financial management - long term investment decision process and relevant cashflows

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

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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.

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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.

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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,

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(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.

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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.

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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)

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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.

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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


Year3 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 = = 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





Pay back period

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.

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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

________________________________________________________________________

Year Cash flows (Sh.)

1 5 million 80 million

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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.

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.

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NPV = PV of cash inflows – Initial Investment (II)

NPV =

(6.1)

=

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

Project B

Year Cash Inflows PVIF PV

1 28million .909 25.452m

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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

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.

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

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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 = , 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.

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%

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We can interpolate to get a more accurate rate.

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

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.

Discount rate

IRR

NPV

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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

, 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, .

Project B, .

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.

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

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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

Using the PI

Project PI NPV Initial outlay

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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

ExampleSuppose 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

Project A 100% 231 3.31

Project B 25% 29,132 1.29

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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)ExampleAssume 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%

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%

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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.

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

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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.

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

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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* =

3303

NPV of chain 8638

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)

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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.

PROBLEMS5.1 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 returnA 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.(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 1002009 1502010 2002011 2502012 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

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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 8012009 1,175 8842010 1,300 9182011 1,425 9432012 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 7642009 1,175 8392010 1,300 9142011 1,425 9892012 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>Required

a. Calculate the initial investment associated with each alternativeb. Calculate the incremental operating cash flows associated with each

alternativec. 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

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1 Sh.800,0002 700,0003 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 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

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(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 N0 (Initial investment) -Sh.28,500,000 -Sh.27,000,0001 (Operating cash flows) +Sh.10,000,000 +Sh.11,000,0002 . +Sh.10,000,000 +Sh.10,000,0003 +Sh.10,000,000 +Sh.9,000,0004 +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.

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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 B0 (Initial investment) -130 million -85 million1 (Operating cash flows) 25 million +40 million2 35 million +35 million3 45 million +30 million4 50 million +10 million5 55 million +5 millionRequired

(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 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 -3601 (Operating Cash flows) +128 +882 +182 +1203 +166 +964 +168 +865 +450 +207

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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 latheb. Assess the acceptability and ranking using (1) NPV and (2) IRRc. Summarize project rankings according to the 3 techniques above. Is there any

conflictsd. Which lathe should ultimately be accepted? Why?

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financial management - long term investment decision process and relevant cashflows

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