a and f investment appraisal mdv tcm4-117031

7/29/2019 A and f Investment Appraisal Mdv Tcm4-117031

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NATIONAL QUALIFICATIONS CURRICULUM SUPPORT

Accounting and

Finance

Investment Appraisal

Staff Development Materials

[ADVANCED HIGHER]


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This edition first published 2001

Electronic version 2001

Learning and Teaching Scotland 2001

This publication may be reproduced in whole or in part for educational purposes by

educational establishments in Scotland provided that no profit accrues at any stage.

Acknowledgement

Learning and Teaching Scotland gratefully acknowledge thi s contribution to the

Higher Still support programme for Accounting and Finance. The original writer

was John McDonagh, of the Institute of Chartered Accountants of Scotland, and the

publicat ion firs t appeared in 1993 in the Scot ti sh CCC series of staff d evelopmentmaterials for the Certificate of Sixth Year Studies.

ISBN 1 85955 894 1

Learning and Teaching Scotland

Gardyne RoadDundee

DD5 1NY

www.LTScotland.com


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ACCOUNTING AND FINANCE i i i

CONTENTS

Introduction iv

Section 1: Accounting Rate of Return (ARR) 1

Section 2: Payback 5

Section 3: Discounted Cash Flow 7

Section 4: Net Present Value (NPV) 9

Section 5: Internal Rate of Return (IRR) 13

Section 6: Profitability Index (PI) 18

Section 7: Advantages and Disadvantages of the Various Methods 19

Appendix: Discount Table 20


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iv ACCOUNTING AND FINANCE

INTRODUCTION

1. Investment appraisal is the technique used by management in deciding

how money will be spent (invested) on fixed assets. Investment

appraisal, also known as project appraisal, thus considers capital

expenditure. The possible relationships between projects are as

follows.

2. Mutually Exclusive

Projects may be mutually exclusive. This means that from a range of

alternatives the choice of one totally precludes the choice of another,

e.g. construction of a power station requires a decision on whether to

build one powered by nuclear or fossil fuel.

3. Projects may be Independent

From a given range of alternatives the decision taker may choose any

single project or combination of projects, or all of the projects.

4. Projects may be Dependent

Here the installation of a new machine may require substantial

alteration to the existing electrical system, or layout of the factory.

5. Method of Investment Appraisal

(a) Accounting Rate of Return

(b) Payback

(c) Net Present Value

(d) Internal Rate of Return(e) Profitabili ty Index


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ACCOUNTING RATE OF RETURN (ARR)

ACCOUNTING AND FINANCE 1

SECTION 1

1.1 The accounting rate of return compares as a percentage the average

profit flowing from the project (investment) with either

(a) the original capital expenditure incurred or

(b) the original capital expenditure averaged over the life of the

project .

1.2 Example 1

Firm X is considering the purchase of a machine which will cost

10,000. The machine will have a life of 5 years and be scrapped at theend of that time. It is estimated that the residual scrap value will be

zero. The cash inflows from the investment will be as follows.

Year Cash Inflow

1 6,000

2 4,000

3 4,000

4 3,000

5 1,000

18,000

The total cash flowing in from purchasing this machine is 18,000.

However, ARR deals with profit flowing from the project. It is,

therefore, essential to adjust cash flows to profit. In the absence of any

further information the following can be assumed to be the profits from

the purchase of the machine.

Year Cash Inflow Depreciation Profit

1 6,000 (2,000) 4,000

2 4,000 (2,000) 2,000

3 4,000 (2,000) 2,000

4 3,000 (2,000) 1,000

5 1,000 (2,000) (1,000)

The total profit, after allowing for depreciation, is 8,000.


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2 ACCOUNTING AND FINANCE

A quicker means of arriving at the profit is to simply deduct the total cost of

the machine from the total cash flows resulting from the project.

e.g. Total Cash Inflows 18,000

Less Capital Cost 10,000

Profit 8,000

ARR = Average Profits

Original Capital Expenditure

Average Profits = 8,000 = 1,6005

ARR = 1,600 x 100 = 16%10,000

or

ARR = Average Profits

Original Capital Expenditure averaged over life of Project

ARR = 1,600 x 100 = 80%

2,000

The timing of the cash flows is never considered. Under ARR, profit rather

than cash flows is the criterion by which projects are appraised.

1.3 Example 2

Firm Y has the choice between Projects A and B.

