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

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Chapter 11 The required rate of return on investment and Shareholder Value Analysis 275

4 Taxation

In Chapter 6, we argued the importance of allowing for taxation in project appraisal

when estimating cash flows. Consistency seems to require discounting post-tax cash

flows at a tax-adjusted cost of finance.

A project’s NPV can be found on a post-tax or a pre-tax basis. If the NPV model is

used on a pre-tax basis, both denominator and numerator must be on a pre-tax basis,

and vice versa. If, for example, we wish to work in post-tax terms, the standard NPV

expression for a one-off end-of-year cash flow, X, is:

where T is the rate of Corporation Tax and is the required return adjusted for tax. If

shareholders seek a return of, say, 10 per cent after tax at 30 per cent, the company has

to earn a pre-tax return of In principle, computation

on a pre-tax basis should generate the same NPV as that produced by a post-tax cal-

culation, so long as the discount rate is suitably adjusted. However, this relationship

is complicated by access to capital allowances. As a result, it is usual to compute NPVs

on a post-tax basis.

The rate of tax applicable to corporate earnings might appear to be the rate of

Corporation Tax. However, the picture is clouded by the prevailing type of tax regime

(e.g. whether classical or an imputation tax system), and by the forms in which share-

holders receive income (i.e. the balance between dividend income and capital gains,

and the relevant rates of tax on these two forms of income). In other words, it is impor-

tant to consider the interaction between the system of corporate taxation and the sys-

tem of personal taxation.

Under an imputation tax, a shareholder receives a tax credit for the income tax

component incorporated into the profits tax. Shareholders subject to tax at the stan-

dard rate face no further tax liability, while higher rate taxpayers face a supplemen-

tary tax demand. To add to the complexity, some imputation systems allow investors

to reclaim all the tax paid on their behalf (full imputation), while others involve a

discrepancy between the rate of corporation tax and the relevant rate of income tax

(partial imputation). Since partial imputation applies in the UK, we will consider

only this form.

When we calculated using the DGM, the computation was based on the net-of-

tax dividend payment, so it may appear that we have met the requirement to allow

for taxation. However, the UK tax system imposes two possible tax distortions. First,

the relative tax treatment of capital gains and dividend income has differed over

time, and second, as we have just seen, different shareholders are subject to tax in

different ways.

Regarding the differential tax treatment of dividends and capital gains, a major pol-

icy change occurred in 1988. Capital gains achieved after 1982 became taxable at the

same rate as dividends (although with a much higher threshold), thus largely remov-

ing the tax penalty on dividends, especially as the top rate of income tax was simulta-

neously lowered to 40 per cent. Many companies reacted by sharply increasing their

dividend payouts, which distorted the growth pattern of dividends.

A major problem facing a company is divining the tax status of its shareholders.

Inspection of the shareholder register may provide much information, but there is no

easy solution to this problem. The share price is set by the market as a result of the

interaction of the supply and demand for its shares as expressed by thousands of

investors. Although each may well be in a different tax position, the resulting share

price is the result of investors assessing whether the shares represent good value or

not. In other words, the market automatically takes into account the average tax posi-

tions of its participants.

10%>11  30%2  14.3 per cent.

NPV 

X11  T2

11  k

CFAI_C11.QXD 10/26/05 11:38 AM Page 275

276 Part III Investment risk and return

Self-assessment activity 11.2

Specify the two situations under which the DGM breaks down completely. (You may have

to revisit Chapter 4.)

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

Under this view, it is not the function of the company to gauge the tax require-

ments of the investor and to adjust the discount rate accordingly. This is impossible

in a capital market with large numbers of investors. The market imposes a required

return for particular companies, and then it is up to individual investors to make their

own arrangements regarding taxation. The market-determined rate of return can be

regarded as the return that the company must make on its investments. This becomes

the after-tax return that the company should use to discount the after-tax cash flows

from capital projects. (The only adjustment that the company should make is to allow

for the tax shield on debt, as explained in Chapter 18.)

To summarise: in principle, we could discount pre-tax cash flows, but the identi-

fication of the appropriate pre-tax required return is complicated by the existence

and timing of capital allowances. Hence, a post-tax computation is preferable.

Theoretically, we ought to allow for investors’ personal tax positions as well as

Corporation Tax (i.e. discount project cash flows net of both Corporation Tax and

investors’ personal tax liabilities). But this requires such detailed knowledge of the

relevant tax rates applicable to shareholders as to render it impracticable. As a result,

it is usual to discount post-Corporation Tax cash flows at the market-expressed

required return, assuming that shareholders have made their own tax arrangements.

