UNIVERSITY OF NAIROBI SCHOOL OF BUSINESS

DFI 501: FINANCIAL MANAGEMENT

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UNIVERSITY OF NAIROBI SCHOOL OF BUSINESS

DEPARTMENT OF FINANCE AND ACCOUNTING

DFI 501: FINANCIAL MANAGEMENT COURSE OUTLINE: MAY-AUGUST 2009

PRE-REQUISITE: DAC 501: FINANCIAL ACCOUNTING INSTRUCTORS: Kamasara V.O. and Lisiolo Lishenga COURSE OBJECTIVE Finance continues to advance rapidly both in the theory and in its real-world applications. As management struggle to create value within the corporate setting, financial management as a discipline is assuming a greater strategic focus. Conflicting stakeholder interests, informational and financial signaling implications, the globalization of finance, the growth of e-commerce, the emergence of strategic alliances, the rise of outsourcing and the advent of the virtual corporation now permeate and pose challenges to the field of financial decision-making. The primary objective of this course is to introduce students to the fundamental principles of financial management and the role of finance in the success of the business. Emphasis will be placed on the theories and models of finance and their application in financial decision making by individuals and business enterprises. COURSE CONDUCT AND EVALUATION: The course will be conducted by way of lectures and class discussions. Students are expected to acquire at least one copy of the recommended texts at the beginning of the course. An acquaintance of the material to be covered prior to the lectures enhances appreciation of the subject matter during the lecture. This will then be enhanced when student revises in light of lecture. Students should expect, and constantly practice on, quantitative questions. Students will be evaluated as follows: Quizzes 20% Tests 30 Final Exam 50 Total 100% READING MATERIALS:

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1) Brealey, R.A; Myers, S.C et al (20007): Principles of Corporate Finance, Mc

Graw Hill. 2) Van Horne, J.C (2007): Financial management and Policy, 12th edition, Prentice

hall. 3) Ross, S.A; Westerfield, R.W et al (2007): Principles and Applications of

Corporate Finance, Mc Graw Hill/Irwin. 4) Gitman L.J (2006): Principles of Managerial Finance, 11th Edition, Pearson

Addison-Wesley. 5) Pandey I.M (2005): Financial Management, 9th Edition, Vikas Publishing House,

India. 6) Other reading materials to be assigned in class. COURSE CONTENT

1. Fundamental Concepts of Financial Management • An Overview of Financial Management • The Nature of Financial Markets • Agency Theory and Corporate Governance • Risk and Return 2. Valuation of Securities • The Concept of Valuation • Time Value of Money • Valuation of Bonds • Valuation of Stocks • Corporate Valuation 3. Investment Decisions

• Basics of Capital Budgeting • Cash flow Determination • Capital Budgeting Techniques • Uncertainty in Capital Budgeting • Capital Rationing

4. Cost of Capital • Cost of Component Sources of Capital • WACC and MCC 5. Financial Planning and Forecasting.

• Analyzing Financial Performance • Approaches to Financial Planning • Cash Budgets

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6. Financing Decisions • Capital Structure Decision • Dividend decision

7. Working Capital Management

• Issues in Working Capital Management • Management of Cash and Short Term Financing • Management of Accounts Receivables • Management of Inventory • Management of Accounts Payables

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LECTURE ONE: OVERVIEW OF FINANCIAL MANAGEMENT

1.0 Introduction

This lecture discusses the objectives and scope of financial management, the factors that shape the operating environment of financial managers, and the owner/manager agency problem and possible solutions to the problem

Objectives At the end of this lecture students should be able to:

1. Define finance and discuss the scope and decision areas in financial management.

2. Describe the environments that impact on financial management decision.

3. Discuss the goals of financial management.

4. Explain the shareholder/management (agency) conflicts and possible solutions.

. 1.1 Scope of Finance We begin the study of finance by taking a broad overview of it as an academic discipline as well as a professional practice. It will become clear that the field of finance is dynamic in its orientation and pervasive in its impact on the lives of almost every economic person. The discipline borrows and interfaces with many other academic disciplines and offers diverse and varied career opportunities. 1.1.1 DEFINITION OF FINANCIAL MANAGEMENT Financial management can be defined as the art and science of managing money. Every organization and individual who has an objective must decide from where to source for money, in what assets to invest the money, and how to manage its assets in the most efficient way. Finance is concerned with the process, institutions, markets, and instruments involved in the transfer money among and between individuals, businesses and the government.

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1.1.2 WHY STUDY FINANCE

All managers in a firm work with finance personnel to justify manpower requirements,

negotiate operating budgets, deal with performance appraisals, and sell proposals based

on their financial merits. Clearly, those managers who understand the theories, concepts,

and practices of financial management will perform their responsibility efficiently and

will also justify their needs for financing. Career opportunities in finance are many and

diverse. Proficiency in financial management could enable one work as financial analyst,

investment analyst, project finance manager, treasurer, and credit manager, pension fund

manger, to mention but a few. Although this course focuses on profit making

organizations, the decision-making principles are just as relevant for public, non-profit

making organizations and even individuals.

1.1.3 DECISION FUNCTIONS OF FINANCE MANAGER

Financial management is concerned with the acquisition, financing and management of

assets with the goal f maximizing shareholders wealth. These three broad decisions

functions of financial managements are briefly discussed below.

The Investment Decision

This is one the most important decision contributing to value creation. It entails the

decision of the amount of assets to be held and the composition of the assets (asset

structure).

The Financing Decision

The function involves deciding on the optimal capital structure (the proportion of debt

and share capital) to be employed by the firm. The long term sources of financing which

form the capital structure of the firm comprise basically three components: debt capital,

preference share capital, and ordinary share capital. These components each have

different costs and it is the responsibility of the finance manager to ensure the firm’s

overall cost of financing is as low as possible.

The financing decision encompasses the dividend decision of the firm. The value of

dividends paid to shareholders must be balanced against the opportunity cost of retained

earnings lost as a means of equity financing.

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The Asset management decision

The asset acquired must be managed effectively. The task requires an analysis of the risk

and return of the various assets in order to ensure firm’s assets are held in efficient

combinations. While the responsibility of managing fixed assets may reside with the

operating managers, the financial manager will have to devote considerable attention to

the management of current assets and liabilities (working capital management).

1.2 Financial Management Environments

The environments that impacts on the functions of a financial manager can be broadly

viewed in terms of social, political, economic, and legal contexts. Although all four

environments affect a finance manager’s functions and decisions, the political and social

dynamics are driven by events on which the manager has little or no influence.

Consequently, in this section we restrict the discussion only to aspects of the legal and

economic environment, namely the various types of business organizations, the tax

legislation, and the financial system (market institutions and intermediaries).

1.2.1 BUSINESS ORGANISATIONS

The three basic forms of business organizations are a proprietorship, a partnership and a

corporation (limited liability companies)

Sole Proprietorship

A proprietorship is an organization in which a single person owns the business, holds title

to all the assets and is personally responsible for all liabilities. The main virtue of a

proprietorship is that it can be easily established and is subject to minimum government

regulation and supervision. The proprietorship’s shortcomings include the owner’s

unlimited liability for the all business debts, the limitations in raising capital, and the

difficulty in transferring ownership.

The proprietorship pays no separate income taxes. Rather the income or losses from the

proprietorship are included on the owner’s personal tax return.

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Partnership

A partnership is similar to a proprietorship, except that it is owned by two or more

persons. The profit of the partnership is taxed on the individual partners after sharing.

A potential advantage of a partnership compared to a proprietorship is that a greater

amount of capital can be raised.

In a general partnership each partner is personally responsible for the obligations of the

business. A formal agreement (partnership deed) is necessary to set forth the privileges

and duties of each partner, the distribution of profits, capital contributions, procedures for

admitting new partners and modalities of reconstitutions of the partners in the event of

death or withdrawal of a partner.

In a limited partnership, limited partners contribute capital and their liability is confined

to that amount of capital. There must be however, at least one general partner in the

partnership who manages the firm and his liability is unlimited.

Corporation

A corporation is an “artificial entity” created by law. A corporation is empowered to own

assets, to incur liabilities, engage in certain specified activities, and to sue and be sued.

The principal features of this form of business organization are that the owner’s liability

is limited; there is ease of transfer of ownership through sale of shares; the corporation

has unlimited life apart from its owners and; the corporation has the ability to raise large

amounts of capital.

A possible disadvantage is that corporation profits are subject to double taxation. A minor

disadvantage is the difficulties and expenses encountered in the formation. Corporation

are owned by shareholders whose ownership is evidenced by ordinary stocks

shareholders expect earn a return by receiving a dividend or gain through increasing

share pries.

Corporations are formed under the provisions of the Companies Act (CAP486). A Board

of Directors, elected by the owners, has ultimate authority in guiding the corporate affairs

and in making strategic policy decisions. The directors appoint the executive officers

(often referred to as management) of the company, who run the company on a day-to-day

basis and implement the policies established by the directors. The chief executive officer

(CEO) is responsible for managing day-to-day operations and carrying out the policies

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established by the board. The CEO is required to report periodically to the firm's

directors.

Figure 1.1 Strengths and weaknesses of the basic forms of business organizations

Sole proprietorship Partnership Corporation

Strengths

1. Owner receives all

profits (as well as losses)

1. Can raise more

capital than a sole

proprietorship

1. Owners have

limited liability which

guarantees they cannot

lose more than they

invest.

2.Low organizational costs 2. Borrowing power

enhanced by more

owners

2. Growth is not

restricted by lack of

funds. (can see shares)

3. Not taxed separately:

rather income included on

proprietor’s return.

3. More available

brainpower and

managerial skills

3. Ownership (shares)

is readily transferable

4. A high degree of

independence

4. Not taxed

separately. The

partners are taxed

after receiving share

of profits

4. Endless life of firm

(does not depend on

life of owners)

5. A degree of secrecy is

achievable

5. Can hire

professional managers

(separation of

ownership from

control)

6. There is ease of

dissolution

6. Can raise funds

more easily

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Weaknesses

1. owner has unlimited

liability – total wealth can

be taken to satisfy debts

1.Owners have

unlimited liability

and may have to

cover the debts of

other partners

1. Taxes generally

higher due to double

taxation- on

dividends and

corporate profits

2. Limited fund raising

ability tends to inhibit

growth

2. Partnership is

dissolved on the

death or withdrawal

of a partner

2. More expensive

to organize

3. proprietor must be a jack-

of-all-trades

3. Difficult to

liquidate or transfer

partnership interest

3. Subject to greater

regulation

4.Difficult to motivate

employees’ career prospects

4. Lacks secrecy,

because

stockholders must

receive financial

report

5. Continuity dependent on

presence of proprietor

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1.2.2 TAX ENVIRONMENT

Taxation by central and local government has profound influence on the behavior of

business and their owners. Tax considerations are especially important in financial

management. Let us also appreciate that tax laws are so numerous and complex and their

impact so profound that firms require the input of a tax expert in many decisions.

Ordinary income tax. The income of all business organizations is liable to tax by the

government. As we noted before the income of proprietorships and partnerships added to

that of its owners and taxed at graduated rates for individuals. How much tax is charged

depends on the personal tax status of the owners. A corporation’s taxable income is found

by deducting all allowable expenses from the revenue. The taxable income is then subject

to the corporate tax rate to determine the amount of tax liability (The current corporate

tax rate in Kenya is 30%).

Capital allowance and tax credit. Capital allowance is allowable in place of depreciation

and is granted to businesses engaged in investment activities and that operate fixed asset.

Tax credits are reduction in tax liability granted by the government to a taxpayer. Capital

allowances and tax credits lower the purchase price of capital assets and a major

consideration in investment decisions. The government grants the allowance and credits

for the purpose of stimulating economic development.

Interest Vs dividends Interest paid on outstanding corporate debt is a tax-deductible

expense. However dividends paid to shareholders are not tax deductible. Thus, for a

profitable company, the use of debt (bonds) in its financing mix results in significant tax

advantage relative to the use of share capital.

Capital gains tax. This is the tax levied on the gain (or loss) on the sale of fixed assets.

The capital gains tax rate is usually lower than the ordinary income tax rate (Capital gains

tax is currently suspended in Kenya).

1.2.3 FINANCIAL SYSTEM

The primary role of the financial system in the economy is to facilitate in the

transformation of saving into investments. The financial system provides the principal

means by which a person who has saved money out of current income can transfer their

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savings to someone else who has productive investments opportunities and is in need of

money to finance them.

This transfer of money results in the creation of a financial asset for the saver and a

financial liability for the borrower. Consequently, the financial system provides the

means for risk transfer and risk sharing among the market participants.

Figure 1.2 illustrates the instruments used in financial system, the way they flow and the

main participants in the system.

Figure 1.2 The financial system comprises of financial markets, financial

institutions that intermediate, the financial instruments that represent claims, and

the savers and demanders of funds who are the government, individuals and

businesses.

Financial institutions Banks, insurance companies, Pension funds Saccos etc

Demanders of funds (Investors) Business, Government Households

Private placement

uriti

es

Fund

s

Suppliers of funds (Savers) Business, Government Households

Sec

Financial markets Primary v SecondaryMoney v Capital

Deposit /shares

Funds

Loans

Funds

Funds

Securities

Securities

Securities

Funds

Funds

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Financial assets

Financial assets are divided into three general classes; money, debt and shares. Money is

issued by government as currency notes and coins and by some commercial banks

through their checking accounts. The issuer of debt promises to pay the creditor a specific

amount of money at a future date whereas the company that issues shares is selling

ownership rights in the company to the shareholder.

Savers and demanders of funds

The key suppliers and demanders of funds are individuals, businesses, and governments.

The savings of individuals provide financial institutions with a large portion of their

funds. Individuals are not only suppliers of funds, but also demand funds from financial

institutions in the form of loans. Individuals as a group are the net suppliers for financial

institutions: They save more money than they borrow.

Business firms also deposit some of their funds in financial institutions, primarily in

checking accounts with various commercial banks. Firms, like individuals, also borrow

funds from these institutions. As a group, business firms are net demanders of funds:

borrowing more money than they save.

Governments maintain deposits of temporarily idle funds, certain tax payments, and

Social Security payments in commercial banks. Although governments do not borrow

funds directly from financial institutions, by selling their securities to various institutions,

they indirectly borrow from them. The government is typically a net demander of funds

(budget deficits).

Financial Intermediaries

Financial intermediaries facilitate the indirect transfer of money from savers to lenders.

Intermediaries confer the following advantages to those who consume their services.

1. Flexibility and liquidity Intermediaries provide a large sum of money to a

borrower by pooling the savings several investors. They also engage in maturity

transformation of assets and claims, providing investors with financial assets

which maybe liquid money at the same time as they are making long-term loans.

2. Diversification By sourcing funds from savers with diverse characteristics the

intermediary is able to provide relatively low risk capital to investors.

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3. Convenience By dealing with an intermediary a person gets a variety of financials

services provided at one point in time and place.

4. Expertise Because of continuous engagement in financial transactions the

intermediary accumulates expertise that can be availed to customers.

The major financial institutions in Kenya economy are commercial banks, savings and

loans, credit unions, savings banks, life insurance companies, pension funds, and mutual

funds. These institutions attract funds from individuals, businesses, and governments,

combine them, and make loans available to individuals and businesses. A brief

description of the major financial institutions follows.

Institution Description

Commercial bank Accepts both demand (checking) and time (saving) deposits. Also

offers negotiable order of withdrawal (NOW), and money market

deposit accounts. Commercial banks also make loans directly to

borrowers or through the financial markets.

Saving and loan These are similar to a commercial bank except chat it may not hold

demand (checking) deposits. They obtain funds from savings,

negotiable order of withdrawal (NOW) accounts, and money

market deposit accounts. They lend primarily to individuals and

businesses in the form of real estate mortgage loans.

Credit union Commonly known as Savings co-operative societies (Saccos),

credit unions deal primarily in transfer of funds between members.

Membership in credit unions is generally based on some common

bond, such as working for a given employer. Credit unions accept

members’ savings deposits, NOW account deposits, and money

market account deposits and lend funds to members, typically to finance

automobile or appliance purchase, or home improvements.

Savings banks These are similar to a savings and loan in that it holds savings,

NOW, and money market deposit accounts. Savings banks lend or

invest funds through financial markets, although some mortgage

loans are made to individuals.

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Life insurance

Company It is the largest type of financial intermediary handling individual

savings. It receives premium payments and invests them to

accumulate funds to cover future benefit payments. It lends funds to

individual, businesses, and governments, typically through the

financial markets.

Pension fund Pension funds are set up so that employees can receive income

after retirement. Often employers match the contribution of their

employees. The majority of funds is lent or invested via the

financial market.

Mutual fund Pools funds from the sale of shares and uses them to acquire bonds

and stocks of business and governmental units. Mutual funds

create a professionally managed portfolio of securities to achieve a

specified investment objective, such as liquidity with a high return.

Hundreds of funds, with a variety of investment objectives exist.

Money market mutual funds provide competitive returns with very

high liquidity.

Unit trusts Unit trusts are investment funds which are open ended, that is, the

size of the fund and number of shares or units issued depends on

the level of demand from the investor. More units are issued as

and when investors subscribe, additional money to the fund. The

value of this unit is based on the market value of the investment

held by the trust.

Unit trust provides 2 main services to individual investors.

(a) Opportunity to invest in relatively will diversified portfolio

(b) The expertise of professional investment managers. The cost

of the management services are reflected in the purchase price

of the units.

In order to safeguard the interest of the unit holders, trustees

are appointed under the terms of the trust deed. A management

company will also be appointed with responsibility both for

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marketing and selling the units and investing the funds

subscribed.

Financial Markets

Financial markets provide a forum in which suppliers of funds and demanders of funds

can transact business directly. Whereas the loans and investments of intermediaries are

made without the direct knowledge of the suppliers of funds (savers), suppliers in the

financial markets know where their funds are being lent or invested. It is important to

understand the following distinctions in the market.

Money versus Capital markets. The two key financial markers are the money market and

the capital market. Transactions in the money market take place in short-term debt

instruments, or marketable securities, such as Treasury bills, commercial paper, and

negotiable certificates of deposit. The market brings together government units,

households, businesses and financial institutions who have temporary idle funds, and

those in need of temporary or seasonal financing.

Long-term securities—bonds and stocks—are traded in the capital market. The main

actor in the capital markets is the securities exchanges, which provide the market place in

which demanders can raise long-term funds and investors can maintain liquidity by being

able to sell securities easily. The Nairobi Stock Exchange (NSE) was established in 1954

and is one of the most active stock markets in sub-Saharan Africa. It currently (2005) has

48 companies listed and 20 brokerage company members.

Private placements versus Public offerings. To raise money, firms can use either private

placements or public offerings. Private placement involves the sale of a new security

issue, typically bonds or preferred stock, directly to an investor or group of investors,

such as an insurance company or pension fund. However, most firms raise money

through a public offering of securities, which is the nonexclusive sale of either bonds or

stocks to the general public,

Primary market versus Secondary market. All securities, whether in the money or capital

market, are initially issued in the primary market (Initial public offerings ( IPOs) and

seasoned equity offerings (SEOs)). This is the only market in which the corporate or

government issuer is directly involved in the transaction and receives direct benefit from

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the issue. That is, the company actually receives the proceeds from the sale of securities.

Once the securities begin to trade in the stock exchange, between savers and investors,

they become part of a secondary market. The primary market is the one which “new”

securities are sold; the secondary market can be viewed as “used,” or “pre-owned,”

securities market.

1.3 The Goal of the Firm in Market Economy

A market economy is one in which goods and services are bought and sold at prices

determined in free competitive markets. Business firms are the principal agents charged

with the task of producing as efficiently as possible the goods and services the society

needs. Given this broad goal of efficiency, what standard or benchmark should financial

management practice be measured? In sum, what is the goal of the firm from a financial

management perspective?

1.3.1 PROFIT MAXIMIZATION

Microeconomic theory of the firm is founded on profit maximization as the principal

decision criterion: markets managers of firms direct their efforts toward areas of

attractive profit potential using market prices as their signals. Choices and actions that

increase the firm’s profit are undertaken while those that decrease profits are avoided. To

maximize profits the firm must maximize output for a given set of scarce resources, or

equivalently, minimize the cost of producing a given output.

Applying Profit-Maximization Criterion in Financial Management

Financial management is concerned with the efficient use of one economic resource,

namely, capital funds. The goal of profit maximization in many cases serves as the basic

decision criterion for the financial manager but needs transformation before it can

provide the financial manger with an operationally useful guideline. As a benchmark to

be aimed at in practice, profit maximization has at least four shortcomings: it does not

take account of risk; it does not take account of time value of money; it is ambiguous and

sometimes arbitrary in its measurement; and it does not incorporate the impact of non-

quantifiable events.

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Uncertainty (Risk) The microeconomic theory of the firm assumes away the problem of

uncertainty: When, as is normal, future profits are uncertain, the criteria of maximizing

profits loses meaning as for it is no longer clear what is to be maximized. When faced

with uncertainty (risk), most investors providing capital are risk averse. A good decision

criterion must take into consideration such risk.

Timing Another major shortcoming of simple profit maximization criterion is that it does

not take into account of the fact that the timing of benefits expected from investments

varies widely. Simply aggregating the cash flows over time and picking the alternative

with the highest cash flows would be misleading because money has time value. This is

the idea that since money can be put to work to earn a return, cash flows in early years of

a project’s life are valued more highly than equivalent cash flows in later years.

Therefore the profit maximization criterion must be adjusted to account for timing of

cash flows and the time value of money.

Subjectivity and ambiguity A third difficulty with profit maximization concerns the

subjectivity and ambiguity surrounding the measurement of the profit figure. The

accounting profit is a function of many, some subjective, choices of accounting standards

and methods with the result that profit figure produced from a given data base could vary

widely.

Qualitative information Finally many events relevant to the firms may not be captured

by the profit number. Such events include the death of a CEO, political development, and

dividend policy changes. The profit figure is simply not responsive to events that affect

the value of the investment in the firm. In contrast, the price of the firms share (which

measures wealth of the shareholders of the company) will adjust rapidly to incorporate

the likely impact of such events long before they are their effects are seen in profits.

1.3.2 VALUE MAXIMIZATION

Because of the reasons stated above, Value-maximization has replaced profit-

maximization as the operational goal of the firm. By measuring benefits in terms of cash

flows value maximization avoids much of the ambiguity of profits. By discounting cash

flows over time using the concepts of compound interest, Value maximization takes

account of both risk and the time value of money. By using the market price as a measure

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of value the value maximization criterion ensures that (in an efficient market) its metric is

all encompassing of all relevant information qualitative and quantitative, micro and

macro. Let us note here that value maximization is with respect to the interests of the

providers of capital, who ultimately are the owners of the firm. – the maximization of

owners’ wealth is the principal goal to be aimed at by the financial manager.

In many cases the wealth of owners will be represented by the market value of the firm’s

shares - that is the reason why maximization of shareholders wealth has become

synonymous with maximizing the price of the company’s stock. The market price of a

firms stocks represent the judgment of all market participants as to the values of that firm

- it takes into account present and expected future profits, the timing, duration and risk of

these earnings, the dividend policy of the firm; and other factors that bear on the viability

and health of the firm. Management must focus on creating value for shareholders. This

requires Management to judge alternative investments, financing and assets management

strategies in terms of their effects on shareholders value (share prices).

1.3.3 AGENCY CONFLICTS AND WEALTH MAXIMIZATION

Two difficulties complicate the achievement of the goal of shareholder wealth

maximization in modern corporations. These are caused by the agency relationships in a

firm, and the requirements of corporate social responsibility.

I.3.3.1 Agency Problem

In modern corporations, control (vested in management) is divided from ownership

(vested in shareholders). This separation is the cause of myriad conflicts of interests

between management and owners. During the past years a body of financial theory, the

agency theory, has emerged dealing with the conflict between shareholders and the

resolution of these conflicts.

The genesis of the conflict is the opportunistic behavior of management, which makes

them place their (management) interest above that of shareholders. Consequently,

shareholders’ wealth maximization goal is sacrificed. For instance, they may grant

themselves excessive salaries, consume large amounts of perquisites, engage in empire

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building, and make sub-optimal investment decisions (retaining profits and investing in

negative NPV projects rather distributing profits as dividends).

Mechanism to Align Shareholder/Management Interests

In order to ensure that managers act in the best interests of the shareholders several

mechanisms may be employed. The most common measures are discussed below.

(i). Monitoring

Shareholders design mechanism to monitor management actions to ensure their interests

are not hurt. Monitoring of management by shareholders themselves is, however,

complicated for the following reasons:

- It is impossible for a shareholder without exception expertise to know to what

extend management have under performed management can even conceal

alliaceous frauds they have committed form shareholders and throughout.

- Underperformance may result from extraneous circumstances beyond

management’ control. For example, changes in world prices of important inputs

(oil) could escalate costs, or changing tastes may make demand for a company’s

product to evaporate (i.e. cigars and pipe tobacco).

Shareholders are obligated to contract with external parties in order to effectively

monitor management. Some of the monitoring arrangements include the following:

Hiring auditors- who report annually to shareholders at the Annual General Meeting

(AGM) on the management’s stewardship of the company.

Board of directors- a properly constituted board plays the oversight role on management

for the shareholders

Bonding insurance. Taking fidelity insurance whereby the firm is compensated if the

insured management commits an infringement.

(ii). Executive compensations schemes

Appropriate compensation schemes should be designed to address management’s

aversion to risk and their obsession with short-term decision horizon. Such schemes

include;

- Stock options that make managers part owners help align interest of management

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and shareholders - Cash and stock bonus pegged to performance.

(iii). Shareholder-activism

The threat of bad publicity by disgruntled shareholders who can confront management

and create dissent among other stockholders, if the grievance is founded. can act as a

deterrent to managerialsm.

(iv). Legal sanctions

Corporate boards and management also face legal liability for their acts of commission

and omission which betray their fiduciary duty to shareholders.

(v). Corporate takeover market (market for corporate control)

The possibility of an outside takeover of the company can be a powerful deterrent to

mismanagement. Management of firms that under-perform become target for take-over

bids. If a takeover bid succeed incumbent management teams vacate their positions to

replaced by new management teams

(vi). Market for executive labor.

In an efficient labor market, executives who under perform will lose their jobs and this

may adversely affect their reputational capital. They will find it hard to secure similar

positions in other companies. On the other hand managers who maximize shareholders

wealth can keep their jobs. Inefficient managers will thus be driven out of the executive

labor market or be forced to take less rigorous jobs.

1.3.3.2. Social Responsibility and Ethics

It has been argued that the unbridled pursuit of shareholders wealth maximization makes

companies unscrupulous, anti social, enhances wealth inequalities and harms the

environment. The proponents of this position argue that maximizing shareholders wealth

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should not be pursued without regard to a firm’s corporate social responsibility. The

argument goes that the interest of stakeholders other than just shareholders should be taken

care of. The other stakeholders include creditors, employees, consumers, communities in

which the firm operates and others. The firm will protect the consumer; pay fair wages to

employees while maintaining safe working conditions, support education and be sensitive to

the environment concerns such as clean air and water. A firm must also conduct itself

ethically (high moral standards) in its commercial transactions.

Being socially responsible and ethical cost money and may detract from the pursuit of

shareholders wealth maximization. So the question frequently posed is: is ethical behavior

and corporate social responsibility inconsistent with shareholder wealth maximization?

Scholars and practitioners concur that, in the long run, the firm has no choice but to act in

socially responsible ways. It is argued that the corporation’s very survival depend on it being

socially responsible. The implementation of a pro-active ethics ad corporate social

responsibility (CSR) program is believed to enhance corporate value. Such a program can

reduce potential litigation costs, maintain a positive corporate image, build shareholder

confidence, and gain the loyalty, commitment and respect of firm’s stakeholders. Such

actions conserve firm’s cash flows and reduce perceived risk, thus positively effecting firm

share price. It becomes evident that behavior that is ethical and socially responsible helps

achieve firm’s goal of owner wealth maximization.

The existence of non- financial objectives do not negate financial objectives, but they do

mean that the simple theory of corporate finance, that the objective of the firm is to maximize

the wealth of the share holders is too simplistic. It may be necessary to sacrifice financial

objectives in order to be a responsible corporate citizen.

22

REVIEW QUESTIONS

1. What are the problems in the relationship between shareholders and

management?

2. Contrast the liability provisions of a sole proprietorship, a partnership, a

limited partnership, and a corporation.

3. Explain the relationship among the following:

a) Authorized shores;

b) Outstanding shares;

c) Treasury stock, and

d) Issued shares.

4. What are the key differences between debt capital and equity capital?

5. Differentiate between standard debt provisions and restrictive covenants

included in a bond indenture.

6. What is the Euro currency market? What is the London Inter-bank Offered

Rate (LIBOR)?

7. Distinguish between a Eurobond and a foreign bond.

8. What is the agency problem? What are agency costs?

9. For what three basic reasons is profit maximization inconsistent with wealth

maximization?

10. Describe the role of corporate ethics and social responsibility. Reconcile the

need for ethics and social responsibility with shareholder wealth

maximization.

11. What are the three key activities of a financial manager? Relate them to the

firms balance sheet.

12. Describe the field of managerial finance. Why is the study of finance

important to all professionals and managers?

13. What are the principal functions:

1. Financial markets and,

2. Financial intermediaries in a financial system?

23

PROBLEMS

QUESTION ONE

Makau Munyao has invested sh.25 million in Mbooni Ltd. The firm has recently been

declared bankrupt and has Sh.60 million in unpaid debts. Explain the nature of payments

if any, by Mr. Munyao in each of the following situations:

a) Mbooni Ltd. is a sole proprietorship owned by Mr. Munyao

b) Mbooni Ltd. is a 50-50 partnership of Mr. Munyao and Mr. Mutiso.

c) Mbooni Ltd is a corporation.

QUESTION TWO

For each of the following situations explain the agency conflict inherent, the cost the firm

might incur, and the likely remedies:

a) The front desk receptionist routinely takes extra 20 minutes of lunch on his

personal errands.

b) Division managers are padding cost estimates in order to show short term

efficiency gains.

c) The firm’s CEO has secret talks with a competitor about the possibility of a

merger in which she would become CEO of the combined firms.

d) A branch manager lays off experienced full-time employees and replaces them

with temporary workers to lower employment costs. The manager’s bonus is

based on profitability of the branch.

QUESTION THREE

Unity Trading Company’s charter authorities issuance of Sh.2,000,000 ordinary hours.

Currently, 1,400,000 shares are outstanding and 100,000 shares are being held as treasury

stock. The firm wishes to raise sh.48,000,000 for plant expansion. The sale of new

ordinary shares will net the firm sh.60 per share.

24

a) Determine maximum member of ordinary shares the firm can issue without

shareholders approval.

b) Will the firm be able to raise needed funds without further authorization.

c) What must the firm do to get authorization to issue more than the shares as

determined in (a) above.

25

LECTURE TWO: THE TIME VALUE OF MONEY

2.0 INTRODUCTION

In this lecture you will be provided with compounding and discounting skills required in

making many financial decisions. Because you can earn interest on money you have, a

shilling today would grow to more than a shilling later. Our goal in this lesson is to

evaluate the trade-off between money held today and money promised at some future

point in time.

Objectives At the end of this lecture you should be able to:

1. Discuss the role of time value in finance

2. Explain the concept of future value and

perform compounding calculations.

3. Explain the concept of present value and

perform discounting calculations.

4. Apply the mathematics of finance to

accumulate a future sum, preparing loan

amortization schedules, and determining

interest or growth rates.

2.1 THE TIME VALUE OF MONEY

Time value of money is one of the most important concepts in finance. The techniques

and skills you learn in this lesson will be essential in handling many of the financial

decision situations in latter lessons, so you should pay particular care to the material

26

presented. Time value computations will be necessary in many and diverse decision

situations, such as financial structure decisions, lease versus purchase of capital assets

choices, bond refinancing decisions, valuation of securities , cost of capital, among

others.

The concept of time value of money is based on the fact that, in general, a shilling

received today is more valuable than a shilling to be received at future point in time (“a

bird in hand is worth two in the bush”). This concept recognizes that the passage of time

affects the value of money: A shilling in ones possession today is more valuable than a

shilling to be received in future because, first, the shilling in hand can be put to

immediate productive use, and, secondly, a shilling in hand is free from the uncertainties

of future expectations (It is a sure shilling).

2.1.1 Time value Concepts

We begin the lesson by considering two views of time value:

• Future value (FV)

• Present value (PV)

Financial values and decisions can be assessed by using either future value (FV) or

present value (PV) techniques. These techniques result in the same decisions, but adopt

different approaches to the decision.

Future value techniques measure cash flow at the some future point in time – typically

at the end of a projects life. The Future Value (FV), or terminal value, is the value at

some time in future of a present sum of money, or a series of payments or receipts. In

other words the FV refers to the amount of money an investment will grow to over some

period of time at some given interest rate.

Present value techniques measure each cash flows at the start of a projects life (time

zero).The Present Value (PV) is the current value of a future amount of money, or a

series of future payments or receipts. Present value is just like cash in hand today.

To illustrate the two concepts of time value, a time line could be employed. A time line

is a horizontal line on which time zero appears at the left most end and future periods are

marked from left to right. Figure 2.1 depicts cash flows occurring over time and the

associated future values and present values.

27

Because money has time value, all of the cash flows associated with an investment must

be measures at the same point in time. Typically the point is chosen is either at the end or

the beginning of the investment’s life.

FV techniques use compounding to find the future value of each cash flow at the given

future date and the sums those values to find the value of cash flows. Alternatively the

PV techniques use discounting to find the PV of each cash flow at time zero and then

sums these values to find the total value of the cash flows.

Although FV and PV techniques result in the same decisions, since financial managers

make decisions in the present, they tend to rely primarily on PV techniques.

FIGURE 2.1Time line depicts an investment's cash flows covering five periods, and

FV and PV concepts. The timeline represents the case where an initial investment of

Sh. 100,000 at time zero is followed by cash inflows for the next five years of

Sh.30,000, Sh. 50,000, Sh.40,000, Sh030,000, and Sh.20,000 respectively

-100,000 30,000 50,000 40,000 30,000 20,000

0 1 2 3 4 5

FV

PV

2.2 FUTURE VALUE OF A SINGLE AMOUNT

The question of whether or not interest is earned on the preceding years’ interest earnings needs to be addressed first. Two forms of treatment of interest are possible. In the case of

28

Simple interest, interest is paid (earned) only on the original amount (principal) borrowed. In the case of Compound interest, interest is paid (earned) on any previous interest earned as well as on the principal borrowed (lent). Compound interest is crucial to the understanding of the mathematics of finance. In most situations involving the time value of money compounding of interest is assumed.

