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Chapter 11 The required rate of return on investment and Shareholder Value Analysis 285

Table 11.3

Divisional Betas for

Whitbread plc

Weighted

Activity % share of sales Surrogate company Beta beta

Hotels 33% Millennium and 1.1 0.363

Capthorne

Pubs and 56% J.D. Wetherspoon 0.84 0.470

restaurants

Sports, health 11% Springhealth Leisure 0.89 0.098

and fitness

Totals 100 0.931

Source: Whitbread plc Report and Accounts, Risk Measurement Service (RMS), September–December 2004.

Self-assessment activity 11.4

What is the company Beta for the firm shown in Figure 11.1 if activities A and B consti-

tute 65 per cent and 35 per cent of its assets respectively?

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

■ The divisional cut-off rate

We need now to consider what are suitable Betas for the three Whitbread divisions.

However, no Betas are recorded for company divisions, simply because no market

trades securities representing title to a firms’ divisional assets. Instead, we need to look

for three surrogate companies and use their ungeared Betas as the ‘stand-in’ estimates

for the Betas of the three Whitbread divisions. This involves using what Fuller and Kerr

(1981) called the pure play technique. It relies on the principle that: ‘the risk of a divi-

sion of a conglomerate company is the same as the risk of an undiversified firm in the

same line of business (adjusted for financial risk)’.

Consulting the RMS, we look for suitable surrogate companies whose Betas we can

use as proxies for those of the Whitbread divisions. The dangers of doing this should

not be understated. Ideally, the surrogate should be a close match for the relevant

Whitbreads division, i.e. they should conduct the same activity or mix of activities in

the same proportions, and should also be ungeared. (If they use debt finance, the gear-

ing effect on their Betas should be stripped out, as explained in Chapter 19.) In princi-

ple, the weighted averages of these Beta values will coincide with the overall Beta of

Whitbread plc if we have selected good surrogates. The weightings ought to be based

on market values, but as these are unknown for company divisions, book values of net

operating assets could be used. Not all companies reveal divisional asset values, so a

proxy measure such as sales or operating profits may have to be used. For Whitbread,

share of sales has been used.

pure play technique

Adoption of the Beta value of

another firm for use in evalu-

ating investment in an

unquoted entity such as an

unquoted firm, or a division of

a larger firm

Let us use Whitbread plc to illustrate the derivation of the appropriate discount rate

at different levels of an organisation. It is organised into three broad product division

lines, as shown in Table 11.3, which lists the three operating divisions. These titles sug-

gest quite different activities, although a firm’s own description of its division is not

always a reliable guide to the nature of those activities.

We performed a CAPM calculation earlier in relation to the equity of Whitbread,

obtaining a result of 9.6 per cent. Should we apply this rate to all investments under-

taken by Whitbread? The answer is ‘no’, if we believe there are risk differences

between the divisions, in which case, we should calculate tailor-made discount rates.

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286 Part III Investment risk and return

revenue sensitivity factor

The sensitivity to economic

fluctuations of a project’s sales

in relation to that of the divi-

sion to which it is attached

Table 11.3 shows that the weighted average Beta for Whitbread is 0.93, a shade

below the value of 0.96 given in the RMS. The discrepancy could be due to the fol-

lowing reasons:

■ The chosen surrogates are not close enough matches for Whitbread’s array of

activities.

■ Differences in gearing. As we will see in a later chapter, gearing has the effect of

raising Beta values as shareholders seek an extra premium to compensate for the

financial risk that gearing imposes. The RMS Beta values are all equity Betas – they

include the effect of gearing, and, of course, different firms may have different gear-

ing ratios. Hence, if we take a Beta from a low-geared firm and apply it to a high-

geared one, our weighted average calculation will understate the true Beta of the

focus firm, and vice versa. Ideally, we should compare like with like, either strip out

the effect of gearing altogether, and work in terms of pure equity (or activity) Betas,

or ungear the Betas of the surrogates, and then re-gear them to reflect the gearing

of the focus firm. These issues we defer to Chapter 19.

■ The project cut-off rate

If any division undertakes a new venture that takes it outside its existing risk parame-

ters, clearly we must look for different rates of return – in effect, we need to obtain esti-

mates for individual project Betas. Without access to internal records, our analysis can

only be indicative, but the following principles offer broad guidance.