This means that shareholders will gravitate to those companies whose dividend

policies most suit their tax positions. This personal clientéle effect is discussed fur-

ther in Chapter 17.

11.3 THE REQUIRED RETURN IN ALL-EQUITY FIRMS: THE CAPM

In Chapter 10, we saw how the security market line (SML) traces out the systematic

risk–return characteristics of all the securities traded in an efficient capital market. The

SML equation is:

is the return required on the shares of company j, and is therefore the same as

is the risk-free rate of return, and is the expected return on the market port-

folio. We saw in Chapter 10 that, in order to utilise the CAPM, we needed either to

measure or to make direct assumptions about these items. (Refer back to the discus-

sion of measurement difficulties and the application to British Airways.)

However, despite these problems, the CAPM has major advantages over the DGM.

The DGM usually involves extrapolating past rates of growth and accepting the valid-

ity of the market’s valuation of the equity at any time. If we suspect that past growth

rates are unlikely to be replicated and/or that a company’s share price is over- or

under-valued, we might doubt the validity of an estimate of derived from the DGM.

The CAPM does not require growth projections; nor does it totally depend on the

instantaneous efficiency of the market. Recall that the Beta is derived from a regres-

sion model relating the returns from holding the shares of a particular company j to

the returns on the market over a lengthy period. Taking, say, monthly observations

over five years (60 in all) effectively irons out short-term influences. This requires

semi-strong market efficiency for the period and a reasonably consistent relationship

between security returns and the returns on the market portfolios.

 R

 b

1ER

 R

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Chapter 11 The required rate of return on investment and Shareholder Value Analysis 277

LEX COLUMN

Counting the cost

There are few more essential

items in the corporate finance

tool-kit than a company’s cost

of capital – the return its

investors expect as compensa-

tion for putting their funds in

one business rather than

another. Estimating this cost

of capital, however, involves as

much art and guesswork as it

does science, and the results

can vary widely.

Three years ago, those com-

panies that publish a figure for

their cost of capital – usually

those which have adopted a

form of economic profit or eco-

nomic value added perform-

ance framework – often came

out with figures 1–2 percent-

age points higher than those

implied by market values, or

estimated by stock market

analysts. Today, the gap has in

many cases reversed. Lloyds

TSB, for example, calculates

its economic profit using a cost

of equity of 9 per cent. Yet its

share price appears to imply,

even if you assume it will

halve its dividend, a cost of

equity in excess of 10 per cent.

Why does this matter? To

create value for shareholders,

companies need to make

returns greater than their cost

of capital. If companies are

underestimating cost of capi-

tal, they will make acquisi-

tions or invest in projects that

destroy value. Conversely, if

the market is setting the hur-

dle too high, investors will

miss out on value-creating

investments.

CAPM

Computing the cost of debt is

fairly straightforward, at least

for companies whose bonds are

traded. The cost of equity is

more complicated. The stan-

dard formula remains the capi-

tal asset pricing model, or

CAPM, devised separately by

William Sharpe, John Lintner

and Jack Treynor. Though many

academic studies have raised

doubts about its empirical valid-

ity, three out of four chief finan-

cial officers use CAPM.

CAPM’s starting point is the

risk-free rate – typically a 10-

year government bond yield.

To this is added a premium,

which equity investors require

to compensate them for the

extra risk they accept. This

equity risk premium is multi-

plied by a factor, known as

beta, to reflect a company’s

volatility and correlation with

the market as a whole. Beta is

designed to capture the risk

that an investor cannot diver-

sify away by holding a portfo-

lio of other shares; a company

whose share price tends to rise

and fall more than the market

will have a high beta. There

are difficulties with all three

of these elements. Govern-

ment bond yields are currently

very low, by historical stan-

dards. A company contemplat-

ing a long-term investment

can lock in these low rates for

its debt, but if interest rates

then rise so will its cost of

equity. It may generate the

cash flows it anticipated from

its investment, but these will

no longer cover its cost of cap-

ital. It may be appropriate to

use a somewhat higher nor-

malised risk-free rate. Yet it

looks as though many equity

analysts have taken insuffi-

cient account of the fall of risk-

free rates in their cost of

capital estimates.