The future value of present amount is found by applying compound interest over a

specified period of time

The Equation for finding future values of a single amount is derived as follows:

Let FVn = future value at the end of period n

PV (Po) =Initial principal, or present value

k= annual rate of interest

n = number of periods the money is left on deposit.

The future value (FV), or compound value, of a present amount, Po, is found as follows.

At end of Year 1, FV1 =Po (1+k) = Po (1+k)1

At end of Year 2, FV2=FV1 (1+k) = Po(1+k) (1+k) = Po ( 1+k)2

At end of Year 3, FV3 = FV2 (1+k) = Po ( 1+k) ( 1+k) (1+k) = Po (1+k)3

A general equation for the future value at end of n periods can therefore be formulated as,

FVn = Po ( 1+k)n (2-1)

.

Take note Equation (2-1) is the basic relationship in the time-value-of-money formulations. All other equations and relationships we shall discuss later derive from this equation

Example 1

Jane deposited Sh.800,000 in a saving account paying 6% interest compounded annually

and would like to know the money the account after 3, 6,7, and 10 years.

Solution

At the end of 3 years, FV3 = 800,000 ( 1+0.06)3 = Sh.952,813

29

At the end of 6 years, FV6 = 800,000 ( 1+0.06)6 = Sh. 103,9534

At the end of 7 years, FV7 = 800,000 ( 1+0.06)7 = Sh. 1,202,904

At the end of 10 years, FV10 = 800,000 ( 1+0.06)10 = Sh. 1,432,678

2.2.1 Using Tables to Find Future Values

Unless you have financial calculator at hand, solving for future values using Equation

2.1 can be quite time consuming because you will have to raise (1+k) to the nth power.

Luckily, there are published tables available giving values of (1+k)n for various values of

k and n. Appendix A at the back of this manual contains a set of these interest rate tables.

Appendix A table A-1 gives the future value interest factors. These factors are the

multipliers used to calculate at a specified interest rate the future values of a present

amount as of a given date. The future value interest factor for an initial investment of

Sh.1 compounded at k percent for n periods is referred to as FVIFk n.

Future value interest factors = FVIFk n. = (1+k)n . (2.2)

We can, consequently, rewrite Equation 2.1 as follows.

FVn = Po * FVIFk,n (2.3)

The FVIF for an initial principal of Sh.1 compounded at k percent for n periods

can be found in Appendix Table A-1 by looking for the intersection of the nth row

an the k % column. A future value interest factor is the multiplier used to calculate

at the specified rate the future value of a present amount as of a given date.

Example 2 We refer to Example 1 where Jane wanted to find out the amount in

her account at future dates given prevailing interest rate of 6%.

Solution Using Table A-1 we find the relevant factors by looking at the

intersection of k-column, and n-row, and multiply by initial deposit.

FV after 3 years will be, 800,000*FVIF 6%,3yrs = 800,000*1.191 = Sh.952,800

FV after 6 years will be 800,000 * FVIF 6%,6yrs = 800,000*1.419 =Sh.1,135,200

FV after 8 years will be, 800,000 * FVIF 6%,8yrs = 800,000*1.594 =Sh.1,275,200

FV after 10yearswill be, 800,000 * FVIF 6%,10yrs = 800,000*1.791 =Sh.1,432,800

30

Example

What is the value of Jane’s deposit after six years assuming the following annual interest

rates; 3%, 5%, 8%, 10%, and 15%.

FV with 3% rate is 800,000*FVIF3%,6yrs=800,000 x 1.194=Sh.955,200

FV with 5% rate is 800,000*FVIF5%,6yrs=800,000 x 1.340=Sh.1,072,000

FV with 8% rate is 800,000*FVIF8%,6yrs=800,000 x 1.587=Sh.1,269,600

FV with 10% rate is 800,000*FVIF10%,6yrs=800,000 x 1.772=Sh.1,417,600

FV with 15% rate is 800,000*FVIF15%,6yrs=800,000 x 2.313=Sh.1,850,400

A Graphic View of Future Value

Figure 2.1 Influence of time and interest rates on the FVIFs.

30

25

20

15

10

5%

5

1 0%

0 2 4 6 8 10 12 14 16 18 20

FV of 1/=

5%

Periods

150

100

200

Future values are normally stated at the end of the given period. Figure 2.1 graphically

illustrates the relationships between interest rate, the time periods, and the future value

interest factors. The relationships can be summed as follows:

31

1. The higher the interest rate, the higher the future value of Sh.1.

2. The longer the period of time, the higher the future value of Sh.1.

3. When the interest rate is zero there is no growth and the future value equals

the present value of Sh.1.

2.2.2 Compounding More Frequently.

Interest is often compounded more frequently than once a year. Financial institutions

compound interest semi-annually, quarterly, monthly, weekly, daily or even

continuously.

Semi Annual Compounding

This involves the compounding of interest over two periods of six months each within a

year. Instead of stated interest rate being paid once a year one half of the stated interest is

paid twice a year..

Example

Jane decided to invest Sh.100,000 in savings account paying 8% interest compounded

semi annually. If she leaves the money in the account for 2 years how much will she have

at the end of the two years?

She will be paid 4% interest for each 6-months period. Thus her money will amount to.

FV4 = 100,000 ( 1+.08/2)2*2 =100,000(1+.04)4 =Sh.116,990

Or

Using tables = 100,000 x FVIF 4%,4periods =100,000*1.17 = Sh.117,000

Quarterly Compounding

This involves compounding of interest over four periods of three months each at one

fourth of stated annual interest rate.

Example

Suppose Jane found an institution that will pay her 8% interest compounded quarterly.

How much will she have in the account at the end of 2 years?

FV8 = 100,000(1+.08/4)4*2=100,000(1+.02)8 =100,000 x 1.1716 =

117,160

Or,

32

Using tables 100,000 x FVIF 2%,8periods = 100,000*1.172 = 117,200

As shown by the calculations in the two preceding examples of semi-annual and quarterly

compounding, the more frequently interest is compounded ,the greater the rate of growth

of an initial deposit. This holds for any interest rate and any period.

General Equation for Compounding more Frequently than Once a Year.

Let;

m = the number of times per year interest is compounded

n= number of years deposit is held.

k= annual interest rate. nm

kn mkPFV

*

0,1 ⎟

⎠⎞

⎜⎝⎛ += (2.4)

Continuous Compounding.

This involves compounding of interest an infinite number of times per year, at intervals

of microseconds - the smallest time period imaginable. In this case m approaches infinity

and through calculus the Future Value equation 2.1 would become,

FVn (continuous compounding) = Po * e k x n (2.5)

Where e is the exponential function, which has a value of 2.7183. The FVIFk,n

(continuous compounding) is therefore ekn , which can be found on calculators.

Example

If Jane deposited her 100,000/= in an institution that pays 8% compounded continuously,

what would be the amount on the account after 2 years?

Amount = 100,000 x 2.718.08*2 = 100,000 x 2.7180.16 =100,000*1.1735 =117,350

Nominal Rate versus Effective Annual Rate (EAR) of Interest.

When interest is compounded more frequently than once annually, then the actual interest

earned or paid would be higher than the nominal or stated interest rate. The nominal

(stated, or quoted) annual rates is the contractual annual rate of interest charged by a

lender or promised by a borrower.

33

The Effective annual rate (EAR) is the annual rate of interest actually paid or earned.

The EAR is best viewed as the interest rate expressed as if it were compounded once per

year.

The effective annual rate reflects the impact of compounding frequency, whereas the

nominal annual rate does not. At times ,interest rates may be quoted in ways that mislead

borrowers and investors regarding the real interest burden or return they are contracting.

To correctly assess the interest involved one should go beyond the stated rate and work

out the effective annual rate and compare with the stated annual rates.

We can calculate the EAR by the following equation

11 −⎟⎠

⎜⎝+=

mEAR (2.6) ⎞⎛

mk

Where m is the frequency of compounding per year, and k is the stated annual rate.

al rate

hen interest is compounded (1) annually, (2) semi annually, and (3) quarterly

;

AR = (1 + 0.08 )1 -1 = ( 1+0.08)1-1 = 8%

1 = ( 1+0.04 )2-1 = 8.16%

rom the foregoing answers, we can note two points:

Example

Jane wishes to find the effective annual rate associated with 8% nominal annu

w

Solution

Using the above equations

1. Annual compounding

E

2. Semi annual compounding

EAR = ( 1+ 0.08/2 )2 –

3. Quarterly

EAR = ( 1 + 0.08/4)4 – 1 = ( 1 + 0.02)4 – 1 = 8.24%.

F

34

Take note 1) The effective annual rate increases with

increasing compounding frequency.

2) The nominal and effective rates are equivalent

for annual compounding.

2.3 FUTURE VALUE OF AN ANNUITY.

An annuity is a series of payments or receipts of equal amounts (i.e. a pensioner

receiving Sh.100,000 per year for ten years after his retirement). The two basic types of

annuities are the ordinary annuity and the annuity due. An ordinary annuity is an

annuity where the cash flow occurs at the end of each period. In an annuity due the cash

flows occur at the beginning of each period. This means that cash flows are sooner

received with an annuity due than for a similar ordinary annuity. Consequently, the future

value of an annuity due is higher than that of an ordinary annuity because the annuity

due’s cash flows earn interest for one more year.

2.3.1 Finding the Future Value of an Ordinary Annuity.

The determination of the future value of an ordinary annuity can be illustrated using the

following example.

Example

John wishes to determine how much money he will have at end of 5 years if he deposits

Sh.100,000 annually at the end of the 5 years into an account paying 7% annual interest.

The following time line and Table 2.2 depicts the situation faced by John.

131100

122500

114500

107000

100000

35

575100

0 1 2 3 4 5

100,000 100,000 100,000 100,000 100,000

Table 2.2 Future value of a Sh.100,000 5-year ordinary annuity compounded at 7%

End of

year

(1)

Amount

deposited

(2)

Number of

years

companied

(3)

Future value interest

factor (FVIF) from

discount tables

(4)

Future value at

end of year

(5)

(2) *(4)

1 100000 4 1.311 131100

2 100000 3 1.225 122500

3 100000 2 1.145 114500

4 100000 1 1.070 107000

4.751

5 100000 0 1.000 100000

FVIFA and the FV after 5 years 5.751 Sh.575100

Using Tables to Find Future Value of an Ordinary Annuity

Annuity calculations can be simplified by using an interest table. The value of an annuity

is founding by multiplying the annuity with an appropriate multiplier called the future

value interest factor for an annuity (FVIFA) which expresses the value at the end of a

given number of periods of an annuity of Sh.1 per period invested at a stated interest rate.

The formula for the future value interest factor for an annuity when interest is

compounded annually at k percent for n periods (years) is ;

kkkFVIFA

nn

t

t

nk

]1[ 1()1(1

1

,

−==

+∑ +=

− (2.7)

)

36

The future value interest factor for an n-year, k%, ordinary annuity (FVIFA) can also be

VIFs to 1.00 llows;

FVIFA = 1.000 +

found by adding the sum of the first n-1 F 0,as fo

∑−1

k,n=

n

using the following expression. The future value of an annuity (PMT) can be

found by,

-2

ives the PVIFA for an ordinary annuity given the appropriate k percent and n-periods.

is 5.751

Thus future value of John’s Sh.100,000 5-year annuity is

FVA = 100,000 x 5.751 Sh.575,100

1,

ttkFVIF

Applying the future value interest factor of an annuity, the future value of an annuity is

determined

FVAn = PMT x (FVIFAk, n) (2.8)

Where FVAn is the future value of an n-period annuity, PMT is the periodic payment or

cash flow, and FVIFAk,n is the future value interest factor of an annuity. The value

FVIFAk,n can be accessed in appropriate annuity tables using k and n. The Table A

g

Example

Using Table A-2, the appropriate FVIFA at 7%, for 5 years

=

Activity

Find the future value of an annuity of Sh.100,000,

e) at 35% for 2 years

a) at 12% for 7 years

b) at 18% for 4 years

c) at 9% for 15 years

d) at 20% for 50 years

2.3.2 Finding Value of an Annuity Due.

37

We can demonstrate the calculation of the future value of an annuity due by using the

preceding example, only that now John makes the deposits at the beginning of the year

ther than at the end.

hn wants to find now much money he will have at the end of five years if he deposits

0 annually at the beginning of each of the next 5 years.

The Time line and Table below shows the future value o

due compounded at 7%.

Timeline

107,000

ra

Jo

Sh.100,00

Solution

f a Sh.100,000 5-year annuity

140,300

131,100

122,500

114,500

615,400

0 3 4

,0 100 100,000

Table

Beginning of year

deposit

No of years interest

compounded

FV at the end of

the year 5

1.225

4 2 1.145 114500

107000

1 2

100 00 100,000 ,000 100,000

FVIF

1 5 1.403 140300

2 4 1.311 131100

3 3 122500

5 1 1.070

Sh.615,400

Using Tables to Find Future Value of an Annuity Due

38

A simple conversion can be applied to use the FVIFA (ordinary annuity)in Table A-2

with annuities due.

The Conversion is represented by Equation 2.6 below.

Fk,n(annuity due) = FVIFk,n(ordinary annuity) x ( 1 +k) (2.6)

an ordinary annuity.

sing e future value of the preceding annuity

due as follows

FVIFA7%,5yrs (a yrs(ordinary) x ( 1 + k)

herefore future value of the annuity due = 100, 000 x 6.154 = Sh.615, 400.

beginning of the period rather than at

may arise in which we know the future value of a present sum as well as the

Suppose you are offered an opportunity to invest Sh.100’000 today with an assurance of

receiving exactly Sh.300,000 in eight years. The interest rate implicit in this question can

be found by re

8-period row in the FVIFs table (Table A-1) we find the factor that

59 and is found in the 15% column. Because 3.059

FVI

The conversion is necessary because each cash flow of the annuity due earns interest for

1 more year than

Example

U the expression above, we can calculate th

.

nnuity due) = FVIFA7%,5

= 5.751 x (1+.07)

= 5.751 x 1.07

=6 .154

T

Because the annuity due’s cash flows occur at the

the end, its future value is greater than that of a similar ordinary annuity..

2.3.3 Finding unknown Interest Rate

A situation

number of time periods involved but do not know the compound interest rate implicit in

the situation. The following example illustrates how the interest rate can be determined.

Example

arranging Equation 2.1 as follows.

FV8 = P0 (FVIF k, 8 )

300,000 = 100,000 (FVIFKk,8)

FVIFk, 8 = 300,000 / 100,000 = 3.000

Reading across the

comes closest to our value of 3 is 3.0

39

is slightly larger than 3 we conclude that the implicit interest rate is slightly less than 15

, recognize that

+k)8

know how long it will take for a shilling invested today to grow to a

ertain future value given a particular compound rate of interest.

grow to Sh.1900 if invested at compound annual

eading down the 10% column in the FVIF table we look for the FVIF in that column

9 comes closest to 1.900 and

is in the 7-period row. Because 1.949 is a bit larger than 1.900 we

conclude that the implicit compounding periods are slightly less than 7 periods.

rite FVIF10%,n as ( 1+0.1)n and solve for n

=n

Using natural logarithms,

percent.

To be more accurate

FVIFk,8 = (1+k)8

(1 = 3

(1+k) = 31/8 = 30.125

1+k = 1.1472

k = 0.1472 = 14.72%

2.3.4 Finding the Number of Compounding Periods.

We may need to

c

Example

How long will it take Sh.1000 to

interest of 10%.

Using Equation 2.1 we rewrite it as:

FVn = P0 (FVIFk%, n )

1900 = 1000 ( FVIF10%, n)

FVIF10%,n = 1.900

R

that is closest to our calculated value 1.900. We see that 1.94

that the number

For accuracy, rew

( 1 + 0.1)n = 1.9

9.1)1.1(

40

n ln1.1 = ln 1.9

n= (ln1.9)/ (ln 1.1) = 6.73 years

Rule of 72

given

annual rate to double the amount (or, what interest the principal must earn for a given

2 can be used to make this

Occasionally you may want to estimate how long a given sum must earn at a

number of periods for the principal to double); the rule of 7

estimate.

rateinterest Annual72 1. Numbers of years to double amount =

2. The interest rate to double amount = deposited. isamount years of No

72

xamples

At 2% interest it would take ~

E

36 years (72/2)

At 9% interest it would take ~ 8 years

If you keep money for 4 years you ne

If you keep money for 6 years you need to earn approximately 12% (72/6) to double it.

(72/9)

ed to earn approximately 18% (72/4) to double it.

Activity

Using discount tables, test the accuracy of Rule 72

2.4 PRESENT VALUES

We may be interested in determining how much a given sum of money to be received at a

future date is worth at present. To do this we use the concept of the present value. The

present value (PV) is the current shilling value of a future amount i.e. the amount of

money that would have to be invested today at a given interest rate to equal the future

amount.

41

The process of finding present values is referred to as discounting. It is the inverse of

FV(a future value)

pital, or opportunity cost.

Paul has an opportunity to receive Sh.30,000 one year from now. If he can earn 6% on his

investm nts wh

We are required to determine how much he needs to invest now at 6% in order to

compounding and seeks to answer the question. “If I can earn k% on my money, what is

the most I will be willing to pay now for an opportunity to receive

shillings n periods from now?” The annual rate of return k% is referred to as the discount

rate, required rate of return, cost of ca

Example

e at is the most he should pay for this opportunity now?

accumulate Sh.30,000 after one year.

Let PV (or Po) equal this amount.

PV (1+0.06) = 30,000

PV = 302,28000,30=

06.1

ar from now is Sh.28,302.

n to be received n periods from now assuming an

aking

The PV of Sh.30,000 received one ye

Equation for Present Value

The PV of some future amount FV

opportunity cost k% is calculated by rearranging our basic future value equation 2.1,

P0m (PV) the subject as follows.

)1()k n

1(, knnnk ++

(2.8)

xamp

aul wishes to find PV of Sh.170,000 that he will receive 8 years from now. Paul’s

ubstituting in Equation 2.7,

1*FVFVPV n ==

E le

P

opportunity cost is 8%

S

PV8%,8yrs = 170,000/( 1 + 0.8)8 =170000/1.851 = Sh.91,842

42

Time line depicting the present value of a sum

PV=Sh.91,842 F

to be received 8 years from now.

V8 = Sh.170,000

2.4.1 Using Pr

The factor in Equation 2.8 denoted by

0 1 2 3 4 5 6 7 8

esent Value Interest Factor (PVIF) Tables

)1()1(

,1 Kk

n

n or ++

− is called the present

date. The PVIFk,n

is the p ed at k% for n-periods.

herefore the present value (PV)of a future sum ( FVn) can be found by

(2.9)

xample

-2 gives a factor of 0.540 for 8% and 8 years.

PV = 170,000 x 0.540 = Sh.91,800.

resent Value Relationships

0 2 4 6 8 10 12 14 16 18 20 22 24

value interest factor (PVIF). The PVIF is the multiplier used to calculate at a specified

discount rate the present value of an amount to be received at a future

resent value of one shilling discount

T

PV = FVn x (PVIFk, n).

E

In the preceding example the PV could be found by multiplying Sh.170,000 by the

relevant PVIF. Table A

P

PVIFs

1.00 0% 0%

0.75 5%

0.5 15% 20%

0.25

43

Remember that PV calculations assume

period.

Periods

that FV are measured at the end of the given

Take note T

PV.

he figure above shows that

1. The higher the discount rate the lower the

2. The longer the period of time, the lower

the PV

3.PVIFs cannot be greater than 1 nor less than zero.

Note that PVIFK, n = 1/FVIFk,n, thus given a table for FVIFs one can find

types of cash flow streams are possible: the mixed stream (unequal cash

w reflects no

whil pattern of equal periodic cash flows.

Present Value of a Mixed Stream

We determine the PV of each future amount and then add together all the individual PVs

Example

The following is a mixed stre cash flows occurring at the end of year

ar Cash flow

Sh.’000’

5 300

corresponding PVIFs.

2.4.2 Present Value of Cash Flow Streams

Two basic

flows) and the annuity (uniform cash flows). A mixed stream cash flo

particular pattern e an annuity is a

am of

Ye

1 400

2 800

3 500

4 400

44

a firm has been offered the opportunity and if it’s

uired rate of return t is the most it should pay for this opportunities?

ble 2.4 PV of mixe of cash flows

ar (n) , n

If to receive the above amounts

req is 9% wha

Ta d stream .

Ye Cash flow PVIF9% PV

1 00,000 7 4 0.91 366,800

2 800,000 0.842 673,600

3 500,000 0.775 386, 000

4 400,000 0.708 283,200

5 300,000 0.650 195,000

PV 1,904,600

Present Value of an Annuity

thod for finding the PV of an annuity is similar for that of a m

be simplified using present value interest factor of an annuity (PVIFA) tables.

eriods is

=

The me ixed stream but can

The present value interest factor of an annuity with end–of-year cash flows that are

discounted at k per cent for n p

( )∑+=

n

tnk1 1

1 =⎥⎥⎥PVIFAK,n

⎦⎣

Table A

⎤

⎢⎢⎢⎡− ⎟

⎠⎞

⎜⎝⎛+k

n

k 11

11 (2.9)

-3 provides the PVIFAk,n, which can be used in calculating the present value of

(2.10)

an annuity (PVA) as follows:

PVA = PMT* PVIFAk n

Example

Mark wants to find the PV of a 5- year annuity of Sh.700,000, assuming opportunity cost

of 8%.

The PVIFA at 8% for 5 years (PVIFA8%,5yrs) from Table A-3 is 3.993.

Therefore, PVA = 3.993 X 700,000 = Sh.2,795,100

45

2.4.3 Present Value of Perpetuity

flow at the

rmine the PV of a Sh.1000 perpetuity discounted at 10%.

he present value of the perpetuity is 1000 x PVIFAk, α = 1000 x 1/0.1= Sh.10,000.

d is worth only Sh .10,000

aw Sh.1000 annually without touching the

e the expression below, which is a rewriting of Equation 2.3.

umulated, and

an n-year annuity discounted at k%.

ne needs to accumulate Sh. 5 million at the end of 5 years to make special purchase.

ake deposits in an account that pays 10% interest compounded annually. How

Suppose you want to buy a house in 5 years from now and estimate that the initial down

will be required at that time. You wish to make equal annual

A perpetuity is an annuity with an infinite life – never stops producing a cash

end of each year forever.

The PVIF for a perpetuity discounted at the rate k is

PVIFAk, α = 1/k (2.11)

Example

Rose wishes to dete

T

This implies that the receipt of Sh.1,000 for an indefinite perio

today if Rose can earn 10% on her investments (If she had Sh.10,000 and earned 10%

interest on it each year, she could withdr

initial Sh.10,000).

2.4.4 Deposits to Accumulate a Future Sum. It may be necessary to find out the periodic deposits that should lead to the built of a

needed sum of money in future.

We can us

PMT = FVAn/FVIFAk n (2.10)

Where PMT is the periodic deposit, FVAn is the future sum to be acc

FVIFAk n is the future value interest factor of

Example

Ja

She can m

much should she deposit in her account annually to accumulate this sum?

Solution

PMT = FVAn/FVIFAk n = 5,000,000/6.105 = Sh.819,000

Example

payment of Sh. 2 million

46

end of year deposits in an account paying annual interest of 6%. Determine the size of the

determining the

equired for an installment – type loan. The distinguishing features of this loan

oans, auto loans, consumer loans etc.

ion Schedule. An amortization schedule is a table showing the timing of

rincipal necessary to pay off a loan by maturity.

nd of the year payment necessary to amortize fully a Sh.600,000,

e pa i-

olution

irst compute the periodic payment

/ k,n.

Using tables w VIF rs = 3.170, and we know that PVAn = S

PMT = 600,000/3.170 = Sh.189, 274 per year.

able 2.4 Loa ortization hedule

Payme

annual deposit.

FVAN = PMT X FVIFAK, N

PMT = FVAn/ FVIFAk n

PMT = 2,000,000/5.637= Sh.354,799

2.4.5. Amortizing a Loan

An important application of discounting and compounding concepts is in

payments r

is that it is repaid in equal periodic (monthly, quarterly, semiannually or annually)

payments that include both interest and principal. Such arrangements are prevalent in

mortgage l

Amortizat

payment of interest and p

Example

Determine the equal e

10% loan over 4 years. Assum yment is to be rendered (i) annually, (ii) sem

annually.

S

(i) Annual repayments

F

PMT = PVAn PVIFA

e find the P A10%,4y h.600,000

T n Am sc

nts

End of year Loan Beg. Of Interest Principal End of year

47

payment

l

l. year

principa

principa

[10%x (2)] 2) – (4)] [ (1) – (3) [ (

(1) (2) (3) (4) (5)

1 189,274 600,000 60,000 129,274 470,726

2 189,274 470726 47,073 142,201 328,525

3 189,274 328525 32,853 156,421 172,104

4 189,274 172104 17,210 172,064 -

(ii) Sem

or semi-annual repayments the number of periods, n, is 8 and the discount rate is 5%.

PMT = VAn /PVIFAk .

he PVIF e kn n =

,000 2 = Sh.92,833 per year.

able 2.4 Loa Amortization schedule

Payme

i-annual repayments

F

Lets compute the periodic payment.

P ,n

Using tables we

PMT

find t

= 600

A5%,8periods =6.46

/6.463

32, and w ow that PVA Sh.600,000

T n

nts

End of

riod

months)

t

Of

l

al of

l.

pe

(6

Loan

paymen

Beg.

year

principa

Interest Princip End

period

principa

[5%x (2)] ) ] [ (1) – (3 [ (2) – (4)

(1) (2) (3) (4) (5)

1 92833 600,000 30,000 62,833 537,167

2 92,833 537,167 26,858 65,975 471,192

3 92,833 471,192 18 23,559 69,274 4019

4 92,833 401, 918 20,096 72,737 329,181

5 92,833 329,181 16,459 76,374 252,807

6 92,833 252,807 12,481 80,192 172,615

48

7 92,833 172,615 8,631 84,202 88,413

8 92,833 88,413 4,421 88,412 -0-

2.4.6 Determining Interest or Growth Rate

It is often necessary to calculate the compound a growth rate implicit in a

h flows. We can use either PVIFs o roceed by way of

llowing illustration.

ow ollowing series of cash flows

Cash flow (Sh.)

2000 1,250,000

rate corresponding to factor 0.822. In the row for 4 year in table of

able A-3 of PVIFs, the factor for 5% is .823, almost equal to 0.822. Therefore interest

r growth rate is approximately 5%.

ote that the (1,520,000/1,250,000) is 1.216. . In the row for 4 year in table

f Table A-1 of FVIFs, the factor for 5% is 1.2155 almost equal to 1.216.We estimate the

rowth rate to be 5% as before.

nnual interest or

series of cas r FVIFs tables. Let’s p

the fo

Example

Roy wishes to find the rate of interest or gr th rate of the f

Year

2004 1,520,000

2003 1,440,000

2002 1,370,000

2001 1,300,000

Solution

Using 2000 as base year, and noting that interest has been earned for 4 years, we proceed

as follows:

Divide amounts received in the earliest year by amount received in the latest year.

1,250,000/1,520,000 = 0.822. This is the PVIF . We read across row for 4 yrsk 4,

years for the interest

T

o

FVIF yrsk 4,N

o

g

49

REVIEW

1. Why does money have time value? 2. List five different applications of time value of money.

of daily, monthly, or quarterly pounding, which would you choose? Why?

5. 6.

7. due

ice each year, and Bank III compounds interest each

a)

b)

c) deposit his money?

Bank IV is different from the others only in the sense that compounding is done

Bank

2.2.

her investments, how much must she deposit at the end of each year to meet this

QUESTIONS

3. If, as an investor, you had a choicecom

4. Describe the procedure used to amortize a loan into a series of equal annual payments. What is a loan amortization schedule? What is perpetuity? What is continuous compounding? What effect does frequency of compounding have on the effective annual rate (EAR)? Explain the difference between an ordinary annuity and an annuity

PROBLEMS

2-1 Tom Mapesa has Sh.500,000 that he can deposit in any of three savings accounts

for a 3 years period. Bank I compounds interest on an annual basis, Bank II

compounds interest tw

quarters. All the three Banks have a stated annual interest rate of 4%.

Compute the amount in each bank account at the end of 3 years.

What is the effective annual rate (EAR) that is earned from each bank?

In which bank should Tom

d)

continuously. What would be the amount at end of 3 years if it was deposited in

IV.

Flo Waridi wishes to accumulate Sh.800,000 by the end of 5 years by making

equal annual end-of-year deposits over the next 5 years. If Flo can earn 7% on

goal?

50

2- The East African Railways Ltd has outstanding an issue of 4 percent perpetual

bonds and promises to pay Sh.2000 semiannually forever. If the market rate of

interest for similar bonds is 9%

3

,at what price should be perpetual bond sell

rent

2-4

estimat

a) sits in the account necessary to

accumulate the required sh.600,000. Assume first deposit first deposit is

ost of living increases 4 percent per year over the next 5

years. What would be the effective purchasing power in year 5 of your

2-5 loan of Sh.1,500,000. The terms of the loan require you to

the loan in five equal annual installments of sh.416,100. The first

p t will b year fr h tive annual rate of

i est on this

2-6 a) Determine the end-off- payments required each year over the

l of the loans following table to repay them fully during the stated

he loan.

A Sh. 120,000 8% 3 years

750,000 10 30

D 0 15 5

cur ly.

Gina Watseka wants to take a holiday in Las Vegas 5 years from today. It is

ed that the trip will cost Sh. 600,000.

Determine the periodic annual depo

made 1 year from today.

b) How much will Gina have to deposit annually if the final deposit is made

1 year before the holiday.

c) Suppose the c

deposits calculated in part (a) above?

A Bank offers a

payback

aymen e made a om today. W at it the effec

nter loan.

equal annual year

ife shown in the

term in t

Loan Principal Interest rate Term of loan

B 600,000 12 10

C

40,00

51

b) Prepare a loan schedule for each of the loans in (a).

c) Explain why interest on the loan declines with the passage of time.

flow

n interest rate of 10 per cent cal late the single amount that is equivalent in

) 1

)

Problems 2-8. u have :

2-9 How much

a.

2-1 f

amortization

2-7 An investment promises the following end-of-year cash flows

Year Cash

1 Sh. 100,000

2 300,000

3 200,000

Assuming a cu

value to the cash flow stream.

a If received today )

b If received at the end of year

c If received at the end of year 2

d) If received at the end of year 3

If you invest Sh.12,000 today, how much will yo a. In 6 years at 7%. b. In 15 years at 12 %.

c. In 25 years at 10 %. d. In 25 years at 10 % compounded semi-annually.

would you have to invest today to get: Sh.12,000 in 6 years at 12%.

b. Sh.8,000 in 5 years at 20% c. Sh.15,000 in 15 years at 8%. d. Sh.30,000 each year for 20 years at 6%. e. Sh.40, 000 each year for 40 years at 5%.

0 Brian Makamu borrows Sh.7,000,000 at 12% interest rate toward the purchase oa new house. His mortgage is for 30 years.

a. How much will his annual payments be? b. How much interest will he pay over the life of the loan? c. How much should he be willing to pay to get out of a 12% mortgage and

into a 10% mortgage with 30 years remaining on the mortgage?

52

2-11 llege fees wilyea fiveyou ears to have the necessary funds for Sus edu .

2-12 You areare asked t i-annually to accumulate a sum of Sh.5,000,000 after 10 years at 8% annual rate (20 payments).

the day after the sixth payment is made ( the beginning of the fourth year), the

be

should be annual payments remaining).

e of the fourth year.

ther tod f 40 years if you decide to make the initial deposit today rather than 10 years from tod

2-14 Lumum ve Sh.1,500,000 at the end of 5 years in order to fulfill his goa is willing to invest the amount as a lump sum tod but w estment return he will need to earn. Figure out the annual com eeded in each of the following cases.

. 020,000 today.

c. 2-15

Sh.15012%.

given the Sh.150,000

2-16 Rita Wanda wishes to select the better of two ten-year annuities.

Your younger sister, Susie, will start college in one year’s time. The col amount to Sh.80,000 per year for four years payable at the beginning of each r. Anticipating Susie’s ambition, your parents started investing Sh.10,000 per year years ago and will continue to do so for five more years. How much more will r parents have to invest for the next five yie’s cation.. Use 10% as the appropriate interest rate throughout the question

the chairperson of the investment retirement fund for Actors Fund. You o set up a fund of semi-annual payments to be compounded sem

The first payment into the fund is to take place 6 months from now, and the last payment is to take place at the end of the tenth year.

a. Determine how much the semi-annual payment should be. On interest rate goes up to 10% annual rate, and you can earn 10% on the funds that have accumulated as well as on all future payments into the fund. Interest is tocompounded semi-annually on all funds. b. Determine how much the revised semi-annual payments

after this rate change (there are 14 semi-The next payment will be in the middl

2-13 You can deposit Sh.100,000 into an account paying 9% annual interest eiay or exactly 10 years from today. How much better off would you be at the end o

ay. ba needs to ha

l of purchasing a sports car. Heay onders what type of inv

pound rate of return na Lumumba can invest Sh.1,b. Lumumba can invest Sh.815,000 today

Lumumba can invest Sh.715,000 today Lucas wishes to determine the future value at the end of two years 0f a

,000 deposit made today into an account paying a nominal interest rate of

a. Find the future value of Lucas’ deposit assuming that interest rate is compounded:

1) Annually 2) Quarterly

3) Monthly 4) Continuously b. Using your findings in a demonstrate the relationship between

compounding frequency and future value c. What is the maximum future value obtainable

deposit, 2-year time period, and 12% nominal rate? Using your findings in a to explain.

53

Annuit

a. Find the future value of both annuities assuming that Rita can earn (1) 10%

2-17 ow

rge a fund will you need when you retire in 20 years to provide the

b. s a lump sum to provide the amount

2-18 dreams. It . The only catch is that Chris is 40and plans to continue working till he is 65. Chris expects property values to

h a house wh

a. If inflation is expected to average 5% for the next 25 years what will Chris dream house cost when he retires/

b. How much must Chris invest at the end of each of the 25 years in order to have the cash purchase price of the house when he retires?

c. If Chris invests at the beginning instead of at the end of teach of the 25 years, how much must he invest each year?

-19 Rodgers Masengo just closed a Sh.2,000,000 business loan that is to be repaid in 3 equal end-of year repayments . The interest rate on the loan is 13%.

Prepare an amortization schedule for the loan.

