Pike Robert, Neal Bill. Corporate finance and investment: decisions and strategy

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Questions with a coloured number have solutions in Appendix B on page 697.

1 Explain the importance of risk in capital budgeting.

2 Explain the distinction between project risk, business risk, financial risk and portfolio risk.

3 The ‘wood pulp’ project has an initial cost of £13,000 and the firm’s risk-free interest rate is 10 per cent. If cer-

tainty equivalents and net cash flows (NCF) for the project are as below, should the project be accepted?

Chapter 8 Analysing investment risk 215

Year Certainty equivalents Net cash flows (£)

1 0.90 8,000

2 0.85 7,000

3 0.80 7,000

4 0.75 5,000

5 0.70 5,000

6 0.65 5,000

7 0.60 5,000

Probability Year 1 net cash flow (£) Year 2 net cash flow (£)

0.2 400 300

0.3 500 400

0.3 600 500

0.2 700 600

Number of 100 ml containers sold Probability of occurrence

11,000 0.3

14,000 0.6

16,000 0.1

4 Mystery Enterprises has a proposal costing £800. Using a 10 per cent cost of capital, compute the expected

NPV, standard deviation and coefficient of variation, assuming independent interperiod cash flows.

5 Mikado plc is considering launching a new product involving capital investment of £180,000. The machine

has a four-year life and no residual value. Sales volumes of 6,000 units are forecast for each of the four years.

The product has a selling price of £60 and a variable cost of £36 per unit. Additional fixed overheads of £50,000

will be incurred. The cost of capital is 12.5 per cent p.a. Present a report to the directors of Mikado plc giving:

(a) the net present values

(b) the percentage amount each variable can deteriorate before the project becomes unacceptable

6 Devonia (Laboratories) Ltd has recently carried out successful clinical trials on a new type of skin cream,

which has been developed to reduce the effects of ageing. Research and development costs in relation to the

new product amount to £160,000. In order to gauge the market potential of the new product, an independent

firm of market research consultants was hired at a cost of £15,000. The market research report submitted by

the consultants indicates that the skin cream is likely to have a product life of four years and could be sold to

retail chemists and large department stores at a price of £20 per 100 ml container. For each of the four years

of the new product’s life sales demand has been estimated as follows:

If the company decides to launch the new product, production can begin at once. The equipment necessary

to make the product is already owned by the company and originally cost £150,000. At the end of the new

product’s life, it is estimated that the equipment could be sold for £35,000. If the company decides against

QUESTIONS

Continued

CFAI_C08.QXD 10/28/05 3:59 PM Page 215

launching the new product, the equipment will be sold immediately for £85,000 as it will be of no further use

to the company.

The new skin cream will require two hours’ labour for each 100 ml container produced. The cost of labour

for the new product is £4.00 per hour. Additional workers will have to be recruited to produce the new prod-

uct. At the end of the product’s life the workers are unlikely to be offered further work with the company and

redundancy costs of £10,000 are expected. The cost of the ingredients for each 100 ml container is £6.00.

Additional overheads arising from the product are expected to be £15,000 p.a.

The new skin cream has attracted the interest of the company’s competitors. If the company decides not to

produce and sell the skin cream, it can sell the patent rights to a major competitor immediately for £125,000.

Devonia (Laboratories) Ltd has a cost of capital of 12 per cent.

Ignore taxation.

Required

(a) Calculate the expected net present value (ENPV) of the new product.

(b) State, with reasons, whether or not Devonia (Laboratories) Ltd should launch the new product.

decisions.

(Certified Diploma)

7 Plato Pharmaceuticals Ltd has invested £300,000 to date in developing a new type of insect repellent. The

repellent is now ready for production and sale and the marketing director estimates that the product will sell

150,000 bottles per annum over the next five years. The selling price of the insect repellent will be £5 per bot-

tle and the variable costs are estimated to be £3 per bottle. Fixed costs (excluding depreciation) are expected

to be £200,000 per annum. This figure is made up of £160,000 additional fixed costs and £40,000 fixed costs

relating to the existing business which will be apportioned to the new product.

