Investment Appraisal Techniques: Further

examples

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5-2

Project Evaluation Methods Used by the Entities Surveyed

(a) The aggregate percentage exceeds 100% because most

respondents used more than one method of project evaluation.

Source: Graham, J.R. & C.R. Harvey (2001)

Selected project evaluation methods used by a survey

Method Percentage

Accounting Rate of Return 20.29

Profitability Index 11.87

Internal Rate of Return 75.61

Net Present Value 74.93

Payback Period 56.74

Project Evaluation Methods: Reviewed

•Net Present Value (NPV)

•Internal Rate of Return (IRR)

•Benefit Cost Ratio (BCR)

•Accounting Rate of Return (ARR)

•Profitability Index

•Payback Period

The average investment is calculated as :

(Initial investment + final or scrap value)

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2

Calculating the accounting rate of return

Equipment item Equipment item

X Y

Capital Cost 80,000 150,000

Life 5 years 5 years

Profits before depreciation

Year 1 50,000 50,000

Year 2 50,000 50,000

Year 3 30,000 60,000

Year 4 20,000 60,000

Year 5 10,000 60,000

Disposal value 0 0

ARR is measured as the average annual profit after depreciation, divided by the average net book value of the assets. Which item of the equipment should be selected, if any , if the company’s target ARR is 30 % ?

SolutionEqpmnt X EqpmntY

Total profit over life

Before depreciation 160,000 280,000

After depreciation 80,000 130,000

Average annual profit

After depreciation 16,000 26,000

(Capital Cost +disposal Value) /240,000 75,000

ARR 40% 34.7%

Both projects would earn a return in excess of 30%, but

since equipment X would earn a bigger ARR, it would be

preferred to equipment Y, even though the profits from Y

would be higher by an average of 10,000 a year.

Advantages

0 It is quick and simple to calculate.

0 It involves a familiar concept of a percentage return.

0 Accounting profits can be easily calculated from financial statements.

0 It looks at the entire project life

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Disadvantages

0 It is based on accounting profits rather than cash flows, which are subject to a number of different accounting policies.

0 It is a relative measure rather than an absolute measure and hence takes no account of the size of the investment.

0 It takes no account of the length of the project.

0 Like the payback method, it ignores the time value of money

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Pay Back Period

The time required for the cash inflows from a capital investment project to equal the initial cash outflow(s)

It simply means the time it takes an investment to pay back the amount invested.

The decision rule is that projects with the minimum pay back time are acceptable.

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Example 1

PAYBACK PERIOD (when the cost of investment has been

paid off)4 YEARS

YEAR CASHFLOW (£) CUMULATIVE CASH

FLOW (£)

0 (10,000) (10,000)

1 2,000 (8,000)

2 3,000 (5,000)

3 4,000 (1,000)

4 1,000 0

5 2,000 2,000

EXAMPLE 2

YEAR MACHINE A MACHINE B

0 (10000) (10000)

1 3000 1000

2 5000 3000

3 3000 5000

4 2000 4000

5 3000 6000

YEAR MACHINE

A

0 (10000)

1 3000

2 5000

3 3000

4 2000

5 3000

CUMULATIVE

CASH FLOW (£)

(10000)

(7000)

(2000)

1000

3000

6000

PAYBACK PERIOD IS

BETWEEN 2 AND 3 YEARS

THEREFORE THE FOLLOWING

CALCULATION IS USED.

INCOME REQUIRED X12

NET CASH FLOW FROM NEXT YEAR

INCOME REQUIRED =£2000

NET CASH FLOW FROM NEXT YEAR = 3000

MONTH OF PAYBACK =8 MONTHS

(2000/3000) X12

PAYBACK PERIOD =2 YEARS 8 MONTHS

YEAR MACHINE

B

0 (10000)

1 1000

2 3000

3 5000

4 4000

5 6000

CUMULATIVE

CASH FLOW (£)

(10000)

(9000)

(6000)

(1000)