Essentially, we look for sources of risk that make the individual project more or less

chancy relative to existing operations. There are two broad reasons why projects have

different risks to the divisions where they are based – different revenue sensitivity and

different operating gearing.

■ Revenue sensitivity

Imagine Whitbread is looking at developing a new restaurant brand. The sales gener-

ated by the projected facility may vary with changes in economic activity to a greater

or lesser degree than existing sales in the relevant division. For example, we may expect

that, for a specified rise in the level of GDP, whereas overall retail sales of Whitbread

existing restaurants increase by 7 per cent, the sales of the new brand rise by 9 per cent.

■ The revenue sensitivity factor

This magnifying effect is measured by the revenue sensitivity factor (RSF). The RSF is

calculated as follows:

This relationship may stem from the nature of the product – if it is pitched at dis-

cretionary spenders (e.g. people who frequent more ‘upmarket’ outlets), it may be

more closely geared to the economy as a whole.

■ Operating gearing

This concerns the extent to which the project cost structure comprises fixed charges.

The higher the proportion of fixed costs in the cost structure, the greater the impact of

a change in economic conditions on the operating cash flow of the project, thus magni-

fying the revenue sensitivity effect. Again, the project may exhibit a degree of operat-

ing gearing different from that of the division as a whole.

To illustrate the impact of operating gearing, consider the figures in Table 11.4,

where the firm applies a 50 per cent mark-up on variable cost. An increase in sales

RSF 

Sensitivity of project sales to economic changes

Sensitivity of divisional sales to economic changes



 1.29

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Chapter 11 The required rate of return on investment and Shareholder Value Analysis 287

Table 11.4

The effect of operating

gearing (£m)

Sales revenue Variable costs Fixed cash costs Operating cash flow

90 60 5 25

60 40 5 15

Self-assessment activity 11.5

Determine the required return on a project whose revenue sensitivity is 50 per cent and

operating gearing 80 per cent compared to the division where it is located. The divisional

Beta is 1.2, the risk-free rate is 5 per cent and the market risk premium 6 per cent.

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

revenue of 50 per cent will lead to an increase in net operating cash flow of 67 per cent

because of the gearing effect. There is thus a magnifying factor of 1.34. This so-called

project gearing factor (PGF) may well differ from the gearing factor(s) found else-

where in the division.

To measure the relative level of gearing, the operating gearing factor (OGF) is used.

This is defined as:

If the divisional gearing factor is 1.80, for example, the project’s

The second step in assessing the project discount rate brings together these two

sources of relative project risk into a project risk factor (PRF).

■ The project risk factor

This is the compound of the revenue sensitivity factor and the operating gearing factor:

In our example, this is equal to In this case, the project is less

risky than the ‘average’ project within the division and merits the application of a

lower Beta. Based on the Whitbread pubs and restaurant Beta, shown in Table 11.3, this

is given by:

The final step calculates the required return using the basic CAPM equation, based

on a 4.75 per cent risk-free rate and a market risk premium of 5 per cent:

Required return  0.0475  0.8010.052  0.0475  0.04  0.875 1i.e. 8.8%2

Project Beta  10.95  0.842  0.80

11.29  0.742  0.95.

Project risk factor  RSF  OGF

0.74.

OGF  1.34>1.80 

OGF 

Project gearing factor

Divisional gearing factor

project gearing factor

The proportionate increase in a

project’s operating cash flow in

relation to a proportionate

increase in the project’s sales

operating gearing factor

The operating gearing factor of

an individual project in relation

to that of the division to

which it is attached

■ Project discount rates in practice

Considering the informational requirements for obtaining reliable tailor-made discount

rates for particular investment projects, few firms go to these lengths. A far more com-

mon practice is to seek an overall divisional rate of return, which becomes the average

cut-off rate, but is then adjusted for risk on a largely intuitive basis, according to the

perceived degree of risk of the project. For example, many firms group projects into

‘risk categories’ such as the classification in Table 11.5. For each category, a target or

required return is established as the cut-off rate.

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288 Part III Investment risk and return

11.7 ANOTHER PROBLEM: TAXATION AND THE CAPM

Empirical studies of the risk premium usually reveal gross-of-personal-tax results. To

adjust for tax, one might consider the tax status of interest income from the risk-free

asset, normally taken as government stock of some form, and the tax status of the

return on the market portfolio.