In order to produce the repellent, machinery and equipment costing £520,000 will have to be purchased

immediately. The estimated residual value of this machinery and equipment in five years time is £100,000. The

company calculates depreciation on a straight-line basis.

The company has a cost of capital of 12 per cent. Ignore taxation.

Required

(a) Calculate the net present value of the product.

(b) Undertake sensitivity analysis to show by how much the following factors would have to change before

the product ceased to be worthwhile:

(i) the discount rate

(ii) the initial outlay on machinery and equipment

(iii) the net operating cash flows

(iv) the residual value of the machinery and equipment

(d) State, with reasons, whether or not you feel the project should go ahead.

(Certified Diploma)

8 The managing director of Tigwood Ltd believes that a market exists for ‘microbooks’. He has proposed

that the company should market 100 best-selling books on microfiche, which can be read using a special

microfiche reader that is connected to a television screen. A microfiche containing an entire book can be

purchased from a photographic company at 40 per cent of the average production cost of best-selling

paperback books.

The average cost of producing paperback books is estimated at £1.50, and the average selling price of

paperbacks is £3.95 each. Copyright fees of 20 per cent of the average selling price of the paperback books

would be payable to the publishers of the paperbacks plus an initial lump sum that is still being negotiated,

but is expected to be £1.5 million. No tax allowances are available on this lump-sum payment. An agreement

with the publishers would be signed for a period of six years. Additional variable costs of staffing, handling

and marketing are 20p per microfiche, and fixed costs are negligible.

Tigwood Ltd has spent £100,000 on market research, and expects sales to be 1,500,000 units per year at an

initial unit price of £2.

The microfiche reader would be produced and marketed by another company.

216 Part III Investment risk and return

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Tigwood would finance the venture with a bank loan at an interest rate of 16 per cent per year. The com-

pany’s money (nominal) cost of equity and real cost of equity are estimated to be 23 per cent p.a. and 12.6 per

cent p.a., respectively. Tigwood’s money weighted average cost of capital and real weighted average cost of

capital are 18 per cent p.a. and 8 per cent p.a., respectively. The risk-free rate of interest is 11 per cent p.a. and

the market return is 17 per cent p.a.

Corporation Tax is at the rate of 35 per cent, payable in the year the profit occurs. All cash flows may be

assumed to be at the year end, unless otherwise stated.

Required

(a) Calculate the expected net present value of the microbooks project.

(b) Explain the reasons for your choice of discount rate in the answer to part (a). Discuss whether this rate is

likely to be the most appropriate to use in the analysis of the proposed project.

before the project was no longer expected to be viable:

initial outlay

annual contribution

the life of the agreement

the discount rate

(ii) What are the limitations of this sensitivity analysis?

(d) What further information would be useful to help the company decide whether to undertake the micro-

book project?

(ACCA)

9 The general manager of the nationalised postal service of a small country, Zedland, wishes to introduce a new

service. This service would offer same-day delivery of letters and parcels posted before 10 a.m. within a dis-

tance of 150km. The service would require 100 new vans costing $8,000 each and 20 trucks costing $18,000

each. One hundred and eighty new workers would be employed at an average annual wage of $13,000, and

five managers on average annual salaries of $20,000 would be moved from their existing duties, where they

would not be replaced.

Two postal rates are proposed. In the first year of operation letters will cost $0.525 and parcels $5.25. Market

research undertaken at a cost of $50,000 forecasts that demand will average 15,000 letters per working day and

500 parcels per working day during the first year, and 20,000 letters per day and 750 parcels per day there-

after. There is a five-day working week. Annual running and maintenance costs on similar new vans and

trucks are estimated to be $2,000 per van and $4,000 per truck, respectively, in the first year of operation. These

costs will increase by 20 per cent p.a. (excluding the effects of inflation). Vehicles are depreciated over a five-

year period on a straight-line basis. Depreciation is tax-allowable and the vehicles will have negligible scrap

value at the end of five years. Advertising in Year 1 will cost $500,000 and in Year 2 $250,000. There will be no

advertising after Year 2. Existing premises will be used for the new service, but additional costs of $150,000

per year will be incurred.