The equity risk premium is

the element that has generated

most controversy. In the early

1990s, most companies used

numbers in excess of 6 per

cent, drawing on data from

lbbotson Associates and oth-

ers. Then market analysts

started to use equity risk pre-

miums of 3–4 per cent and

these numbers began to filter

into corporate use. Historical

performance data compiled by

Elroy Dimson, Paul Marsh and

Mike Staunton give a world

equity premium over bonds of

3.8 per cent over the last 103

years. Marakon Associates, the

strategic consultancy, derives

an equity risk premium of 5.3

per cent, rather higher than

the recent average, from the

implied internal rate of return

of 1,190 stocks, but of 3.6 per

cent on the basis of dividend

yield and growth. Splitting the

difference, that gives an esti-

mate of about 4.5 per cent.

Beta

Beta can be even trickier to

calculate. Ideally, companies

would use a forward looking

beta but estimates depend on

historical trading data. Yet as

McKinsey analysts pointed

out in a recent study, the TMT

bubble of 1998–2001 has dra-

matically lowered the appar-

ent betas of unaffected sectors.

They calculate an improbably

low current beta of 0.02 for the

food, beverage and tobacco

sector, against an average of

0.85 for 1990–97. Individual

company betas can also deliver

counter-intuitive results. An

accident-prone company may

have a very low beta, because

its mishaps mean it shows less

correlation with the overall

market.

Continued

CFAI_C11.QXD 10/26/05 11:38 AM Page 277

278 Part III Investment risk and return

Now that we know how required rates of return can be estimated, it is appropriate to

show how these can be used in valuation of firms. To achieve this, we draw on the ear-

lier treatment of value drivers and firm valuation in Chapter 4.

As we have observed, in recent years, there has been much greater appreciation of

the need for managers to optimise the interests of shareholders. In general terms, this

can be achieved by generating a rate of return on investment which, at the very least,

matches their required return on investment, i.e. the cost of equity. Remember that

11.4 USING VALUE DRIVERS – SHAREHOLDER VALUE ANALYSIS (SVA)

Take Allianz as an example:

the German insurer bases its

embedded value calculations

on an 8.15 per cent risk dis-

count rate for Europe and the

US. This is based on a 5 per

cent long-term view of risk-

free rates, a 3.5 per cent equi-

ty risk premium and a beta of

0.9. This beta, in particular,

might raise an eyebrow, since

the vulnerability of the com-

pany’s capital base to equity

market declines would prompt

most investors to call it a

high beta stock. Substituting

a historical German equity

risk premium of 5.7 per cent –

according to Dimson, Marsh and

Staunton – and a Bloomberg-

calculated beta of 1.14 would

yield a cost of equity of 11.5

per cent.

The finer points of CAPM

mattered less when nominal

interest rates were high. Take

a company whose cash flows

are growing at 3 per cent:

using a 12 per cent cost of cap-

ital to discount these cash

flows, only one third of its

value lies more than 10 years

out but, at 7 per cent, more

than half is accounted for by

these more distant years.

Small adjustments to the cost

of capital will also have a larg-

er impact on the overall valua-

tion at these lower rates. This

effect weighs even more on

non-financial companies with

a significant amount of debt

on their balance sheets, as

their weighted average cost of

capital will be lower than

their cost of equity.

In most corporate invest-

ment decisions, the odd half

point makes little difference,

though in pricing acquisitions

the precise cost of capital may

be more significant. With equi-

ty markets still jittery, howev-

er, companies are better off

setting a higher hurdle rate for

investment than a straightfor-

ward CAPM calculation would

imply. That might not be con-

sistent with academic theory

but it will, in practice, make

them choose more carefully

between their business units

in allocating capital and lead

to less wasteful investment

than in the past.

Source: Financial Times, 24 March 2003.

■ Applying the CAPM to Whitbread plc

The Risk Measurement Service quoted a Beta of 0.96 for Whitbread shares as at

September 2004. In late 2004, the yield on three-month Treasury Bills was 4.75 per cent.

Using a market risk premium of 5 per cent yields the following required return:

This is considerably below the DGM result. As the two approaches, in principle,

should yield about the same result, some reconciliation is required. At the time of this

calculation, market interest rates were historically low, at least in money terms, gener-

ating expectations of low interest rates for the future. It is doubtful whether Whitbread

can sustain 12 per cent divident growth in the future, so it right be more prudent to

use a rate nearer to that of the industry as a whole.