Annuity X is an ordinary annuity of Sh.250,000 per for 10 years. y Y is an annuity due of Sh.220,000 per for ten years.

annual interest, (2) 20% annual interest. b. Briefly explain the differences between the values

You plan to retire in exactly 20 years. Your goal is to create a fund that will allyou to draw Sh.200,000 per for 30 years between retirement and probable death. Youwill be able to earn 11% during the retirement period..

a. How la30-year Sh.200,000 annuity. How much would you need today acalculated in a above if you earn only 9% during the 20 years preceding retirement?

While vacationing in Lamu Island Chris Musundi saw the vacation home of his was listed with a sale price of Sh.20,000,000

increase at the general rate of inflation. Chris can earn 9% annually and is willing to invest a fixed amount for the 25 years to fund the cash purchase of suc

en he retires.

2

54

LECTURE 3: RISK AND RETURN

3.0 INTRODUCTION In this lecture we explain how risk and return between risk and return. We also introduc h fect, and the concept of market efficiency.

s of an asset are measured and the trade-offe portfoe t lio theory, the diversification ef

ObAt the e

1. undamentals of risk, return, and risk preferences.

2. Describe the procedures for measuring risk and return of single assets and portfolio of

g

jectives nd of this lecture you should be able to:

Explain the f

assets. 3. Show the effect of correlation and

diversification on risk and return. 4. Discuss the meaning of beta and explain

ther basics of the capital market pricinmodel (CAPM) and the security market line (SML).

Valuation and an understa

nding of the trade-off between risk and return form the

lth maximization. Each financial decision presents certain

e unique combination of these characteristics

foundation of shareholders wea

risk and return characteristics, and th

impacts on the value of the firm. We shall consider risk and return as they relate to both

single assets (arising share) and to a portfolio of assets.

3.1 FUNDAMENTALS OF RISK, RETURN AND

PREFERENCES

55

3.1.1 Risk

The term risk is used interchangeably with the term uncertainty to refer to the variability

those expected from a given asset. It is the chance of an

ntees its

d, a Sh.1000 investment in a certain company’s shares which over the

to the high variability of

returns.

ent over a given

s any cash

k = (C + [P – Pt-1])/ Pt-1 (3.1)

ired rate of return during period t

et atend of time period t-1

ne year or 10 years. When it is one year kt represents an

erence behaviors among managers are – risk-aversion, risk-

Risk-indifference, is the attitude toward risk in which no change in return would be

required for an increment risk

Risk-aversion is the attitude toward risk in which an increased return would be required

for an increase in risk.

of actual returns from

unexpected financial loss (or gain). The greater the variability the higher risk. Different

assets will have varying risk levels. For example, a government bond that guara

holder Sh 100 interest after 30 days has no risk – it is risk free, because the return is

certain. On the han

same period could earn from Sh.0 to Sh.200 is very risky due

3.2.2 Return

The return on an asset is the total gain or loss experienced on an investm

period of time. It is commonly measured as the change in value plu

distribution during the period, expressed as a percentage of the beginning of the period

investment value.

The following equation captures the essence of this value.

t t t

Where kt = actual, expected, or requ

Pt = Price (value) of asset at end of time period t

Pt-1 = Price value of ass

Ct = Cash (flow) received from the asset investment in the time period t.

t may be one day, one month, o

annual rate of return. The return could be positive or negative in the event of a loss.

3.2.3 Risk Preferences

The three basic risk pref

indifference and risk-seeking.

56

Risk seeking is the attitude toward risk in which a decreased return would be accepted

for an increase in risk.

increase in risk they require an,

crease in returns. Consequently, managers and investors tend to be conservative rather

ise, a risk averse

ct to

ble values that a random variable can assume and

their associated probabilities of occurrence). This probability distribution for normal

Figure 3.1 graphically illustrates the three risk preferences.

Figure 3.1 shows the three risk preferences of risk aversion, risk seeking and risk

indifference

Most managers and investors are risk-averse; for an

Risk seeking

Risk indifference

Risk averse

Return

Risk

in

than aggressive in accepting risk. Accordingly, unless specified otherw

financial behavior will be assumed in this lecture.

3.3 RISK AND RETURN OF A SINGLE ASSET

For risky securities the actual rate of return can be viewed as a random variable subje

a probability distribution (a set of possi

57

populations) can be summarized in terms of two parameters: (1) the expected return

he expected return is the weighted average of possible returns, with the weight being the

1

here

Pri = Probability of occurrence of the ith outcome

= Number of outcomes considered.

and 2 in the table below. Using the data

the two columns, the expected return and the standard deviations (risk) of the asset are

computed in columns 3 and 4 in the same table.

(1) (2) (3) (4)

Possible returns Probability of

occurrence

Expected return Variance

(mean), and (2) the standard deviation

3.3.1 Expected Return

T

probabilities of occurrences. The expected value of a return, k, is

( )k * (3.2)∑=

=n

iiik Pr

W ki = return for the ith outcome

n

Example

Asset A’s return distribution is given in column 1

in

ki Pri k = ki P* ri ( )Prikk i−

2

0.20 0.10 0.020 0.0011236

0.28 0.05

0.10 0.05 0.005 0.0000018

0.02 0.10 0.002 0.0005476

0.04 0.20 0.008 0.0005832

0.09 0.30 0.027 0.0000048

0.14 0.20 0.028 0.0004232

0.014 0.0017298

∑= 00.1 ∑= 094.0 ∑= 004414.0

58

k , is 9.4% as computed in columThe expected return, n 3 above.

an asset’s

sk. The equation for determining the standard deviation (s.d.) is as follows

3.3.2 Standard Deviation

The risk of a return can be measured by the returns’ standard deviation or variance. The

standard deviation is a statistical measure of the dispersion of a distribution around the

expected value. It is the square root of the variance (the sum of squared deviations) of the

distribution. The standard deviation is the most common statistical measure of

ri

∑ −= Pr)( 2

ikk i (3.3)

ceding example n 4 of the table.

kσ

Using above pre we determine variance as in colum

004414.0=σ k = 0.0664

= 6.64%.

expected

V is a measure of risk that neutralizes the influence of size of the

The greater the standard deviation, the riskier the asset.

3.3.3 Coefficient of Variation

The standard deviation can sometimes be misleading in comparing the risk of investment

alternatives if the alternatives differ in size. The coefficient of variation, CV, is a measure

of relative dispersion that is useful in comparing the risk of assets with differing

returns. The C

investment.

The coefficient of variation (CV) is given by the formula,

k

CV kσ= (3.3)

The CV , thus, represents the amount of variation in the returns per unit of return.

The higher the CV, the greater the risk. The real utility of the CV comes in comparing

e risk of assets that have different expected returns. th

59

Example

Consider investment opportunities A and B whose normal probability distributions of

e as follows.

Investment A Investment B

dard deviation

t is evident that Investment B has the lower risk. B should therefore

e preferred over A.

cessary given that investors usually hold assets not singly but in combinations

must sum up to 100%) The general formula

r the expected return of a portfolio, kp, is

one-year return ar

Characteristics

Expected return 0.08 0.24

Stan 0.06 0.08

CV 0.75 0.33

Based solely on the standard deviation, Investment B would be riskier than A (‘A’ would

be preferred). This would not be a rational investment decision because if one considers

the coefficient of variation, which measures the relative dispersion of risk – risk per unit

of expected return – i

b

3.4 RISK AND RETURN IN A PORTFOLIO CONTEXT

A portfolio is a combination of two or more assets. The risk of any single proposed asset

investment should not be viewed independently of other assets. New investment must be

considered in light of their impact on the risk and return of the portfolio of asset held by

an investor. The goal should be to create an efficient portfolio – one that minimizes risk

for a given level of return (or that maximizes returns for a given level of risk). We need

to extend our analysis of risk and return to portfolios of assets. Indeed this is only

ne

.

3.4.1 Portfolio Return

The expected return on a portfolio is the weighted average of the expected returns of the

assets (securities) comprising that portfolio. The weights are equal to the proportions of

total funds investor in each security (weight

fo

60

(3.5)

e total number of different securities in the

olio.

standard deviation of a single a i.e.

∑ ==

n

j jjp kwk 1*

Where wj, is the proportion in weight of total funds invested in security j; k j

is the

expected return for security j; and n is th

portf

3.4.2 Standard Deviation of a portfolio

The standard deviation of a portfolio returns is found by applying the formula for the

sset.. Specifically equation 3.2 would be applied,

∑ −= Pr)( 2

ik kk iσ (3.6)

ce is due to the covariance

fferent assets comprising the portfolio, which

ns.

f one asset increase (decrease) the returns of the other asset decrease

tion would imply that the two variables show no tendency to vary

together.

Portfolio risk and co-variation

While the portfolio expected return is a weighted average of return on the individual

assets, the portfolio s.d is not the simple weighed average of the standard deviations of

the individual assets making up the portfolio. The differen

relationships between the returns on di

affects risk without affecting retur

Covariance (correlation)

Covariance (correlation) is a statistical measure of the degree to which two variables (i.e.

securities return) move together over time. Positive correlation means that, on average,

the returns of the two assets move in the same direction (i.e. when the returns of one asset

increase (decrease) those of the other asset also increase (decrease)). Negatively

correlation suggests the returns of the two assets move in opposite directions (i.e. when

the returns o

(increase)). Zero correla

61

The degree of correlation (co variation) is measured by a correlation coefficient, which

ranges from +1 for perfectly positively correlated series to -1 for perfectly negatively

correlated series. Uncorrelated series will have a coefficient of zero.

The two figures below, Figure 3.2 and Figure 3.3 show the effect of correlation on risk.

N

M

Return

Return

Time

Figure 3.2 A perfectly positively correlated returns of two assets M and N (no reduction in risk)

62

Return

Time

N

M

Figure 3.3 Perfectly Negatively Correlated returns of two assets , M and N (variability (risk) reduced to nil).

Covariance (correlation) between the returns of assets provides for the possibility of

eliminating some risk without reducing potential return. The result could be that a

combination of individual risky assets could deliver a low risk portfolio as long as the

individual assets’ returns do not move in lock step ( i.e. perfectly positively correlated).

Diversification

Diversification is the combining of assets (securities) in away that reduces risk (it

depends on how the returns of the assets co-vary not on the number of assets in the

basket). Diversification reduces risk because some of each individual security’s

variability is offset by the variability in the opposite direction of other securities Benefits

of diversification, in the form of risk reduction, occur as long as the security are not

perfectively positively correlated. Combining assets with perfect positive correlation does

not diversify risk. Combining assets with perfect negative correlation in returns confers

the greatest diversification impact as it reduces risk to the minimum. Combining assets

63

with correlation coefficients between +1 to -1 will result in diversification benefits,

whose magnitude depends on how far away the returns are from being perfectly

positively correlated. To reduce overall risk, it is best to combine or add to the portfolio

assets that have a negative or a low positive correlation.

component assets x and y.

Correlation, Diversification, Risk and return

The calculation of portfolios sad can be found using the following formula:

Portfolio std. deviation = √ ∑∑= =

n

jj

n

kikj RRww COV

1 1),(

Where n is the total number of different securities in the portfolio, and are the

proportions of total funds invested in securities k and j, and COV ( is the

covariance between possible return for securities j and k.

wk wj

), RR kj

For a portfolio of two assets, X and Y, the portfolio’s standard deviation can be directly

calculated from the standard deviations of both assets using the following formula.

),(22222 RRwwww yxyxyyxp COVxx++= σσσ . Or, alternatively,

σσρσσσ yxxyyxyyxp wwww xx22222 ++=

Where and are the proportion of funds invested in assets x and y, wx wy σ x and σ y

are the standard deviations of the returns of assets x and y, is the ),( RR yxCOV

64

covariance of the returns of assets x and y, and ρ xy is the correlation coefficient between

the returns of component assets x and y. Note that ρ xy=

σσ yx

yx RRCOV ),(.

The correlation coefficient takes values between -1, for perfectly negatively correlated

returns, through 0 for uncorrelated returns, to +1 for perfectly positively correlated

returns.

Example

Consider the following terms returns for three different assets A, B and C. Two

portfolios are to be formed from the assets: (i) AB and (2) AC.

The portfolios are formed by combining equal proportions of the component assets.

Asset A Asset B Asset C

8% 16 8%

10% 14% 10%

12% 12% 12%

14% 10% 14%

10% 8% 16%

Find expected returns of the two portfolios. Determine the Std. deviations of the two

portfolios. Comment on the diversification impacts of the portfolios formed.

The expected returns on the assets are as below.

A B C

pri ka

%

kp ari kb

%

kp bri kc

%

kp cri

0.2 8 1.6 16 3.2 8 1.6

0.2 10 2.0 14 2.8 10 2.0

0.2 12 2.4 12 2.4 12 2.4

0.2 14 2.8 10 2.0 14 2.8

0.2 16 3.2 8 1.6 16 3.2

Expected return 12 12 12

65

The standard deviations of the returns of the assets are similar as follows:

Asset A

=))12.016.0()12.014.0(

)12.012.0()12.01.0()12.008.0(22

2.02.0

2.02.02.0

−−

−−−++

+⎜⎝⎛ +

222

= (0.00032 + 0.00008+ 0+0.00008+0.00032)

=2.83%

Likewise the standard deviations of Asset B and C are 2.83%

Next we need to determine the covariance of returns of the assets being combined.

We begin with portfolio AB.

COV ( = ), RR ba ∑ ))(( RRRRp bbaari−−

0.2(0.08-0.12) (0.16-0.12) = -0.00032

0.2(0.10-0.12)(0.14-0.12) = -0.00008

0.2(0,12-0.12)(0.12-0.12) = -0.0000

0.2(0.14-0.12)(0.10-0.12) = -0.00008

0.2(0.16-0.12)(0.08-0.12) -0.00032

-0.0008

Covariance of returns of portfolio AC = ∑ ))(( RRRRp ccaari−−

66

0.2 0.08-0.12)(0.08-0.12) = 0.00032

0.2(0.10-0.12)(0.10-0.12) = 0.00008

0.2(0.12-0.12)(0.12-0.12) 0

0.2(0.14-0.12)(0.14-0.12) 0.000008

0.2(0.16x0.12)(0.16-0.12) 0.00032

0.0008

Expected returns of portfolio AB = 0.5x12+0.5x12=12%

Standard deviation of returns of portfolio AB

),(22222 RRwwww bababbapabCOVax

++= σσσ

0008.0*5.0*5.0*2** 0283.05.00283.05.0 2222 −++=x

pabσ =

= 0

Assets A and B are perfectly negatively correlated and combining them in a portfolio

completely eliminates any variability (risk) in returns.

The expected returns of portfolio AC= 0.5x12+0.5x12=12%

Standard deviation of returns of portfolio AC =

),(22222 RRwwww cacaccapac COVax++= σσσ

0008.0*5.0*5.0*2** 0283.05.00283.05.0 2222 ++=x

pacσ

67

=√ (0.0008)

= 0.0283

=2.83%

Assets A and C are perfectly positively correlated (correlation coefficient of

+1).Combining the two assets in a portfolio has no diversification effect as shown by the

unchanged portfolio standard deviation of 2.83%.

Most assets are positively correlated but with a correlation coefficient of less than +1.

Combining them in a portfolio will result in diversification gains depending on how far

from +1 the correlation coefficient is.

3.5 THE CAPITAL ASSET PRICING MODEL (CAPM)

One of the basic theories that links together risk and return for all marketable assets is the

capital asset pricing model (CAPM) initially developed by Sharpe (1964) and Lintner

(1965). A number of other economists subsequently tested, advanced, refined and

extended its applicability (Black (`972), Merton (1973)).

3.5.1 Systematic Vs. Unsystematic Risk

The total risk of an asset can be decomposed into two basic components:

Total blediversifianonrisk −= blediversifiarisk + risk

Unsystematic (Diversifiable) Risk

This is that part of total risk that can be diversified away by holding the investment in a

suitably wide portfolio. Research has shown that on average, most of the reduction

benefits of diversification can be gained by forming portfolios containing 15 -20

randomly selected securities. Diversifiable risk is the portion of total risk that is

associated with random (idiosyncratic causes which can be eliminated through

diversification. At the limit the market portfolio, comprising an appropriate portion of

68

each asset in the market has no undiversifiable risk The causes are firm-specific and

include labour unrests, law suits, regulatory action, competition, loss of a key customer

etc.

Non-diversifiable (Systematic) Risk

This is the risk inherent in the market as a whole and is attributable to market wide

factors. This risk component is not diversifiable and must thus be accepted by any

investor who chooses to hold the asset. Factors such as war, inflation, international

incidents, government macroeconomic policies and political events account for non-

diversifiable risk.

Because any investor can costlessly create a portfolio of assets that will eliminate

virtually all diversifiable risk, the only risk relevant in determination of the prices and

returns of an asset is its non-diversifiable risk.

Interpretation

The CAPM links together non-diversifiable risk and the return for all assets. The model is

concerned with: (1) how systematic risk is measured , and (2) how systematic risk affects

required returns and share values. The CAPM theory includes the following propositions:

a. Investors require a return in excess of the risk-free rate to compensate them for

systematic risk.

b. Investors require no premium for bearing unsystematic risk because it can be

diversified away.

c. Because systematic risk varies between companies, investors will require a higher

return from investments where systematic risk is greater.

The Formula

The CAPM can be stated as follows.

69

)( RRRR fmifi −+= β (3.7)

Where: is the expected return from asset i. Ri

is the risk-free rate of return (return on the 91-day treasury bill R f

Rm is the return from the market as a whole: The market portfolio will ,

by definition be fully diversified as it comprises all marketable assets.

β i is the beta factor of asset i..

RR fm − is the market premium

The Beta Coefficient and the Market Premium

The beta coefficient, β i, measures the non-diversifiable risk. It is an index of the degree

of volatility of asset i’s returns in terms of the volatility of the returns of the market

portfolio (market’s risk). The beta factor for the market portfolio is 1.0: the risk free asset

will have a beta of 0. Assets that are riskier than the market will have betas > 1.0 while

those which are less risky will have betas less than 1.0.

Example

ABC Ltd. wishes to determine the required return on asset Z which has a beta of 1.5. The

risk-free rate of return is found to be 7%; the return on the market portfolio is 11%. Find

the required rate of return on asset Z.

Using the CAPM formula,

)( RRRR fmzfz −+= β

= 7% + 1.5(11% - 7%) =7% + 6% = 13%

70

The markets risk premium of 4% (11% - 7%), when adjusted for asset Z’s index of risk

(beta) of 1.5 results in the asset’s risk premium of 6% (1.5 * 4%). That risk premium

when added to 7% risk-free rate, results in a 13% required rate.

Security Market Line (SML)

When the CAPM is depicted graphically it is called the security market line (SML). In

the graph, risk, as measured by beta, is plotted on the X-axis and the required return are

shown on the Y-axis. Two points to note in graphing the SML are:

(i) The risk-free asset has a beta of 0.

(ii) The market portfolio has a beta of 1.The risk-return trade-off is clearly shown

by the SML. For the preceding example ,the SML will appear as below

return

E(ri) SML

m

rf 7%

0 1 beta

(i) Figure 3.1 The figure show the Security Market Line with beta on the x-axis and expected return on the y-axis. Note that the market portfolio has a beta of 1 and the risk free asset of 0.

71

REVIEW QUESTIONS

1. Define the terms return and risk as they relate to financial decision making.

2. What is the coefficient of variation? When is it preferred over the standard

deviation when company risk?

3. What is an efficient portfolio? Why is the correlation between asset return

important.

4. What is the relationship of total risk, non diversifiable risk and diversifiable

risk? Why is non diversifiable risk the only relevant risk in asset pricing?

5. If corporate managers are risk averse, does this mean that they will not take

risks? Explain.

PROBLEMS

3.1 Mbalamwezi Ltd must choose between two assets purchases: The annual rate of

return and related probabilities for the assets are shown below:

Project ABC Project XYZ Rate of return Probability Rate return Probability

-10% 10% 20% 30% 40% 45% 50% 60% 70% 80% 100%

0.01 0.04 0.05 0.10 0.15 0.30 0.15 0.10 0.05 0.04 0.01

10% 15 20 25 30 35 40 45 50

0.05 0.10 0.10 0.15 0.20 0.15 0.10 0.10 0.05

72

a) For each projects, compute

i) The range of possible rates of return

ii) The expected value of return

iii) The standard deviation of returns

iv) The coefficient of variations.

b) Construct a bar chart of each distributions of rates of return.

c) Which project would you consider less risky? Why?

3-2 The following data has been gathered in order to help in graphically estimating

the betas of two assets A and B.

Actual return

Year Market portfolio Asset A Asset B 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

6% 2 -13 -4 -8 16 10 15 8 13

11% 8 -4 3 9 19 14 18 12 17

16% 11 -10 3 -3 30 22 29 19 26

a) On a set of market return (x-axis) – asset return (y-axis) axes, use the data above

to draw the characteristics line for asset A and for asset B (On the same set of

axes).

b) Use the characteristic lines from (a) to estimate the betas for assets A and B.

c) Use the betas in (b) to comment on the relative risks of assets A and B.

3.3 The risk free rate in the economy is currently 8%, with the market return at 12%.

Asset A has a beta of 1.10

a) Draw the security market line (SML)

b) Use CAPM to calculate the required return on asset A. Depict asset A’s

position on the SML in (a)

73

c) Assume as a result of recent economic events the risk free rate and the

market return have declined to 6% and 10% respectively. Draw the new

SML on same axes as used before and show new position of asset A.

d) Assume as a result of recent events, the market return has risen to 13%.

Ignoring the shift in.

c) Draw the new SML on same axes as before and show the new position for

asset A.

3.5 A company is considering developing and raising two apartment complexes, WA

and HA. The following estimate of cash flows has been generated for each

apartment.

WA HA Probability Annual cash flows Probability Annual cash

flows 0.1 0.2 0.4 0.2 0.1

1,000.000 1,500,000 3,000.000 4,500.000 5,000.000

0.2 0.3 0.4 0.1

1,500.000 2,500.000 3,500.000 4,500.000

a) Find the expected cash flows from each apartment complex.

b) What is the coefficient of variation for each apartment complex

c) Which apartment complex has more risk?

3-6 The company in the preceding question will hold the apartments for 10 years.

Either apartment would cost sh.10,000,000. The company uses risk adjusted

discount rate when considering investments with coefficient of variation (CV)

greater than 0.35. He estimates the cost of capital to be 12%. For projects with

CV between 0.35 and 0.40, he adds 2% to the cost of capital and for projects with

CV between 0.40 and 0.50 he adds 4%. The company would not consider an

investment with a CV more than 0.50.

74

a) Compute the risk adjusted net present values for WA and HA apartments.

(Use cash flows from previous problem).

b) Which investment should company accept if the investments are mutually

are exclusive?

c) If projects are not mutuality exclusive, and in the absence of capital

positioning, how would your decision in (b) be affected.

3.6 Tobacco Company of Kenya (TCK) is a stable company with sales growth of

about 5% per year in good or bad economic conditions. Because of this stability

(correlation coefficient with economy of +0.3 and standard deviation of sales of

about 5% from the mean) the management the company can absorb some small

risky outfits, which could add quite a bit of a return with affecting company’s

risk. Two alternative outfits are being considered for acquisition (i.e. ABC and

XYZ) TCK cost of capital is 10%.

Probability After tax cash flows for 10 years

Sh ‘000’

Probability After tax cash flows for 10 years Sh ‘000’

0.3 0.3 0.2 0.2

6000 10,000 16,000 25,000

0.2 0.2 0.2 0.3 0.1

(1,000) 3000 10,000 25,000 31,000

a) What is the expected cash flow from each outfit.

b) Which outfit has the lower coefficient of variation

c) Compute the net present value of each outfit

d) Which outfit would you pick based on NPV.

e) Would you change your mind if you added the risk dimensions into the problem?

Explain.

f) If ABC had a correlation coefficient with the economy of 0.5 and XYZ had one of

-0.1, which outfit would give you best portfolio effects for risk reduction? Which

would give the highest potential return?

g) What might be the effect of the acquisitions on the market value of TCK shares?

75

LECTURE FOUR: LONG TERM SECURITIES AND

VALUATION

4.1 INTRODUCTION

In lecture three we discussed two key finance concepts of risk and return. This lecture

examines how the two concepts determine the value of long tem securities. Although we

focus mainly on financial assets, the principles and methods discussed are just as relevant

and applicable to the valuation of real assets.

Learning Objectives

At the end of this lecture you should be able to:

1. Discuss the characteristic s of long

term security instruments.

2. Distinguish among the various

valuation concepts.

3. Describe the key inputs in, and the

basic valuation model.

4. Apply the basic valuation model to the

valuation of bonds, preferred stock, and

ordinary shares

4.2 CHARACTERISTICS OF LONG TERM SECURITIES

Long term securities are the claims held as evidence by those who have provided long

term financing to a firm. They, typically, comprise bonds and debentures, preference

shares, and ordinary shares.

76

4.2.1 Bonds

A bond is a debt instrument indicating that a corporation or government has borrowed a

certain amount of money and promises to repay it in the future under clearly defined

terms. Corporate bonds are issued by corporations while the government issues

government bonds.

Bonds are usually issued with a maturity of 10-30 years and with a par or face value of

Sh. 1000. The coupon interest rate on a bond represents the percentage of the bonds par

value that will be paid annually (typically in 2 equal semi- annual payments) as interest.

At maturity the bondholders are repaid the principal amount – par value.

Legal Aspect of Corporate Bonds (Agency Problem)

In order to mitigate the agency problem, whereby management (and shareholders) of

firms may be tempted to expropriate the wealth of bondholders, the law protects

bondholders through indenture and the provision of a trustee.

I. Bond indenture

A bond indenture is a complex legal document stating the conditions under which a

bond has been issued with the aim of protecting bondholders once they have lend to the

issuer of the bond. It specifies the rights of the bondholders and the duties of the issuing

corporation in the contract in which the corporation borrows from bondholders. Included

in the indenture are the interest and principal payments, various standard and restrictive

provisions, sinking-fund requirements and security (collateral) interest provisions. In the

following sections we briefly discuss the contents of an indenture.

Standard provisions are provisions in a bond indenture specifying certain criteria of

satisfactory record keeping and general business maintenance on the part of the borrower.

Normally, they do not place a burden on financially sound business. They typically

require the borrower to:

- Maintain satisfactory accounting records (consistent with generally

accepted accounting principles – GAAPs, and international accounting

standards - IASs)

77

- Periodically supply audited financial statements

- Pay taxes and other liabilities when due

- Maintain all facilities in good working order

Restrictive provisions These are contractual clauses that place operating and financial

constraints on the borrower. The most common restrictive covenants include:

- Require the borrower to maintain minimum level of liquidity (to insure

against loan default and ultimate failure).

- Prohibit borrowers from discounting accounts receivable to generate cash.

This could cause a long run cash shortage if proceeds are used to meet

current obligations

- Impose fixed asset restrictions on the borrower (the liquidation or

encumbrance of fixed assets could damage firms ability to repay the

bonds).

- Constrain subsequent borrowing. Either additional debt is prohibited or is

subordinated to the original loan (subsequent creditors have to wait until

claims of senior or prior debt are satisfied).

- Limit the firm’s annual cash dividends payments to a specified amount or

percentage.

The violation of any standards or restrictive provision by the borrower gives the

bondholders (through their trustee) the right to demand immediate repayment of the debt.

Sinking fund requirement

A sinking fund provides for the systematic retirement of bonds prior to their maturity.

The corporation makes semi- annual or annual payments to a trustee who uses these

funds to retire bonds by purchasing in the market, or sets up a fund that accumulates until

maturity when the fund is applied in the liquidation of the bond.

Security collateral interest

The bond indenture identifies carry asset pledged as collateral. The protection of bond

collateral is crucial to interests of bondholders.

78

II Trustee

A trustee is a paid third party to a bond indenture (individual, corporation or commercial

bank’s trust department) who is paid to act as a watchdog on behalf of the bondholders

and is empowered to take specific actions if terms of indenture are violated. The

provision for a trustee for a bond issue recognizes the fact that atomistic and diffuse

bondholders, individually, may not have the capacity and incentive to ensure compliance

with the terms of issue by effective monitoring of the issuer of bonds.

General Features of a Bond Issue

Three common features of a bond issue are conversion, call (redemption) and stock

purchase warrants.

Conversion feature

This is a feature of convertible bonds that allows bondholders to change each bond

into a stated number of shares of common stock (ordinary shares). Bondholders will

exercise the option if the share price is greater than the conversion price (this feature

is advantageous to the issuer because he does not have to give up immediate control

as in issuing stock: to the holder it provides a possibility of a future speculative gain).

Call feature

The feature gives the issuer the opportunity to repurchase bonds prior to maturity at a

stated call price that include a premium ( in most cases, the call price exceeds the par

value by an amount equal to 1 year’s interest). The feature is advantageous to the

issuer because when interest rates fall in the economy an issuer can call outstanding

bonds and reissue a new bond at a lower interest rate but when interest rates rise the

call option is not exercised.

Putable provision

In contrast to the call feature, the putable provision allows the investors the option of

requiring the issuer to repurchase bonds at specified times prior to maturity. Investors

will exercise this option when they need cash or when interest rates have risen since

bonds were issued.

Stock purchase warrants

79

Stock purchase warrants are instruments (sweeteners) attached to bonds that give the

warrant holders the right to purchase a certain amount of a firms ordinary shares at a

specific price over a certain period of time ( they enable firms to raise needed funds at

slightly lower interest rates and less restrictive provisions).

4.2.2 Common Stock (Ordinary Shares)

The true owners of business forms are the ordinary shareholders. Sometimes referred to

as residual owners, they receive what is left after satisfaction of all other claims. The

fundamental aspects of ordinary shares are.

Ownership

The ordinary shares of a firm may be owned privately (family) or publicly with shares

being traded in the stock exchange.

Par value

The par value of an ordinary share is relatively useless value, established in the firm’s

corporate charter (memorandum). It is generally very low- Sh.5or less.

Pre-emptive rights

Allow shareholders to maintain their proportionate ownership in the corporation when

new shares are issued. The feature maintains voting control and protects against dilution.

Rights offering

The firm grants rights to its shareholders to purchase additional shares at a price below

market price, in direct proportion to their existing holding.

Authorized, outstanding and issued shares

Authorized shares are the number of shares of common stock that the firm’s charter

(articles) allows without further shareholders’ approval.

Outstanding shares is the number of shares held by the public

Issued shares are the number of share that has been put in circulation; they represent the

sum of outstanding and treasury stock.

Treasury stock is the number of shares of outstanding stock that have been repurchased

by the firm (not allowed by the Companies Act of Kenya Laws).

80

Voting rights

Generally each ordinary share entitled the holder to one vote at the Annual General

Meeting for the election of directors and on special issues.

Dividends

The payment of corporate dividends is at the discretion of the Board of Directors.

Dividends are paid usually semi- annually (interim and final dividends). Dividends can

be paid in cash, stock (bonus issues) and merchandise.

4.2.3 Preference Shares

These are a hybrid between debt and ordinary shares. Preference shares:

- Are promised a fixed periodic return which is stated as a % of par value

- Do not have a voting right at the annual general meeting (AGM) of shareholders.

- Have preference over ordinary shares with respect to distribution of earnings

- Have preference over ordinary shares on the liquidation of asset

Preference shares may have several distinguishing features such as; Cumulation

Most preferences shares are cumulative with respect to any dividend passed over.

Dividend in arrears together with current dividends must be paid first before distribution

is made to ordinary shareholders.

Callable (redeemable)

The issuer can retire outstanding stock within a certain period of time at a specific price.

Conversion

This feature allows holders to change each share into a stated number of ordinary shares.

81

Summary of differences between debt and ordinary shares

Debt Ordinary share

Voice in management No Yes

Claims on income and assets Senior to Equity Subordinate to debt

Maturity Stated None

Tax treatment Interest is tax deductible Dividend is not deductible

4.3 VALUATION OF LONG TERM SECURITIES (BONDS

AND SHARES)

Valuation is the process that links return and risk to determine the worth of an asset. The

key inputs to the valuation process include cash flows, their timing and the risk (required

return) associated with the cash flows.

Cash flows. The value of an asset depends on the cash flows it is expected to provide

over the ownership period. The cash flow could be regular, intermittent or single. The ash

flows from stocks are dividends and capital gains and from bonds are interest and the

redemption value.

Timing. We must incorporate the timing of the cash flows in valuation calculations. For

computational convenience and custom the cash flows are assumed to occur at the end of

the period, unless otherwise stated.

Risk (required return). In general the greater the risk (the less certain) of a cash flow,

the lower its value of the cash flow. In the valuation process the required return is used to

incorporate risk in the analysis. The higher the risk the greater the required return: the

lower the risk the less the required return. The required return could range from the risk

free rate upwards depending on level of risk.

82

4.3.1 Valuation Concepts

The term value could mean different things to different people. A brief description and

contrasts of some of the major concepts of value follows.

Liquidation vs. going concern value

Liquidation value is the amount of money that could be realized if an asset (or group of

assets) is sold separately from its operating organization. Going concern value of a firm

is the amount the firm could be sold for as a continuing operating business. The valuation

models we discuss assume that we are dealing with going concerns.

Book value vs. market value

Book value is the accounting value of an asset as given by the asset cost less

accumulated depreciation. Market value is the market price at which an asset trades in

an open market price.

Intrinsic value

Intrinsic value is the price a security ought to have based on all factors bearing on its

valuation. This is the economic value of a security.

4.3.2 Basic Valuation Model

The value of any asset is the present value of all future cash flows it is expected to

provide over the relevant period.

)1()1()1(...2

21

10 k

CFk

CFk

CFV nn

++++++= (4.1)

Where V0 = The current value of asset (at time 0)

Cash flow expected at end of time period t =CF t

k = required return

n = relevant time period

Using PVIF notation the basic valuation equation can be stated as;

83

CF=v0 1 x (PVIFk,1) + CF2 x (PVIFk,2) +…+ CFn x (PVIFk,n)

Firm’s long term securities include bonds, preferred stock and ordinary shares. Our

discussion in the remainder of the lecture will focus on the mechanics of valuing each of

these financial assets. We start first with bonds, followed by preference shares and end

with the ordinary shares, which poses the most challenging valuation difficulties.

4.3.3 Bond Valuation

Bonds are long-term debt instruments used by business and government to raise money.

Most pay interest semi annually at a slated coupon interest rate, have an initial maturity

of 10-30 years and have a par or face value of Sh.1000 that must be repaid at maturity.

The simplest and common type of bond is one that pays the bondholder two forms of

cash flows if held to maturity i.e. periodic interest and the bonds face value at maturity.