All the above cost data are current estimates and exclude any inflation effects. Wage and salary costs and

all other costs are expected to rise because of inflation by approximately 5 per cent p.a. during the five-year

planning horizon of the postal service. The government of Zedland will not permit annual price increases

within nationalised industries to exceed the level of inflation.

Nationalised industries are normally required by the government to earn at least an annual after-tax

return of 5 per cent on average investment and to achieve, on average, at least zero net present value on their

investments.

The new service would be financed half by internally generated funds and half by borrowing on the

capital market at an interest rate of 12 per cent p.a. The opportunity cost of capital for the postal service is

estimated to be 14 per cent p.a. Corporate taxes in Zedland, to which the postal service is subject, are at

the rate of 30 per cent for annual profits of up to $500,000 and 40 per cent for the balance in excess of

$500,000. Tax is payable one year in arrears. All transactions may be assumed to be on a cash basis and to

occur at the end of the year, with the exception of the initial investment, which would be required almost

immediately.

Chapter 8 Analysing investment risk 217

Continued

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Required

(a) Acting as an independent consultant, prepare a report advising whether the new postal service should be

introduced. Include a discussion of other factors that might need to be taken into account before a final

decision was made. State clearly any assumptions that you make.

(b) Monte Carlo simulation has been suggested as a possible method of estimating the net present value of a

project. Briefly assess the advantages and disadvantages of using this technique in investment appraisal.

(ACCA)

218 Part III Investment risk and return

Describe the types of risks associated with investment decisions in a firm known to you. (If necessary, read the

Annual Report of a major company, like BP plc, to familiarise yourself with a company.) Suggest how these risks

should be formally assessed within their investment appraisal process.

Practical assignment

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Relationships between investments:

portfolio theory

Learning objectives

This chapter is designed to explore the financial equivalent of the maxim ‘don’t put all your eggs in

one basket’. In particular, it aims:

■ To give the reader an understanding of the rationale behind the diversification decisions of both

shareholders and companies.

■ To illustrate the mechanics of portfolio construction with a user-friendly approach to statistics,

using numerical examples.

■ To explain why optimal portfolio selection is a matter of personal choice.

■ To examine the drawbacks of portfolio analysis as an approach to project appraisal.

A good grasp of the principles of portfolio analysis is an essential underpinning to understanding the

Capital Asset Pricing Model, to be covered in Chapter 10.

LEX LIVE

Metro and the weather

Diversified investment strate-

gies can be marvellous things.

Suppose you face a choice of

buying shares in a maker of

sunscreen or in a maker of

umbrellas. The textbook

response is to invest in both.

This guarantees a relatively

high return at moderate risk

levels, whatever the weather.

The same logic should apply

to companies, too. Unfortuna-

tely, that has not been the

recent experience of investors.

On Friday, Metro, the German

retail conglomerate, joined the

growing list of companies

blaming their lacklustre per-

formance on a rainy European

summer.

Wet weather may indeed

have hit Metro’s food sales.

But the argument would carry

more weight had the very

same Metro a year ago not put

weak department store sales

down to last summer’s heat.

Groups such as Unilever and

Cadbury Schweppes have also

been keen to use the weather

excuse in recent years, freely

invoking the vagaries of the

climate to explain away their

performance.

This might sound like harm-

less spin, but it contains a real

danger. This is that companies

may actually believe their own

PR and start to overlook struc-

tural challenges, such as the

growth of own labels and dis-

count retailers. These affect

both Unilever and – arguably –

Metro. The German retailer’s

weak like-for-like sales growth

partly reflects lacklustre

demand. But it also raises

some doubts about the returns

of its foreign expansion. When

companies diversify, they take

on a huge extra burden of

management. If Metro cannot

even cope with whatever is

thrown at it by the weather

gods, it should reconsider its

foray abroad – and leave the

task of diversifying to

investors.

Source: Financial Times, 29 October 2004.