Franks and Broyles (1979) recommended two adjustments. First, adjust the risk-free

rate for the shareholders’ rate of personal tax (at present, UK basic-rate tax on interest

income is 20 per cent), then adjust the risk premium according to the relative propor-

tions of excess return earned in dividends and in capital gain form. Grubb (1993/4)

shows that over 1960–92, about half of the return on equities was from dividends and

half from capital gain. Two major problems follow. Capital Gains Tax (CGT) was only

introduced in 1965, and has been applied at varying rates, while the basic rate of

income tax has also changed many times over this period. Moreover, in reality, very

few shareholders are liable to CGT. However, taking 20 per cent as an average rate of

CGT and 25 per cent as an average rate of tax on dividends thus yielding a weighted

average tax rate (WAT) of the calculation of the

post-tax required return on Whitbread’s ordinary shares would be:

There are obvious problems in taking average rates of tax over periods when tax

regimes have altered. Wilkie (1994) argues that such a calculation is conceptually

flawed, being based on the assumption that individuals would have invested in a tax-

inefficient vehicle (government stock) – although many do! Most personal investors

would have been subject to higher rates of income tax and thus would have taken

steps anyway to shelter their income from tax. Finally, he points out that the securities

market historically has been dominated by tax-exempt investors, in terms of both the

 0.075 i.e. 7.5%

 0.038  0.037

 0.047511  0.22  0.9630.054

 R

11  present income tax rate2  b3market risk premium431  WAT4

1ER

10.5  0.202  10.5  0.252  22.5%,

Imagine the divisional required return is 18 per cent, the rate applicable to projects

that replicate the firm’s existing activities. Around this benchmark are clustered activ-

ities of varying degrees of risk, and as the perceived riskiness increases, the target

return rises in tandem.

In all these cases, we are discussing a discount rate derived from the ungeared Beta.

In other words, we are separating out the inherent profitability of the project from any

financing costs and benefits. Analysis of financing complications is deferred to

Chapters 18 and 19.

Table 11.5

Subjective risk

categories

Project type Required return (%)

Replacement 12

Cost saving/application of advanced manufacturing technology 15

‘Scale’ projects, i.e. expansion of existing activities 18

New project development:

Imitative products 20

Conceptually new products, i.e. no existing competitors 25

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Chapter 11 The required rate of return on investment and Shareholder Value Analysis 289

11.8 PROBLEMS WITH ‘TAILORED’ DISCOUNT RATES

The pure play technique is an appealing device for estimating discount rates for spe-

cific activities, but suffers from a number of practical difficulties.

1 Selecting the proxy. To select a proxy, the firm needs to examine the range of appar-

ently similar candidates operating in the relevant sector. However, no two compa-

nies have the same business risk due to diversity of markets, management skills

and other operating characteristics. How one chooses between a range of ‘fairly

similar’ candidates is essentially an issue of judgement.

2 Divisional interdependencies. In practice, it is difficult to make a rigid demarcation

of divisional costs and incomes, since most divisionalised companies share facil-

ities, ranging from the highest decision-making level to joint research and devel-

opment, joint distribution channels and joint marketing activities. Indeed, access

to shared facilities often provides the initial motive for forming a diversified con-

glomerate, enabling the elimination of duplicated services and the exploitation

of scale economies. If carefully evaluated and implemented, the merging of activ-

ities should create value and reduce business risk. Only when a merger has no

operating impact across divisional lines can it be suggested that business risk

itself is unaffected. Even so, there may well be synergies at the peak decision-

making level.

3 Differential growth opportunities. Using a cut-off rate based on another firm suggests

that the division in question has the same growth prospects as the surrogate.

However, opportunities to grow are determined by dividend policy, the extent of

capital rationing and the interaction between divisions, e.g. competition for scarce

investment capital. In reality, because the firm’s own decision processes help to

determine the potential for growth, it is not accurate to assume that growth oppor-

tunities are externally derived.

4 Joint ventures. The use of differential discount rates may destroy the incentive to

cooperate on projects that straddle divisional boundaries. For example, a joint

venture whose expected return lies between the cut-off rates of the two divi-

sions will be attractive to one and unacceptable to the other. Here, some form of

mediation is required at peak level, which reassures the ‘loser’ of the decision

that subsequent performance will be assessed after adjusting for having to oper-

ate with a project that it did not want, or without a project that it did wish to

undertake.

percentages of share value held and, more crucially, the flow of new funds to the mar-

ket, which dictates market prices. He concludes that little accuracy is lost by using the

gross-of-tax risk premium, and ignoring any tax effect on the risk-free rate, especially

as future tax rates on investment income are likely to be lower than past rates, follow-

ing widespread tax cuts in the 1990s.