The interest is an annuity and the face value is a single payment received at a specified

future date. The basic equation for the value of such a bond with n years to maturity and

which pays interest ,I , annually is;

....)1()1()1()1( 210

kkkkB

d

M

d

I

d

I

d

Inn ++++

++++= (4.2)

Where

B0 = current value of the bond (at time zero).

I = annual interest paid in shillings (coupon interest x face value)

n = number of years to maturity

M = par value (face value) in shillings

kd = required return on a bond

The interest payments can be discounted using PVIFA tables while the payment at

maturity will be discounted using PVIF tables. The discounting notation is;

)*)* (( ,,0 PVIFPVIFAB nn kM

kI

dd

+=

84

Example

Mills Co has issued a 10% coupon interest rate, 10 year bond with a Sh. 1000 par value,

which pays interest annually. The required rate of return of similar bonds is 10%. What is

the value of the bond?

The values of the variables are;

I = per value x coupon rate = 1000*10% = Sh 100

M = 1000

kd = 10%

n = 10 years

Substituting the values in the valuation formula for bonds leads to,

B0 = 100 x (PVIFA10%,10yrs) + 1000x (PVIF10%,10yrs)

= 1000 x 6.145 + 1000 x .386 =Sh.1000.50.

The answer is the same as the par value of Sh.1000 except for rounding differences

In practice, however, the value of a bond in the market place is rarely equal to its par

value. Some may be quoted above their par value, and some below: It all depends on the

bond’s required return and the time to maturity. We will discuss the effect of these two

on the value of bonds.

Required Returns and Bond Values

Whenever the required return on bond differs from its coupon interest rate the bonds

value will differ from its par value. (The required return may differ for two reasons:

1. Economic conditions may have changed since the bond was issued, causing a

shift in cost of long term funds

2. The firm’s risk class may change.

When the required return is greater the coupon interest rate, the bond value, B0, will be

less than its par value M, and the bond sells at a discount M-B0. When the required return

falls below the coupon interest rate, the bond value, B0, will be greater than par, M, and

the bond sells at a premium equal to B0-M.

85

Example Example

In the preceding example of Mills Company, the required return equalled the coupon

interest rate and the bonds value equalled its Sh.1000 par value.

In the preceding example of Mills Company, the required return equalled the coupon

interest rate and the bonds value equalled its Sh.1000 par value.

If required return were greater than the coupon rate of 10% i.e. 12%, the value of the

bond would be as follows;

If required return were greater than the coupon rate of 10% i.e. 12%, the value of the

bond would be as follows;

B0 = 100 x (PVIFA12%,10yrs) + 1000x (PVIF12%,10yrs) B0 = 100 x (PVIFA12%,10yrs) + 1000x (PVIF12%,10yrs)

= 100 x 5.650 + 1000 x .322 = Sh.887.00. = 100 x 5.650 + 1000 x .322 = Sh.887.00.

The bond will sell at a discount of Sh.113 (1000-887) and is said to be a discount bond.

Conversely, if the bond’s required return fell to say, 8%, the bond’s value would be:

The bond will sell at a discount of Sh.113 (1000-887) and is said to be a discount bond.

Conversely, if the bond’s required return fell to say, 8%, the bond’s value would be:

B0 = 100 x (PVIFA8%,10yrs) + 1000x (PVIF8%,10yrs) B0 = 100 x (PVIFA8%,10yrs) + 1000x (PVIF8%,10yrs)

= 100 x 6.710 + 1000 x .463 = Sh.1134.00 = 100 x 6.710 + 1000 x .463 = Sh.1134.00

The bond will sell at a premium of Sh.134 (1134 – 1000). The bond is called a premium

bond

The bond will sell at a premium of Sh.134 (1134 – 1000). The bond is called a premium

bond

Figure 4.1 The relationship between value of a bond and the required rate of return.

The graph is downward sloping, implying that bas interest rates rise bonds lose value.

Figure 4.1 The relationship between value of a bond and the required rate of return.

The graph is downward sloping, implying that bas interest rates rise bonds lose value.

Market value of bonds (Sh.)

2 4 6 8 10 12 14 2 4 6 8 10 12 14

Required return, kd% Required return, kd%

1200 1100 1000 900 800

Time to Maturity and Bond Values Time to Maturity and Bond Values

The value of bond will approach par value as the message of time moves the bond’s value

closer to maturity (when required return equals the coupon rate the bond’s value remains

at par until it matures).

The value of bond will approach par value as the message of time moves the bond’s value

closer to maturity (when required return equals the coupon rate the bond’s value remains

at par until it matures).

86

Market value of bonds

1200 premium bond

1100

1000 required return = par value

900

800 discount bond

10 9 8 7 6 5 4 3 2 1 0

Figure 4.2 Relationship between maturity and value of a bond Time to maturity

Interest Rate Risk

The chance that interest rate will change and thereby change the required return and bond

value is called interest rate risk. How much interest rate risk a bond has depends on how

sensitive its price is to changes in interest rates This sensitivity directly depends on two

things: the time to maturity and the coupon rate. Investors in bonds should keep in mind

the following;

1. All other things equal, the longer the time to maturity, the greater the interest

rate risk.

2. All other things equal, the lower the coupon rate, the greater the interest rate

risk.

Bondholders are more concerned with rising rates which decrease bond values. The

shorter the amount of time until maturity the less responsive is the bonds market value to

a given change in the required.

Also, if two bonds with different coupon rates have the same maturity, then the value of

the one with lower coupon is more dependent on the face amount to be received at

maturity. As a result its value will fluctuate more as interest rates change. In other words,

87

the bond with the higher coupon has a larger cash flow early in its life, so its value is less

sensitive to changes in the discount rate.

If time will return when interest rates are volatile financiers prefer lining shorter to hedge

against interest rate risk.

Perpetual Bonds

This is a bond that never matures- a perpetuity. A consol is an example. The present

value of a perpetual bond is equal to the capitalized value of an infinite stream of interest

payments. If a bond promises, fixed annual interest payment, I, forever its value at

investors required rate of return, kd, is,

)1()1()1(...210

kkkB

d

I

d

I

d

I

+++++= α

This should reduce to

kB

d

I=0 (4.3)

Example

You intend to buy a bond that pays Sh. 500 per year forever. If your required rate of

return is 12%, what is the maximum you should pay for the bond?

The PV of the security would be

B0 = 500/0.12 = Sh.4166.7

This is the amount you will be willing to pay for this bond.

Zero Coupon Rate Bonds

Zero coupon rate bonds make no periodic interest payment but instead the bond is sold at

a deep discount from its face value. The bond is then redeemed at face value on its

maturity. The valuation formula for a zero coupon bonds is truncated version of that used

for normal interest paying bond. The present value of interest payment is loped off

leaving only the payment at maturity.

88

Therefore,

)1(0

kB

d

Mn+

= (4.4)

= )( ,PVIF nkMd

Example

ABC Ltd., issues a zero coupon bond having a 10 year maturity and a face value of Sh.

1000. Investors require a return of 12%. How much should an investor pay for the bond?

B0 = 1000/(1.12)10

= 1000 (PVIF12%,10yrs)

= 1000 x 0.322

= Sh 322

The bond is worth Sh.322.

Semi – Annual Compounding Interest

Most bonds pay interest twice a year. As a consequence the valuation equation changes

∑++=

+=n

tnt

kkB

d

M

d

I2

120 )2/1()2/1(

2/ (4.5)

= PVIFPVIFAB nn kMkIdd

2,212,

210 **

21

+=

Notice that the assumption of semi- annual accounting once taken applies even to the

maturity value.

Example

10% coupon bonds of ABC Ltd., have 12 years to maturity and annual required rate of

return is 14%. What is the value of a Sh.1000 par value bond that pays interest semi-

annually?

89

)(*)(*2 24%,724%,70 PVIFPVIFAB MI

+=

= 50 (11.469) + 1000 (.197) = Sh.770.4

Yield to Maturity (YTM)

When investors evaluate and trade bonds, they consider yield to maturity (YTM), which

is the rate of return investors earn if they buy a bond at a specific price and hold it until

maturity. The YTM is analogous to the Internal rate of return from an investment in the

bond. The yield to maturity on a bond with current price equal to its par value (i.e. B0

=M) will always equal the coupon rate. When the bond value differs from par, the yield

to maturity will differ from the coupon rate.

The yield to maturity on a bond can found by sowing equation for kd in the equation

below.

∑++=

+=n

tnt

kkB

d

M

d

I1

0 )1()1( (4.6)

The required return is the bond’s yield to maturity. The YTM can be found by trial and

error procedures.

Example

Mills Company bond which currently sells for Sh.1080, has a 10% coupon rate and

Sh.1000 par value, pays interest annually and has 10 years to maturity. Find YTM of the

bond.

∑++=

+=10

110)1()1(

10001001080t

t

kk dd or,

PVIFPVIFA kk dd10,10, *1000*1001080 +=

90

Trial and error

We know that when Kd = 10% (equal coupon rate), then B0 = 1000. Thus the discount

rate to result in 1080 must be less than 10%. (Try a lower rate if the PV of cash flows at a

given rate is lower than the market price of the bond).

Try 9% = 100 x 6.418 + 1000 x .422 = 1063.80 (The 9% rate is not low

enough to get Sh.1080).

Next try 8% = 100 x 6.710 + 1000 x .463 = 1134

Because 1080 lies between 1063.80 and 1134 the YTM must be between 8% and 9%.

Because 1080 is closer to 1063.80, the YTM to the nearest whole per cent is 9%.

By using interpolation, we find the more precise YTM value to be 8.77% as follows;

Interpolation

1134 – 1063.80 = 70.20

1080 – 1063.80 = 16.20

YTM = 9% - 16.20 = 9% - 0.2307692

70.20

= 8.77%)

Using a financial calculator, we get 8.766%.

4.4 Preference Shares Valuation

A type of stock that promises a fixed dividend but at the discretion of the Board of

directors. It has preference over ordinary shares in the payment of dividends and claims

on the assets it has no maturity date (unless redeemable) and give the fixed nature of the

dividend is similar to a perpetuity.

Thus the PV of a preferred stock, V , is p

kDV

p

pp = (4.7)

91

Where Dp is the stated annual dividend, per share and kp is the appropriate discount rate.

Example

A company had issued a 9% Sh.100 par value preference shares and an investors require

a rate of return of 14% on this investment. Find the value of a preference share to

investors.

Dp = 9%*100 = Sh.9

kp = 0.14

The value of the preference share is,

Vp = 9/0.14 = Sh.64.29

Example

A preferred stock paying a dividend of Sh. 5 and having a required return of 13% will

have a value of Sh.38.46 (5÷0.13)

4.5 Valuation of Ordinary Shares

Common shareholders expect to be rewarded through periodic cash dividends and an

increasing share value. It is the expectation of future to dividends and a future selling

price (which itself is based on future dividends) that gives value to a share. Cash

dividends are broadly defined to mean all cash distributions and are the foundation for

valuation of shares.

Dividend discount models are designed to compute the intrinsic value of a share under

specific assumptions as to the expected growth patterns of future dividends and the

appropriate discount rate to apply.

Basic stock valuation equation

The value of a share is equal to the PV of all future dividends it is expected to provide

over an infinite time horizon (from a valuation viewpoint only dividends are relevant).

k

Dk

Dk

DPsss +++

+=1()1()1(

...22

11

0 αα (4.8)

92

Where P0 = current value of ordinary share

ks = required return on ordinary shares

Dt = per share dividend at end of year t.

We illustrate the use of this formula to estimate the value of ordinary stock under three

dividend growth assumptions i.e. zero growth in dividends, constant growth in dividends,

and variable growth phases.

Zero growth assumes a constant, non-growing dividend stream i.e. D1 = D2 = … = Dα =

D. The dividend stream is a perpetuity and can be valued as such i.e.

kP

s

D=0 (4.9)

Example

The dividend of Den Company is expected to remain constant at Sh. 3 indefinitely. If

required return on its stock is 15% the value of its ordinary share would be Sh.20 ( i.e.

2015.03

= )

Constant Growth

The constant growth model, assumes that dividends will grow at a constant rate, g. If we

let D0 equal the most recent dividend, then

)1()1(

)1()1(

)1()1( 0

2

2

01

1

00

kgD

kgD

kgDP

sss ++

++

++

+−−−++=α

α or, (4.10)

)1()1()1( 22

11

0

kD

kD

kDP

sss ++++−−−++= α

α

The equation can be simplified and rewritten as

93

gk

DPs−

= 10 (4.11)

(D1 is the coming years dividend , ks is the required return on the stock and g is the

constant growth rate in dividends). Gordon’s model is a common name for the constant

growth model.

Example

Lama Company has paid the following dividends over the past years

Year div per share

1999 1.00

2000 1.05

2001 1.12

2002 1.20

2003 1.29

2004 1.40

The average growth of dividends for the past five years is expected to persist in the

foreseeable future. You are required to determine the value of the company’s shares after

payment of the dividend of 2004.

First find the average rate of growth in dividend over last five years. Let the average

growth rate be g. Then the dividend of year 2004 denoted by D2004 is found by growing

the dividend of year 1999 as follows:

D2004 = D1999 x (1+g)5

(1+g) 5 = D2004/D1999

00.140.1

5%,=FVIF g

= 1.40

By looking across the table for FVIFs (in the 5-year row) the factor closest to 1.40 for 5

years is 7%. Therefore, g is 0.07.

gkDPs−

= 10 =

07.015.050.1−

=Sh.18.75

94

The value of the stock is Sh.18.75

Variable Growth Model

The dividend valuation approach can be manipulated to allow for changes in the dividend

growth rates. For instance the model could be based on the assumptions that dividends

initially grow at a supernormal rate for a number of years followed by normal growth rate

into the foreseeable future. In such a situation our dividend model can be modified as

follows.

Let gs equal the initial growth rate (supernormal growth for n years),and gn equal the

subsequent growth rate (normal growth to infinity) and Dt be the dividend paid at end of

time period t

The formula for the value of the share, P0, is

∑++

+=

+

−+=

n

tn

ns

nt

t

kgkD

kgDP

ss

s1

10

0 )1()1()1 1*

)(

( (4.12)

The first term on the left hand side, represents the present value of dividends during the

initial phase of supernormal growth; the second term, Dn+1/( ks-gs)*1/(1+ks),represent the

present value of the price of the stock at the end of the initial growth period.

STEPS

1. Find the value of dividends at the end of each year Dt, during the initial growth

years 1 to n by

Dt = D0 x (1 + gs)t

2. Find present value of the dividends expected during the initial growth phase i.e.

∑++

=

n

tt

t

kgDs

s1

0

)1()1(

= ∑=

n

ttt PVIFD k s1

, )(

3. Find value of stock at the end of the initial growth phase i.e.

95

gkDP

ns

nn −= +1 (Same as Gordon’s constant growth model)

Next we discount Pn to the present i.e. PVIFP nn k s,*

4. Add the PVs in 2 and 3 to find the value of stock.

Example

Waka Industries has just paid the 2004 annual dividend of Sh. 1.50 per share. The firm’s

financial manager expects that these dividends will increase at 10% annual rate over the

next 3 years. At the end of the3 years, (end of 2007) the growth rate will decline to 5%

for the foreseeable future. The firm’s required rate of return is15%. Estimate the current

value of Waka share i.e. the value at end of 2004 (P0 = P2004).

Solution

Find value of cash dividends in each of the next 3 years and their PVs at end of year

2004 as below:

Remember D0 =D2004 =Sh.1.50

Year(t) End of year Dividend

=D0 (1.1)tPVIF t%,15 Present value

1 2005 1.65 0.870 1.44

2 2006 1.82 0.756 1.38

3 2007 2.00 0.658 1.32

Present value of dividends during initial growth phase Sh.4.14

Next the price of the stock at the end of the initial growth phase (at the end of 2007) can

be found first by calculating the dividend to be paid at end of the year 2008

( )20081 DDn =+

D2008 = D2007 x (1 + 0.05) = 2.00 x 1.05= Sh.2.10.

96

Using Gordon’s constant growth model, the price of the stock at end of 2007 is

calculated as follows;

21.05.015.0

10.2200812007 Sh

gkDP

ns

=−

=−

=

The value of Sh.21 at end of year 2007 must be converted into PV (end of 2004). Using

15% as the required return, (PVIF 15%,3yrs) x 21 = 0.658 x 21 = Sh.13.82.

Finally, we add the present values to get the value of the stock i.e.

P2004 = 4.14 + 13.82 = Sh.17.96

97

REVIEW QUESTIONS

1. Define valuations. Briefly describe three key inputs to the valuation process.

2. Briefly explain the meaning of the efficient markets hypothesis (EMH).

3. What is meant by a bonds yield to maturity (YTM)?

4. What relationship between the required return and coupon rate will caused

bond to sell (a) at a discount? (B) At a premium? And (c) it per value ?

Explain.

5. Describe compare and contrast the following common stock valuation models:

a) zero-growth, b) constraint – growth and c) variable-growth.

98

LECTURE 5: LONG-TERM INVESTMENT DECISION PROCESS AND RELEVANT CASH FLOWS

5.0 INTRODUCTION

Long-term investment decisions are important and take up a considerable amount of a

financial manager’s attention because of two reasons:

(1) They consume quite a sizable amount of a firm’s funds

(2) The decisions determine the future viability and competitiveness of the firm.

Objectives

At the end of this lecture you should be able to:

1. Explain the motives for capital expenditure

and the steps followed in the capital

budgeting process.

2. Define and explain the basic terminologies

used to describe projects, funds

availability, decision approaches and cash

flow patterns.

3. Discuss and compute the major

components of relevant cash flows.

4. Calculate, interpret and evaluate the pay

back period, the net present value, the

profitability index and the internal rate of

return of investment proposals.

5. discuss difficulties and conflicts in using

discounted cash flow methods

.

In this lecture we shall discuss the motives, terminologies and procedures in the capital

budgeting process. We will also explain the major components of the cash flows

employed in making the long-term investment decision. The next lecture will complete

99

the discussion by examining the specific techniques employed in making the long-term

investment decision.

5.1 THE BASICS OF CAPITAL BUDGETING PROCESS

Capital budgeting is the process of evaluating and selecting long term investments

consistent with the firm’s goal of owner wealth maximization.

For a manufacturing firm, capital investment are mainly to acquire fixed assets-property,

plant and equipment. Note that typically, we separate the investment decision from the

financing decision: first make the investment decision then the finance manager chooses

the best financing method.

5.1.1 Capital Expenditure Motives

A capital expenditure is an outlay of funds by the firm that is expected to provide

benefits over a period of time greater than one year (In contrast, operating expenditure’s

benefits are received within one year). The basic motives for capital expenditures are to

expand’ replace, or renew fixed assets, or obtain some other less tangible benefit over a

long period of time. These key motives for making capital expenditures are briefly

outlined below.

1. Expansion: The most common motive for capital expenditure is to expand the

cause of operations – usually through acquisition of fixed assets. Growing firms

need to acquire new fixed assets rapidly.

2. Replacements – As a firm’s growth slows down and it reaches maturity, most

capital expenditure will be made to replace obsolete or worn out assets. Outlays of

repairing an old machine should be compared with net benefit of replacement.

3. Renewal – An alternative to replacement may involve rebuilding, overhauling or

refitting an existing fixed asset.. A physical facility could be renewed by rewiring

and adding air conditioning.

100

4. Other purposes – Some expenditure may involve long-term commitments of

funds in expectations of future return i.e. advertising, R&D, management

consulting and development of view products. Other expenditures include

installation of pollution control and safety devises mandated by the government.

5.1.2 Steps in Capital Budgeting Process

The capital budgeting process consists of five distinct but interrelated steps. It begins

with proposal generation, followed by review and analysis, decision making,

implementation and follow-up. These six steps are briefly outlined below.

1. Proposal generation: Proposals for capital expenditure are made at all levels

within a business organization. Many items in the capital budget originate as

proposals from the plant and division management. Project recommendations may

also come from top management, especially if a corporate strategic move is

involved ( for example , a major expansion or entry into a new market). A capital

budgeting system where proposals originate with top management is referred to a

top-down system, and one where proposals originate at the plant or division level

is referred to as bottom-up system. In practice many firms use a mixture of the

two systems, though in modern times has seen a shift to decentralization and a

greater use of the bottoms-up approach. Many firm offer cash rewards for

proposal that are ultimately adopted.

2. Review and analysis: Capital expenditure proposals are formally reviewed for

two reasons. First, to assess their appropriateness in light of firm’s overall

objectives, strategies and plans and secondly, to evaluate their economic viability.

Review of a proposed project may involve lengthy discussions between senior

management and those members of staff at the division and plant level who will

be involved in the project if it is adopted. Benefits and costs are estimated and

converted into a series of cash flows and various capital budgeting techniques

applied to assess economic viability. The risks associated with the projects are

also evaluated.

3. Decision making: Generally the board of directors reserves the right to make final

decisions on the capital expenditures requiring outlays beyond a certain amount.

101

Plant manager may be given the power to make decisions necessary to keep the

production line moving (when the firm is constrained with time it cannot wait for

decision of the board.

4. Implementation: One approval has been received and funding availed

implementation commences. For minor outlays the expenditure is made and

payment is rendered: For major expenditures, payment may be phased, with each

phase requiring approval of senior company officer.

5. Follow-up: involves monitoring results during the operation phase of the asset.

Variances between actual performance and expectation are analyzed to help in

future investment decision. Information on the performance of the firm’s past

investments is helpful in several respects. It pinpoints sectors of the firm’s

activities that may warrant further financial commitment; or it may call for retreat

if a particular project becomes unprofitable. The outcome of an investment also

reflects on the performance of those members of the management involved with

it. Finally, past errors and successes provide clues on the strengths and

weaknesses of the capital budgeting process itself.

5.1.3 Basic Terminology

Before we develop the concept, lecturing and practices of capital budget some basic

terminology need to be explained.

Independent versus Mutually Exclusive Projects

Independent projects are those whose cash flows are unrelated or independent of one

another; the acceptance of one does not eliminate the others from further considerations

(if a firm has unlimited funds to invest, all independent project that meet it minimum

acceptance criteria will be implemented i.e. installing a new computer system, purchasing

a new computer system, and acquiring a new limousine for the CEO.

Mutually exclusive projects are projects that compete with one another, no that the

acceptance of one eliminates the acceptance of one eliminates the others from further

consideration. For example, a firm in need of increased production capacity could either,

102

(1) Expand it plant (2) Acquire another company, or (3) contract with another company

for production of required items.

Unlimited Funds versus Capital Rationing

Unlimited funds This is the financial situation in which a firm is able to accept all

independent projects that provide an acceptable return (Capital budgeting decisions are

simply a decision of whether or not the project clears the hurdle rate).

Capital rationing This is the financial situation in which the firm has only a fixed

number of shillings to allocate among competing capital expenditures. A further decision

as to which of the projects that meet the minimum requirements is to be invested in has to

be taken.

Conventional versus Non-Conventional Cash flows

Conventional cash flow pattern consists of an initial outflow followed by only a series of

inflows. ( For example a firm spends Sh.10 million and expects to receive equal annual

cash inflows of Sh.2 million in each year for the next 8 years)

Cash inflows 2m 2m 2m 2m 2m 2m 2m

0 1 2 3 4 5 6 7 8

Cash 10m

Outflow End of year The cash inflows could be unequal

Non-conventional cash flows This is a cash flow pattern in which an initial outflow is

not followed only by a series of inflows, but with at least one cash outflow. For example

the purchase of a machine may require Sh.20 million and may generate cash flows of

Sh.5 million for 4 years after which in the 5th year an overhaul costing Sh.8million may

be required. The machine would then generate Sh.5 million for the following 5 years.

103

Inflows 5m 5m 5m 5m 5m 5m 5m 5m 5m 5m 5m

Outflows

10m 8m

Evaluating projects with unconventional patterns poses challenges that require an

analyst’s special attention

Relevant versus Incremental Cash flows

To evaluate capital expenditure alternatives, the firm must determine the relevant cash

flows which are the incremental after-tax initial cash flow and the resulting subsequent

inflows associated with a proposed capital expenditure. Incremental cash flows

represent the additional cash flows (inflowing and outflows) expected to result from a

proposed capital expenditure.

Sunk Costs versus Opportunity Cost

Sunk costs are cash outlays that have already been made (past outlays) and therefore

have no effect on the cash flows relevant to a current decision. Therefore sunk costs

should not be included in a project’s incremented cash flows.

Opportunity costs are cash flows that could be realized from the best alternative use of

an owned asset. They represent cash flows that can therefore not be realized, by

employing that asset in the proposed project. Therefore, any opportunity cost should be

included as a cash outflow when determining a project’s incremental cash outflows.

5.2 CASH FLOW COMPONENTS

The cash flows of any project can include three basic components:

(1) An initial investment

(2) Operating cash flows

(3) Terminal cash flows.

All projects will have the first two; some however, lack the final components. We will

discuss these components in following sections.

104

5.2.1 Initial Investment

The initial investment is the relevant cash outflow for a proposed project at time zero. It

is found by subtracting all cash inflows occurring at time zero from all cash outflows

occurring at time zero. Atypical format used to determine initial cash flow is shown

below.

Cost on new asset XX

Installation cost XX

Installed cost of new asset XX

Proceeds from sale of old assets XX

+ Tax on sale of old assets (XX)

After-tax proceeds from sale of old asset XX

+ Change in Net working capital XX

Initial Investment XX

We will elaborate some of the items appearing in the above determination. The installed cost of new asset = cost of new asset (acquisition cost) + installation cost

(additional cost necessary to put asset into operation) +After-tax proceeds from sale of

old asset. The last variable in the equation is explained as follows.

After tax proceeds from sale of old asset = The difference between old assets sale proceeds and any applicable taxes or tax refunds resulting from the sale of existing assets

Proceeds from sale of old assets + Cash inflows net of any removal or cleanup cost resulting from the sale of an existing asset(** by the co)

Tax on sale of old asset

Tax that depends upon the relationship between old assets sale proceeds and its written down value(Capital Gains Tax)

105

Change in networking capital (NWC) Net working capital is the difference between

current assets (CA) and current liabilities (CL) i.e. NWC = CA –CL. Changes in NWC

often accompany capital expenditure decisions. If a company acquires a new machinery

to expand its levels of operation, levels of cash, accounts receivables, inventories,

accounts payable, accruals will increase. Increases in current assets are uses of cash while

increases in current liabilities are sources of cash. As long as the expanded operations

continue, the increased investment in current assets (cash, accounts receivables and

inventory) and increased current liabilities (accounts payables and accruals) would be

expected to continue.

Generally, current assets increase by more than the increase in current liabilities, resulting

in an increase in NWC which would be treated as an initial outflow (This is an internal

build up of accounts with no tax implications, and a tax adjustment is therefore

unnecessary).

5.2.2 Operating Cash Flows

These are incremental after tax cash during its lifetime. Three points should be noted:-

- Benefits should be measured on after tax basis because the firm will not have the

use of any benefits until it has satisfied the government’s tax claims.

- All benefits must be measured on a cash flow basis by adding back any non-cash

charges (depreciation)

- Concern is only with the incremental (relevant) cash flows. Focus should be only

on the change in operating cash flows as a result of proposed project. The

following income statement format is useful in the determination of the operating

cash flows.

106

Shs

Revenue XX

Expenses (XX)

Profits before depreciation XX

Depreciation (XX)

Profit before tax XX

Taxes (XX)

Profit after taxes XX

Add back depreciation XX

Operating Cash flows XX

5.2.3 Terminal Cash Flows

The cash flows resulting from the termination and liquidation of a project at end of its

economic life are its terminal cash flow. Terminal cash flow is determined as incremental

after tax proceeds from sale or termination of a new asset or project. The format below

can be used to determine terminal cash flows.

Proceeds from sale of new assets Project XX

± Tax on sale of new asset XX

XX

Proceeds from sale of old asset XX

± Tax on sale of old asset XX XX

± Change in NWC XX

Terminal Cash Flow XX

Note that for a replacement decision both the sale proceeds of the old asset and the new

asset are considered. In the case of other decision (other than replacement), the proceeds

of an old asset would be zero. Note also that with the termination of the project the need

for the increased working capital is assumed to end. This will be shown as a cash inflow

due to the release of the working capital to be used business needs. The amount recovered

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at termination will be equal to the amount shown in the calculation of the initial

investment.

5.3 CAPITAL INVESTMENT TECHNIQUES

The preferred technique should time value procedures, risk and return considerations and

valuation concepts to select capital expenditures that are consistent with the firm’s goals

of maximizing owner’s wealth. The three most popular techniques are the payback

period, net present value, and internal rate of return. We will use one basic problem to

illustrate all the techniques.

Example

The problem concerns MALI Limited, a medium sized metal fabricator that is currently

contemplating two projects: project A requires an initial investment of Sh.42million and

project B requires an initial investment of Sh.45million. The projected relevant cash

flows for the two projects are shown below.

PROJECT A PROJECT B

Initial Investment (yr 0) Sh.42 million Sh.45 million

Operating cash flows

Year 1 Sh.14 million Sh.28 million

Year 2 Sh.14 million Sh.12 million

Year3 Sh.14 million Sh.10 million

Year 4 Sh.14 million Sh.10 million

Year 5 Sh.14 million Sh.10 million

Average Sh.14 million Sh.14 million

5.3.1 Payback Period

The payback period is the exact amount of time required for the firm to recover its

initial investment in a project as calculated from cash inflows. In case off an annuity the

pay back period can be found by dividing initial investment by annual cash inflow. For a

mixed stream of inflows the yearly cash inflow must be accumulated until the initial

investment is recovered.

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Decision Criteria

When pay back period is used to make accept/reject decision, the decision criteria are as

follows:

• If the Pay back period is less than the maximum acceptable Pay back period set

by management accepts the project.

• If the pay back period is greater than the maximum acceptable pay back period,

reject the project

The length of the maximum acceptable pay back period is subjectively determined by

management based on factors such as the type of project (i.e. replacement or expansion),

the risk of the project, and the perceived relationships between pay back period and share

values, past experiences and future prospects. It will be the length of time management

feels results in good value-creating investment decisions.

Calculating Pay Back Period for MALI Limited

For project a (annuity Stream)

Pay back period = 1442 = 3.0 years

For project B (a mixed stream), the initial investment of Sh.45million will be recovered

between the 2nd and 3rd year-ends.

Year Cash flow (Sh) Cumulative cash flow (Sh.)

1 28million 28million

2 12million 40million

3 10million 50million

4 10million 60million

5 10million 70million

Pay back period years5.21052 =+

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Only 50% of year 3 cash inflows of Sh.10million are needed to complete the pay back

period of the initial investment ofSh.45million. Therefore pay back period of project B is

2.5 years.

If MALI Ltd.’s maximum acceptable Pay back period was 2.75 years, Project A would be

rejected and project B would be accepted. If projects were being ranked, Project B would

be preferred.

5.3.1.1 Strengths and Weaknesses of the Pay Back Period

Method

The Pay back period is widely used by (1) large firms to evaluate small projects; (2)

small firms to evaluate most projects.

Advantages of the pay back period. The pay back period boasts the following strengths:

- Is simple and has intuitive appeal

- It considers cash flows rather than accounting projects

- Can be viewed as a measure of risk exposure

- can be used as a supplement to other sophisticated techniques

Weaknesses of the pay back period. The method suffers from the following

shortcomings:

1. The benchmark Pay back period used is merely a subjectively set number y

management (the maximum number of years management decides cash flows

must breakeven – no link to wealth maximization).

2. Fails to take fully into account time factor in the value of money. This weakness

can be demonstrated using the following example.

Example

A company is considering two projects, Project Gold and Project Silver, whose relevant cash flows are given below. Project GOLD Project SILVER

Initial Investment Sh. 50million Sh.50 million

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________________________________________________________________________

Year Cash flows (Sh.)

1 5 million 80 million

2 5 million 2 million

3 40 million 8 million

4 10 million 10 million

5 10 million 10 million

Pay back period 3 years 3 years

Both projects have 3-year Pay back periods but more of the Sh.50million of the initial

investment in project Silver is received sooner than is recovered for project Gold

within the 3-year Pay back periods.

3. Failure to recognize cash flows after the pay back period.

Example

Take the following data for two projects, X and Y.

X Y

Initial Investment Sh.10million Sh. 10million

Year Cash flow

1 Sh.5million Sh.3 million

2 5 million 4million

3 1 million 3million

4 0.1 million 4million

5 0.1 million 3 million

Pay back period 2 years 3 years

Strict adherence to pay back period suggests that project X be preferred. But we looked

beyond Pay back period we see that Project X returns a paltry Sh.1.2million while project

Y would bring in Sh.7million.

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5.3.2 Net Present Value (NPV)

A sophisticated capital budgeting technique; found by subtracting a project’s initial

investment from present value of its cash inflows discounted at a rate equal to the firms

cost of capital.

NPV = PV of cash inflows – Initial Investment (II)

NPV = )(1 )1(

InvestmentInitialIIn

tt

t

kCF∑+=

− (6.1)

= IIn

ttkt PVIFCF −∑

=1,*

Decision Criteria

When NPV is used to make accept – reject decisions, the decision criteria are as follows:

• If the NPV is greater than 0, accept the project

• If the NPV is less than 0, reject the project.

If NPV > 0, the firm will earn a return greater than its cost of capital, thereby enhancing

the market value of the firm and shareholders wealth.

Calculating NPV for MALI Limited.

Project A

Annual Cash inflow (annuity) Sh.14million

PVIFA 10%, 5 years (table A-4) * 3.791

PV 53.074million

Less initial Investment 42.million

Net Present Value 11.074million

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Project B

Year Cash Inflows PVIF PV

1 28million .909 25.452m

2 12m .826 9.912m

3 10m .751 7.510m

4 10m .683 6.830m

5 10m .621 6.210m

Present Value 55.914m

Less initial investment 45.000m

NPV 10.912m

5.3.3 The Internal Rate of Return (IRR)

Probably the most sophisticated capital budgeting technique, the internal rate of return

(IRR) is the discount rate that equates the PV of cash inflows with the initial investment

associated with the project (thereby causing NPV = 0). In other words, it is the compound

annual rate of return , which would cause the investor to be indifferent between investing

in the project and not investing in it.the firm will earn if it invests in the project and

received the given cash flows.

Mathematically, the IRR is found by solving the following equation for k

)(1 )1(

InvestmentInitialIIn

tt

t

kCF∑+=

=

Decision Criteria The IRR is used to make accept-reject decision as follows:

If the IRR is greater than the cost of capital, accept the project.

If the IRR is less than the cost of capital, reject the project.

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The decision rule guarantees that the firm earns at least its required return (cost of

capital) which should enhance its market value and the wealth of its owners.