It appears that estimates of obtained by either method are susceptible to the date

of the calculation and prevailing expectations for the future. More fundamentally,

whereas the DGM looks at performance over a number of years, the CAPM is essen-

tially a one-period model, although it is commonly used for long-term purposes.

 0.0475  0.048  0.0955 1i.e. 9.6%2

 R

 b1ER

 R

2  0.0475  0.9610.052

CFAI_C11.QXD 10/26/05 11:38 AM Page 278

Chapter 11 The required rate of return on investment and Shareholder Value Analysis 279

shareholders incur an opportunity cost when subscribing capital for firms to use and

managers are legally obliged to safeguard those funds with all due diligence.

Sometimes, managers feel that ‘their’ companies are not ‘correctly’ valued by the stock

market – there has been a steady trickle of firms de-listing from the main UK market since

the late 1990s, largely for this reason. Moreover, share prices can swing quite violently in

the short term, which tends to undermine managers’ faith in market efficiency. Often

nonplussed by such gyrations, both managers and shareholders may require a more

objective and reliable measure of value than simply the prevailing market price.

Such a measure can be provided by the shareholder value approach, propounded

by Alfred Rappaport, drawing on Michael Porter’s ideas. You met the concept of a

value driver in Chapter 4 – here we make use of this idea to analyse inherent share-

holder value (SV), which may be thought of as the fundamental, or inherent, value of

the firm to its owners. The SV figure also provides a cross-check on the market’s cur-

rent valuation of the company. This may be regarded as a more stable and possibly

more reliable indicator of the fundamental value of the firm that is unaffected by the

short-term vagaries of the market.

The following example of Safa plc is the vehicle for investigating the SVA approach.

But first, a refresher on value drivers may be useful.

Rappaport developed a simple but powerful model to calculate the fundamental

value of a business to its owners by focusing on the key factors that determine firm

value. He identified seven value drivers, comprising three cash flow variables and

four parameters:

■ Sales, and its speed of growth

■ Fixed capital investment

■ Working capital investment

■ Operating profit margin

■ Tax rate on profits

■ The planning horizon

■ The required rate of return

In its simplest form, SVA takes the last four drivers as given, and assumes that

the first three, the cash flow variables, change at a constant rate. The key to the

analysis, as with any budgeting exercise, is the level of sales and the projected rate

of increase. From the sales projections, we can programme the operating profits and

cash flows over the planning horizon and discount at a suitable rate to find their

present value.

In the full model, the value of the firm comprises three elements, the value of the

equity, the value of the debt and the value of any non-operating assets, such as mar-

ketable securities. However, to keep the analysis simple, we focus on an all-equity-

financed company with no holdings of marketable assets. In addition, we need to

explain the treatment of investment expenditure. To generate value, firms have to

invest, i.e. to generate future cash flows requires preliminary cash outflows. These

appear to reduce value in the short-term but should generate a more than compensat-

ing increase in value via future cash flows.

■ Categories of investment

Investment in working capital, especially inventories, is required to support a

planned increase in sales. Often, companies attempt to apply a roughly constant ratio

of working capital to sales so that a 7 per cent sales increase needs an equivalent

increase in working capital investment. This is called incremental working capital

investment.

Replacement investment is undertaken to make good the wear and tear due to

using equipment, or ‘depreciation’. However, there are phasing issues to consider. In

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280 Part III Investment risk and return

11.5 WORKED EXAMPLE: SAFA PLC

The board of Safa plc is concerned about its current stock market value of £95 million,

especially as board members hold 40 per cent of the existing 100 million ordinary shares

(par value £1) already issued. They are vaguely aware of the SVA concept and have

assembled the following data:

Current sales

100 million

Operating profit margin* 20 per cent

(*After depreciation. On average, depreciation provisions match ongoing investment requirements

and are fully tax-deductible.)

Estimated rate of sales growth 5 per cent p.a.

Rate of corporation tax 30 per cent (with no delay in payment)

Long-term debt zero

Net book value of assets £120 million (net fixed assets plus net

current assets)

To support the increase in sales, additional investment is required as follows:

(i) Increased investment in working capital will be 8 per cent of any concurrent sales

increase.

(ii) Increased investment in fixed assets will be 10 per cent of any concurrent sales

increase.

The risk-free rate of interest is 7.6 per cent, Safa’s Beta coefficient is 0.8 and a con-

sensus view of analyst’s expectations regarding the overall return on the market port-

folio is 15.6 per cent.

