952 7,111

Labour (900) (1,476) (2,232) (3,147)

Supervisors (101) (165) (250) (352)

Deduct WDA (200) (200) (200) (200)

Taxable 724 1,374 2,270 3,412

Tax (20%) (145) (275) (454) (682)

Add back WDA ____ 200 200 200 200 ____

Remitted (800) 924 1,429 2,195 3,158 (682)

Exchange rate 140 233.3 354.3 496.0 647.6 796.3

£000

Received (5,714) 3,961 4,033 4,425 4,876 (856)

UK tax (465) (582) (686) (790)

Net cash flow (5,714) 3,961 3,568 3,843 4,190 (1,646)

Discount factor (14%) 1.000 0.877 0.769 0.675 0.592 0.519

Present value (5,714) 3,474 2,744 2,594 2,480 (854)

Net present value +£4,724,000

(c) Effect of hyper-inflation

If the purchasing power parity theory holds true, then rapidly increasing

inflation during the period of the joint venture is likely to lead to a higher net

present value for the project. The sales, wages and supervisory costs all

increase at a constant rate per annum, so it is immaterial in NPV terms

whether the national inflation is low or high, but the favourable effect comes

from the tax payment.

The writing down allowance is calculated on the original cost of the

machinery, so there is some benefit lost as inflation rises. However this loss

will be more than compensated by the one year delay in payments of

taxation. The higher that inflation is, the lower the tax payment becomes in

real terms, so that the expected NPV of the project will rise as the inflation

level rises. If the government’s previous attempts at controlling inflation have

failed, it is likely that so will the current inflation reduction programme,

leading to a more attractive NPV prospect.



50576969 acca p4 class notes june 2011 version

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