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220 Part III Investment risk and return

Activity A

Activity B

overall

enterprise

Time

Rate of return

Figure 9.1

Equal and offsetting

fluctuations in returns

9.1 INTRODUCTION

This chapter deals with the theory underlying diversification decisions. Diversification

is a strategic device for dealing with risk. Whereas the previous chapter examined

methods of risk analysis that focused on individual projects, here we study how the

financial manager can exploit interrelationships between projects to adjust the risk-

return characteristics of the whole enterprise. In the process, we will show why many

firms develop a wide spread of activities or portfolios. The term ‘portfolio’ is usually

applied to combinations of securities, but we will show that the principles underlying

security portfolio formation can be applied to combinations of any type of asset, includ-

ing investment projects.

Many firms diffuse their efforts across a range of products, market segments and

customers in order to spread the risks of declining trade and profitability. If a firm can

reduce its reliance on particular products or markets, it can more easily bear the

impact of a major reverse in any single market. However, firms do not reduce their

exposure to the threat of new products or new competitors for entirely negative rea-

sons. Diversification can generate some major strategic advantages: for example, the

wider the spread of activities, the greater the access to star performing sectors of the

economy. Imagine an economy divided into five sectors, with one star-performer each

year whose identity is always random. A company operating in a single sector is like-

ly to miss out in four years out of five. In such a world, it is prudent to have a stake in

every sector by building a portfolio of all five activities.

Diversification is designed to even out the bumps in the time profile of profits and

cash flows. The ideal form of diversification is to engage in activities that behave in

exactly opposite ways. When sales and earnings are relatively low in one area, the

adverse consequences can be offset by participation in a sector where sales and prof-

its are relatively high. With perfect synchronisation, the time profile of overall returns

will describe the pattern shown in Figure 9.1. This shows the returns from two activi-

ties: A, which moves in parallel with the economy as a whole; and B, which moves in

an exactly opposite way. The equal and opposite fluctuations in the returns from these

two activities would result in a perfectly level profile for a diversified enterprise com-

prising both activities. In generally adverse economic conditions, the returns from

activity A, closely following the economy as a whole, will be depressed, but involve-

ment in activity B has an exactly compensating effect. The reverse applies when the

economy is expanding. The returns from B are said to be contra-cyclical, and the

dampening effect on the variability of returns is called a portfolio effect.

For firms planning to diversify, there are two important messages. First, it is not

enough simply to spread your activities. Different activities are subject to different

types of risk, which are not always closely related. For an internationally diversified

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Chapter 9 Relationships between investments: portfolio theory 221

*The real reason is probably that they have applied for shares in a privatisation, or been given shares

in a building society demutualisation!

The theory of diversification was developed by Markowitz (1952). It can be reduced to

the maxim ‘don’t put all your eggs in one basket’. This is a simple motto, but one that

many investors persistently ignore. How often do we read heart-rending stories of

small investors who have lost all their savings in some shady venture or other? Why do

more than 50 per cent of private investors persist in holding a single security in their

investment portfolios? Perhaps they are unaware of the advantages of spreading their

risks, or have not understood the arguments. Perhaps they are not risk-averse or are

simply irrational.* Rational, risk-averse investors appreciate that not all investments

perform well at the same time, that some may never perform well, and that a few may

perform spectacularly well. Since no one can predict which investments will fall into

each category in any one period, it is rational to spread one’s funds over a wide set of

investments.

A simple example will illustrate the remarkable potential benefits of diversification.

■ Achieving a perfect portfolio effect

An investor can undertake one or both of the two investments, Apple and Pear. Apple

has a 50 per cent chance of achieving an 8 per cent return and a 50 per cent chance of

returning 12 per cent. Pear has a 50 per cent chance of generating a return of 6 per cent

and a 50 per cent chance of yielding 14 per cent. The two investments are in sectors of

the economy that move in direct opposition to each other. The investor expects the

return on Apple to be relatively high when that on Pear is relatively low, and vice versa.

What portfolio should the investor hold?

First of all, note that the expected value (EV) of each investment’s return is identical:

At first glance, it may appear that the investor would be indifferent between Apple

and Pear or, indeed, any combination of them. However, there is a wide variety of

possible expected returns according to how the investor ‘weights’ the portfolio.