This view is very appealing, both in view of the rapid growth in the popularity of

tax breaks like the old TESSAs and PEPs, and now ISAs; and also for simplicity.

Difficulties over specifying discount rates may go some way to explaining the contin-

uing popularity of the payback method. Significantly, this is usually used in conjunc-

tion with the IRR, which does not require the pre-specification of a discount rate. This

combination becomes a convenient means of communicating criteria of investment

acceptability throughout a company without requiring continuous updating of the

discount rate for the tax position. A survey of over 200 firms conducted for the CBI by

Junankar (1994) found that 56 per cent of those that used the IRR method applied it on

a pre-tax basis.

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290 Part III Investment risk and return

Modern strategic planning has moved away from crude portfolio planning devices

such as the Boston Consulting Group’s market share/market growth matrix towards

capital allocation methods that emphasise the creation of shareholder value. Central to

value-based approaches is discounting projected cash flows to determine the value to

shareholders of business units and their strategies. A key feature of the DCF approach is

the recognition that different business strategies involve different degrees of risk and should be

discounted at tailored risk-adjusted rates.

However, critics such as Reimann (1990) suggest that differential rates will increase

the likelihood of internal dissension, whereby a manager of a ‘penalised’ division

may resent the requirement to earn a rate of return significantly higher than some of

his colleague-competitors. This resentment may be worsened by the observation that

longer-term developments, especially in advanced manufacturing technology and

other risky, but potentially high value-added activities, may be ‘unfairly’ discrimi-

nated against. As a result, managers may be reluctant to propose some potentially

attractive projects.

As we saw in Chapter 8, risk-adjusted discount rates have the effect of compound-

ing risk differences, making ostensibly riskier projects appear to increase in risk over

time. One school of thought contends that in order to avoid this risk penalty, the

attempt to tailor discount rates to divisions should be modified, if not abandoned. For

example, instead of using differential discount rates, firms might use a more easily

understood and acceptable, company-wide discount rate for projects of ‘normal’ risk,

but appraise high-risk/high-return projects using different approaches.

Underlying these arguments is the familiar assertion that diversification by firms

differs crucially from shareholder diversification, so that applying the CAPM to the

former could be misleading. If an investor adds a new share to an existing portfolio,

the market risk of the portfolio will alter according to the Beta of the new security. If

its Beta is higher than that of the existing portfolio, then the portfolio Beta increases,

and vice versa. With corporate diversification, however, we are not dealing with a bas-

ket of shares of unrelated companies, which may be freely traded on the market. A

firm that diversifies rarely adds totally unrelated activities to its core operations. It

may add value if the new activity possesses synergy, or detract from value if the mar-

ket views the combination as merely a bundle of disparate, unwieldy activities that are

hard to manage.

Market risk can be altered by strategic diversification decisions at two levels. At the

corporate level, decisions concerning business and product mixes, and operating and

financial gearing can affect market risk. The effect of both types of gearing can be mag-

nified by the business cycle, so that a firm which engages in contra-cyclical diversifi-

cation may dampen oscillations in shareholder returns and thus reduce market risk.

At the business level, market risk can be reduced by tying up outlets and supplier

sources (i.e. by increasing market power), and by developing business activities that

enjoy important interrelationships, such as common skills or technologies (i.e. by

exploiting economies of scale).

Many managers feel that the emphasis on hurdle rates is probably misplaced inso-

far as accurate cash flow forecasts are more important to creating business value than

the particular discount rate applied to them. This probably helps explain the continu-

ing popularity of the payback method, and the reluctance, at least in the UK, to adopt

CAPM-based approaches. It may also explain why so many successful firms place

great emphasis on post-auditing capital projects in order to sharpen up the cash flow

forecasting and project appraisals of subordinate staff. Furthermore, there is evidence

11.9 A CRITIQUE OF DIVISIONAL HURDLE RATES

*This section relies heavily on arguments used by Reimann (1990).