Calculating the IRR

It is not usually a simple matter to determine the internal rate of return of an investment

without a financial calculator, a computer, or solving high order equations. In practice, a

method of approximation (Trial and error) which gives answers accurate to two decimal

places in the percentage figure is employed.

Trial and Error Approach

For an annuity calculating the IRR is considerably easier than calculating it for a mixed

stream of operating cash inflows. The steps of the trial and error process are as follows:

(1) Calculate Pay back period for the project

(2) Find, from PVIFA, tables for the life of the project, the PVIFA closest to the Pay

back period calculated in (1) above.

(3) The discount rate associated with the factor is the project’s IRR

For Mali Company Project A has an annuity stream

Payback period = 42,000,000/14,000,000 = 3.000.

According to table of PVIFAs (Table A4), the PVIFA closest to 3.000 for 5years, is

3.058 (for 19%) and 2.991(for 20%). The value closest to 3.000 is 2.991; therefore,

the IRR of the project A, to the nearest 1%, is 20%.

Interpolating = %)19%20%(1*99.2058.3991.2000.320 −

−−

− , will give a more accurate IRR

of 19.86%.

Since the cost of capital for Mali Ltd is 11% the project is acceptable.

For Mixed cash flow Stream Steps.

Project B has a mixed operating cash flow stream. Having already worked out the

project’s NPV at the discount rate of 11% to be Sh.10.922 million, the discount rate that

should result to zero NPV would have to be considerably higher than 11%.The trial and

error steps proceed as follows, and are summarized in Table 5.4 below.

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We try first a discount rate of 20%, which gives an NPV of Sh.1,282,000. We have to try

a higher rate, say, 21%. The NPV is Sh.+494,000. A higher discount rate of 22% makes

the NPV to turn negative to Sh. -256,000. The IRR lies between 21% and 22%: to the

nearest 1% it is 22%

We can interpolate to get a more accurate rate. %66.21256494

256022 =−−

−+

Table 5.4: determining IRR through trial and error process

Try 20% Try 21% Try 22%

Year CFs PVIF PV PVIF PV PVIF PV

0 -45m 1.000 -45m 1.000 -45m 1.000 -45m

1 +28m .833 +23.324m ..826 +23.128m .820 +22.96m

2 12m .694 +8.328m .683 +8.196m .672 +8.064m

3 +10m .579 +5.79m .564 +5.640m .551 +5.510

4 +10m .482 +4.82m .467 +4.670 .451 +4.410m

5 +10m .402 +4.02m .386 +3.860 .370 +3.700

+1.282 +.494 -.256

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5.3.4 NPV Profile

In general the NPV and the IRR methods lead to the same accept reject decision. The

graph

Discount rate

IRR

NPV

Shows the relationship between NPV and discount k.. When discount rate is zero NPV is

simply total cash inflows less total cash outflows. (The highest NPV will occur with 0%

discount rate). As the discount rate increases, the NPV falls and the graph slopes

downwards to the right. When the curve intersects the horizontal axis NPV is zero and

the discount rate at this point, by definitions, represents the IRR.. For discount rates

higher than the IRR, the NPV is negative. It is clear from the profile that the NPV rule

will be consistent with the IRR decision rule: If the cost of capital (required rate of

return) is less than the IRR, the project will be accepted because NPV is positive. For

required rates greater than the IRR we would reject project because the NPV would be

negative.

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5.3.5 Profitability Index

The profitability index (PI) or benefit – cost ratio of a project is the ratio of the PV of

future net cash flows to the initial cash outlay. It can be expressed as

IIPIn

tt

t

kCF /

1 )1(∑

+=

= , where II is the initial outlay.

Acceptance Criterion. As long as the PJ is 1.00 or greater the investment proposal is

acceptable. For most projects, the NPV method and the PI method give the same

accept/reject signals.

Using Mali Ltd examples the PIs of the two projects are:

Project A, 26.1000,000,42000,074,53)(

===estmentInitialInv

CFsPVPI .

Project B, 24.1000,000,45000,914,55)(

===estmentInitialInv

CFsPVPI .

Both projects are acceptable as their Profitability indexes are greater than 1.0. However,

Project A is marginally better than Project B.

5.4 POTENTIAL DIFFICULTIES IN USING DISCOUNTED CASH FLOW METHODS

For a single conventional, independent projects, the IRR, NPV and PI methods lead

us to make similar accept/reject decision. Various types of circumstances and

projects differences can cause ranking difficulties. Four situations that could cause

inconsistencies arise: (1) when funds are limited necessitating capital rationing and,

(2) when ranking two or more project proposals with varied lives, (3) when ranking

two or more projects with different Investment scales, and (4) when projects have

opposite cash flow patterns.

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5.4.1 Capital Rationing

Occurs any time there is a budget constraint or ceiling on the amount of money that can

be invested during a specific period of time (For example, the company has to depend on

internally-generated funds because of borrowing difficulties, or a division can make

capital expenditures only up to a certain ceiling).

With capital rationing, the firm attempts to select the combination of investments that

will provide the greatest increase in the firm of the value subject to the constraining limit.

Example

Assume your firm faces the following investment opportunities:

Project Initial Cash Flows IRR NPV PI

Shs.000 Sh.000

A 50,000 15% 12,000 1.24

B 35,000 19 15,000 1.43

C 30,000 28 42,000 2.40

D 25,000 26 1,000 1.04

E 15,000 20 10,000 1.67

F 10,000 37 11,000 2.10

G 10,000 25 13,000 2.30

H 1,000 18 100 1.10

If the budget ceiling for initial cash flows during the present period is Shs.65,000,000 and

the proposals are independent of each other, your aim should be to select the combination

projects that provide the highest in firm value the Shs.65 m can deliver.

Selecting projects in descending order of profitability according to various discounted

cash flows methods, which exhausts Sh.65 million reveals the following:

Using the IRR Using the NPV

Project IRR NPV Initial outlay Project NPV Initial flow

Sh 000 Shs.000 Sh 000 Sh.000

A 37% 11,000 10,000 C 42,000 30,000

B 28 30,000 30,000 B 15.000 35,000

C 26 25,000 25,000 57,000 65,000

54,000 65,000

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Using the PI

Project PI NPV Initial outlay

Sh000 Sh000

C 2.40 42,000 30,000

G 2.30 13,000 10,000

F 2.10 11,000 10,000

E 1.67 10,000 15,000

76,000 65,000

With capital rationing you would accept projects C, E, F and G which deliver an NPV of

Sh.76million. The universal rule to follow is “When operating under a constraint, select

the projects that deliver the highest return per shilling of the constraint (the initial

investment outlay)”. Put another way, select that mix of projects that gives you “the

biggest bang for the buck”. We achieve this buy employing the profitability index which

ranks projects on the basis of the return per shilling of initial investment outlay.

Under conditions of capital rationing it is evident that the investment policy is less than

optimal – Optimal policy requires that no positive NPV projects be rejected.

5.4.2 Scale Differences

Example Suppose a firm has two mutually exclusive projects that are expected to generate

following Cash flows

End of Year Project A Project B

Cash flows (Sh) Cash flows (Sh)

0 -1000,000 -100,000,000

1 0 0

2 400,000 156,250,000

If the required rate of return is 10% the NPV, IRR and PI of the projects are as below:

IRR NPV PI

Sh000

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Project A 100% 231 3.31

Project B 25% 29,132 1.29

Ranking of projects based on our results

RANKING IRR NP PI

1st A B A

2nd B A B

Using the IRR and PI shows preference for project A, while NPV indicates preference

for Project B. Because IRR and PI are expressed as a proportion the scale of the project is

ignored. In contrast results of NPV are expressed in absolute shilling increases in value of

the firm. With regard to absolute increase in value of the firm, NPV is preferable.

5.4.3 Differences in Cash Flow Patterns (Multiple IRR) Example Assume a firm is facing two mutually exclusive projects with following cash flow

patterns.

End of year Project C Project D

Cash flows Cash flows

Sh000 Sh000

0 -1,200 -1,200

1 1,000 100

2 500 600

3 100 1,080

Note that project C’s cash flows decrease while those of project D increase over time.

• The IRR for projects are as follows

Project C - 33%

Project D - 17%

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• For every discount rate> 10% project C’s NPV and PI will be> than project D’s.

• For every discount rate < 10% project D’s NPV and PI will > project C’s.

K<10% K>10%

RANKING IRR NPV PI NPV PI

1st C D D C C

2nd D C C D D

When we examine the NPV profiles of the two projects, 10% represents the discount rate

at which the two projects have identical NPVs. This discount rate is referred to as

Fisher’s rate of intersection. On one side of the Fisher’s rate it will happen that the

NPV and PI on one hand, and the IRR on the other give conflicting rankings.

We observed conflict is due to the different implicit assumption with respect to the

reinvestment rate on intermediate cash flows released from the project. The IRR

implicitly assumes that funds can be reinvested at the IRR over the remaining life of the

project. With the IRR the implicit reinvestment rate will differ from project to project

unless their IRRs are identical.

For the NPV and PI methods assume reinvestment at a rate equal to the required rate of

return as the discounts factor. The rate will be the same for all projects.

Since the reinvestment rate represents the minimum return on opportunities available to

the firm, the NPV ranking should be used. In this way, we identify the project that

contributes most to shareholder wealth.

5.4.4 Differences in Project Lives

When projects have different lives, a key question is what happens at the end of the short-

lived project? Two alternatives assumptions can be considered. (1) Replace with (a)

identical project or (b) a different project. (2) Do not replace. The Do not replace

alternative is considered first.

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Example

Suppose you are faced with choosing between 2 mutually exclusive investments X and Y

that have the following Cash flows.

End of year Project X Project Y

Cash flows Cash flows

Sh. ‘000’ Sh. ‘000’

0 - 1000 - 1000

1 0 2000

2 0 0

3 3,375 0

If the required rate of return is 10% we can summarize our investment appraisal results as

follows:

IRR NPV PI

Sh000

X 50% 1536 2.54

Y 100% 818 1.82

RANKING

Rank IRR NPV PI

1st Y X X

2nd X Y Y

Once again a conflict in ranking arises. Both the NPV and the PI prefer project X to Y,

while The IRR criterion choose Y over X.

Again, in this case of no replacement, the NPV method should be used because it will

choose projects that add the greatest absolute increment in value to the firm.

Replacement Chain When faced with a chose between mutually exclusive investments

having unequal life that will require replacement, we can view the decision as one

involving a series of replications – or a replacement chain – of respective alternatives

over some common investment horizon.

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Repeating each project until the earliest rate that we can terminate each project in the

same year results in a multiple like-for-like replacement chains covering the shortest

common life. We solve the NPV for each replacement chain as follows:

NPV chain =

Where n = single replication project life in years

NPV= singe replication NPV for a project with n- year

R = umber of replications needed

K= discount rate

The value of each replacement chain therefore is simply the PV of the sequenced of NPV

, generated by the replacement chain.

Example

Assume the following regarding mutually exclusive investments alternatives A and B,

both of which requires future replacement

Project A project B

Single replication life (n) 5 years 10 years

Single replication PV calculated at project

specific required rate of return (NPVn) Sh. 5,328 Sh. 8000

Number of replication to provide shortest common life 2 1

Project specific discount rate 10% 10%

At first glance project B looks better than project A (8000 Vs 5328). However the need to

make future replacements dictates that we consider values provided over same common

life i.e. 10 years. The NPV can then be re-worked as follows

NPV for first 5 years = 5328

NPV for replicated project=5328* = PVIF yrs5%,103303

NPV of chain 8638

123

The NPV of project B is already known i.e. Sh. 8000. Comparing with Sh. 8638 present

value of the replacement chain, project A is preferred.

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REVIEW QUESTIONS

1. Define, and differentiate between each of the following sets of capital

budgeting terms; (a) independent vs. mutually exclusive projects (b) unlimited

funds vs. capital rationing (c ) accept/reject vs. ranking approaches (d)

conventional vs. non conventional cash flow patterns. (e) annuity vs. mixed

stream cash flows (f) Bank vs. opportunity cost (g) incremental cash flows vs.

irrelevant cash flows.

2. Describe each of the following input to the initial investment, and show how

the initial investment is calculated by using them. (a) cost of new assets (b)

installation cost (c) proceeds from sale of old asset (d) tax on sale of old

asset; and (e) change in net working capital.

3. What is the terminal cash flow? Explain its determination in a replacement

decisions.

4. What is the internal rate of return (IRR) on an investment? How is it

determined?

5. Do the net present value (NPV) and internal rate of return (IRR) always agree

with respect to talking decisions? Explain.

6. What is capital budgeting?

7. What are the key motives for making capital expenditure?

8. Why does capital budgeting rely for analysis purposes on cash flows rather than net income.

PROBLEMS 5.1 The Mbuni Glass Company uses a process of capital rationing in its decision making

.The firm’s cost of capital is 13% . The company will only invest Sh. 60 million this year. It has determined the internal rates of return for the following projects.

Project Project Size(Shs ‘millions’) Internal rate of return A 10 15% B 30 14% C 25 16.5% D 10 17% E 10 23% F 20 11% G 15 16% Required

(a) Pick the projects that the firm should accept.

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(b) If projects D and E were mutually exclusive, how would that affect your overall answer in (a) above.

5.2 Maringo Ltd.'s chief financial officer (CFO) expects the firms profits after taxes for the next 5 five years to be as follows.

Year Net profits after taxes (Shs ‘millions) 2008 100 2009 150 2010 200 2011 250 2012 320

The CFO is beginning to develop the relevant cash flows needed to analyze whether to renew or replace the company’s only depreciable asset, a machine that originally cost Sh.30 million, has a current book value of zero, and can now be sold for Sh.20 million. He estimates that at the end of 5 years the existing machine can be sold to net Sh.2 million before taxes. The CFO plans to use the following information to develop the relevant cash flows for each of the alternatives. Alternative I: Renew the existing machine at a total depreciable cost of Sh.90 million. The renewed machine will have a 5 year useful life and be depreciated on straight line basis with a salvage value of Sh.10 million. The renewal decision could result in the following projected revenues and expenses (excluding taxes). Year Revenue (millions) Expenses (excldg. Dep’n) (millions2008 1,000 801 2009 1,175 884 2010 1,300 918 2011 1,425 943 2012 1,550 968 The renewed machine would result in an increased investment of Sh.15 million in net working capital. Alternative II: Replace the existing machine with a new machine costing Sh.100 million and requiring installation cost of Sh.10 million. The new machine would have a usable life of 5 years and a salvage value after 5 years of Sh.20 million before taxes. The firm’s projected revenues and expenses (excluding depreciation) if it acquires the machine, would be as follows: Year Revenue ( Shs ‘millions) Expenses (Shs ‘millions) 2008 1,000 764 2009 1,175 839 2010 1,300 914 2011 1,425 989 2012 1,550 998 The new machine would result in an n increased investment of Sh.22 millions in net working capital. The firm is subject to 40% tax on both ordinary income and capital gains>

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Required a. Calculate the initial investment associated with each alternative b. Calculate the incremental operating cash flows associated with each

alternative c. Calculate the terminal cash flows at the end of year 5 associated with

each alternative. d. Based solely on the cash flows (without discounting) which alternative

appears to be better? Why? 5.3 Pima Watch Company Ltd. is considering an investment of Sh.1,500,000, which

produces the following inflows. Year Cash flow

1 Sh.800,000 2 700,000 3 400,000

You are going to use the net present value profile to approximate the value for the internal rate of return. Follow the following steps. (a) Determine the net present value of the project based on a zero discount rate. (b) Determine the net present value of the project based on a 10% discount rate. (c) Determine the net present value of the project based on a 20% discount rate. (d) Draw the NPV profile of the project and observe the discount rate at which the

NPV is zero. This is an approximation of the IRR of the project. (e) Actually compute the IRR by interpolation and compare your answer to the

answer to part (d). 5.4 Waziri Industries is currently analyzing the purchase of a new machine costing

Sh.16,000,000 and requiring Sh. 2,000,000 in installation costs. The use of this machine is expected to result in an increase in net working capital of Sh.3,000,000 to support the expanded level of operations. The firm will write down the installed cost of the machine at a rate of 20% per annum for tax purposes and expects to sell the machine to net Sh.1,000,000 before taxes at the end of its usable life. The firm is subject to 30% tax rate on both ordinary income and capital gains.

Required (a) Calculate the terminal cash flow for a usable life of (1) 3 years (2) 5

years, and (3) 7years. (b) Discuss the effect of usable life on terminal cash flows using your findings

in (b). (c) Assuming a 5 year usable life, calculate the terminal cash flows if the

machine were sold to net (1) Sh.900,000 (2) Sh.17,000,000 before taxes at the end of 5 years.

(d) Discuss the effect of sale price on terminal cash flows using your findings in (c).

5.5 A machine currently in use was purchased two years ago for Sh.4 million. The machine is being depreciated on a straight line basis to write off the cost over a 5 year usable life. The current machine can be sold today to net Sh.3.6 million. After

127

removal and cleanup costs. A new machine with a three year usable life can be purchased today at a price of Sh.14 million. It requires Sh.1 million to install and has a usable life of 3 years. If the new machine were acquired the investment in accounts receivable will increase by Sh.1 million and inventory investment will rise by Sh 2.5 million., and accounts payable would increase by Sh.1.5 million. Profits before depreciation and taxes are expected to be Sh.7 million for each of the next 3 years with the old machine and Sh.12 million in the first year and Sh.13 million for each of the next 2 years with the new machine. At the end of the next 3 years the market value of the old machine will equal to zero, but the new machine will be sold to net Sh.3.5 million before taxes. Both ordinary corporate income and capital gains are taxed at the rate of 30%.

Required (a) Determine the initial investment associated with the proposed

replacement. (b) Calculate the incremental cash flows associated with the replacement

decision for the next 3 years. (c) Calculate the terminal cash flows associated with the replacement

decision. (d) Depict on a time line the relevant cash flows found in (a), (b) and (c)

associated with the proposed replacement decision. 5.6 Molo Limited is developing the relevant cash flows associated with the proposed

replacement of an existing machine tool with a technologically advanced one. Given the following costs associated with the replacement decision explain whether each could be treated as a sunk or opportunity cost.

(a) Molo would be able to use the same tooling it had used on the old machine (which has a book value of Sh.4 million) for the new machine.

(b) Molo would be able to use its existing computer system to develop programs for operating the new machine tool. The old machine tool did not require these programs. Although the firm’s computer system has excess capacity the capacity could be leased to another firm for an annual fee of Sh.1.7 million.

(c) Molo would have to acquire additional space to accommodate the new larger machine tool. The space that would be used is currently being leased to another company for Sh.1 million.

(d) Molo would use a small storage facility to store the increased output of the new machine tool. The storage facility was built by Molo at a cost of Sh.12 million 3 years ago. Because of its unique configuration and location, it is currently of no use to either Molo or any other company.

(e) Molo would retain an existing overhead crane which it had planned to sell for its Sh. 18 million market value. Although the crane was not needed with the old machine it will be used to position raw materials on the new machine tool.

5.7 Bidii Limited is in the process of choosing the better of two equal risk, mutually exclusive, capital expenditure projects. The relevant cash flows for each project are shown below. The firm’s cost of capital is 14%.

Year Project M Project N 0 (Initial investment) -Sh.28,500,000 -Sh.27,000,000 1 (Operating cash flows) +Sh.10,000,000 +Sh.11,000,000

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2 . +Sh.10,000,000 +Sh.10,000,000 3 +Sh.10,000,000 +Sh.9,000,000 4 +Sh.10,000,000 +Sh.8,000,000 Required

(a) Each project’s pay back period (b) The NPV for each project (c) The IRR for each project (d) Summarize the decision criterion for each measure calculated above. (e) Draw the NPV profiles for each project on the same axes and explain

circumstances under which conflicts in ranking may arise. 5.8 Magarini Limited is considering two mutually exclusive projects. The firm which has

a cost of capital of 12% t\has estimated the following cash flows. Year Project A Project B 0 (Initial investment) -130 million -85 million 1 (Operating cash flows) 25 million +40 million 2 35 million +35 million 3 45 million +30 million 4 50 million +10 million 5 55 million +5 million Required

(a) NPV of each project (b) IRR of each project (c) Draw NPV profile of each project on same axes. (d) Evaluate and discuss the ranking of the projects based on your findings above. (e) Explain your findings in (d) in light of the pattern of cash flows associated

with each project. 5.9 Mzima Limited is considering the purchase of a new printing press. The total

installed cost of the printing press is Sh 22 million. This outlay could be partially offset by the sale of an existing press, which has a book value of nil, was purchased at Sh.10 million10 years ago and could be sold to fetch Sh. 12 million currently before taxes. As a result of the new press sales for each of the next 5 years are expected to increase by Sh. 16 million, but product costs (excluding depreciation) will represent 50% of the sales. The new press will not affect the firm’s working capital requirements. The new press will be write-down on declining balance for a period of 5 Years. Assume a tax rate of 40%. Required

(a) Determine the initial investment (b) Operating cash flows attributable to the new press (c) The pay back period. The NPV and the IRR related to the proposed

new press. (d) Make a recommendation to accept or reject the new press and justify

your answer. 5.10 Mugoya Limited, a large machine shop, is considering replacing one of its lathes with either of two new lathes, Bingwa or Hodari. Bingwa is highly automated , computer controlled lathe; Hodari is a less expensive lathe that uses standard technology. A

129

financial analyst has prepared estimates of the initial investment and incremental cash flows associated with the two lathes as shown below. Year Bingwa (Shs, “millions”) Hodari (Shs. “millions”) 0 (Initial investment) -660 -360 1 (Operating Cash flows) +128 +88 2 +182 +120 3 +166 +96 4 +168 +86 5 +450 +207 Fifth year cash flows include the salvage value of the lathes. Mogaya’s cost of capital is 13% and is in the 40% tax bracket and requires all project to have a maximum payback period of 4 years. Required

a. Determine the pay back period for each lathe b. Assess the acceptability and ranking using (1) NPV and (2) IRR c. Summarize project rankings according to the 3 techniques above. Is there any

conflicts d. Which lathe should ultimately be accepted? Why?

130

LECTURE SIX

INTEREST RATE FUNDAMENTALS AND COST OF

CAPITAL

6.0 INTRODUCTION

For economic growth, controlled inflation and full employment in our economy, funds

(money) must flow from savers (suppliers) to investors (demanders). This occurs

through the medium of financial institutions and markets. The interest rate (cost of

money) prevailing in the economy acts as regulating mechanism that control the flow of

these funds from the surplus units (savers) to the deficit units (borrowers). Generally, the

lower the interest rate the greater the flow of funds and the greater the economic growth.

When funds are obtained by selling an ownership interest (equity) the cost to the issuer

(demander) is commonly called the required rate of return.

Objectives At the end of the lecture students should be conversant with: 1. Interest rate fundamentals and term structure of interest rate 2.Sources and costs of long term capital 3. Weighted average cost of capital (WACC) and weighted marginal cost of capital (WMCC) 4. Financing and investment decisions using IOS and WMCC schedules1.

6.1 Interest Rate Fundamentals

Interest rate is the compensation paid by the borrower of funds to the lender, from the

borrower’s perspective it is the cost of funds.

The nominal rate is the actual rate of interest charged by the supplier of funds and paid by

the demander. The nominal rate encompasses:-

i) The real rate

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ii) The inflation premium and,

iii) The risk premium.

This can be expressed as

Ki = K* + IP + RPi ------ (I)

Where

Ki is the nominal rate of interest

K* is the real rate of interest

IP is the risk premium

RPi is the risk premium

Real Rate

This is the rate that creates equilibrium between the supply of savings and the demand for

investible funds in a perfect world, without inflation; where fund suppliers and

demanders have no liquidity preference, and where all outcomes are certain. The real

rate of interest is the most basic cost of money.

Figure 1 below shows that the real rate of interest is an equilibrium for funds (So = D)

and occurs at rate of interest of Ko.

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Real rate of interest

K2 K0

K1

S1

S1

S0

S0

Funds supplied (demanded)

Changing economic conditions, lasts and preference can cause the real interest level to

rise or fall. For example, a trade surplus could shift the supply function of money

downwards and cause the real rate of interest to fall to a new level of K1. (On the other

hand an increase in taxation my shift the supply curves upwards occasioning a rise in real

rate of interest to K2.

Inflationary Premium

The premium for inflationary premium represents the average rate of expected inflation

over the life of a loan or investment. A rise in the inflation rate depreciates the value of

money: suppliers of money will demand a higher compensation in nominal terms

resulting in higher premium for inflation. Factors that cause inflationary pressure such as

government fiscal policies, consumer tastes, costs of raw materials and political events

impact the inflationary premium.

Risk Premium

The risk premium consist of a number of issuer and issue related characteristics including

default risk, maturity risk, liquidity premium, contractual provisions and tax risk. The

highest premium for risk comes with high risk of default, long term maturity, unfavorable

contractual provisions and strongest tax conditionalities defined as the required return on

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a risk free asset (91 day treasury bills). It embodies the real rate of interest plus

inflationary expectation. It can be represented as:-

RF = K* + IP …………………..2

Recall equation (1) giving as the nominal rate of interest. Introducing RF, the equation

can be rewritten as:-

Ki = RF + RPi

Thus the nominal rate of interest has two basic components; the risk free rate and the risk

premium. For a risky assets, therefore the real rate of interest could be estimated by:-

K* = RF – IP

6.1.1 TERM STRUCTURE OF INTEREST RATES

Definition: For bonds of similar risk the term structure of interest rate relates the interest

rate or required rate of return to the time to maturity of the securities.

Yield to Maturity (YTM)

The annual rate of interest on a security purchased on a govendary and Yield to Maturity

(YTM). The yield to maturity, Ki is computed exactly in the same way you would solve

for the internal rate of return (IRR) on a security. A bond that promises to pay 15%

coupon at end of each year for 3 year, then pay a face-value of Kshs1,000. If the current

market price is obscured to be Sh.977.54 then the YTM can be found by solving fork d,

in the following expression.

977.54 = ∑++=

+3

13)1()1(

1000150t

t

kk dd

k d can through trial and error determined to be 16%. This is the security’s yield to

maturity.

134

Yield Curves

It is a graph of the term structure of interest rates that depict the relationship between the

yield to maturity of a security of (y axis) and the time to maturity (x – axis): It shows the

pattern of interest rates on securities of equal quality but different maturities. We have 3

zero coupon bonds that pay a force value of Kshs1,000 upon maturity. The three bonds

have maturities of one, two and three years and are observed to have a current market

price of Kshs826.45, 718.18 and 640.66 respectively.

The implied yields to maturity can be found by solving for k d in the following

relationship, )1(0

kB

d

Mn+

=

For the three bonds are the YTMs are:-

One year bond 21%

Two year bond 18%

Three year bond 16%

135

We can plot a yield curve relating yields to maturity with time to maturity as below:-

Yield curve

Time of maturity 1 2 3

The yield curve could take several forms;

1. Invested yield curve - is a downward sloping yield curve that indicates generally

cheaper long term borrowing costs than short term borrowing costs.

2. Normal yield curve – an upward sloping yield curve that indicates generally

cheaper short term borrowing costs than long term borrowing costs.

3. Flat yield curve – a yield curve that reflects relatively similar borrowing costs for

both short and long term loans.

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Inverted Flat

Time to maturity Time to

maturity Time to maturity

YTM YTM YTM

Normal

The shape of the yield curve provides useful insights into future interest rate expectations

which could affect a firm’s financial decisions. When a firm is faced with a downward

sloping curve a financial manager is likely to rely on long term financing. When the

yield is upward sloping the manager will use cheaper short term financing.

6.2 THEORIES OF TERM STRUCTURE

The theories of term structure attempt to explain why yield curves take on different

shapes. Three theories are the expectation hypothesis, liquidity preference theory, and

market segmentation theory.

Expectation hypothesis

This hypothesis suggests that the yield curve reflects investor’s expectations about future

interest rates. For example, differing inflation expectations associated with different

maturities will cause nominal interest rates to vary. An increasing inflation expectations

results in an upward sloping yield curve; a decreasing inflation expectation results in

downward sloping yield curve and a stable inflation expectation results in a flat yield

137

curve. The observed strong relationship between inflation and interest rates supports this

widely accepted theory.

Liquidity preference theory -

It suggest that for any issuer, long term interest rates tend to be higher than short term

rates due to the lower liquidity and higher responsiveness to general interest rate

movement of longer term securities.

This happens because:-

i) Investors perceive less risk in short term securities than in longer term

securities because short term securities are more liquid.

ii) Borrowers are generally willing to pay higher rate for long term funds because

they are saved the need to arrange roll over of short term debt – may be at a

higher interest rate. In general therefore, longer maturities tend to call for

higher interest rates than shorter maturities.

Market Segmentation Theory.

The theory suggests that the market for loans is segmented on the basis of maturity and

that the supply of, and demand for loans within each segment determine the prevailing

interest rate. The scope of the yield curve will be determined by the general relationship

between the rates prevailing in each segment. Modigliani and Sutch (1966) argue that

there is relatively little substitution between assets of different maturities because

investors have preferred “habitats”. The equilibrium between suppliers and demanders of

short term funds (seasonal business loans) would determine prevailing short term rates

and the equilibrium suppliers and demanders of long term funds (real estate loans) would

determine prevailing long term rates. Therefore low rates in the short term segment and

high rates in the long term segment should cause the yield curve to be upward sloping,

vice versa.

138

6.3 COST OF CAPITAL

Cost of capital acts as a major link between the firm’s investment decision and the wealth

of the owners of a firm. It is the ‘magic number’ that is used to decide whether a

proposed corporate stock price. Our concern is with long-term sources, which supply the

permanent financing.

Definition

Cost of capital can be defined as the rate of return that a firm must earn on its project

investments to maintain the market value of its shares. Or,

As the minimum rate of return required by suppliers of capital firm to attract their

funds to the firm.

If risk is held constant, projects with rate of return above the cost of capital will increase

the value of the firm, vice versa.

Cost of capital and risk

The following equation explains the general relationship between risk and financing

costs.

Kfpbprk iifi ++= 1

Where:

ki = specific cost of the type of long term financing

r f = risk free cost of the given type of financing

bpi = business risk premium of firm i

fpi = financial risk premium faced by firm i

The equation indicates that the cost of each type of capital depends on the risk free cost

of that type of funds, the business risk of the firm and the financial risk of the firm.

139

Business risk is the risk to the firm of being unable to cover operating costs. Financial

risk is the risk of the firm of being unable to cover required

6.3.1 SPECIFIC SOURCES OF CAPITAL

The right hand side of the balance sheet comprises current liabilities, long-term debt,

preferences shares capital, and ordinary share capital. Our concern is only with the long-

term sources of funds because they supply the permanent financing.

COST OF DEBT

Before tax cost of debt

The before tax cost of debt can be derived by solving for the discount rate k d, that

equates the market price of the bond with present value of cash flows from the bond over

its life (interest plus principal payments). This is the same as funding the internal rate of

return (IRR) on the bond’s cash flows.

This cost,k d, also know as the yield to maturity can be calculated by using the formula

∑+=

+=

n

tt

tto

kPIBd1 )1(

Where , is the current market price of bold (net proceeds (minus any flotation

costs).

B0

Pt and I t are the payment of principal and interest in period t .

If principal payment occurs only at maturity and if the interest payments are constant the

relationship would simplify to: -

∑++=

+=n

tnto

kkB

d

M

d

I1 )1()1(

140

Where M is the payment at maturity and I is the periodic interest payment.

By solving fork d, the discount rate the equates the present value of cash payments to

suppliers of debt to current market price of debt, we find the rate of return required by

the lenders.

Example

A company intends to sale a bond to raise capital. The features of the bond are:

Par value Kshs. 1,000

Coupon rate 9%

Discount on issue Kshs. 20

Flotation cost 2% of par value

Find the cost of debt financing

Soution

Net proceeds of from sale of bond = 1000 – 20 – 2% x 1000 = 960

The cash flows associates with ABC Company’s bond issue are as follows

End of year CF

0 +960

1 – 20 -90

20 -1000

We work out the cost of debtk d, through trial and error. The discount rate must be

higher than the 9% (because 960 < 1000, the par value. The present value at a k d of

9% is Sh. 1000, same as par value. Lets try 10%.

The present value of cash flows is given by

90* =Sh. 915.26. PVIFPVIFA yrsyrs 20%,1020%,10*1000+

141

Because 960 is between 1000 and 915.26 the k d must be between 9% and 10%. It is

however 9% to the nearest whole %,

By using interpolation the bond’s before tax cost is

%47.98540%9 =+

k d = 9.47

After tax cost of debt

The specific cost of financing must be selected on an after tax basis. Because interest on

debt is tax deductible it reduces taxes by an amount equal to the product of the interest

payment and firms tax rate. The after-tax cost of debt will be substantially lower than the

before –tax cost and will be given by )1( Tkk di−=

Where k d is the before tax cost of debt and is T is the firms tax rate.

If the ABC Co is in the 40% tax bracket, the after tax cost of debt will be

9.47 x (1-0.4) = 9.47 x 0.6

= 5.68%

Typically the explicit of debt is less than the cost of alternative forms of long term

financing primarily because of the tax deductibility of interest. The higher the rate of

corporation tax is, the greater the tax benefits in having debt finance when compared

with equity finance. In the example above, if the rate of tax had been 50%, the cost of

debt would have been 9.47(1-.5) =4.74%

142

Example:

Owen Allot plc has in issue 10% debentures of a nominal value of Sh.1000. the market

price is Sh.900 ex interest. Calculate the cost of this capital if the debenture is:

a. Irredeemable;

b. Redeemable at par after 10 years.

Ignore taxation.

Solution

The cost of irredeemable debt capital is I %1.11900100

0

==BI

The cost of redeemable debt capital. The best trial and error figure to try first is, 12%.

Year Cash flow Discount PV Discount PV Factor factor 12% £ 11% £ 0 Market value (900) 1.000 (900.00) 1.000 (90.00) 1-10 Interest 100 5.650 565.00 5.889 58.89 10 Capital repayment 1000 0.322 322.00 0.352 35.20 (13.00) 40.90

The approximate cost of debt capital is, therefore %76.1100.1390.40

00.1312 =+

−

The cost of debt capital estimated above represents the cost of continuing to use the finance rather than redeem the securities at their current market price. It would also represent the cost of raising additional fixed interest capital if we assume that the cost of the additional capital would be equal to the cost of that already issued. If a company has not already issued-any fixed interest capital, it may estimate the cost of doing so by

Approximating before tax cost of debt

Therefore tax cost of debt k d, for a bond with Kshs.1000 par value center approximate

using following equation:

143

21000

1000

+

−+

=N

Nk

d

d

dn

I

Where I = annual interest payments

N d = net proceeds from sale of debt

n = number of years to bonds maturity

Substituting in previous example:

2100096020

960100090

+

−+

=kd = 9.4%.