Moreover, a badly-weighted portfolio can offer wide variations in returns in different

time periods.

For example, when Pear is the star performer, a portfolio comprising 20 per cent of

Apple and 80 per cent of Pear will offer a return of:

Apple

10.2  8%2 

Pear

10.8  14%2 

Portfolio

11.6%  11.2%2  12.8%

Investment Pear:

EV  10.5  6%2  10.5  14%2  13%  7% 2  10%

Investment Apple: EV  10.5  8% 2  10.5  12%2  14%  6%2  10%

firm the factors affecting, say, domestic operations may be quite different for these

affecting overseas operations. If changes in these influences are random and relative-

ly uncorrelated, diversification may significantly reduce the variability of company

earnings. Second, to generate an appreciable impact on overall returns, diversification

must usually be substantial in relation to the whole enterprise. Hence, two key mes-

sages of portfolio diversification are: look for unrelated activities, and engage in significant

diversification.

9.2 PORTFOLIO ANALYSIS: THE BASIC PRINCIPLES

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222 Part III Investment risk and return

When Apple is the star, the return is only:

Although there should be as many good years for Apple as for Pear, resulting over

the long-term in an average return of 10 per cent, in the shorter term, the investor would

be over-exposed to the risk of a series of bad years for Pear. Happily, there is a portfo-

lio which removes this risk entirely.

Consider a portfolio invested two-thirds in Apple and one-third in Pear. When

Apple is the star, the return on the portfolio, is a weighted average of the returns

from the two components:

Conversely, when Pear is the star, the portfolio offers a return of:

With this combination, the risk-averse investor cannot go wrong! The portfolio

completely removes variability in returns as there are only two possible states of the

economy. Any rational risk-averse investor should select this combination of Apple

and Pear to eliminate risk for a guaranteed 10 per cent return. Here, the portfolio

effect is perfect, like that shown in Figure 9.1. However, not every investor would

necessarily opt for this particular balanced portfolio. Super-optimists might load

their funds entirely on to Pear, hoping for 14 per cent returns every year. This may

work for a year or two, but the chances of achieving a consistent return of 14 per

cent year after year are very low. The chance of achieving 14 per cent in the first

year is 50 per cent, but the chance of getting 14 per cent in each of the first two years

is and so on. Diversification is usually the

safest (and often the most profitable) policy. We will study later in the chapter how

different portfolio weightings affect the overall risk and return.

In this example, the opportunity to eliminate all risk arises from the perfect negative

correlation* between the two investments, but this attractive property can only be

exploited by weighting the portfolio in a particular way.

Regrettably, cases of perfect negative correlation between the returns from securi-

ties are rare. Most investment returns exhibit varying degrees of positive correlation,

largely according to how they depend on overall economic trends. This does not rule

out risk-reducing diversification benefits, but suggests they may be less pronounced

than in our example. As we will see, the extent to which portfolio combination can achieve

a reduction in risk depends on the degree of correlation between returns. Later in the chap-

ter, we will examine rather more realistic cases, but first we need to explore more

fully the nature and measurement of portfolio risk.

150 per cent2  150 per cent2  25 per cent

 12>3  8%2  11>3  14%2  15.33%  4.67%2  10%

 12>3  12%2  11>3  6%2  18%  2%2  10%

10.2  12%2  10.8  6%2  12.4%  4.8%2  7.2%

*Readers lacking a grounding in elementary statistics may want to consult an introductory text such

as C. Morris, Quantitative Approaches in Business Studies (Pearson Education), in order to study the con-

cept of correlation. Correlation is measured on a scale of (perfect negative correlation) through zero

to (perfect positive correlation).1

1

Self-assessment activity 9.1

What are the two required conditions for total elimination of portfolio risk?