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Chapter 11 The required rate of return on investment and Shareholder Value Analysis 291

We have considered the relative merits of using the DGM and the CAPM to derive the

rate of return required by shareholders. The case for and against using tailor-made dis-

count rates for particular business segments and projects was also discussed.

Key points

■ The return required on new investment depends primarily on two factors: degree

of risk and the method of financing the project.

■ In ungeared companies, the return required by shareholders can be estimated using

either the DGM or the CAPM.

■ The DGM relies on several critical assumptions: in particular, sustained and con-

stant growth, and the instantaneous reliability of the share price set by the market.

■ The CAPM relies on a Beta estimate obtained after smoothing short-term distor-

tions, but the estimated may be affected by random influences on the risk-free

rate.

Continued

SUMMARY

(Pruitt and Gitman, 1987; Pohlman et al., 1988) that senior managers manifest their sus-

picion of subordinates’ cash flow predictions by deflating the figures presented to

them when projects are submitted for approval.

In view of these arguments, there may be a case for reconsidering the merits of

using certainty equivalents – adjusting the cash flow estimates and then discounting

at the risk-free rate. However, this has not been widely adopted. Apart from the diffi-

culty of specifying the risk-free asset, there is the problem of determining the certain-

ty equivalent factors, which involves specifying the probabilities of different possible

cash flows as a basis for assessing their utility values. While techniques are available

for doing this (Swalm, 1966; Chesley, 1975), it has not been practicable in most firms.

Reimann (1990) suggests a ‘management by exception’ approach. The firm should

establish and continuously update a corporate cost of capital, based on CAPM princi-

ples. This should be applied as a common hurdle rate for the majority of business

activities, which, he argues, typically exhibit very similar degrees of risk. At the busi-

ness level, major emphasis should be given to careful cash flow estimation, based on

evaluation of long-term strategic opportunities and competitive advantage. A key ele-

ment should be a multiple scenario approach, whereby the implications of ‘best’,

‘worst’ and ‘most likely’ states of the world are examined. For projects that, by their

very nature, have a demonstrably greater level of risk, other procedures may be appro-

priate. Rather than adjust the corporate discount rate, Reimann suggests the risk adjust-

ment be made to the cash flow estimates by the business unit executives themselves, i.e.

those with closest knowledge both of the market and of competitors’ behaviour pat-

terns. Again, a multiple scenario approach should be adopted. This avoids the effect of

compounding risk differences over time and thus penalising longer-term projects,

which may have a demotivating effect on staff engaged in pursuing high-risk activities.

This discussion may seem to downgrade the importance of DCF and CAPM

approaches in project appraisal. However, it is really intended to remind you that

apparently neat mathematical models rarely hold the whole answer. If the rigid appli-

cation of a numerical routine leads managers to question the basis of the routine itself

(one which we believe offers powerful guidance in many situations) and to exhibit

dysfunctional behaviour, it is far better to modify the routine itself to reflect real world

practicalities.

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292 Part III Investment risk and return

Further reading

■ Application of a uniform company-wide discount rate to all company projects can

lead to accepting projects that should be rejected and to rejecting projects that

should be accepted.

■ To resolve the problem of risk differences between divisions of a company, the Beta of

a surrogate firm (adjusted for gearing) can be used to establish divisional cut-off rates.

■ If individual projects within the division also differ in risk, the divisional Beta can be

adjusted for differences in revenue sensitivity and/or differences in operating gearing.

■ Not all academics and business people accept the need to define discount rates so

carefully, preferring instead to concentrate on the problems of cash flow estimation.

■ Reimann argues that a divisional cut-off rate should be used as a rough benchmark

for projects, but alternative methods of risk analysis should be applied to explore

more fully the risk characteristics and the acceptability of investment proposals.

Analyses of the ‘tailored’ discount rate can be found in Dimson and Marsh (1982) and Andrews

and Firer (1987). Gup and Norwood (1982) and Harrington (1983) provide practical illustrations

of how US corporations apply divisional discount rates, while Reimann (1990) gives a critique of

the whole approach.

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Chapter 11 The required rate of return on investment and Shareholder Value Analysis 293

Questions with a

coloured number have solutions in Appendix B on page 701.

1 The ordinary shares of Rasal plc have a market price of £10.50, following a recent dividend payment of £0.80

per share. Dividend growth has averaged 4.5 per cent p.a. over the past five years. What is the rate of return

required by shareholders implied by the current share price?