COST OF PREFERRED STOCK

The cost of irredeemable preferred stock, is the ratio of the preferred stock

dividend to the firm’s net proceeds from sale of the preferred stock ( Market price minus

any flotation costs and discounts).

k p

NDk

p

pp=

Where cost of preferred stock, annual dividend, and the net proceeds from

sale of preference shares, excluding any flotation costs. Because preferred stock dividend

are paid out of the firm’s after tax cash flows, a tax adjustment is not required as was in

the case of debt.

k p Dp N p

Example

144

ABC Co is contemplating issuance of a 10% preferred stock expected to sell for its

Kshs.87 per share par value. The cost of selling the stock is expected to be Shs.5 per

share. Find the cost of preferred stock

Dp = 10% x 87 = Kshs.8.70

N p = 87 – 5 = Kshs. 82

%6.108270.8

==k p

COST OF ORDINARY SHARE CAPITAL

The cost of equity is the return required on by investors in the market place. The cost,

ks , is the rate at which investors discount the expected dividends of the firm to

determine its share value.

There are 2 forms of equity financing

1. Retained earnings

2. New issues of equity.

In the context of the dividend discount model approach the cost of equity ks can be

thought of as the discount rate that equates the present value of cash flows with the

current market price of the share. Recall from valuation.

∑+=

=α

10 )1(t

tt

kDP

s

Where P0 = current market price per share, is dividend expected to be paid at the

end of period t and

Dt

k sis discount rate, the cost of equity.

145

In estimating future dividend, assumptions necessary. The most frequently used

assumptions are zero growth in dividends, constant growth in dividends, and variable

growth rates.

Constant Growth Rate

If future dividends are expected to grow at a constant rate, the expression to use in

estimating cost of equity is

gg

g

kD

kDP

ss−

=−

+= 10

0

)1(

Therefore, cost of equity is ggg

PD

PDks +=+

+=

0

1

0

0 )1(

Example

ABC dividends are expected to grow at a constant rate of 5% into the foresable future.

The company has just paid dividend of Shs.3.80 and is share is selling at a market price

of Shs.50 calculate of cost of equity.

%98.1205.05099.305.0

50

)05.01(80.3 =+=++

=ks

Growth Phases

If growth in dividends is expected to vary in future a modification in the dividend model

will be in order. Usually above normal growth is followed by normal growth.

For instance, if dividend were expected to growth 15% compound rate for 5 years, at

10% for next 5 years, and the gowth at 5% rate into the firescible future the equation

would be: -

146

)1()1()10.01(

)1(15.01(

1011

5

1

10

6

500

1*05.0 kk

Dk

Dk

DPsss st t

t

t

t

t

+∑ ∑

++

++

−++=

= =

If current dividend paid is 2/= and current market price is Sh.70, the k s would be

10.42%.

Cost of Retained Earnings

The cost of retained earning, Kr, to the firm is the same as the cost of equity.

kr = k s

It is not necessary to adjust the cost of retained earnings for flotation costs because

retention is an internal financing received without incurring these costs. The cost of

retained earnings for ABC Co as calculate above for Ks.

Cost or retained earnings is always lower than cost of a new issue due to absence of

flotation costs when financing projects with retained earnings.

Cost of new issues

The cost of new issue of equity kn is determined by calculating the cost of equity net of

any discounts and associated flotation costs. Because of flotation costs and discounts the

proceeds from an issue will be less than current market price of the stock and hence its

cost will be more expensive.

The cost of new issues can be calculated by modifying equations as follows.

If net proceeds = N n i.e. ( Price - Flotation cots). The cost of equity,

under the two assumptions of no growth. and constant growth will be

147

No Growth Nk

nn

D=

With constant growth = gNDk

nn

+= 1

Example:

The Co estimates that to sell a new issue the shares will have also to be priced at Sh.47,

and in addition flotation costs of Sh..2.50 per share will be incurred. What is cost of new

issue if the company has and will experience a constant growth in dividend of 5%, and is

currently selling at a price of Sh.50. Dividend next year is expected to be Sh. 4.00 per

share.

%1405.050.247

00.4=+

−=kn

This is the value to be used in subsequent calculations of a firm’s cost of capital.

6.3.2 WEIGHTED AVERAGE COST OF CAPITAL

WACC reflects the expected average future cost of funds over the long run; found by

weighing the cost of each specific source of capital by its proportion in the firm’s capital

structure.

148

The calculation of the WACC is performed by multiplying the specific cost of each form

of financing by its proportion in the firms capital structure and summing the weighted

values

kwkwkw ssppiiWACCk ***)( ++=

Where

= proportion of long term debt in capital structure wi

= proportion of preference stock in capital structure wp

ws = proportion of equity in capital structure

wi + + = 1 wp ws

the firms equity weight is multiplied by either the cost if retained earnings ws kr or cost

of new equity kn, which cost is used depend on whether the firm’s equity will come

from retained earnings on new issues.

Example:

ABC Co costs of various types of capitals are

Cost of debt ki = 5.6%

Cost of preference = 10% k p

Cost of retained earnings kr = 13%

Cost of new equity kn = 14%

The Co target capital structure proportions are: -

149

Weight

Debt 40%

Preferred stock 10%

Equity 50%

100%

The company has a sizable amount of retained earnings that it intends to use for future

investments. Find company’s WACC

Weight Cost Weighted Cos

Debt 0.4 5.6% 2.2%

Preferred stock 0.1 10.6 1.1

Equity 0.5 13.0 6.5

9.8

WACC = 9.8%

Arguments for using WACC

The weighted average cost of capital is recommended for use in investment appraisal on

the assumptions that:

a. Net investments must be financed by new sources of funds; retained earnings, new share issues, new loans and so on;

b. The cost of capital to be applied to project evaluation must reflect the marginal cost of new capital; and

c. The weighted average cost of capital reflects the company’s long-term future

capital structure, and capital costs. If this were not so, the current weighted

average cost would become irrelevant because eventually it would not relate

to any actual cost of capital.

150

It has been argued that the current weighted average cost of capital should be used to

evaluate project, because a company’s capital structure changes only very slowly over

time; therefore the marginal cost of new capital should be roughly equal to the weighted

average cost of current capital.

If this view is correct, then by undertaking investments, which offer a return in excess of

the WACC, a company will increase the market value of its ordinary shares in the long

run. This is because the excess returns would provide surplus profits and dividends for

the shareholders.

Arguments against using the WACC

The arguments against using the WACC as the cost of capital for investment appraisal are

based on criticism of the assumptions that are used to justify use of the WACC.

The main arguments against the WACC are as follows.

a. New investments undertaken by a company might have different business

risk characteristics from the company’s existing operations. As a

consequence, the return required by investors might go up (or down) if the

investments are undertaken, because their business risk is perceived to be

higher (or lower).

b. The finance that is raised to fund a new investment might substantially

change the capital structure and the perceived financial risk of investing in

the company. Depending on whether the project is financed by equity or

by debt capital, the perceived financial risk of the entire company might

change. This must be taken into account when appraising investments.

c. Many companies raise floating rate debt capital as well as fixed interest

debt capital. With floating rate debt capital, the interest rate is variable,

and is altered every three or six months or so in line with changes in

151

current market interest rates. The cost of debt capital will therefore

fluctuate as market conditions vary. Floating rate debt is difficult to

incorporate into a WACC computation, and the best that can be done is to

substitute an ‘equivalent’ fixed interest debt capital cost in place of the

floating rate debt cost.

WEIGHTING SCHEME

Weights can be calculated based on book value or market value and using historic or

target proportions.

Book value vs. Market value

Book value weights use historical accounting values to measure the proportion of each

type of capital in the firm’s financial structure. Market value weights measure the

proportion of each type of capital at its current market value. Market value weights are

appealing, because the market value of securities closely approximate the actual shilling

amounts to be received from their sale. In addition the long term cash flows from

investments to which cost of capital is applied are estimated in terms of current as wells

future Market values.

Historic versus Target

Historic weights are either book or market value weights based on the proportions of each

type of capital in the existing capital structure while target capital structure is the desired

optimal capital structure proportions.

From a purely theoretical point of view the preferred weighting is target market value

proportion.

WEIGHTED MARGINAL COST OF CAPITAL

As volume of financing increase the cost of various types of financing will increase,

raising the firms WACC. Therefore, it is useful to calculate WMCC, which is the firms

152

WACC associated with its next shilling of total new financing. The marginal cost is the

WACC relevant to current decisions.

As larger amounts of financing are raised the greater the risk to the funds providers.

Therefore the WMCC is an increasing function of the level of total new financing.

Another factor that causes WACC to increase is that as retained earnings are exhausted

equity will have to be sourced through more expensive new issues.

Finding Breaking points

To calculate WMCC, we must calculate the breaking points, which reflect the level of

total new financing at which cost of one of the financing components rises. The

following general equation can be used to find breaking points.

BPj = Afj

Wj

Where:

BPj = breaking point for financing source j

AFj = amount of funds circulable from source j at a given cost (before BP)

Wj = capital structure weight for financing source j.

Example

ABC Co has Kshs.300,000 of retained earnings available whose cost is 13%. If it

exhausts the returned earnings it must use more expensive new issue of equity whose cost

is 14%.

The firm expects that it can borrow only Kshs.400,000 of debt at the 5.6% cost,

additional debt will have an after tax cost of 8.4%.

Unlimited amounts of funds can be raised by issuing preferred stock at cost of 10.6%

The company target capital structure proportions are:

153

Weight

Debt 40%

Preferred stock 10%

Equity 50%

100%

Required:

- Determine the breaking points

- Calculate the WMCC after each breaking point

- Draw WMCC schedule.

Solution

(a) Breaking points:

Two breaking points exist (1) When the Kshs.300,000 of retained earnings is

exhausted and (2) When the Kshs.400,000 of debt costing 5.6% is exhausted.

BP equity = AF = 300,000 = Sh.600,000

Ws 0.5

BP debt = AFj = 400,000 = Sh.1,000,000

Wj 0.4

No breaking is caused by increase use of preference shares.

(b) Calculating WMCC

Next we calculate the WACC between breaking points. First find WACC between

total financing of Sh.0 – Sh.600,000, then WACC from Sh.600,000 – Sh.1,000,000

then above Sh.1,000,000.

WACC for ranges of total financing:

154

Sh.0 – 600,000 0.4 (5.6) + 0.1 (10.6) + 0.5 (13) = 9.8%

Sh .600,000 – 1,000,000 0.4 (5.6) + 0.1 (10.6) + 0.5 (14.0) = 10.3%

Sh.1,000,000 and above 0.4 (5.6) + 0.1 (10.6) + 0.5 (14.0) = 11.5%

(c) WMCC graph

(c) 12

11.5%

10.3%

10 9.8%

0 600,000 1,000,000

Total new finances

INVESTMENT OPPORTUNITY SCHEDULE (IOS) AND THE WMCC

SCHEDULE

The investments made by firm depend on two things.

- The returns on investment opportunities

- The cost of financing the opportunities.

The firms IOS is a ranking of investment possibilities from best to worst (lowest

return). As the cumulative amount of money invested in a firm’s capital project

increase, its IRR on the projects will decrease. The first project selected will have the

highest return, followed by the second highest and so on until the funds available are

exhausted. We can use the concept of the investment opportunity schedule and the

WMCC schedule to simultaneously illustrate the interdependence of the investment

and the financing decisions.

155

Lets go back to the preceding example of ABC company. Suppose ABC has the

following investment opportunities available during a given year.

Investment

opportunity

Opportunity’s

IRR

Initial

Investment

Sh. ‘000’

A 15% 100

B 10.0 100

C 12.0 300

D 11.0 200

E 14.0 400

F 13.0 100

G 14.5 200

The following IOS can be prepared ranking the projects according to their IRRs from

the most to the least preferable. company has prepared the following investment

opportunity schedule:

Investment

opportunity

Opportunity’s

IRR

Initial

Investment

Sh. ‘000’

Cum.

investment

Sh. ‘000’

A 15% 100 100

G 14.5 200 300

E 14.0 400 700

F 13.0 100 800

C 11.0 300 1100

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D 11.0 200 1300

B 10.0 100 1400

We can plot the project returns against the cumulative investment on the same axes as

the WMCC schedule the firm should accept projects up to the point at which the

marginal return on its investment equals its weighted marginal cost of capital.

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A 15

14 G

13

12.5 E

12

F

11.5

WMCC

11

C

10.5

10 D IOS

9.5

*

200 400 600 800 1000 1200 1400

By using the WMCC and IOS schedules the firms optimal capital budget is

determined as (1,100,000).

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By raising Sh. 1100,000 of new financing and investing in projects AGEF and C the

firm should maximize shareholder width.

Review Questions

1. A cost of capital can be said to consist of three elements. What are they? 2. What is the dividend valuation model formula for the cost of equity:

(a) with no dividend growth? (b) with dividend growth?

3. How is the after-tax cost of debt of debt capital calculated? 4. Why should a weighted average cost of capital be used as the discount rate,

instead of the cost of the funds that are specifically used to finance each new investment?

5. On what assumption is it appropriate to use the weighted average cost of capital as the discount rate for investment evaluation?

6. Should weightings be based on the market values or the book values of the sources of capital?

Problems

6.1 Explain and distinguish between:

a) Weighted average cost of capital, and

b) Marginal weighted average cost of capital.

Nyuki Ltd is a company operating in eh telecommunications industry. The company’s

balance sheet as at 31 March 2007 is as below:

Liability and Owners Equity

Sh ‘000’ Sh ‘000’

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Current liabilities 18% debentures (sh. 000) 10% preference shares Ordinary shares (sh.10 par) Retained earnings

12,500 16,000 6,250 12,500 28,125

Current assets Net fixed asset

32,500 42,875

75,375 75,375

Additional Information

1. The debentures are selling at Sh. 950 in the market and will be redeemed 10

years from now.

2. By the end of last financial period the company had declared and paid sh.500

as dividend per share. The dividends are expected to grow at an annual rate of

10% in the forecast future. Currently the company’s shares are trading at

sh.38 per share at the local stock exchange.

3. The preference shares were floated in 2002 and their prices have remained

constant.

4. Most Banks are lending out money at an interest rate of 22% per annum.

5. The corporation tax rate is 40%.

Required:

i) The market weights average cost of capital for the firm.

ii) Why are markets value weights preferable to book value weight when

determining the weighted average cost of capital for a firm.

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LECTURE EIGHT

ANALYSIS AND INTERPRETATION OF FINANCIAL

STATEMENT

8.1 Introduction

Financial statements are essentially historical and static documents. They tell us what has

happened during a particular period or series of periods of time. The most valuable

information to most users of financial statements or reports, however, concerns what

probably will happen in the future. In this lecture we will discuss how financial statement

analysis can assist statement users in predicting the future by means of comparing and

evaluating financial trends and cross-sectional positions of firms.

Objectives At the end of this lecture you should be able to:

1. Discuss the needs of the users of

financial statements.

2. Discuss the types of comparison used

in financial statement analysis

3. Compute financial ratios and use them

to evaluate financial strengths and

weaknesses

4. Use the Dupont system to carry out a

complete ratio analysis of the firm

5. Explain common size and index

analysis

6. Discuss the limitations of financial

statement analysis

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8.2 DEFINITION AND OBJECTIVES OF FINANCIAL

ANALYSIS

Financial analysis is the process or critically examining in detail, accounting information

given in financial statements and reports. It is a process of evaluating relationship

between component parts of financial statements to obtain a better understanding of a

firm’s performance. Financial statement analysis involves three basic procedures:

Selection This involves the selection from the total information available about an

enterprise, the information that is relevant to the decision under consideration.

Relation This involves arranging the information in a manner that will bring out a

significant relationship(s).

Evaluation This involves the study of the relationship and interpretation of the result

thereof.

The specific objectives of financial statement analysis are to:

(a). assess the past, present and future earnings of an enterprise,

(b). assess the operational efficiency of the firms a whole and its various divisions or

departments

(c). asses the short term and tong term solvency of the firm,

(d). assess the performance of one firm against another or the industry as whole and the

performance of one division against another.

(e) Assist in the developing of forecasts and preparing of budgets,

(f) Assess the financial stability of the business under review, and

(g) Assist in the understanding of the real meaning and significance of financial

Information.

Financial statements are essentially a record of the past. Business decisions naturally

affect the future. Analysts therefore study financial statements as evidence of past

performance that may be used in the prediction of future performance.

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8.3 SOURCES OF INFORMATION

The first procedure in financial statement analysis is to obtain useful information. The

main sources of financial information include, but are not limited to, the following;

Published reports

Quoted companies normally issue both interim and annual reports, which contain

comparative financial statements and notes thereto. Supplementary financial information

and management discussion as well as analysis of the comparative years' operations and

prospects for the future will also be available. These reports are normally made available

to the public as well as the shareholders of the company.

Registrar of Companies

Public companies are required by law to file annual reports with the registrar of

companies. These reports are available for perusal upon payment of a minimum fee.

Credit and Investment Advisory Agencies

Some firms specialize in compiling financial information for investors in annual

supplements. Many trade associations also collect and publish financial information for

enterprises in various industries. Major stock brokerage firms and investment advisory

services compile financial information about public enterprises and make it available to

their customers. Some brokerage firms maintain a staff or research analysis department

that study business conditions, review published financial statements, meet with chief

executives of enterprises to obtain information on new products, industry trends, negative

changes and interpret the information for their clients.

Audit Reports

When an independent auditor performs an audit the audit report-is usually addressed to

the shareholders of the audited enterprise. The audit firms frequently also prepare a

management report, which deals with a wide variety of Issues encountered in the course

of the audit Such a management report is not a public document, however, it is a useful

source of financial information.

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Government Statistics and Market Research Organizations

8.4 COMPARISONS IN FINANCIAL ANALYSIS

The figures in the financial statements are rarely significant or important in themselves. It is their relationships to other quantities, amounts and the direction of change from one point in time to another point in time that is of importance. It is only through comparison of data that one can gain insight and make intelligent judgments. Analysis thus involves establishing significant relationships that points to changes as well as trends.

The two comparisons widely used for analytical purpose involve trend and cross-

sectional analyses.

Trend Analysis This is also known as time series analysis, horizontal analysis or temporally analysis. It

involves the comparison of the present performance with the result of previous periods

for the same enterprise. Trend analysis is therefore usually employed when financial data

is available for three or more periods. Developing trends can be seen by using multiyear

comparisons and knowledge of these trends can assist in controlling current operations

and planning for the future. It can be carried out by computing percentages for the

element of the financial statement that is under observation. Trend percentage analysis

states several years' financial data in terms of a base year, which is set to be equal to

100%.

In conducting trend analysis the following need to be taken into account:

(i) Accounting principles and policies employed in the preparation of financial

statement must be followed consistently for the periods for which an analysis is

being made to allow comparability.

(ii) The base year selected must be normal and a representative year.

(iii) Trend percentages should be calculated only for these items, which

have logical relationship.

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(iv) Trend percentages should be carefully studied after considering the

absolute figures, otherwise they may lead to misleading conclusions.

(v) To make meaningful comparisons, trend percentage should be

adjusted in light of price changes to the base year.

Example

Assume that the following data is extracted from the books of ABC Ltd.

2004 2003 2002 2001 2000

Sh. Million Sh. Million Sh. Million Sh. Million Sh. Million

sales 725 700 650 575 500

Net income 99 97.5 93.75 86.25 75

From the above absolute figures, there appears to be a general increase in safes and

income over the years. When expressing the above date in terms of percentages with

2000 being the base year, the following trend percentage is observed.

. 2004 2003 2002 2001 2000

Sales 145% 140% 130% 115% 100%

Net Income 132 % 130 % 125 % 115 % 100 %

Net income/Sales 13.7% 13.9% 14.4% 15% 15%

From the above table it can be observed that:

i) Sales and net income have grown over the years but at a 'increasing rate,

ii) Net income has not kept pace with growth in sates. When net income is

expressed as a percentage of rates,

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iii) It is further observed that net income as a percentage of sates is decreasing

over the years and this needs to be investigated.

Financial statement analysis is not an end by itself; rather the analyses enable the right

questions, for which management has to look for answers.

Graph

percentage

years

2000 2001 2002 2003 2004

150 140 130 120 110

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From the line graph, one can observe that the growth rate for sales has decreased. The

same applies is net income as shown by the slope of the curves. One may also conclude

from the curves that between 2001 and 2000 sales and income have grown at the same

rate. Subsequently, growth in net income failed to keep pace with the growth in sates.

Problems of Trend analysis

(a). To ensure comparability of figures, the results of each year will have to be

adjusted using consistent accounting policies. The task of adjusting statements to

bring them to a common basis could be taunting.

(b). Comparison becomes difficult when the unit of measurement changes in value

due to general inflation. Comparisons become quite difficult over time.

(c). If the enterprise's environment changes over time with the result that performance

that was considered satisfactory in the past may no longer be considered so. More

specific measures rather than general trends may be preferred in such instances.

Cross Sectional Analysis

This involves the comparison of the financial performance of a company against

other companies within its industry or industry averages at the same point in time. It

may simply involve comparison of the present performance or a trend of the past

performance. The idea under this approach is to use bench-marking, whereby areas in

which the company excels benchmark companies are identified, and more

importantly areas that need improvement highlighted. The typical bench-marks used

in cross-sectional analysis may be a comparable company, a leader in the industry, an

average firm or industry norms (averages).

Problems Of Cross Sectional Analysis

(a). It is difficult to find a comparable firm within the same industry. This is because

firms may have businesses which are diversified to a greater or lesser extent.

Further, industry averages are not particularly useful when analyzing firms with

167

multi-product lines. The choice of the appropriate benchmark industry for such

firms is a difficult task.

(b). Businesses operating in the same Industry may be substantially different in that,

they may manufacture tile same product but one may be using rented equipment

while the another uses its own making comparison difficult .

(c). Two firms may use accounting policies, which are quite different resulting in

difference m financial statements It is usually very difficult for an external user

to identify differences in accounting policies yet one must bear them in mind

when interpreting two sets of accounts.

(d). The analyst must recognize that ratios with large deviations from the norm are

only the symptoms of a problem. Once the reason for the problem is known

management must develop prescriptive actions for eliminating it. The point to

keep in mind is that ratio analysis merely directs attention to potential areas of

concern; it does not provide conclusive evidence as to the existence of a problem.

8.4 RATIOS

The most common tools of financial analysis are ratios. A ratio is simply a mathematical

expression of an amount or amounts in terms of another or others. A ratio may be

expressed as a percentage, as a fraction, or a stated comparison between two amounts.

The computation of a ratio does not add any information not already existing in the

amount or amounts under study. A useful ratio may be computed only when a significant

relationship exists between two amounts. A ratio of two unrelated amounts is

meaningless. It should be re-emphasized that a ratio by itself is useless, unless compared

with the same ratio over a period of time and/or a similar ratio for a different company

and the industry. Ratios focus attention on relationships which are significant but the full

interpretation of a ratio usually requires, further investigation of the underlying data.

Thus ratios are an aid to analysis and interpretation and not a substitute for sound

thinking.

8.4.1 Classification of Ratios

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Financial ratios may grouped into four basic categories: liquidity ratios, debt ratios,

activity ratios and profitability and investment ratios.

Liquidity Ratios.

Liquidity refers to an enterprise's ability to meet its short-term obligations as and when

they fall due. Liquidity ratios are used to assess the adequacy of a firm’s working capital.

Shortfalls in working capital may lead to inability to pay bills and disruptions in

operations, which may be the forerunner to bankruptcy. The tree basic measures of

liquidity are (1) net working capital, (2) the current ratio, and (3) the quick (acid-test)

ratio. As will become clear, for all the three measures, the higher their values the more

liquid the firm is. It should however be emphasized that excessive liquidity sacrifices

profitability even as inadequate liquidity may lead to insolvency – a trade-off exists

between profitability and liquidity (risk).

Net Working Capital Net working capital ,although not a ratio is a common measure of

a firm’s overall liquidity it is calculated as follows:

Net working capital = current assets – current liabilities Net working capital represents current assets that are financed from long term capital

resources that do not require repayment in the short-run, implying that the portion is still

available for repayment of short-term debts.

Example

2004 2003

Sh.000 Sh.000

Current assets 26,400 15,600

Current liabilities (13,160) (6,400)

Net working capital 13,240 9,200.

In the year 2003 Sh.9.2 million of working capital is available to repay Sh.6.4 million of

current liabilities and in 2004 Sh.13.24 million is available of working capital to pay

sh.l3.16 million of current liabilities. This reflects a strong liquidity position in the years.

169

The figure of net working capital, being an absolute figure requires standardization

before its use for comparing performance of different firms. For example net working

capital as a percent of sales can be calculated and used for such comparison. A time-

series comparison of the firm’s net working capital is often helpful in evaluating its

operations.

Current ratio The current ratio is one of the most commonly cited financial ratios and

tests, in short-term, the debt-paying ability of an enterprise. A high current ratio is

assumed to indicate a strong liquidity position while a low current ratio is assumed to

indicate a relatively weak liquidity position. The RULE of the thumb is that current-assets

should be twice current liabilities. The current ratio is expressed as follows:

Current ratio = Current assets / Current liabilities

Example

Using the data from the previous example the current ratios for the two years is arrived as follows.

2004 2003

26400 /13,160 15600/6400

= 2: 1 = 2.4: 1

Observation

The enterprise appears to nave a strong liquidity position. There has been, however, a

slight drop from year 2003 to year 2004.

For every shilling that is owed in 2004, the firm has Sh.2 to pay the debt and for every

shilling0wed in 2003 , the firm has Sh.2.40 available to meet the liability. If the firm’s

current ratio is divided into 1.0 and the resulting value is subtracted from 1.0, the

difference when multiplied by 100 represents the percent by which the firm’s current

assets can shrink without making it impossible for the firm to cover its current liabilities.

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A current ratio of 2 means that the firm can still cover its current liabilities even if its

current assets shrink by 50 percent ([1.0 – (1.0/2.0)]* 100).

Quick ratio or Acid test ratio.

The current ratio has further been refined to Quick ratio or Acid Test Ratio. This ratio

tests the short-term debt paying ability of an enterprise without having to rely on

inventory and prepayments Inventories are generally the least liquid current asset and

prepayments are generally not convertible to cash. Therefore for a company whose

inventories include work-in-progress, and slow-moving items the quick ratio is a better

indicator of liquidity than the current ratio. The rule of the thumb is for every shilling of

current liability owed, the enterprise should have a shilling of current quick assets

available to meet it i.e. a quick ratio of 1.0.

It is given by;

(Current assets-inventories-prepayments)/(Current liabilities)

Activity Ratios

Activity ratios measure the speed with which accounts are converted into sales or cash.

Activity ratios can be categorized into two groups: The first group measures the activity

of the most i9mportant current accounts, which include inventory, accounts receivable,

and accounts payable1. The second group measures the efficiency of utilization of total

assets and fixed assets.

Inventory Ratios

Average sales period ( Age of inventory) This ratio measures the average number of

days taken to sell the average inventory carried by a firm. It is given by:

(Average inventory x 365 days )/(Cost of sales)

Where, average inventory =(Beginning inventory+ Ending inventory)/2

1 In order to calculate activity ratios using current accounts the averages of these amounts during the year are preferred.. These averages can be approximated by summing the beginning-of-year and the-end-of year account balances and dividing by 2. When data needed to find the averages are unavailable, year-end values may be used to calculate activity ratios for current accounts.

171

Inventory turnover ratio. Inventory turnover ratio measure the number of times a

company's inventory has been sold during the year.

Inventory turnover = Cost of sales/Average Inventory

Accounts Receivable Ratios

Average Collection Period (Age of accounts receivable or days sales outstanding)

The ratio measures the average number of days taken by an enterprise to collect its trade

receivables. The ratio is computed as follows

(Average trade receivables X 365 days)/ (Credit sales)

Or, 365 days/(Accounts receivable turnover ratio)

Where, average trade receivables = (Beginning + Ending trade receivables)/2

The average collection period should only be judged in relation to a firm’s credit terms.

Only then can one draw definitive conclusions about the effectiveness of a firm’s credit

and collection policies.

Accounts receivable turnover ratio The accounts receivable turnover ratio measures the

number of times an enterprise has turned accounts receivable into cash during the year.

The higher the times the more efficient a company will be assumed to be in collecting its

debts. The ratio is computed as follows:

Accounts receivable turnover = Annual Credit sates/Average trade receivables

Trade Creditors Ratios

(vi) Average payment period (Age of trade payable) ratio. This ratio measures the

average number of days taken to pay an accounts payable. It is computed as follows:-

(Average trade payables X 365 days)/Credit purchases

Or

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365 days/(Accounts payable turnover ratio)

Where average accounts payable=(Beginning + Ending accounts payable)/2

Accounts payable turnover ratio. The accounts payable turnover ratio measures the

efficiency with which firms pay their trade creditors. The higher the number of times, the

more efficient the enterprise is assumed to be in paying its creditors. It is calculated as

follows;

Accounts payable turnover ratio = Annual Credit purchases/Average trade payables

Leverage ratios

A firm is said to be financially leveraged whenever it finances a portion of its assets by

debts. Debts commit a firm to payment of interest and repayment of capital. Borrowing

increases the risk of default and it is only advantageous to shareholders if the return

earned on the funds borrowed is greater than the cost of the funds. There two

classifications of measures of debt: (1) Measures of the degree of indebtedness measure

the amount of debt relative to other significant balance sheet amounts. Common measure

of the degree of indebtedness include the debt ratio, the debt/equity ratio, and the debt –

to-total capitalization, (2) Measures of the ability to service debt assesses a firm’s ability

to make the contractual payments required on a scheduled basis over the life of the debt.

Commonly referred to as coverage ratios, they include times-interest earned, and the

fixed charge coverage ratios.

Debt to equity ratio This ratio measures the proportion of assets provided by

providers of long-term debt funds for each shilling of assets provided by the

shareholders. It is computed as follows:

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Total long term debt/Total stockholders funds

Debt to total assets ratio (Debt ratio) This ratio measures the proportion of assets

financed by outsiders. It is calculated as follows;

Total liabilities / Total assets

Debt/total capitalization ratio Indicates the proportion of capital provided by outsiders.

The formula for Debt/Total capitalization ratio is;

Long-term debt/(Long-term debt + Shareholders funds)

The times interest earned ratio This is also known as the interest cover ratio. This ratio

measures the ability of a firm to meet its interest payment out of the current earnings. It

reflects the likelihood that creditors will continue to receive their interest payments.

It is It is computed as follows:-

Earning before interest and tax/Interest expense

Fixed charge coverage ratio The fixed payment coverage ratio measures the firm’s

ability to meet all fixed payment obligations. Loan interest, principal payments, on debt,

scheduled lease payments, and preferred stock dividends are commonly included in this

ratio. The formula for the fixed charge coverage ratio is as follows:

(Earnings before interest and tax + lease payments)/(interest + lease payments

+{(principal payments + preferred stock dividends)*[1/(1-T)]}

Where T is the corporate tax rate applicable to the firm’s income. The term [1/(1-T)] is

included to adjust the after tax principal and preferred stock dividend payments back to a

before-tax equivalent that is consistent with the before-tax values of all other terms.

The fixed payment coverage ratio measures the risk the firm will be unable to meet

scheduled fixed payments and thus be driven into bankruptcy. The lower the ratio the

greater the risk to both lender and owners.

174

Profitability Ratios

Profitability ratios evaluate the firm’s earnings with respect to a given level of sales, a

certain level of assets, the owner’s investment, or share value. Evaluating the future

profitability potential of the firm is crucial since in the long run, the firm has to operate

profitably in order to survive. The ratios are of importance to long term creditors,

shareholders, suppliers, employee’s and their representative groups. All these parties are

interested in the financial soundness of an enterprise. The ratios commonly used to

measure profitability include:

Gross Profit Margin

This ratio measures the percentage of each shilling of sales remaining after the firm has

paid for its goods. The higher the gross profit margin the better, and the lower the relative

cost of merchandise sold. The formula for calculating the gross profit margin is as

follows:

Gross profit margin = (Sales – cost of goods sold)/ Net Sales

= Gross profits/ Net Sales

Operating Profit Margin

This ratio measures the percentage of each shilling of sales that remains after paying of

for the goods sold and the operating expenses. This is a measure of “pure profits” because

they measure only the profits earned on operations ignoring any financial charges and

government taxes. The operating profit margin is calculated as follows:

Operating profit margin = Operating profits/Net Sales

= Earnings before interest and taxes/Net Sales

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Net Profit Margin

The net profit margin measures the percentage of each shilling of sales remaining to the

owners of the firm after paying off all expenses, including financing charges and taxes.

The higher the firm’s net profit margin the better for the owners. The ratio is calculated

as follows:

Net profit margin = Profit after taxes/Net Sales

Return on Total Assets (ROA)

This ratio is also called the return on investment (ROI) and measures how well

management has employed available assets in generating profits from its assets. The

return on total assets is calculated as follows:

Return on total assets = Profit after taxes/ Total assets

Return on Equity (ROE)

The return on equity measures the return earned on the owner’s investment in the firm. This ratio measures the ability of an enterprise to generate income for its owners. Return on equity is calculated as follows:

Return on equity = (Profits after taxes – preference dividend)/Ordinary Shareholders’ funds Where, ordinary shareholders’ equity =Total shareholders’ funds less preference share

capital.

Investment Ratios

Investment ratios help equity shareholders and other investors to assess the value of an

investment in the ordinary shares of a company, The value of an investment in the

ordinary shares in a listed company is its market value, and so investment ratios must

have regard not only to information in the company published accounts, but also to the

current price. The following are the common investment ratios.

Earnings per Shape (EPS)

This ratio represents or reflects the amount of shillings or cents earned per ordinary

share. It is considered so critical that the accounting profession requires its disclosure on

the face of the income statement for quoted companies(IAS 33).

176

It is given by

EPS = (Profit after taxes -Preference dividends)/The number

of ordinary Shares outstanding

Dividend pay-out ratio.

This ratio reflects a company's dividend policy. It indicates the proportion of

earnings per share paid out to ordinary shareholders as divided. It is

computed as follows:

Dividend pay-out ratio = Dividends per ordinary share / Earnings per share

Where ordinary dividends per share = Ordinary dividends/

Number of ordinary shares

Dividend Yield Ratio

This shows the dividend return being provided by the share. It is given by

Dividend yield = Dividends per share / Market price per share

Price Earnings Ratio (The P/E Ratio)

This ratio is used in comparing stock investment opportunity. It is an index of

determining whether shares are relatively cheap or relatively expensive. It measures the

amount investors are willing to pay for each shilling of the firm’s earnings.