Project A Project B

Capital Outlay 10,000 10,000

Cash Inflows Year 1 6,000 6,000Year 2 4,000 4,000

Year 3 3,000 6,000

Year 4 3,000

Year 5 1,000

Year 6 1,000

Both Project A and Project B require a capital outlay of 10,000 each.


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1.4 Example 3

Firm Z

Project A Project B

Capital Outlay 5,000 5,000

Cash Inflows Year 1 5,000 1,000

Year 2 4,000 2,000

Year 3 3,000 3,000

Year 4 2,000 4,000

Year 5 1,000 5,000

Total Profits

Cash Inflows 15,000 15,000

Less Capital Outlay 5,000 5,000

10,000 10,000

ARR as percentage of Capital Outlay

2,000 x 100 2,000 x 100

5,000 1 5,000 1

= 40% 40%

Both Projects have the same ARR but if asked which was the better

Project, most people would select Project A, the reason being that it is

better to collect the large sums of money as soon as possible. In other

words, the timing of cash flows must have some relevance in

investment appraisal. However, ARR ignores the timing of such cash

flows and all s are treated as being equal.


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PAYBACK


SECTION 2

2.1 Payback represents an assessment of the time taken by a project to

recover in full the initial capital outlay. In other words it is the length

of time a project takes to pay for itself. The time taken for a project to

pay for itself is known as the Payback Period.

Payback is a popular method because of its simplicity. The length of

time that the capital is at risk is known. However, as with the

accounting rate of return, the actual timing of the cash flows is ignoredand there is a built-in discrimination in favour of short-term

investments. It should also be observed that cash flows afterthe

payback period are ignored.

2.2 Example

Project X Project Y

Cash Outlay 20,000 20,000

Cash Inflow Year 1 10,000 12,000

Year 2 6,000 8,000

Year 3 4,000 1,000

Year 4 4,000 1,000

Year 5 4,000

Year 6 4,000

Year 7 4,000

Calculation of the payback period is as follows.


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PAYBACK


Project X Project Y

Cash Outlay 20,000 20,000

Cash Inflows Annual Cumulative Annual Cumulative

Year 1 10,000 10,000 12,000 12,000

Year 2 6,000 16,000 8,000 20,000

Year 3 4,000 20,000 1,000 21,000

Year 4 4,000 24,000 1,000 22,000

Year 5 4,000 28,000

Year 6 4,000 32,000

Year 7 4,000 36,000

Time taken to

pay back Capital 3 Years 2 Years

The rule in investment appraisal as far as payback is concerned is that

the sooner a project pays for itself the better. Thus, if two projects are

mutually exclusive, the project with the shorter payback period is

considered to be the superior project. If the two project s above are

mutually exclusive then Project Y would be chosen. The shortcomings

of payback as a means of investment appraisal, however, should beimmediately apparent.

While it is true that Project Y does have a shorter payback period, cash

flows after the payback period are ignored. Some firms in the United

Kingdom have cut-off periods for project payback. The result of this is

that investments must pay for themselves within a certain period, e.g. 2

or 3 years. If a proposed project will take longer than the firms cut -off

period, then it will not be considered. Unlike ARR, payback does at

least consider cash flows and not profit.

Because of the shortcomings of methods which ignore the timing of

cash flows, attention should be turned to techniques which recognise

the concept of present value. Such methods use discounted cash flow

techniques and consist of the Net Present Value model and the Internal

Rate of Return model.


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DISCOUNTED CASH FLOW


SECTION 3

3.1 Assume you have 1.00 and inflation runs at 10% for 1 year. How

much will you pay in one years time for an item costing 1.00 now?

1.00 x 1.10 = 1.10

3.2 Assume inflation continues to run at 10% for another year. How much

will you have to pay at the end of the second year for an item costing

1.00 just now?

1.10 x 1.21

3.3 If inflation runs at 10% for a third year how much will you pay for an

item costing 1.00 just now?

(1.21 x 1.10) = (1.10 x 1.10 x 1.10) = (1.10)3 = 1.331

3.4 This is known as Compounding. However, when we discount we

simply reverse the procedure. If inflation runs at 10%, an item costing

1.00 in one years time will cost how much just now? 1

The answer is 1.10 = 0.9090

3.5 If inflation runs at 10% for a second year, an item costing 1.00 in 2

years time will cost how much just now?1

The answer is 1.102

= 0.8264

3.6 Again, if inflation continues to run at 10% for a third year then an item

costing 1.00 in 3 years time costs how much just now?