(Answer in Appendix A at the back of the book)

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Chapter 9 Relationships between investments: portfolio theory 223

9.3 HOW TO MEASURE PORTFOLIO RISK

We have just seen the importance of the degree of correlation between the returns from

two investments. We saw also how the return from a portfolio could be expressed as a

weighted average of the individual asset returns, the weights being the proportions of

the portfolio accounted for by each of the various components. A similar relationship

applies before the event: that is, if we consider the expected value of the return from the

portfolio. The expected return on a portfolio comprising two assets, A and B,

whose individual expected returns are and respectively, is given by:

(9.1)

where and are the respective weightings of assets A and B, with

The riskiness of the portfolio expresses the extent to which the actual return may

deviate from the expected return. This may be expressed by the variance of the return,

or by its standard deviation,

Portfolio risk

The (rather fearsome!) expression for the standard deviation of a two-asset investment

portfolio, is:

(9.2)

where

We need now to explain the meaning of the covariance. The covariance, like the cor-

relation coefficient, is a measure of the interrelationship between random variables, in

this case, the returns from the two investments A and B. In other words, it measures the

extent to which their returns move together, i.e. their co-movement or co-variability.

When the two returns move together, it has a positive value; when they move away from

each other, it has a negative value; and when there is no co-variability at all, its value is

zero. However, unlike the correlation coefficient, whose value is restricted to a scale

ranging from to the covariance can assume any value. It measures co-movement

in absolute terms, whereas the correlation coefficient is a relative measure.

The correlation coefficient between the return on A and the return on B, is sim-

ply the covariance, normalised or standardised, by the product of their standard

deviations:

The covariance, between the returns on the two investments, A and B, is

given by:

(9.3)

where is the realised return from investment A, is the expected value of the

return from A, is the realised return from investment B, is the expected value

of the return from B, and p

is the probability of the ith pair of values occurring.

cov



i 1

 ER

21R

 ER

cov

Correlation coefficient between A and B’s returns  r



cov

 s

1,1

cov

 the covariance of the returns on A and B.

 the variance of the return on asset B.

 the variance of the return on asset A.

11  a2  the proportion of the portfolio invested in asset B.

a  the proportion of the portfolio invested in asset A.

 23a

 11  a2

 2a11  a2cov

a  11  a2  1.

11  a2a

 aER

 11  a2ER

1ER

covariance

A statistical measure of the

extent to which the fluctua-

tions exhibited by two (or

more) variables are related

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224 Part III Investment risk and return

Equation (9.3) tells us to calculate, for each pair of simultaneously occurring out-

comes, their deviations from their respective expected values; next, to multiply these

deviations together and then to weight the resulting product by the relevant probabil-

ity for each pair. Finally, the sum of all weighted products of paired divergences

between expected and actual outcomes defines the covariance. This relationship is

more easily understood with a numerical example. Table 9.1 shows possible returns

from two assets under four different economic conditions, with associated probabili-

ties. First, do Self-assessment activity 9.2. Then, check through the calculation in

Table 9.2.

In this case, there is no co-variability at all between the returns from the two assets.

If the return from A increases, it is just as likely to be associated with a fall in the

return from B as a concurrent increase. If the covariance (which measures the degree

of co-movement in absolute terms) is zero, we should expect to find the correlation

coefficient (the relative measure of co-movement) is also zero. We may now demon-

strate this:

The case of zero covariance is a very convenient one, as we can see from looking at

the expression for portfolio risk, (Equation 9.2 from page 223).

 23a

 11  a2

 2a11  a2cov

Correlation coefficient

between A and B’s returns  r



cov

 s



130  402

 0

Self-assessment activity 9.2

With the figures in Table 9.1, check that the expected values for both A and B are 20 per

cent, and that their respective standard deviations are 30 per cent and 40 per cent, using

the formulae presented in Chapter 8.

(Answer in Appendix A at the back of the book)

Table 9.1

Returns under different

states of the economy

State of the economy Probability Return from A Return from B

0.25

60%50%E

20%50%E

20%10%E

60%10%E

Table 9.2

Calculating the

covariance

Weighted

Product Probability product

20 20 0.25

Note: Although the rate of return figures are percentages, they have been treated as integers to

clarify exposition.

covariance

 0

300

120040306050

300120040302050

300120040302010

300120040306010

 ER

21R

 ER

2ER

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