2 Insert the missing values in the following table:

(i) 11% £8.00 3% ?

(ii) 14% ? 4% £0.350

(iii) ? £5.00 6% £0.155

(iv) 12% £4.60 ? £0.250

3 Lofthouse plc has paid out dividends per share over the past few years, as follows:

1996 11.0p

1997 12.5p

1998 14.0p

1999 17.0p

2000 20.0p

In March 2000, the market price per share of Lofthouse is £5.00 ex-dividend. What is the rate of return required

by investors in Lofthouse’s equity implied by the Dividend Growth Model?

4 The all-equity financed Lasar plc has a Beta of 0.8. What rate of return should it seek on new investment:

(i) with similar risk to existing activities?

(ii) with 25 per cent greater risk compared to existing activities?

(iii) with 25 per cent lower risk compared to existing activities?

The risk-free rate of interest is 6 per cent, and the expected return on the market portfolio is 11 per cent.

5 Salas Ltd is an unquoted company that operates four divisions, all focused on single activities as shown in the

table below. Salas identifies a proxy quoted company for each activity in order to calculate cut-off rates for

new investment.

Division Proxy beta Assets employed (£m)

Construction (C) 0.7 3.00

Engineering (E) 1.1 8.00

Road Haulage (R) 0.8 4.00

Packaging (P) 0.6 5.00

The risk-free rate is 7 per cent, and the expected return on the market portfolio is 15 per cent.

Required

(i) Calculate the required return at each division.

(ii) Calculate Salas’ overall required rate of return.

6 Megacorp plc, an all-equity financed multinational, is contemplating expansion into an overseas market. It is

considering whether to invest directly in the country concerned by building a greenfield site factory. The

expected payoff from the project would depend on the future state of the economy of Erewhon, the host coun-

try, as shown below:

QUESTIONS

Continued

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State of Erewhon economy Probability IRR from project (%)

0.1 10

0.2 20

0.5 10

0.2 20

Megacorp’s existing activities are expected to generate an overall return of 30 per cent with a standard devi-

ation of 14 per cent. The correlation coefficient of Megacorp’s returns with that of the new project is

Megacorp’s returns have a correlation coefficient of 0.80 with the return on the market portfolio, and the new

project has a correlation coefficient of with the UK market portfolio.

■ The Beta coefficient for Megacorp is 1.20.

■ The risk-free rate is 12 per cent.

■ The risk premium on the UK market portfolio is 15 per cent.

■ Assume Megacorp’s shares are correctly priced by the market.

Required

(a) Determine the expected rate of return and standard deviation of the return from the new project.

(b) If the new project requires capital funding equal to 25 per cent of the value of the existing assets of

Megacorp, determine the risk–return characteristics of Megacorp after the investment.

Ignore all taxes.

7 PFK plc is an undiversified and ungeared company operating in the cardboard packaging industry. The Beta

coefficient of its ordinary shares is 1.05. It now contemplates diversification into making plastic containers.

After evaluation of the proposed investment, it considers that the expected cash flows can be described by the

following probability distribution:

State of economy Probability Internal rate of return (%)

Recession 0.2

No growth 0.3 8

Steady growth 0.3 12

Rapid growth 0.2 30

The overall risk (standard deviation) of parent company returns is 20 per cent and the risk of the market

return is 12 per cent. The risk-free rate is 5 per cent and the FTSE-100 Index is expected to offer an overall return

of 10 per cent per annum in the foreseeable future.

The new project will increase the value of PFK’s assets by 33 per cent.

Required

(a) Calculate the risk–return characteristics of PFK’s proposed diversification.

(b) It is believed that the plastic cartons activity has a covariance value of 40 with the company’s existing

activity.

(i) Calculate the total risk of the company after undertaking the diversification.

(ii) Calculate the new Beta value for PFK, given that the diversification lowers its overall covariance with

the market portfolio to 120.

(iii) Deduce the Beta value for the new activity.

(iv) What appears to be the required return on this new activity?

You may ignore taxes.

8 Lancelot plc is a diversified company with three operating divisions – North, South and West. The operating

characteristics of North are 50 per cent more risky than South, while West is 25 per cent less risky than South.

In terms of financial valuation, South is thought to have a market value twice that of North, which has the

5

0.10

0.36,

294 Part III Investment risk and return

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