1

The answer is 1.103

= 0.7513

3.7 What this means to business people is that if inflation is at 10%, 1.00

received in one years time is exactly the same as being given 0.9090

just now. Also, 1.00 being received in 2 years time is exact ly the

same as receiving 0.8264 just now and 1.00 received in 3 years time

is the same as receiving 0.7513 just now.


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DISCOUNTED CASH FLOW


3.8 This is described as Present Value and is stated thus

at 10%,

1.00 in one years time has a present value of 0.9090 1.00 in two years time has a present value of 0.8264

1.00 in three years time has a present value of 0.7513

3.9 Investment appraisal can make use of present values by converting all

future cash flows back to present value and thus comparisons can be

made between projects in which all cash flows and the timing of the

cash flows are considered.

3.10 The conversion of future cash flows into present value amounts is done

through discount factors. The discount factor a firm uses to convert

future s to present value is based on the cost of borrowing to that firm

and is known as the cost of capital.


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NET PRESENT VALUE (NPV)


SECTION 4

4.1 The Net Present Value (NPV) model as a means of investment appraisal

considers all future cash flows but converts all future s to their worth

at this moment in time. The result of this procedure is that allcash

flows from a project are considered and, since all future cash flows are

converted to present values, then a true comparison can be made

between competing projects.

4.2 Example 1

Cost of Project 20,000

Years Cash Inflows

1 10,000

2 6,000

3 4,000

4 4,000

5 4,000

4.3 Discount (or present value) factors are used to convert future s to

present value. Present value tables are provided in the Appendix on

page 20. The present values are based on the cost of borrowing to the

firm. Assume this to be 10%. Looking at the present value table, we

move to the 10% column and not the discount factors for the 5 years of

the project. These are:

Years Discount factor

1 .9091

2 .82643 .7513

4 .6830

5 .6209

4.4 In other words at 10%, 1 in 1 years time has a present value of

0.9091 just now. At 10%, 1 in 2 years time has a present value of

0.8264 just now and so on.


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4.5 We can use these present value factors to convert the future cash

inflows into present value as follows.

Years Cash Flows x Discount Factor @ 10% = Present Value

0 (20,000) 1.00 (20,000)

1 10,000 .9091 9,091

2 6,000 .8264 4,958

3 4,000 .7513 3,005

4 4,000 .6830 2,732

5 4,000 .6209 2,484

Net Present Value 2,270

Points to Note

All cash flows are considered, including the cash outflow (the investment) as

well as the cash inflows.

The cash outflow to fund the project is made now in Year 0. Year 1 cash

inflows come into the firm one year from now. Thus the discount factor in

Year 0 (now) is always 1.00.

All cash flows are converted into present value by multiplying the cashflows by the appropriate discount (present value) factor.

Net Present Value is found by adding together all cash inflows and

deducting all cash outflows.

In this example the net present value of the project is 2,270. This means

that shareholders wealth is increased by 2,270.

If an investment gives a positive NPV then the project should be accepted

(unless we are dealing with mutually exclusive projects).

The greater the net present value the greater is the increase in shareholders

wealth. Thus, if there are two projects which are mutually exclusive, the

project providing greater NPV will be chosen.

If NPV is found to be negative, then the project should not be accepted

because shareholders wealth is, in effect, reduced.


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4.6 Example 2

A project will cost 20,000 and will bring in the following cash flows.

Years Cash Inflows

1 15,000

2 10,000

3 6,000

4 3,000

5 (8,000)

The firms cost of capital is 12%.

Before deciding on whether the project should be accepted or rejected,

it should be noted that Year 5 cash flow is bracketed, thereby denoting

that it is a cash outflow. Such a situation is becoming more common

nowadays as environmental issues become more important. A cash

outflow at the end of a project may come about because a firm has to

restore land to the way it was prior to the project being carried out, e.g.

restoring countryside after the laying of a pipe line, or removing an oil

platform from the North Sea after depleting the oil reserves.

Calculations are as follows.

Years Cash Flows Discount Factor @ 12% Present

Value

0 (20,000) 1.00 (20,000)

1 15,000 .8929 13,394

2 10,000 .7969 7,969

3 6,000 .7118 4,271

4 3,000 .6355 1,907

5 (8,000) .5674 (4,539)


This project should therefore be accepted. Now assume interest rates

rise to 18%. The project must be recalculated at the new cost of capital.


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Years Cash Flows Discount Factor @ 18% Present

Value

0 (20,000) 1.00 (20,000)

1 15,000 .8475 12,713

2 10,000 .7182 7,182

3 6,000 .6086 3,562

4 3,000 .5158 1,547

5 (8,000) .4371 (3,497)


NPV is reduced from 3,002 to 1,507.