It is given by

PER=Market price per ordinary share/Earnings per share

This price earnings ratio reflects the consideration that investors are willing to pay for a

stream of a shillings of earnings in the future. The price-earnings ratio is widely used by

investors as a general guideline in gauging stock values. Investors increase or decrease

the price-earnings ratio that they are willing to accept for a share of stock according to

how they view its future prospects. Companies with ample opportunity for growth

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generally have high price-earnings ratio, with the opposite being for companies with

limited growth.

LIMITATIONS OF RATIOS

1. Ratios are insufficient in themselves as a basis of judgment about the future. They

are simply indicators or what to investigate. Therefore, they should not be viewed as

an end but as a starting point.

2. They are useless when used in isolation. They have to be compared over time for the

same firm or across firms with the industry's average.

3. Ratios are based on financial statements. Any weaknesses of the financial statements

are also captured within the ratios.

4. Comparing ratios across firms may be difficult because the firms may not be

comparable. Data among companies may not provide meaningful comparisons

because of factors such as use of different accounting policies and the size of the

company.

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LECTURE TEN

WORKING CAPITAL MANAGEMENT

10.0 INTRODUCTION Investment decisions apply to both current assets and plant and equipment assets.

However, the investment decision techniques for current assets may differ because

current assets have some unique characteristics:

(1) The amount of investment in each asset may vary from day to day

(2) Decisions regarding investment in one type of current asset may impact on the

investment in other current assets. For example, a relaxation in credit terms

that leads to an increase in debtors may call for an increased investment in

stocks.

This lesson has two goals: First we will discuss the concepts underlying the management

of working capital as a whole. Secondly, we will specifically focus on the management of

current liabilities. The next lesson will complete the topic by discussing the management

of current assets.

Objectives

At the end of this lecture you should be able to:

1. Provide a definition and explanation of

working capital concepts

2. Discuss the two polar working capital

strategies: aggressive and conservative

strategies.

3. Describe the basic types and

characteristics of current liabilities

(short term financing)

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10.1 DEFINITIONS AND GENERAL CONCEPTS OF WORKING

CAPITAL

Definitions of Working Capital Working capital can be defined from two perspectives.

(1) Net working capital is defined as the difference between the firm’s current asset

and the firm’s current liabilities.

(2) Net working capital is the firm’s current assets financed with long-term funds.

Working Capital Management Decisions In principle, current asset investment decisions, as in the case of investment in fixed

assets, calls for a cost-benefit evaluation of a large number of alternatives, and the

selection of that alternative that produces the greatest net benefit. The typical process

will feature the following activities:

(1) The financial manager estimates the costs and benefits of each alternative.

(2) The net present value (NPV) must be calculated for each alternative given the

discount rate approximate to the degree of risk involved

(3) The alternative with the highest NPV is chosen and implemented.

In practice, however, the NPV approach is rarely used for evaluating working capital

investment decisions. The alternative approach, commonly used, is to maximize average

net profit, with the amount invested treated as its equivalent annual cost. The

management of working capital boils down to balancing the risks and benefits of holding

excessive, to those of holding too little, working capital.

In this lesson and the next, we focus our attention on the management of each of the

individual current asset and current liability times. This is a preferred approach given the

fact that each item has its own unique characteristics. Generally, it is to be expected that

current liabilities be the preferred source of financing current assets (because current

liability is a cheap source of finance and the maturity of current liabilities parallels the

180

liquidity of current assets). Management, however, must weigh the desire of a higher

return against the risk of insolvency (if, for example, the bank suspends its overdraft

facilities or creditors demand earlier payment).

Overcapitalization and Overtrading The finance manager must be wary of two polar extremes in working capital

management. These extremes are, (i) over-capitalization and, (2) over-trading.

Over Capitalization (Conservative Financing Strategy)

If a company manages its working capital, so that there are excessive stocks, debtors and

cash and very few creditors, there will be an over-investment by the company in current

assets. Working capital will be excessive and the company is said to be overcapitalized (

i.e. the company will have too much capital invested in unnecessarily high levels of

current assets). The result of this would be that the return on investment will be lower

than it should, with long-term funds unnecessarily tied up when they could be more

profitably invested elsewhere.

Indicators of over-capitalization

Accounting ratios can assist in judging whether over capitalization is present.

(1) Sales/Working capital ratio:- the volumes of sales as a multiple of

working capital should indicate whether the total volume of working

capital is too high (compared to the past and industry norms).

(2) Liquidity ratio. A current ratio and a quick ratio in excess of the industry

norm or past ratios will indicate over-investment in current assets

(3) Turn-over periods. Excessive stock and debtors’ turnover periods or too

short creditor payment period might indicate that the volume of debtors

and stocks is unnecessarily high, or creditors’ volume too low.

Over-trading (Aggressive Financing Strategy)

Overtrading occurs when a business tries to do too much too quickly with too little long-

term capital: The capital resources at hand are not sufficient for the volume of trade.

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Though initially an over-trading business may operate at a profit, liquidity problems

could soon set in, disrupting operations and posing insolvency problems.

Symptoms of over-trading

Accounting indicators of overtrading include:

(1) Rapid increases in turn-over ratios (over-heating)

(2) Stock turnover and debtor’s turnover might slow down with consequence that

there is a rapid increase in current assets.

(3) The payment period to trade creditors lengthens

(4) Bank over-drafts often reach or exceed the limit of facilities offered by the bank.

(5) The debt ratios rise

(6) The current ratio and quick ratio fall and the net working capital (NWC) could be

negative.

Operating and Cash Conversion Cycles We can understand better the management of working capital by appreciating the inter-

linkages of flows in the current section of the balance sheet. Opportunities to improve

efficiency in collecting, holding and disbursing funds center on flows through this section

of the balance sheet, depicted in the bottom part of Figure 12.1. We diagram these flows

in more detail in Figure 12.2, which shows the steps along the way as funds flow through

the firm’s accounts. Let us assume that KQ Ltd. orders raw materials at point A and

receives them 14 days later at B. Terms of 2/10, net 30 are offered, so the firm pays the

invoice 10 days later at C. However, it takes 2 days for the check to clear, and KQ’s

bank account is not charged until point D. KQ turns its inventory six times per year, so 60

days after the materials are received, the product is sold and the customer is billed. The

collection period is 30 days, 28 for the customer to pay and 2 for the check to arrive by

mail (G), KQ processes the payment and deposits it 2 days later at H. Another 2 days

elapses while KQ’s bank collects the funds from the customer’s bank.

The firm’s total financing requirement is affected by the total time lag from point B to

point J. The firm itself can control some factors that determine the various lags, but some

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it cannot. Some of the lags affect the cash balance, while others affect other components

of working capital such as accounts receivable and inventory. When we address

ourselves to cash management, we are concerned with time period BCD and FGHJ.

Time period AB is beyond the firm’s control and does not directly affect its financial

statements although it may affect production schedules. Time period DE is determined

by the firm’s production process and inventory policy and affects the total investment in

inventory. Time period EF is determined by the firm’s credit terms and the payment

policies of its customers, and affects the total investments receivable.

Operating (trading) cycle (OC)

Operating cycle is the amount of time that elapses from the point when the firm inputs

materials and labour into the production process to the point when cash is collected from

the sale of the resulting finished product. The cycle is made up of two components; the

average age of inventory and the average collection period.

OC = average age of inventory (AAI) + average collection period (ACP). (12.1)

The Cash Conversion Cycle (CCC)

This is the amount of time the firm’s cash is tied up between payment for production

inputs and receipts of payment from the sale of the resulting finished product. For a

manufacturing firm, the cash conversion cycle indicates the length of time it takes for an

investment in raw materials to be ultimately realised as a cash receipt after sale of the

manufactured product. This cycle could be broken into several sub-periods: The period of

time it takes:

(a) Between ordering and receipt of raw materials;

(b) For trade creditors to be paid

(c) For raw materials held in stock to be introduced into the production

process

(d) For the finished goods held in stock to be sold

(e) For cash to be realised from debtors.

It is to be noted that purchase of input on credit allows the firm to partially offset the

length of time resources are tied up in the operating cycle.

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Assuming no time lag between the raising of sales and purchase orders and their

execution, the cash conversion cycle can be determined by:

CCC = Operating Cycle (OC) – Average payment period (APP) (12.2)

Or

CCC = AAI + ACP – APP (12.3)

For a manufacturing company,

CCC = Average age of raw materials + average age of work in

progress + average age of finished goods + average collection

period – average payment period

The cash cycle is thus the period between payment of cash to creditors (cash out) and

the receipt of cash from debtors (cash-in).

The length of period has direct effect on the liquidity of a company. The amount tied

up in working capital (WC) will be equal to the value of raw materials (RM), Work-

in-progress (WIP), finished goods (FG) and debtors less creditors. The more the

amount of WC tied up, the less liquid the company is. If the turn-over periods for

stocks and debtors lengthen, or the payment period to creditors shortens:

(1) The cash cycle will lengthen

(2) The investment in working capital is increased.

Example

ABC Ltd sells merchandise on credit terms, requiring payment within 60 days of sale.

On average it takes 85 days to manufacture, warehouse and sale a finished product. Raw

material suppliers require payment within 45 days and employees are paid every 15 days.

The firm calculates its weighted average payment period for raw materials and labour to

be 35 days.

Determine (1) the operating cycle

(2) the cash conversion cycle.

Solution

(1) Average age of inventories (AAI) = 85 days

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Average collection period (ACP) = 70 days

Operating cycle(OC) = AAI + ACP = 85 + 70 = 155 days

(2) Cash conversion cycle (CCC) = OC – APP = 155 – 35 = 120 days

10.2 MANAGEMENT OF CURRENT LIABLITIES Current liabilities are sources of short term financing which assist firms finance current

assets and meet other short term financing needs. The three broad categories of short

term financing are:

1. Spontaneous sources

2. unsecured sources

3. secured sources

We will briefly discuss the characteristics of each of these sources .

Spontaneous Sources Spontaneous financing arises automatically from the day-to-day operations of the firm.

The most common forms of spontaneous financing come from trade credit from

suppliers, and accrued expenses. This financing is interest free and requires no collateral.

Accounts payable

The purchaser obtains goods and services, agreeing to pay later in accordance with the

credit terms stated on supplier’s invoice. Trade credit is credit extended in connection

with goods purchased for resale. It is this qualification that distinguishes trade credit from

other forms of credit.

Suppliers often give cash discounts on open accounts for payment within a specified

period. The credit terms specify the credit period, the size of the cash discount, the cash

discount period, and the date the credit period begins , which is usually at the end of each

month (EOM). For example, terms of 2/10, net 30 EOM, mean a discount of 2% may be

taken if the invoice is paid within 10 days of the invoice date; otherwise the full payment

is due within 30 days from the end of the month of purchase. If the EOM is not part of

the terms then counting begins from the date of the invoice. Prompt-payment cash

discounts are to be distinguished from quantity (bulk) discounts given for purchase of

large quantities, and also from trade discounts given at different points in the distribution

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chain (wholesale versus retail, etc.). Proper management of credit offered by suppliers

requires that:

1. The firm takes the cash discounts by paying on the last day of the discount period.

The annual percentage cost of giving up cash discounts is quite high. This cost

can be estimated using the following equation.

Cost of giving up discount = CD/(100%-CD)*365/N (12.4)

Where CD = stated cash discount as a percentage

N = number of days payment can be delayed by giving up the cash

discount

Example

ABC Ltd. purchased Sh.100,000 worth of merchandise on 27 February from a supplier extending credit terms of 2/10, net 30 EOM. Calculate the cost of giving up the cash discount. Solution

The annualized effective cost of giving the discount = CD/(100%- CD)*(365/N)

= 2%/(100%-2%)*(365/20)

= 37.24%

This is a very high cost indeed and is equivalent borrowing at 37.24%. (NB If we

were to take the discount the firm would pay on 10 March. By giving up the

discount it costs the firm Sh.2,000 (100,000-98,000)).

2. Stretch accounts payable The firm should pay its bills as late as possible without

damaging its credit rating. The full extent of the credit period should be utilized in

the case where cash discounts are not offered. Caution is to be exercised in

stretching payments as this may harm the firm’s reputation and at worst can cot

the firm its sources of supply.

Accruals

Accruals are the other major source of spontaneous financing. Accrued expenses arise

when a firm consumes services (other than trade services) without having to make

immediate payment for them .Typical expenses that generate accrued financing include

wages and salaries, utilities, rent, etc.

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Unsecured sources of short term financing Unsecured source of financing is one against which no specific assets are pledged as collateral. Businesses obtain unsecured short term credit from three sources i.e. trade credit, banks and commercial paper. Trade credit Most trade credit is extended via the open account that results in accounts payable discussed in the preceding section. There are however two other less common sources of trade credit; The promissory note (trade) and the trade acceptances.

1. Promissory note Is usually called a note payable (trade) on the balance sheet. Such notes bear interest and have specified maturity date. They are used in situations in which a purchaser of goods on credit has failed to meet the terms of an open credit agreement and the supplier wishes a formal acknowledgement of the debt and a specific agreement on a future payment date.

2. Trade acceptances Under this arrangement the purchaser acknowledges the debt formally by accepting a draft drawn by then seller calling for payment on a specified date at a designated bank. After acceptance, the draft is returned to the seller and the goods are shipped.

Bank loans Commercial banks are by far the largest suppliers of unsecured loans to businesses. Businesses need to establish a cordial relationship with their bank that can facilitate lending transactions. For a successful relationship to blossom banks will generally look for honesty and integrity ,managerial competence and frank communication in their clients. In addition detailed and specific information regarding the nature of the financing requirement, the amounts and timing of the need, the uses to which the funds will be put, and when and how the bank will be repaid may be needed. Banks lend unsecured short term loans in three forms: a line of credit, a revolving credit agreement, and a single payment note.

1. Single payment note This is a short term , one-time-loan, payable as a single amount at its maturity. It generally has a maturity of 30-daysto 9 months and may have either a fixed or floating rate.

2. Lines of credit A line of credit is an agreement between a business and a bank showing the maximum amount the business could borrow and owe the bank at any point in time. Lines of credit are not contractual and legally binding upon the bank, but they are nearly always honored. The major benefit, to a business, of a line of credit is its convenience and administrative simplicity. From the bank’s point of view the major attraction of a line of credit is that it eliminates the need to examine the creditworthiness of a customer each time the customer wants to borrow. The terms of a credit line may require a floating interest rate, operating change restrictions, compensating balances, and annual cleanup provisions ( a period usually of 1or 2 months during which the loan is completely paid off). A line of credit is often used to finance seasonal working capital needs or other temporary requirements.

3. Revolving credit agreement Involve a contractual and binding commitment by the bank to provide funds during a specified period of time. Because the bank legally guarantees the availability of funds, the borrower pays a commitment fee of ¼ or ½ percent per year on the average unused portion of the commitment. Revolving credit agreement, like a line of credit, permit the firm to borrow up to a

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certain maximum amount; but unlike a line of credit, are not subject to ‘clean-up ‘ provisions.

Commercial Paper A commercial paper is a form of financing that consists of short term promissory notes issued by firms with high credit standing. Commercial paper is typically sold at a discount from its par value. Consequently, the interest charged is determined by the size of the discount and the time to maturity. Commercial paper distributed through the stock exchange is known as a money market instrument. The use of commercial paper to raise funds is advantageous because the cost is lower relative to bank loans and the borrower avoids the cost of maintaining compensating balances required on bank loans. Additionally , borrowers who need to raise huge amounts of money can satisfy their needs more conveniently by issuing commercial paper. Example A company has issued a Sh.100,000,000 par value worth of commercial paper with a 90-day maturity, for Sh.98,000,000. Find the effective annual rate of interest on the paper. Solution The effective annual rate = (1+D/Nم)ⁿ -1 (12.1) Where D = discount Nم = net proceeds from issue n = 365/time to maturity The effective 90-day rate is = D/Np = 2,000,000/98,000,000 = 0,0204 Therefore ,effective annual rate = (1+0.0204) ⁿ - 1 = 0.0841 = 8.41% (n =365/90 = 4) Secured Sources of Short Term Financing A loan is one obtained by a borrower pledging specific asset(s) as security. In the case of shot term loans, lenders insist on collateral that is reasonably liquid. Inventory, accounts receivable, and marketable securities are the assets commonly used as security. Usually the interest on secured loans is higher than interest on unsecured loans because of the perceived risk and the costs of negotiation and administration. The primary sources of secured loans are the commercial banks and non-bank financial institutions. In considering the use of a company’s asset as security we should keep in mind the adverse effect of such action on unsecured creditors who may take them into account in any future transactions.

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LECTURE ELEVEN

MANAGEMENT OF CURRENT ASSETS

11.0 INTRODUCTION

In this lecture we discuss the effective management and control of specific current asset

items so as to achieve efficient operations consistent with the minimization of holding ,

investment and transaction costs associated with the current assets.

Learning Objectives

Objectives At the end of this lecture you should

be able to:

1. Discuss motives for holding cash and

marketable securities and discuss the

strategies for efficient management of

cash. Describe the basic characteristics

of marketable securities.

2. Explain the credit policy variables and

assess the impact of changes in credit

and collection policy on financial

variables including profits.

3. State the inventory management

fundamentals and apply the basic

inventory management models.

.

11.1 MANAGEMENT OF CASH AND MARKETABLE SECURITIES

Cash management involves five interrelated goals:

(1) How to accelerate the collection of cash

(2) How to control cash disbursements

(3) How the appropriate working balance is determined

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(4) How to invest any temporary idle funds in interest bearing marketable

securities.

(5) How to forecast and manage cash shortages.

Let us consider these goals in some detail

11.1.1 ACCELERATING COLLECTION OF CASH

Quick movement of remittances from dispersed locations to central management prevents

the build up of idle or lazy cash balances. Good cash management practice would aim at

reducing the time by between

(1) When payment is initiated by a debtor sending a cheque in payment and

(2) The time when funds become available for use in the recipients bank account.

Three contributors to a lengthy time lag, which need attention are:

- Transmission delay, when payment is sent through post.

- Lodgment delay, by the payee in presenting, after receipt.

- Clearance delay, by the bank after receipt of cash or cheque.

Measures to reduce the time lag will target these contributory factors and include

1 payee setting up efficient cheque handling procedures to eliminate lodgment

delays.

2 Automation; Facilities such as Bankers Automated Clearing Services (BACS)

enable speedy computerized transfer of funds between banks.

3 For regular payments, standing orders or direct debits may be arranged.

4 Concentration Banking. Firms with regional sales outlets often designate certain

of these offices as regional collection centers. Customers within each region are

instructed to remit payment to these offices, which deposit these receipts in local

banks. The funds are transferred later from these bank branches to a

concentration or disbursing bank from which bill payments are dispatched. The

purpose is to limit mail time. Concentration banking also permits the firm to

reduce the idle balances by storing its cash more efficiently in one (few)

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concentration account(s) rather than in many dispersed accounts. This reduces the

requirement for large working balances.

5 Lock Box System The purpose is to eliminate the time between the receipt of

remittances by the company and their deposit in the bank. In this system the

customer sends the payments to a post office box, which is emptied at least daily

by the firm’s bank. The bank opens the payment envelopes, deposits the checks

in the firm’s account and sends deposit slip to the firm. The lock boxes are

normally geographically dispersed and funds are ultimately transferred to a

disbursing bank.

6 Personal collection of checks by messengers. A messenger shuttles around

collecting checks from customers whose accounts are due.

7 Establishing good bank relations to expedite cheque clearance.

11.1.2 CONTROLLING DISBURSEMENTS

The firm’s objective with respect to payments should be not only to pay slowly but also

slow down the availability of funds to suppliers once the payment has been dispatched.

Some of the methods for lengthening the collection period of a firm’s checks are.

1 Lengthening Mail Delivery Time Payments are placed in the mail at locations

from which it is known that a great deal of time will likely elapse before the

payment is received by the supplier. Payments also may be mailed to the

supplier’s corporate headquarters address rather than the local post office or

regional office.

2. Playing the Float. This refers to the amount of money tied up in checks that have

been written but have yet to be collected or paid on. Playing the float means to

write checks against money not currently in the firm’s checking account. Firms

are able to play the float because they know that a delay will likely exist between

the receipt and deposit of check by their supplier and the actual withdrawal of

funds from their account. Using float firms create what is effectively and interest

free loan.

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3. Use Drafts. This is a slow and awkward payment procedure. Used to pay

salaries: an employee can only cash the draft at this bank after the bank gets

consent from his employer.

4. Accruals. Another tool for stretching a firm’s payment is accruals. Accruals or

C.L. that represent a service or good that has been received by the firm but not yet

paid for – wages, rent, tax.

DETERMINING THE OPTIMAL CASH BALANCE

Cash is the ready currency to which all liquid assets can be reduced. Marketable

securities are short term, interest-earning money market instruments. The level of cash

and money and marketable securities held by firms is determined by the motives of

holding them.

Transaction Motive - Holding cash and marketable securities for the purpose of making

planned payments for items such as purchase of stock and payment of wages.

Safety Motive - Balances held mainly in highly liquid marketable securities to cater for

unexpected demand for cash or emergencies.

Speculative Motive – A firm may want ready funds at hand to quickly take advantage of

any opportunities that may arise.

Safety and speculative motives are together referred to as precautionary motives.

The working balance of cost is maintained for transaction purposes. If the firm has too

small a working balance, it runs out of cash. It then liquidates marketable securities or

borrows both involving transaction costs. If on the other hand the firm maintains too

high a working balance it foregoes the opportunity to earn interest on marketable

securities – an opportunity cost. The optimal working balance occurs total costs

(transaction costs plus opportunity cost) are at a minimum. Finding the optimum

involves a trade-off between falling transaction costs against rising opportunity costs.

Baumol Model

This inventory management model was applied to cash balance problem by Baumol.

Inputs to the Baumol model include:

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1. Total cash outflow (demand) over the period

2. Transactions costs of replenishing cash balance by borrowing or selling securities

3. The interest rate that can be earned on securities.

Let Q = amount converted into cash by selling securities or borrowing

d = Total cash outflow (demand) per period (year)

c = Transaction costs of each sale of securities or borrowing

i = The interest rate that can be earned per period (year) i.e. the cost of

holding cash rather than investing it

Then Q* (Optimal size of cash transfer) = idc2 (13.1)

Example:

The Triad Company anticipates Sh.15 million in cash outlays during the next year. The

outlays are expected to occur equally throughout the year. Triad’s treasurer reports that

the firm can invest in marketable securities yielding 8% and the cost of shifting funds

from marketable securities portfolio to cash is Sh.7, 500 per transaction. Assume the

company will meet its cash demands by selling marketable securities. Using the Baumol

model:

(a) Determine optimal size of Triads transfer of funds from marketable securities to

cash.

(b) What will be Triads average cash balance?

(c) How many transfers from marketable securities to cash will be required during the

year?

(d) What will be the total cost associated with Triads cash requirements?

(e) How would your answers to (a) and (b) change if transaction cost could be

reduced to Sh.5, 000 per transaction? or if Triad could invest in marketable

securities to yield 10%?

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SOLUTION

(a) Q* (Optimal size of cash transfer) = √ (2dc/i)

We can determine that; d = 150 million; i = 0.08; c = 7500.

Therefore,

Q* = √(2 x 150,000,000 x 7500)/0.08

= Sh.5,303,301

(b) Triad’s average cash balance = Q*/2 = 5,303,301/2 = Sh.2,651,650

(c) Number of transfers = 150,000,000/5,303,301 = 28.3

(d) Total costs = holding cost + transaction cost

= 2,651,650 x 0.08 + 28.3 x 7,500

= 212,132 + 212,250

= Sh.424,381.

Miller-Orr Model

This a model that provides for cost-efficient cash balances between determining an upper

limit and the return point for cash balances: This model, unlike the Baumol model that

assumes certainty, is based on the assumption that receipts and disbursements are

completely random. The Miller-Orr model requires the determination of:

(a) An upper limit, which is the maximum amount of cash to be held

(b) Lower limit, which is the minimum amount of cash to be held (assumed to be

zero)

(c) Return point, which is the target cash balance considered optimal.

This control limit model gives an answer in terms of the maximum and the minimum

balances and provides a decision rule, rather than a fixed schedule of transfers. The

important implication of the model is that the greater the variability of a firm’s cash flow

the higher should be the minimum balance.

Setting the Return and Upper Point The value the firm sets for the return point

depends on (1) conversion costs, (2) the daily opportunity cost of funds, and (3) the

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variance of daily net cash flows. The variance is estimated by using daily net flows ( i.e.

inflows minus outflows).

The return point is estimated by:

Return Point = 3 √ [ (3 x conversion cost x variance of daily net cash

flows)/(4* daily opportunity cost)] (13.2)

The upper limit for cash balance in this model is always set at three times the return

point. Therefore

Upper limit = 3x return point. (13.3)

Figure 13.1: Miller-Orr Model: Cash balance control limits

In Figure 13.1 when cash balance reaches the upper limit, at t1, an amount equal to the

upper limit minus the return point are transferred out of the cash account and into

marketable securities.

Cash converted to marketable = upper limit – return point securities (13.4)

The cash balance continues to fluctuate and falls to zero (the lower limit) at t2 when

market securities equal to the return point minus the lower limit are sold and proceeds

transferred to cash working balance.

Marketable securities converted to cash = return balance – lower limit (zero) (13.5)

Example

It costs XYZ Company Sh. 3,000 to convert marketable securities to cash and vice versa;

the firm’s marketable securities portfolio earns an 8% annual return. The variance of

XYZ Company’s daily net cash flows is estimated to be Sh. 2,7000,000.

Determine the return point and the upper limit.

Solution

(i) Return point = 3√[(3 x 3000 x 2,700,0000/(4*0.00022)] = Sh.13,990

(ii) the upper limit line = 3 x return point = 3 x 13,990 = Sh.41,970

NB: Daily opportunity cost = 8%/360 = 0.00022

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11.1.3 INVESTING IDLE CASH – MARKETABLE SECURITIES

It may happen the firm finds itself holding cash balances in excess of its requirements.

Two causes of this build-up could be :-

1. Build up of transactions balances due to the seasonal nature of business, and

2. Build up of precautionary balances needed to take care of emergencies or unexpected

profitable opportunities.

Cash in excess of requirements should be invested in interest bearing assets that can be

converted readily into cash.

Investment Criteria

Because the cash must be available at short notice it will be invested in short-term debt

instruments (rather than shares) after examining three principal characteristics:

1. Default risk – the possibility tat interest or principal might not be paid on time

and in the amount promised.

2. Maturity – the time period over which interest and principal are to be made.

3. Marketability – ease with which an asset can be converted to cash.

Investment Alternatives

The principal types of interest bearing assets that meet the criteria of low default risk,

short maturity and ready marketability are often referred to as money market securities

and include:

1. Government Treasury Bills. These bills are issued weekly by the government

(Treasury), are readily marketable and have maturities ranging from 91 to 360

days.

2. Bank Certificate of Deposit (CDs). Are fixed maturity time deposits placed

with leading commercial banks. CDs of largest banks are marketable, have low

default risk (although not zero) and have maturities ranging from 91 to 360 days.

3. Commercial Paper. These are short term unsecured promissory notes of large

corporations. Commercial papers are usually issued by major finance companies,

banks and some non-financial firms.

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4. Bankers Acceptances. These are drafts drawn against deposits in commercial

banks. They are usually used in foreign trade. The draft has a specific payment

date and has a guaranteed payment at maturity by the bank that accepts it.

DEALING WITH CASH SHORTAGES

Cash flow shortages can arise in several ways.

1. Making losses – perpetual loss making eventually results in cash flow scarcity.

2. Inflation – in periods of inflation, a firm needs ever-increasing amounts of cash

just to replace used up or worn out assets.

3. Growth – growing companies need additional fixed assets and increased levels of

stocks and debtors.

4. Seasonal business – cyclical sales or demand may make cash balances to

fluctuate sharply during the year.

5. One-off expenditures, such as repayment of a loan at maturity, purchase of

expensive asset and natural disasters could lead to a severe strain on cash

reserves.

Easing Cash Shortages.

Shortages may be alleviated by:

1. Postponing capital expenditures that are not crucial and urgent.

2. Disposal of fixed assets which are not core or critical for survival.

3. Renegotiating contracts to defer or even reduce payment obligations. Instances

include:

- Rescheduling loan repayment

- Deferral of corporation tax payment by negotiating with Kenya Revenue

Authority

- Retrenchment of staff

4. Freezing of payment of dividends.

11.2 Accounts Receivable Management

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Account Receivables are amounts of money owed to a firm by customers who have

bought goods and services on credit. Management of receivables aims at determining the

optimal level of investment in receivables, which maximizes the benefits and minimizes

the costs of holding receivables.

Economic conditions, competition, product pricing, product quality and the firm’s

accounts receivables management policies are the chief influences on the level of a firms

accounts receivable. Of all these factors, the last one is under the control of the finance

manager. Our concern is to focus on this last factor.

As with other current assets, the manager can vary the level of accounts receivable in

keeping with the trade-off between profitability and risk.

The firm’s financial manager controls accounts receivable through the establishments and

management of:

(1) credit policy, which is determination of credit selection, credit

standards and credit terms, and

(2) collection policy.

Let us consider these management variables.

11.2.1 CREDIT SELECTION

This is the decision whether to extend credit to a customer and how much credit to

extend. A credit investigation is first carried out on the prospective customer in whom

the five Cs of credit are employed. The five Cs of credit are key dimensions –

character, capacity, capital collateral and conditions – used by the credit analysts to

focus their analysis on an applicant’s credit worthiness. A brief discussion of these

characteristics follows.

Character This refers to the creditor’s willingness to honour obligations. The applicants

record of meeting past obligations – financial, contractual, and moral - is closely

scrutinized. Any past litigation against the applicant would also be relevant.

Capacity This considers the applicants ability to generate cash to repay the requested

credit. Financial statement analysis, especially liquidity and debt rations are useful in

assessing capacity.

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Capital Considers the financial strength of the applicant as reflected by his net worth

position. The applicant’s debts relative to equity and the profitability ratios will be used

in this assessment.

Collateral Looks at the amount of assets the applicant can pledge to secure the credit to

be advanced. The asset structure as revealed in the balance sheet and record of any legal

claims against the applicant will be helpful in this assessment.

Conditions The prevailing economic and business climate as well as unique

circumstance affecting the applicant will be considered.

Character and Capacity receive primary attention; capital, collateral and conditions play

a supplementary role.

Sources of Information on the Debtor

The evaluation of an applicant begins when he fills a form providing basic financial

and credit data and references. Additional information will be obtained from other

sources depending on time and expense and size of credit involved. The credit

analyst may obtain information from the following sources.

Financial Statements The seller may request the audited financial statements of the

applicant for a number of years. The trends shown by the statements would help

gauge financial strengths.

Credit Rating And Reports Credit rating agencies provide subscribers with credit

rating and estimates of overall financial strength for many companies (Dun &

Bradstreet is the largest mercantile credit reporting agency in the world. In Kenya, the

industry is in its infancy with Metropol Rating Agency one among the very few firms

active).

Bank Checking The applicant’s bank could be a good source of information for the

credit analyst. The credit analyst can obtain information such as average cash balance

carried, loan granted and recovery of loan experience. Despite existence of banking

secrecy laws, the credit applicant will allow his bank to provide the information in

order to facilitate his being granted credit.

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Trade checking Credit information is frequently exchanged among companies

selling to the same customer. Companies can ask other supplies about their

experience with an account.

Credit Analysis

Having collected information, the credit analyst must conduct a credit analysis of the

applicant. The analyst must decide on the applicant’s credit worthiness and the

maximum amount of credit the applicant can support – the line of credit (maximum

amount a credit customer can owe the selling firm at any one time). Two approaches to

credit analysis are discussed below.

(a) Investigations Procedures

The following ad hoc procedures are usually employed by small firms and by big firms on small accounts

(1) Applicant’s financial statements and accounts payable ledger can be used to

calculate the “average payment period”

(2) Consult past experience to see whether the firm has sold previously to the account

(applicant) and whether that experience has been satisfactory.

(3) A through ratio analysis of the accounts liquidity activity, debt and profitability.

(4) A credit rating agency’s recommendation could be obtained and used to estimate

the maximum line of credit to extend.

(5) Time series comparison should be performed to uncover any trends.

(6) The credit analyst's own subjective judgment of a firm’s credit worthiness could

be decisive.

(a) Credit scoring systems

These systems employ quantitative approaches to decide whether or not to grant

credit, by assigning numerical scores to various characteristics related to the

applicant’s credit worthiness. The credit score is a weighted average of scores

obtained on key financial and credit characteristics. In consumer credit, plastic credit

cards are often given out on the basis of a credit-scoring system that rates such things

as occupation, duration of employment, home ownership, years of residence and

annual income. Numerical rating systems are also used by some companies

extending trade credit (credit granted from one business to another).

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Credit Decision And Line Of Credit

Once the analyst has marshaled the necessary evidence and analyzed it, two decisions

must be made:

(1) Whether to extend the credit

(2) Whether to establish a line of credit. A line of credit is used where repeat sales

are expected. It is the maximum limit on the amount the firm will permit to be

owed at any one time by the applicant. In essence it is the maximum risk

exposure that the firm will allow itself to undergo for an account.

11.2.2 CREDIT STANDARDS

Credit standards define the minimum criteria for the extension of credit to a customer.

Extension of credit has its costs (risks) even as it has benefits. In determining the

optimal credit standards, marginal costs of credit should be related to the marginal

profits from the increased sales.

Key variables that should be considered in evaluating relaxation or tightening of

credit standards are:

(a) Clerical and collection expenses – If credit standards are relaxed/tightened,

more/less credit is offered and a bigger/smaller credit department is needed to

service accounts.

(b) Investment in Receivable – The higher the firm’s average accounts receivables

are, the more expensive they are to carry, and vice versa. Thus a relaxation of

credit standards can be expected to result in higher carrying costs and a tightening

of credit standards results in a lover carrying costs.

(c) Default and Bad date Expenses: the probability of (risk) of acquiring a bad debt

increases as credit standards are relaxed and decreases as the standards become

more restrictive.

(d) Sales Volume and contribution margin: it is expected that as credit standards

are relaxed, sales (contribution margin) will be expected to increase; a tightening

of credit standards is expected to reduce sales (contribution margin).

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The table below summarizes the basic change and effects on profit expected to

result from relaxation of credit standards.