3000

9000

Now it’s your turn! Calculate the payback period for machine

B

PAYBACK PERIOD =3 YEARS 3 MONTHS

= INCOME REQUIRED X12

NET CASH FLOW FROM NEXT YEAR

INCOME REQUIRED =£1000

NET CASH FLOW FROM NEXT YEAR =4000

MONTH OF PAYBACK =3 MONTHS

(1000/4000) X 12

The payback period for machine A is 2 years 8

months

The payback period for machine B is 3 years 3

months

Therefore the business would select machine A

However machine B generates £6000 as opposed

to £3000 by machine A. This is one of the

disadvantages of this method. The advantages

and disadvantages will now be examined.

A Short Payback Period Can Be Useful When:-

When technology is changing rapidly. A business does not

want to purchase an expensive piece of equipment and find

that it is obsolete before it has been paid for. In certain

circumstances innovations can carry with them cost and

efficiency advantages that can give them the opportunity to

increase their sales and market share.

Products can go out of favour with customers before they

have brought in sufficient revenue to repay the costs of the

investment. This is particularly true of high fashion products

whose life may only be a few months before another product

takes its place. It can also be true of technical products when

innovation is moving rapidly.

Advantages Payback

1. Simple to calculate.

2. Quick screening tool for analysis.

3. It places stress on early return, forecasts of which are likely

to be more accurate.

4. An early return is especially important when liquidity is more

important than profitability.

Disadvantages Payback

1. It disregards all cash flows beyond the payback period so fails

to measure overall profitability.

2. It ignores the time value of money.

3. It discriminates against projects which involve a long payback

period.

4. It fails to recognise that revenue generated early in the payback

period is more valuable than money received later.

Cost of capital

• The cost of capital is the rate of return that the suppliers of capital—bondholders and owners—require as compensation for their contributions of capital. • This cost reflects the opportunity costs of the suppliers of

capital.• The cost of capital is the cost of using the funds of

creditors and owners.• Cost of capital refers to the opportunity cost of making a

specific investment. It is the rate of return that could have been earned by putting the same money into a different investment with equal risk

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Net Present Value (NPV)

This takes into account the time value of money. It is based on the principle that money is worth more than it is in the future. The principle exists for two reasons:

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Risk – money in the future is uncertain.

Opportunity cost –could be in an interest account earning interest.

Discounted Net Cash Flow

•The ARR method of project valuation ignores the

timing of cash flows and the opportunity cost of

capital tied up. Pay back considers the time it takes to recover the original investment cost, but ignores total profits over a project’s life.

•Discounted cash flow, or DCF for short, is an investment appraisal technique which takes into account both the time value of money and also the profitability over a project’s life. DCF is therefore superior to both ARR and pay back as method of investment appraisal.

Important points about DCF

• DCF looks at the cash flows of a project, not the accounting profits. Like the pay back technique, DCF is concerned with liquidity, not profitability. Cash flows are considered because they show the cost and benefits of a project when they occur. For example, the capital cost of a project will be original cash outlay, and not the depreciation charge which is used to spread the capital cost over the asset’s life in the financial accounts.

• The timing of the cash flows is taken into account by discounting them. The effect of discounting is to give a bigger value per $ for cash flows that occur earlier, for example $1 earned after 1 year will be worth more than $1 earned after 2 years, which in turn be worth more that Rs 1 earned after 3 years or so on.

Net Present Value (NPV)

NPV = present value of cash inflows minus present value of cash outflows.

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If the NPV is positive, it means that the cash inflows from a project will yield a return in excess of the cost of capital, and so the project should be undertaken.

If the NPV is negative, it means that the cash inflows from a project will yield a return below the cost of capital, and so the project should not be undertaken.

NPV=PVCI-PVCO

If the NPV is exactly zero, the cash inflows from a project will yield a return which is exactly the same as the cost of capital.

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Discounted Cash Flow Methods

• Discounted cash flow (DCF) methods involve the process of discounting a series of future net cash flows to their present values.

• DCF methods include:

• The net present value method (NPV).

• The internal rate of return method (IRR).