If interest rates do increase, many positive NPVs are transferred into

negative NPVs and projects are not undertaken, e.g. machines are not

bought, new oil dril ling is not carried out. High interest rates can

contribute to a firms stagnation or even contraction.


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INTERNAL RATE OF RETURN (IRR)


SECTION 5

5.1 Like NPV, Internal Rate of Return (IRR) considers the timing of cash

flows and uses discount factors to convert future s to present value.

However, IRR finds the rate of return which brings the net present

value of all cash inflows and outflows to zero. The rate of return which

achieves this is known as the yield of the project. The yield obtained is

compared to the firms cost of capital and if the yield of the project is

greater than the cost of the capital the project should be accepted. The

IRR method of investment appraisal is also known as the yield method.

5.2 A project requires an initial investment of 10,000 and will produce the

following cash inflows. The firms Cost of Capital is 23%.

Years Cash Inflows

1 6,000

2 4,000

3 4,000

4 3,000

5 1,000

The first stage is to create a table similar to that prepared when using NPV. The

only difference is that, instead of using the cost of capital, a discount factor is

chosen which, it is hoped, will bring all future cash inflows and outflows to an

NPV of zero.

Years Cash Flows Discount Factor @ 24% Present Value

0 (10,000) 1.00 (10,000)

1 6,000 .8065 4,839

2 4,000 .6504 2,602

3 4,000 .5245 2,098

4 3,000 .4230 1,269

5 1,000 .3411 341


Since 24% has not brought NPV to zero, another discount factor must

be chosen. The NPV produced is 1,149. A discount factor lower than

24% would produce a higher NPV than 1,149, thus the second discount

factor must be greater than 24%.


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Years Cash Flows Discount Factor @ 32% Present Value

0 (10,000) 1.00 (10,000)

1 6,000 .7576 4,546

2 4,000 .5739 2,296

3 4,000 .4348 1,739

4 3,000 .3294 988

5 1,000 .2495 250

Net Present Value (181)

A discount factor of 32% produces negative NPV of 181. The result

of this is that the discount factor which will bring all cash flows to zero

must lie between 24% and 32%.

To find the discount factor bringing cash flows to zero we could try 25%. If

this did not work we could move to 26% and so on. However, by means of

interpolation we are able to ascertain the discount factor giving zero for the cash

flows.

24% gives an NPV of +1,149

32% gives an NPV of181

8% difference leads to difference of 1,330

To find discount factor giving zero

24% + 1,149 x difference (between percentages)1,330

= 24% + 1,149 x 81,330

= 30.9%

Alternatively

= 32% 181 x 81,330

= 30.9%

Alternatively the following formulae can be used.


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Positive rate + (Positive NPV (Positive NPV + Negative NPV) x

Range of rates)%

24% + (1,149 (1,149 + 181) x 24)%

24% + ((1,149 1,330) x 8)%

24% + (0.8639 x 8)%

24% + 6.91%

30.91%

or

Negative rate (Negative NPV (Positive NPV + Negative NPV) x

Range of rates)%

32% (181 (1,149 + 181) x 8)%

32% ((181 1,330) x 8)%

32% (0.1361 x 8)%

32% 1.09%

30.91%

The figure of 30.9% is the yield of the project and it is now compared to the

cost of capital. If it is greater than the cost of capital, then the project should be

accepted. If it is less than the cost of capital, then the project should be rejected.

5.3 Note that IRR is only useful when comparing projects of the same scale.

Scale is a function of

(a) outlay

(b) cash flow patterns

(c) life.

If projects being compared and assessed differ in any of the above three

areas, then IRR should not be used and firms should look to NPV as a

means of assessing projects.


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5.4 Outlays

An example of the scale problem with regard to capital outlays is tomake a decision between two mutually exclusive options.

Option 1: Give me 1 just now and in an hour I will give you back

1.50.

Option 2: Give me 10 just now and at the end of the hour I will give

you back 11.

An analysis of these two alternatives reveals the following:

Option 1 Option 2

*NPV 1 10

IRR 50% 10%

*No rate is used as the transaction was almost instantaneous. The

question centres on whether people (or shareholders) would prefer to be

1.00 richer rather than 50p richer. In other words, absolute values a re

better indicat ions of increases in wealth than percentages. It follows,

therefore, that IRR may lead to a wrong decision in business. In the

above example, the capital outlays were different and where this is thecase IRR should not be used.

5.5 Cash Flow Patterns

Assume a firm has a cost of capital of 10%. Two mutually exclusive

projects have to be considered and are detailed below.