Table 13.1 Effect of a relaxation of credit standards

Item Direction of Change Effect on Profits

Sales volume(contribution) + +

Average Collection period + -

Bad debt expense + -

The opposite effects result when standards are tightened.

Example

XY Co. is currently making annual sales of 120,000 units at Sh.10 per unit. The variable

cost per unit is Sh.6 and average cost per unit, given the current sales volume is Sh.8.

The firm is contemplating a relaxation of credit standards that is expected to result in

15% increase in unit sales, an increase in average collection period from 30 days to 45

days, and an increase in bad debt loss rate from 2% to 3% of total sales. Additional

working capital (apart from accounts receivable) needed will remain at 25% of sales

even if the credit standards are relaxed. The firm has excess capacity and can increase

sales without a corresponding increment in Fixed Assets. The firm’s cost of capital is

12%. Determine whether it is advisable for the firm to relax its credit standards. Assume

360-day year.

Solution

Additional Profit Contributions from Sales

Current plan

Sales revenue (120,000 x 10) 1,200,000

Less costs

Variable (120,000 x 6) 720,000

Fixed (8-6) x 120,000) 240,000

Total costs 960,000

Net profit 240,000

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Proposed plan

Sales revenue (120,000 x 115% x 10) 1,380,000

Less: Costs

Variables (138,00 x 6) 828,000

Fixed (no change) 240,000

Total costs 1,068,000

Net profit 312,000

Addition profit contribution with new plan = 312,000 – 240,000 = Sh.72,000

Other costs of new plan

Cost of the investment in Accounts receivables (A/R)

Under the current plan:

Average A/R = 1,200,000 x 30 = Sh.100,000

360

Average Investment in A/R = variable cost ratio(VC ratio) x Average A/R

=( 6/10) x 100, 000 = 60,000

Cost of Investment in A/R = 60,000 x 15% = Sh.9,000

Under proposed Plan:

1,380,000 x( 45/360)*VC ratio = 172,500 x 0.60 = 103,500

Cost of investment in A/R = 103,500 x 15% = Sh.15,525

Incremental cost of investment in A/R = 15525-9,000 = Sh. 6,525

Cost of additional working capital (WC) under proposed plan

Current plan’s WC needs = 25% x 1,200,000 = 300,000

Cost working capital = 15% x 300,000 = Sh.45,000

Proposed plan’s WC needs = 25% x 1,380,000 = 345,000

Cost of WC = 15% x 345,000 = Sh.51,750

Marginal increment in cost of WC =51,750-45.000 = Sh.6,750

Bad debt losses

Current plan = 2% x 1,200,000 24,000

Proposed Plan = 3% x 1,380,000 41,000

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Marginal increment in bad debts 17,400

Overall benefits of relaxation in credit standards = 72,000 – 6,525 – 6,750 – 17,400 =

Sh.41.325. Therefore a relaxation in credit standards is advisable.

11.2.3 CREDIT TERMS (TERMS OF SALE)

Credit terms specify the repayment terms required of all credit customers ( i.e. 2/10,net

30. Credit terms make specification on three issues:

(1) the cash discount (2)%

(2) the cash discount period (10 days)

(3) the credit period (30 days)

Changes in any aspect of the firm’s credit terms may have an effect on its overall

profitability of the company.

Cash Discounts

An increase in a cash discount will lead to the following changes and effect, as shown in

Table 11.2

Table 11.2 Shows the effects of a n increase in cash discounts granted on the

financial variable . A decrease will have the opposite effects.

Item Direction of change Effect on profits

Sales volume + +

Average Collection period - +

Bad debt expenses - +

Profit per unit - -

The sales volume increases since the cash discount effectively reduces the price for those

firms ready to pay within the discount period. (assuming demand is elastic). The

Average collection period decreases because the discount acts as an inducement for early

payment. The bad debt expense falls because as people pay earlier, the risk of a bad debt

decreases. The increase in sales, and the decrease in average collection period and bad

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debt expense have a positive effect on net profits. Increased cash discount has however

the negative effect of a decreased profit margin per unit as more people take the discount

and pay the reduced price.

Example

XYZ Co. is contemplating initiating a cash discount of 2% for payment within 10 days of

purchase. The firm’s current average collection period is 30 days.. Credit sales of

120,000 units at a price of Sh.10 are made annually. Variable cost per unit is Sh.6, and

average cost per unit is Sh.8. If the discount is initiated 70% of sales will be on discount

and sales will increase by 10%. The average collection period will drop to 15 days. Bad

debt expenses currently at 2% of sales will fall to 1%. Total working capital needed will

not be affected by the cash discount. The firms required return on investment is 12%.

Assume no additional capital investment will be necessary.

Evaluate the proposal to initiate a discount.

Solution

An additional (10% x 120,000) 12,000 units will be sold whose contributions to profit is

12,000 x 4 = Sh.48,000

Average Investment in A/R (receivables).

Current plan – 120,000/12 = 100,000

Proposed plan = 1,320,000/24 = 55,000

Reduction in Average A/R = 45,000

Savings = 45,000 x 12% = Sh.5,400

Bad debts Expenses

Current plan = 2% x 1,200,000 = 24,000

Proposed plan = 1% x 1,320,000 = 13,200

Saving in bad debt losses 10,800

Cash discount costs

Cash discount 2% x 1,320,000 x 70% = Sh.18,480

Net benefit of cash discount =48,00 + 5,400 + 10,800 – 18,480 = Sh.45,720

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The Cash Discount Period

Increased cash discount period leads to the following changes in profits.

Table 11.3 Shows the impact of an increased cash discount period on the financial

variables of a firm granting credit

Change Effects on profits

Item (increase + ) (profits +)

(Decrease -) (negative –)

Sales volume + +

Average Collection period due to

non discount taker now

paying earlier - +

Profit per unit - -

Bad debt expense - +

Average collection period due to

discount takers still taking the

cash discount but now

paying later + -

When cash discount period is increased, there is a positive effect on profits

because people who formerly were not taking the discount will now take it

thereby reducing the average collection period. On the negative side people who

already were taking the cash discount will be able to still take it and pay later thus

slowing down collection of receivables.

Credit Period

The following effect on profits can be expected form an increase in the credit

period.

Item Change Effect on Profits

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Sales volume + +

Average Collection period + -

Bad debt expense + -

Increasing the credit period should increase sales, the average collection period,

and the bad debts expense.

Example

A company is considering increasing its credit period from 30 to 60 days. The

average collection period currently 45 days is expected to increase to 75 days.

Bad debt expenses currently 1% of sales, are expected to increase to 3%. Sales

(credit) are expected to increase by 15% to 69,000 units. The selling price and

variable cost per unit are Sh.16 and Sh.12 respectively. The firm’s cost of capital

is 15%. Assess the planned increase in discount period.

Solution

Additional profit contribution from sales

9000 x 4 36,000

Cost marginal investment in A/R

Proposed credit period

[(16 x 69,000)/4.8]*0.15 34,500

Present credit period

[(16 x 60,000)/8.0]*0.15 18,075

Cost of marginal investment (16,425)

Cost of marginal bad debts

Bad debts with current plan

0.03 x 1,104,000 33,120

Bad debts with current plan

0.01 x 960,000 9,600

Cost of marginal bad debts (23,520)

Net loss from implementation of proposed plan (3,945)

This suggests that the change should not be made.

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11.2.4 COLLECTION POLICIES

Are the procedures followed to collect account receivables when they are due. The level

of bad debts is a reflection, partially on the effectiveness of a firms collection policies and

partially on the credit policies on which extension of credit is based. If we assume the

level of bad debts attributable to credit policies is constant, increasing collection

expenditures affect the overall level of bad debts as shown below.

Beyond point A additional collection expenditures will not reduce the firm’s bad debt

losses enough to justify the outlay in funds.

Trade-Offs

The trade-offs expected from tightening of collection efforts are as follows

Table13.5 Shows the trade-offs of tightening collection policies.

Item Change Effect on Profits

Bad debt expense + -

A.C.P - +

Sales volume - -

Collection expenditures + -

Increased collection expenditures should reduce the bad debt expense and the average

collection period/thereby increasing profits. The negative effects of this policy

include lost sales and increased collection expenditures. The various strategies for

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tightening or relaxing the collection effort may be assessed by calculating the

marginal cost of increased efforts and the decreased profit contribution from sales and

comparing this to savings from both reduced bad debt expenses and decreased

investment in accounts receivable.

Types Of Collections Techniques

As an account becomes more and more overdue, the collection techniques used

become more personal and strict. The collection techniques used may include.

Letters: When an account becomes long overdue a firm normally sends a polite

letter reminding the customer of his obligation. A second and third more demanding

letter may be sent if the customer does not respond.

Telephone Calls: The credit manager or the company’s lawyer may call the

customer and personally request for pay if letters prove unavailing.

Personal Visits: A local sales person may be sent to confront the customer.

Collection Agencies: A firm engages the services of a debt collector. This technique

should be used sparingly because the fees are normally high.

Legal Action: This step is taken as a last resort. If may force the customer into

bankruptcy.

Cost Consideration

Generally the effort expended in collecting depends upon the size of the account and the

possibility of ultimate collection. Affirm should usually not spend more on collection

fees than the value of the account to be collected (more than what it expects to collect).

Banks may be prepared to spend more so that they are not perceived as always writing off

poor debts.

CLASS ILLUSTRATIONS

Example one R Ltd is considering a change of credit policy, which will result in an

increase in the average collection period from one to two months. The relaxation in

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credit is expected to produce an increase in sales each year amounting to 25% of the

current sales volume.

Selling price per unit Sh.1000

Variable cost per unit 850

Current annual sales 240 million

The required rate of return on investment is 20%. Assume that the 25% increase in sales

would result in additional stocks of Sh.10 million and additional creditors of Sh.2 million.

Advise the Company whether or not to extend the credit period if:

(a) all customers take the longer period of two months.

(b) Existing customers do not change their payment habits; only the new

customers take a full two months credit.

Solution:

The change in credit policy is justifiable if the rate of return on the additional investment

in working capital would exceed 20%.

Contribution/sales ratio 15%

Increase in sales revenue 60 million

Increase in contribution profits 15% x 600 9 million

(a) If all the debtors take 2 months credit

Average debtors after sales increase (2/12 x 300 m 50,000,000

Less current average debtors (1/x x 240 m) 20,000,00

Increase in debts 30,000,000

Increase in stocks 10,000,000

40,000,000

Less increase in creditors 2,000,000

Net increase in WC investment 38,000,000

Cost of investment in WC (38m x 0.2) 7,600,000

Net increase in benefit (9m – 7.6m) 1.400,000

(b) If only new debts take 2 months credit

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Increase in stock 10,000,000

Increase in stocks 10,000,000

Increase in creditors (2,000,000)

Net increase in WC investment 18,000,000

Cost on investment (18m x 0.2) 3,600,000

Net benefit ( 9m – 3.6m) = 5,400,000

It is worthwhile taking on the new credit policy in both cases.

Example 2: Credit Term

LP Ltd has annual credit sales of Sh. 120 million, and three months are allowed for

payment. The Co decides to offer 2% discount for payment made within ten days of the

invoice being sent, and to reduce the maximum time allowed for payment to two months.

It is estimated that 58% of the customers will take the discount. If the company requires

a 20% return on investments, what will be the effect of the discount if the cost per unit is

Sh. 90 and the selling price is Sh. 100? Assume volume of sales will be unaffected by

discount.

Solution:

Current volume of debtors 3/12 x 120m = 30,000,000

Volume of debtors with changed policy

(10/360 x 50% x 120 m) + (2/360 x 50% x 120m) = 11,666,667

Reduction in debtor with change 18,333,333

Saving in cost of investment in debtors (20% x 18,333,333) 3,666,667

Less discount allowance each year (22 x 50% x 120m) (1,200,000)

Net benefit of new discount policy each year 2,466,667

Example Three: Bad Debt risk KK Ltd. achieves current annual sales of Sh.18,million. The cost of sales is 80% of this

amount but bad debts average 1% of total sales, and annual profit is as follows:

Sales 18,000,000

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Less costs of sales (1 4,400,000)

3,600,000

Less bad debts (180,000)

Profit 3,420,000

The company is considering the following effects of changes in its current credit policy.

Present policy proposed policy

Additional sales (%) - 25%

Av. Collection period 1 month 2 months

Bad debt (% of sales) 1 % 3%

The company requires a 20% return on its investment.

If cost of sales is 75% variable and 25% fixed and on the assumption that:

(a) There would be no increase in fixed costs from the extra turnover.

(b) There would be no increase in average stocks or creditors

What is the preferable policy.

Solution:

(1) The increase in profit before cost of additional finance for proposals is:

Increase contribution margin from additional sales is:

25% x 18m x 40%* 1,800,000

Less increase in bad debts:

(3% x 22.5m) – 180,000 (495,000)

Increase in annual profit 1,305,000

* The CM/S ratio is 100% - 75% x 80% = 40%

(2) Proposed investment in debtors

22.5m x 2/12 3,750,000

Less current investment in debtors (18m x 1/12) 1,500,000

Additional investment 2,250,000

Cost of additional finance at 20% 450,000

Net benefit of proposed policy (1 305,000 – 450,000) = Sh.855,000

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Example Four: collection policy CP Ltd requires advice on its debt policy. Should the Current policy be discarded in

favour of Options 1 or 2?

Current policy Option 1 Option 2

Annual expenditure on debt

collection 240,000 300,000 400,000

Bad debt losses (% of Sales) 3% 2% 1%

Average collection period 2 months 1½ months 1 month

Current credit sales are Sh. 4,800,000 and the company requires 15% return on its

investments.

Solution: Current policy Option 1 Option 2

Average Debtors 800,000 600,000 400,000

(a) Savings in cost of investment in

debtors (15% x red) - 30,000 60,000

Bad debt loses (sales value) (144,000) (96,000) (48,000)

(b) Reduction in bad debt losses 48,000 96,000

Benefits of each option (a) + (b) 78,000 156,000

Extra cost of debt collection 60,000 160,000

Net benefit/(loss) from option 18,000 (4,000)

Option 1 is preferable.

11.3 Inventory Management

Inventories ensure the smooth functioning of the production-sale or purchase-sale process

of firms. A stock of raw materials and work-in-progress facilitates the production

function while finished goods stocks provide a buffer that enables the firm to satisfy

sales demands as they arise.

Types of Inventory

The basic types of inventory are:

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(a) Raw materials are necessary for production of the final product. The actual

level of raw materials stocked depends on:

- lead time it takes to receive an order. The longer the lag between

placement and receipt of an order the higher the stock levels.

- The frequency of use. The stocks of frequently used items will be higher.

- The investment required: greater amounts of outlay are necessary for

expensive items.

- The physical characteristics of the inventory itself. Bulky and perishable

items would not be ordered in large quantities.

(b) Work-in-progress (W.I.P) These are partially finished goods that are at

some intermediate stage of production. They occur because production

processes are not instantaneous. The longer the firm’s production cycle the

higher the level of W.I.P inventory expected.

The W.I.P is the least liquid of a firms inventory (it hard to sell partially

finished goods or over use them as security for loans) and has the

characteristics that it builds up in value as it an item is transformed from raw

materials to finished state.

( c) Finished goods – These consist of items already produced but not yet sold.

The level of finished goods inventory is determined by:

- Projected demand. Safety stocks may be maintained as security against

unexpected demand or production stoppages.

- The production process. Scheduling and proper planning of production

process may reduce inventory levels.

- Investment made in finished goods inventory. Inventories of specialized

high-cost items will normally be kept at a minimum.

Inventory as an Investment

The relationship between inventory an account receivable inventory and account

receivable are closely related. A decision to extend credit to a customer may

result in increased sales that can only be supported by higher levels of stocks and

A/R. The credit terms extended will also influence the investment in inventories

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and receivables since longer credit may allow a firm to move items from

inventory to receivables. Since cost of carrying an item as inventory is higher

than as A/R such a strategy is advantageous.

Optimal Investment in Inventories

The inventory is an investment in the sense that it requires the firm to tie up its money.

Average inventory = cost of goods sold

Inventory turnover The management of stocks involves the balancing of the cost of stock shortages against

the costs of holding stocks. Three aspects of stock management are:

(1) The economic order quantity (EOQ) can be used to decide the optimum order

size (which minimizes ordering plus stockholding costs)

(2) Deciding on whether to take advantage of discounts for bulk purchases.

(3) Decision on how to deal with uncertainty in demand and/or the supply lead-

time. The question to be addressed is: How much buffer stock is necessary to

eliminate the risk of “stock-outs”?

Stock Costs

Stock costs can be classified into four groups.

(a) Holding Costs: the cost of capital tied up, warehousing and handling costs,

deterioration, obsolescence, insurance and pilferage.

(b) Procuring costs (ordering costs): for goods purchased externally these comprise,

clerical costs, telephone charges and delivery costs.

(c) Shortage Costs may include:

(i) the loss of a sale and the contribution from the lost sale.

(ii) The extra cost of having to buy an emergency supply of stocks at a

high cost.

(iii) The cost of lost production and sales, where the stock-out bring an

entire process to a halt.

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(d) Cost of the stock itself – the supplier’s price will need to be considered when

bulk discounts are given.

Minimizing inventory costs:

cost (Sh) total operating

stock costs

carrying cost

ordering and stock out costs

inventory levels

The objective is to minimize total costs (holding and ordering costs)

T = (Qh)/2 + (cd)/Q

stock levels

average total hold Q

2

Time

The order quantity (EOQ) which will minimize these total costs (no bulk purchase

discounts) is

EOQ = hcd2 (13.6)

Example:

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The demand for a commodity is 40,000 units a year, at a steady rate. It costs Sh. 2000 to

place an order, and 40/- to hold a unit for a year. Find the order size to minimize stock

costs, the number of orders placed each year, and the length of the stock cycle.

Solution

EOQ = hcd2 =

40000,40*000,2*2

= 2000 units

Number of orders in a year = 40,000/2,000 = 20 orders

The stock cycle = 52 ÷ 20 = 2.6 weeks.

Total inventory cost will be:

Ordering cost = 20 x 2000 = Sh.40,000

Carrying cost = 2000/2)*40 = Sh.40,000

Total costs Sh. 80,000 a year.

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Problems 11.1 Joan Mbaka, a financial analyst for Kuona Mbee Distillers has been asked to investigate a proposed change in the firm's credit terms. The company’s founder and chief executive believes that by increasing the credit period from 30 to 65 days, two important benefits will result: (1) sales will increase as a result of attracting new customers, and (2) some existing customers will purchase merchandise sooner to ensure its availability, given the unpredictable timing of the selling seasons. Annual sales are estimated to increase from the current level of Sh.400 million to Sh.480 million. Eighty percent of this increase is attributable to new customers, and the other 20% is expected to result from existing customers. Because some existing customers will be making their purchases earlier than in the past, their actions will merely result in a shifting of inventory to accounts receivable. Joan estimated that the decline in inventory investment attributable to the actions of existing customers would just equal the additional accounts receivable investment associated with their actions. Joan’s investigation indicates that with the extended credit period, the firm’s average collection period would increase 45 to 90 days. In addition, bad debts would increase from 1 to 2.5 % of sales. The firm’s variable costs are expected to continue to amount to 80% of each Sh.1 of sales. Kuona Mbee Processors currently requires a 16% rate of return on equal-risk accounts receivable investments, and its cost of carrying Sh.1 inventory for 1 year is 26 cents. Required

a. Find the additional annual profit contribution expected from the increased credit period.

b. Determine the increase in Kuona Mbee’s average investment in accounts receivable and the resulting annual cost attributable to the proposed increase in the credit period.

c. Calculate the annual savings resulting from the decrease in inventory investment attributable to the existing customers’ earlier purchases.

d. Calculate the annual cost expected to result from the increase in bad debt expenses attributable to the proposed lengthening of the credit period.

e. Use your findings in a through d to advise Joan on whether or not the proposed increase in the credit period can be financially justified. Explain your recommendations.

f. What impact, if any, would ignoring the effect of the proposed increase in the credit period on the level of inventory investment found in c have on your recommendation in e? Explain.

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DFI 501: FINANCIAL MANAGEMENT CLASS DISCUSSION QUESTIONS

QUESTION ONE

a). Explain the meaning of the term leverage as applied in finance (6 marks) b. Nameless Drapers Ltd. makes a patented headscarf that wholesales for Sh.600. Each scarf has variable operating cost of Sh.350. Fixed operating costs are Sh.5,000,000 per year. The firm pays Sh.1,300,000 interest and preferred dividends of Sh.700,000 per year. At this point the firm is selling 30,000 scarves a year and is in the 40% tax bracket.

Required

i. Calculate Nameless Draper’s operating breakeven point in units and shillings. (4 marks)

ii. Based on the firm’s current sales of 30,000 units, calculate its EBIT and net profits. (2marks)

iii. Calculate the firm’s degree of operating leverage (DOL) (3marks). iv. Calculate the firm’s degree of financial leverage (DFL) (3marks) v. Calculate the firm’s degree of total leverage (DTL). (3 marks) vi. Nameless Drapers Ltd. has entered into a contract to produce and sell an additional

15,000 scarves in the coming year. Use the DOL and the DFL to predict the changes in the EBIT and the net profit (3 marks)

(Total: 25 marks)

QUESTION TWO

(a) The most recent balance sheet of Nguvu Limited is presented below:

Nguvu Limited Balance Sheet-30 June 2007 Sh. “000” Sh. “000” Current Assets 88,000 Trade creditors 22,000 Fixed Assets (net) 132,000 Accrued expenses 22,000 Current Liabilities 44,000 Long term debt 88,000 Ordinary shares 22,000 Retained earnings 66,000 220,000 220,000The company is about to embark on an advertising campaign which is expected to raise sales from their present level of Sh.275 million to Sh.385 million by the end of next financial year. The firm is currently operating at full capacity and will have to increase its investment in both current and fixed assets to support the projected level of sales. It is estimated that both categories of assets will rise in direct proportion to the projected increase in sales. For the year just ended, the firm’s net profits were 6% of the year’s sales but are expected to rise to 7% of the projected sales. To help support its anticipated growth in assets needs next year the firm has suspended plans to pay cash dividends to its shareholders. In years past a dividend of Sh. 6.60 had been paid annually. Nguvu Ltd.’s trade creditors and accrued expenses are expected to vary directly with sales. Notes payable will be used to supply the extra external funds needed to finance next year’s operations that are not forthcoming from other sources.

Required Prepare a pro-forma balance sheet of Nguvu Ltd as at 30 June 2008. (13 marks)

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(b) Biashara Traders are concerned about managing their cash in an efficient manner. On average trade debtors are collected in 45 days. Stocks turns over 4.8 times in a year and trade creditor are paid approximately 30 days after they arise. Assume a 360-day year. Required Calculate the following for the firm: (i) The cash cycle (6marks) (ii) The operating cycle (6marks)

(Total: 25marks)

QUESTION THREE

(a) Identify the five Cs of credit and briefly outline their role in credit selection. (10 marks)

(b) Fashion Furniture is evaluating the extension of credit to a new group of customers. Although

these customers will provide Sh.18million in additional sales, 12 percent are likely to be

uncollectible. The company will also incur Sh 1.4 million in additional collection expenses.

Production and marketing costs represent 80 percent of sales. The firm is in the 40 percent tax

bracket and has a receivable turnover of 5 times. No other asset buildup will be required to

service the new customers.

Required

(i) If Fashion Furniture has a 10% required return determine the financial viability of

extending credit. (6 marks)

(ii) If 15 percent of the new sales prove uncollectible, does this affect your decision in above?

(4 marks)

(iii) Should the credit be extended if receivables turnover drop to 1.5, and 12 percent of

accounts are uncollectible? (5 marks)

(Total: 25 marks)

QUESTION FOUR The following financial statements as at the end of 2004, and historical ratios relate to Biashara limited. Corresponding average ratios for the industry in which Biashara operates are also provided.

Biashara Limited Income Statement

For year ended 31 December 2004

Net sales Sh. Cash 300,000 Credit 9,700,000 Total 10,000,000 Less: cost of goods sold 7,500,000Gross profit 2,500,000 Less: Operating expenses Selling 300,000 General and admin. 700,000

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Depreciation 200,000 1,200,000Operating profit 1,300,000 Less: interest expense 200,000Profit before tax 1,100,000 Less Taxes (40%) 440,000Profits after tax 660,000 Less preference dividend 50,000Earnings available to ordinary shareholders

610,000

Less ordinary dividend 200,000To retained earnings 410,000

Biashara Limited Balance sheet

As at 31 December 2004 ASSETS Sh Current assets Cash 200,000

Marketable securities 50,000 Accounts receivables 800,000 Inventories 950,000 Total current assets 2,000,000 Gross fixed assets 12,000,000 Less: Accumulated dep’n 3,000,000 Net fixed assets 9,000,000 Other assets 1,000,000Total assets 12,000,000LIABILITIES AND EQUITY Current liabilities Accrued liabilities 100,000 Notes payable 200,000 Accounts payable 100,000 Total current liabilities 1,200,000 Long term debts 3,000,000 Shareholders equity Preference shares 1,000,000 Ordinary shares (Sh. 75 par)

3,000,000

Share premium 2,800,000 Retained earnings 1,000,000 Total shareholders equity 7,800,000 Total liabilities and equity 12,000,000 Note: (a) Annual credit purchases of Sh.6,200,000 were made.

(b) The annual principal payment on the long term loan debt is Sh.100,000. (c) The firm has 25,000 shares of Sh.2 preference shares outstanding.

HISTORICAL DATA FOR BIASHARA LIMITED AND INDUSTRY AVERAGES

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DATA INDUSTRY AVERAGE 2004

2002 2003 Current ratio 1.40 1.55 1.85 Net working capital Sh.760,000 Sh.720,000 Sh.1,200,000 Acid test ratio 1.00 .92 1.05 Average age of accounts receivable

45.0 days 36.4 days 35.0 days

Inventory turnover 9.52 9.21 8.60 Average age of accounts payable

58.53 days 60.75 days 45.75 days

Debt ratio .20 .20 .30 Debt-equity ratio .25 .27 .39 Debt-to-total capitalization ratio

.22 .22 .27

Gross profit margin .30 .27 .25 Operating profit margin .12 .12 .10 Net profit margin .067 .067 .058 Total assets turnover .74 .80 .74 Return on investment .049 .054 .043 Return on equity .078 .085 .084 Earnings per share Sh.8.65 Sh.11.05 Sh.7.45 Dividends per share Sh.2.60 Sh.3.65 Sh.2.45 Book value per share Sh.140 Sh.150 Sh.175 Times interest earned 8.2 7.3 8.0 Total debt coverage 4.8 4.5 4.5 Required

(a) Compute the corresponding ratios for Biashara Limited for 2004. (b) Select appropriate ratios and analyze the liquidity, leverage, activity and profitability of the

company both cross-sectionally and trend wise. QUESTION FIVE The following projections of sales have been made in respect of Mugumo Company for the seven months of 2006.The company closes its year and prepares its accounts on 31st December.

January Sh.900,000 February Sh.2,200,000 March Sh.1,350,000 April Sh.2,400,000 May Sh.3,000,000 June Sh.2,700,000 July Sh.2,250,000

Additional Information

1. 10% of the sale are sold for cash and the rest collected as follows: • 60% collected in the month following the month of sale • 30% collected in the second month following the month of sale

2. November and December 2005 sales were Sh.2,200,000 and Sh 1,750,000 respectively 3. Mugumo purchases and pays for the merchandise one month in advance . Cost of goods sold

average 60% of sales price. 4. Salaries and wages average Sh.600,000 per month, 20% of which is always accrued and paid

at the year end.

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5. Monthly rent payments amount to Sh.250,000. In addition the company pays Sh.200,000 in miscellaneous expenses.

6. Depreciation expense per month is Sh. 90,000. 7. Tax payments amounting to Sh.230,000 are to be paid each quarter beginning March. 8. The company’s cash balance at December 31st 2005 was Sh228,000;a minimum balance of

Sh.150,000 must be mantained at all times. 9. All borrowings are to be made at the beginning of the month in even thousands and at an

interest rate of 12% per annum. Monthly interest payments are to be made beginning the month following the month of borrowing

10. Any excess cash is to be used to repay any loans outstanding. This repayment of the principal is to be done in even thousands.

Required (a) Prepare a cash budget for Mugumo Limited covering the first six months of 2006. (b) Explain the uses of a cash budget.

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DFI 501: FINANCIAL MANAGEMENT CONTINUOUS ASSESSMENT TEST 1

KISUMU CAMPUS JULY 2009

Instructions

1. Answer all the four questions. Marks allocated are shown at the end of each question.

2. Be neat and show necessary workings. 3. When appropriate qualitative answers to be brief and in point form. 4. Time allowed: 2 hours.

QUESTION ONE Urembo Fabrics Ltd. (UFL), an apparel manufacturer, is in the process of expanding its productive capacity to introduce a new line of products. Current plans call for a possible expenditure of Sh.1 billion on four projects of equal size (i.e. Sh.250 million), but with different returns. Project A will increase the firm’s processed yarn capacity and has an expected return of 15%. Project B will increase capacity for woven fabrics and carries a return of 13.5%. Project C is a venture into synthetic fibres and is expected to earn 11.2%. Project D is an investment into dye and textile chemicals and is expected to show a 10.5% return. The firm’s capital structure consists of 40 percent debt and 60 percent common equity, and this will continue in the future. UFL has Sh.150 million in retained earnings available for investment. The company’s ordinary share is now selling at Sh.30 and underwriting expenses are estimated at Sh.3 per share if new shares are issued (after exhausting the retained profits). Ordinary dividends for the next year will be Sh.1.50 per share, and earnings and dividends, which have grown consistently at 9%, are expected to maintain this growth rate in future. The yield on comparative bonds has been hovering at 11%. The company’s investment banker feels that the firstSh.200 million of bonds could be sold to yield 11% while additional debt might require a 2% premium. Assume a corporate tax rate of 45%. Required

(a) Determine the break points in the firm’s capital structure. (4 marks) (b) Calculate the marginal average cost of capital before and after each break

point determined in (a) above. (6 marks) (c) Based on the information on the potential returns on the four projects and the

marginal average cost of capital of the firm, determine the firm’s optimal capital investment budget. (4 marks)

(d) Depict your answer in (c) above by graphing the investment opportunity, and the weighted marginal cost of capital schedules on the same axes. (6 marks)

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(e) A key concept in the capital asset pricing model (CAPM) is the beta. Write brief explanatory notes on the beta (5 marks)

(Total: 25 marks) QUESTION TWO

Mark Sang is considering giving up his paid employment and venturing into business on his own account. He is considering purchasing a quarry pit with a ‘life’ of 35 years. To purchase the quarry, Mark will have to pay Sh.2,375,000 now. Mark wishes to work the quarry for the next 20 years, which coincides with the remaining active life in paid employment. Mark earns Sh.250,000 per annum from his current job. Mark predicts that the net operating cash receipts from the business (before any

compensation to himself) will be Sh.625,000 per annum for the first 15 years and

Sh.500.000 per annum for the last 5 years. He thinks that the business could be sold at

the end of 20 years for Sh.750,000.

Further, Mark thinks that certain capital replacements and improvements would be necessary and this would amount to Sh,50,000 per annum for the first 5 years, Sh.75,000 per annum for the next 5 years, Sh.100,000 per annum for the next 7 years and nothing for the last 3 years. These expenditures are to be incurred at the beginning of each year. To finance the purchase of the quarry pit , Mark would have to realize his savings which are invested to yield a rate of return of 10% before tax , and have a comparable risk factor to the Quarry business.

Required

(a) Compute the net present value of the business and advice Mark on whether or not to buy the business (Ignore income tax). (14 marks)

(b) State and explain three circumstances in which the IRR and the NPV techniques could lead to conflicting rankings of investment projects. (6 marks)

(Total: 20 marks)

QUESTION THREE

(a) The Great Rift Valley Company has just finished making an annual dividend payment of Sh.2 per share of its ordinary stock. Earnings and dividends are expected to grow at a 9% annual rate indefinitely. Investors currently require a rate of return of 13%. The company is considering several business strategies and wishes to determine the effect of these strategies on the wealth of its shareholders. Strategy I Continuing the present strategy, which results in the expected growth rate and required rate of return stated above.

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Strategy II Expanding timber holdings, which will increase the expected dividend growth rate to 11% in the foreseeable future, but will increase the risk of the company. As a result the rate of required return will increase to 16%. Strategy III Integrate into retail stores, which will increase the dividend growth rate to 10%, and increase the required rate of return to 14% in the foreseeable future. Strategy IV Acquiring a competitor, which will result in the growth of dividends at an annual rate of 16% for the next five years to be followed by a growth of dividend of 7% thereafter indefinitely. The required rate return would be maintained at 13%. Required

From the standpoint of market price per share, determine the best strategy. (16 marks) (b) Chakaza Betting Ltd. has outstanding a Sh.1000 face value bond with a 14% coupon rate and 3 years until maturity. Interest payments are made semi-annually. Required

(i) The value of the bond if the annual required return is (1) 12%, and (2) 14%. (3 marks)

(ii) The yield to maturity on the bond assuming it is currently selling at Sh. 953.61. (3 marks)

(iii) The value of a bond similar to the one of Chakaza except that the bond is a zero-coupon, pure discount bond, and that the annual required rate of return is 16%.

(Assume semi-annual discounting) (3 marks) (Total: 25 marks) QUESTION FOUR

(a) Squirrel Photocopiers Limited uses 165,000 reams of A-4 paper a year. Its current paper supplier charges Sh.250 per ream. Annual inventory carrying costs are 1.5 percent of inventory value. The costs of placing and receiving an order of paper are Sh.325. Assume that inventory replenishment occurs virtually instantaneously. Required

Determine the following for the company: (i) The Economic Order Quantity (3marks) (ii) The total annual inventory cost (3marks) (iii) The optimal ordering frequency (2marks)

(b) Mtongwe Limited has an average selling price of Sh.100 for a component it manufactures for sale in the local market. Variable costs are sh.70 per unit and fixed costs amount to Sh.1,700,000. The company has financed its assets by have issued 40,000 ordinary shares.

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Another company in the same industry, Bombululu Limited, has the same operating information but has financed its assets with 20,000 ordinary shares and a loan which has an interest payment of Sh.160,000 per year. Both companies are in the 40% tax bracket and have sales of Sh.7,000,000 in the current financial year. Required For each company , determine: (i) The degree of operating leverage (3marks) (ii) The degree of financial leverage (3marks) (iii) The degree of combined leverage (3marks) (iv) The break-even point (3marks)

(c) List and briefly discuss the 5Cs of credit (5marks) (Total: 25marks)

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