Net Present Value (NPV)

• Difference between the PV of the net cash flows (NCF) from an investment, discounted at the required rate of return, and the initial investment outlay.

• Measuring a project’s net cash flows:

• Forecast expected net profit from project.

• Estimate net cash flows directly.

• The standard NPV formula is given by:

n

tt

t Ck

CNPV

1

0 1

0

where:

= initial cash outlay on project

= net cash flow generated by project at time t

= life of the project

= required rate of return

t

C

C

n

k

Net Cash Flow

• Cash inflows:

• Receipts from sale of goods and services.

• Receipts from sale of physical assets.

• Cash outflows:

• Expenditure on materials, labour and indirect expenses for manufacturing.

• Selling and administrative.

• Inventory and taxes.

Evaluation of NPV

• NPV method is consistent with the company’s objective of maximising shareholders’ wealth.

• A project with a positive NPV will leave the company better off than before the project and, other things being equal, the market value of the company’s shares should increase.

• Decision rule for NPV method:

• Accept a project if its NPV is positive when the project’s NCFs are discounted at the required rate of return.

NPV Example

•Example 5.1:

–Investment of $9000.

–Net cash flows of $5090, $4500 and $4000 at the end of years 1, 2 and 3 respectively.

–Assume required rate of return is 10% p.a.

–What is the NPV of the project?

NPV Example (cont.)

Solution:

• Apply the NPV formula given by Equation 5.5.

• Thus, using a discount rate of 10%, the project’s NPV = +$2351 > 0, and is therefore acceptable.

0

1

2 3

1

5090 4500 4000 9000

1.10 1.10 1.10

4627 3719 3005 9000

2351

nt

tt

CNPV C

k

Internal Rate of Return (IRR)

•The internal rate of return (IRR) is the discount rate that equates the PV of a project’s net cash flows with its initial cash outlay.

• IRR is the discount rate (or rate of return) at which the net present value is zero.

•The IRR is compared to the required rate of return (k).

• If IRR > k, the project should be accepted.

5-29

Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson

Slides prepared by Farida Akhtar and Barry Oliver, Australian National University

Calculation of Internal Rate of Return

• By setting the NPV formula to zero and treating the rate of return as the unknown, the IRR is given by:

0

11

0

n

tt

t Ck

C

0

where:

= initial cash outlay on project

= net cash flow generated by project at time t

= life of the project

= internal rate of return

t

C

C

n

r

Calculation of Internal Rate of Return (cont.)

• Using the cash flows of Example, the IRR is:

%25

9000)1(

4000

)1(

4500

1

509032

IRR

IRRIRRIRR

Multiple and Indeterminate Internal Rates of Return

•Conventional projects have a unique rate of return.

•Multiple or no internal rates of return can occur for non-conventional projects with more than one sign change in the project’s series of cash flows.

•Thus, care must be taken when using the IRR evaluation technique.

•Under IRR: Accept the project if it has a unique IRR > the required rate of return.

Choosing Between the Discounted Cash Flow Methods

• Independent investments:

• Projects that can be considered and evaluated in isolation from other projects.

• This means that the decision on one project will not affect the outcomes of another project.

• Mutually exclusive investments:

• Alternative investment projects, only one of which can be accepted.

• For example, a piece of land is used to build a factory, which rules out an alternative project of building a warehouse on the same land.

Choosing Between the Discounted Cash Flow Methods (cont.)

• Independent investments:

–For independent investments, both the IRR and NPV methods lead to the same accept/reject decision, except for those investments where the cash flow patterns result in either multiple or no internal rate(s) of return.

–In such cases, it doesn’t matter whether we use NPV or IRR.

Choosing Between the Discounted Cash Flow Methods (cont.)

•Evaluating mutually exclusive projects:

•NPV and IRR methods can provide a different ranking order.

•The NPV method is the superior method for mutually exclusive projects.

•Ranking should be based on the magnitude of NPV.