Years Project 1 Project 2

0 (100) (100)1 100

2 144 30

Calculation of the IRR is 20% for Project 1 and 24% for Project 2.

Thus, if IRR was the method of appraising investments, then Project 2

would be chosen in preference to Project 1. However, if the NPV is

calculated (using the cost of capital of 10%), it is found that in absolute

terms Project 1 has an NPV of 19 whilst Project 2 has an NPV of 16.


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Project 1 clearly increases shareholders wealth more than does Project

2 and it is clearly advantageous to choose Project 1, yet IRR would

have provided the wrong signals to management regarding whichproject to accept.

5.6 Life

Again it can be shown that IRR is unsuitable when deciding on projects

which are of different lengths.

Example

Two mutually exclusive projects require an initial investment of 100

each. The cash flows are as follows. Assume cost of capital is 10%.

Years Cash Inflows

Project 1 Project 2

0 (100) (100)

1 126

2 144

The IRR for the projects work out at 20% for Project 1 and 26% for

Project 2. Thus using an IRR model as the decision -making tool,management would choose Project 2.

However, the NPV for the projects stands at 19 for Project 1 and 15

for Project 2. In absolute terms Project 1 should be chosen in

preference to Project 2.

Again IRR gives the wrong signals to management regarding which

project to choose.


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PROFITABILITY INDEX (PI)


SECTION 6

6.1 The Profitability Index (or PI) is based on the comparison of the net

present value of the cash flow with the amount of the original

investment. It is, therefore, a measure of the percentage increase in the

capital sum that the net present value represents. Projects are thus

ranked in order of profitability.

The profitability index is calculated in the following manner.

Net present value of cash flows = profitability index

Original amount invested

6.2 The higher the profitability index, the higher the return earned on the

project. The lower the profitabi li ty index, the less profitable the project

and if the index falls below 1, this means that the project has failed to

meet the required rate of return.


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ADVANTAGES AND DISADVANTAGES OF THE VARIOUS METHODS


SECTION 7

7.1 Accounting Rate of Return

Advantages - Simple to understand

- Easy to calculate

Disadvantages - Ignores the timing of cash flows

- Based on profitabili ty rather than cash flows

7.2 Payback

Advantages - Simple to understand

- Easy to calculate

- Indicates length of time capital outlay is at risk

Disadvantages - Ignores cash flows after payback period

- Ignores timing of cash flows

- Biased in favour of short-term projects

7.3 Net Present Value

Advantages - Considers the time value of money

- Considers all cash flows

- Answer is in absolute terms of increase (or

decrease) in shareholders wealth

Disadvantages - May be difficult to calculate

7.4 Internal Rate of Return

Advantages - Considers the time value of money

- Considers all cash flows

Disadvantages - Cannot be used to compare projects of different

scales

- Can give more than one answer

- Confusing

7.5 Profitability Index

This is a derivative of the Net Present Value model and has the same

advantages and disadvantages as NPV.


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DISCOUNT TABLE


APPENDIX

Present value of 1 received aftern years discounted at 1%

i 1 2 3 4 5 6 7 8 9 10

n

1 .9901 .9804 .9709 .9615 .9524 .9434 .9346 .9259 .9174 .9091

2 .9803 .9612 .9426 .9246 .9070 .8900 .8734 .8573 .8417 .8264

3 .9706 .9423 .9151 .8890 .8638 .8396 .8163 .7938 .7722 .7513

4 .9610 .9238 .8885 .8548 .8227 .7921 .7629 .7350 .7084 .68305 .9515 .9057 .8626 .8219 .7835 .7473 .7130 .6806 .6499 .6209

6 .9420 .8880 .8375 .7903 .7462 .7050 .6663 .6302 .5963 .5645

i 11 12 13 14 15 16 17 18 19 20

n

1 .9009 .8929 .8850 .8772 .8696 .8621 .8547 .8475 .8403 .8333

2 .8116 .7969 .7831 .7695 .7561 .7432 .7305 .7182 .7062 .6944

3 .7312 .7118 .6931 .6750 .6575 .6407 .6244 .6086 .5934 .5787

4 .6587 .6355 .6133 .5915 .5718 .5523 .5337 .5158 .4987 .4823

5 .5935 .5674 .5428 .5194 .4972 .4761 .4561 .4371 .4190 .4019

6 .5346 .5066 .4803 .4556 .4323 .4104 .3910 .3704 .3521 .3349

a and f investment appraisal mdv tcm4-117031

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