Benefit-Cost Ratio (Profitability Index)

•The profitability index is calculated by dividing the present value of the future net cash flows by the initial cash outlay:

•Decision rule:

•Accept if benefit–cost ratio > 1

•Reject if benefit–cost ratio < 1

PV of net cash flowsBenefit Cost Ratio

Initial cash outlay

Other Methods of Project Evaluation

•Two major non-discounted cash flow methods that are used:

•Accounting rate of return method (ARR)

•Payback period method (PP)

•These methods are usually employed in conjunction with the discounted cash flow methods of project evaluation.

Accounting Rate of Return

•Earnings (after depreciation and tax) from a project expressed as a percentage of the investment outlay.

•The calculation involves:

•Estimating the average annual earnings to begenerated by the project.

• Investment outlay (initial or average).

Accounting Rate of Return (cont.)

•Fundamental problems of ARR in project valuation:

•Arbitrary measure — based on accounting profit as opposed to cash flows, depends on some accounting decisions such as treatment of inventory and depreciation.

• Ignores timing of the earnings stream — no time value of money concepts are applied, as equal weight is given to accounting profits in each year of the project’s life.

Payback Period; Pro. and Cons..

• The time it takes for the initial cash outlay on a project to be recovered from the project’s after-tax net cash flows.

• Using Example 5.1, assume cash flow occurs throughout year and find the payback period of the project:

Project cost: –9000

Year 1: +5090

3910

Year 2: 3910/4500 = 0.87, so it takes 1.87 years for the project to recover its initial cost.

• Decision:

• Compare payback to some maximum acceptable payback period.

• What length of time represents the ‘correct’ payback period as a standard against which to measure the acceptability of a particular project?

Payback Period (cont.)

•Strengths:

• It is a simple method to apply.

• It identifies how long funds are committed to a project.

•Weaknesses:

• Inferior to discounted cash flow techniques because it fails to account for the magnitude and timing of all the project’s cash flows.

•Does not consider how profitable a project will be, just how quickly outlay will be recovered.

Summary of Evaluation Methods

•Discounted cash flow methods are superior investment appraisal methods as they account for timing of cash flows and the time value of money.

•DCF methods will always give the same accept/reject decision for a conventional project.

• In practice, the above-mentioned alternative project evaluation methods (most likely payback period) may be used in conjunction with DCF methods.

Economic Value Added (EVA)

•Alternative to discounted cash flow methods, accounting rate of return and payback period.

•Key factor is the required rate of return.

•EVA is the difference between the project’s accounting profit and the required return on the capital invested in the project.

•EVA can be improved by increasing accounting profit or by reducing capital employed.

Economic Value Added (cont.)

• EVA is given by:

• Discounted sum of EVAs equals NPV of project.

1 1 t t t t tEVA C I I kI

1

where:

= net cash flow generated by project at time t

= investment value, end of year

= investment value, end of year -1

= required rate of return

t

t

t

C

I t

I t

k

Real Option Analysis

• In practice, company management will often have time flexibility in their investment decision choices and ways to manage project if firm decides to proceed.

• Management choices are often known as real options.

• Option gives a successful tender for a project the right but not the obligation to initiate operation on a project.

• Depending on changes in circumstances successful bidder may or may not take up option immediately. Hence, option gives bidder the right to exploit any advantageous changes in circumstances.

• It is significant to consider value associated with management’s flexibility.

Summary

•NPV method is recommended for project evaluation. The method is consistent with shareholder wealth maximization.

•NPV is also simple to use and gives rise to fewer problems than the IRR method, such as non-uniqueness.

•Independent projects — accept if NPV > 0, reject if NPV < 0.

Summary (cont.)

•Mutually exclusive projects — accept project with the highest NPV.

• In practice, other valuation methods such as accounting rate of return, payback period and economic value added are used in conjunction with NPV, despite a preference for DCF methods.

•This may be to measure some other effect, such as the effect of the project on liquidity — payback period.

•Real option analysis considers managerial flexibility is valuable unlike project evaluation methods, where the idea of management ability to intervene in an ongoing project is ignored.