Safa presently pays out 20 per cent of profit after tax as dividend. The board esti-

mate that Safa can continue to enjoy its traditional source of competitive advantage as

a low cost provider for a further six years, at the end of which it estimates the net book

value of its assets will be £140 million.

What is the inherent underlying value of this company?

reality, in relation to particular items, the act of replacement is infrequent, occurring in

discrete chunks, whereas depreciation in the accounts is an annual provision, so that

in all but the year of replacement, depreciation will likely exceed replacement expen-

diture. However, taken in aggregate, and especially for larger firms, replacement may

be closely related to depreciation provisions.

New investment in fixed assets. This has two dimensions. First, if the firm wants

to expand sales of existing products, then, unless it has spare capacity, it will need to

invest in additional capital equipment to support the planned sales increase. Second,

new investment may be undertaken to accompany a major strategic venture such as

the development of a new product, which will also generate an increase in sales. Taken

together, these may be related to the planned sales increase, although there is likely to

be a time lag before strategic investment comes fully ‘on stream’ and is able to deliver

higher sales quantities. Notwithstanding this qualification, we can link the amount of

investment in new capacity, for whatever reason and which adds to the firm’s stock of

assets, to a planned increase in sales. We call the resulting sum the incremental fixed cap-

ital investment.

In the following demonstration example of Safa plc, replacement investment is

assumed to equal depreciation provisions (which are treated as part of operating

expenses in accounting statements), and both working capital investment and

incremental fixed capital investment are made a percentage of any planned sales

increase.

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Chapter 11 The required rate of return on investment and Shareholder Value Analysis 281

Table 11.2

Cash flow profile

for

Safa plc (ungeared)

£m 0 1 2 3 4 5 6, etc.

1 Sales 100 105 110.25 115.76 121.55 127.63 134.00

(5% growth)

2 Operating profit 20 21 22.05 23.15 24.31 25.53 26.80

margin @ 20%

3 Taxation @ 30% (6) (6.30) (6.62) (6.95) (7.29) (7.66) (8.04)

4 Incremental (0.40) (0.42) (0.44) (0.46) (0.49) (0.51)

working capital

investment @ 8%

of sales increase

5 Incremental fixed (0.50) (0.53) (0.55) (0.58) (0.61) (0.64)

capital investment

@ 10% of sales

increase

6 Free cash flow 13.80 14.48 15.21 15.98 16.77 17.61

7 Present value @ 14% 12.11 11.14 10.27 9.46 8.71 8.02

Accuracy of figures influenced by rounding errors.

These can be taken as operating cash flows given the assumption that

investment.

depreciation  replacement

■ Answer and comments

First of all, we need to find the return required by the shareholders of Safa, using the

CAPM formula. This is:

This becomes the appropriate rate at which to value Safa’s future cash flows.

There is no debt finance so all operating profits (less tax) are attributable to share-

holders. There appears to be no long-term strategic investment programme, and

wear-and-tear is made good at a rate roughly corresponding to tax-allowable depre-

ciation provisions. This means that free cash flows are equal to operating profits

less tax.

The firm enjoys a temporary cost advantage for six years, beyond which cash flows

are uncertain. Post-year-six cash flows can be handled in a number of ways:

1 The year six cash flow figure can be assumed to flow indefinitely. This seems quite an

optimistic assumption to make both in relation to Safa plc and also more generally.

2 A view can be taken on the firm’s efforts to restore competitive advantage and some

growth assumption can then be incorporated. Again, this can only be speculative,

as there is no information on this issue.

3 Perhaps the most prudent assumption to make is that the expected year six book

value of assets will approximate to the value of all future cash flows, i.e. the com-

pany has no further supernormal earnings capacity. This implies that any subse-

quent investment has an NPV of zero.

We adopt the third approach mainly for simplicity.

Table 11.2 shows the cash flows over the competive advantage period, years 1–6

inclusive. The base year (year 0) figures are given to establish a reference line from

which future cash flows will grow.

 17.6%  6.4%2  14%

 7.6%  0.8 315.6%  7.6%

ˇ 4

 R

 b3ER

 R

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282 Part III Investment risk and return

■ Valuing Safa plc

Taking firstly the value created over the competitive advantage period:

PV of operating cash flows (line 7)  £59.5 m

Second, we add in the estimated residual value, our proxy for all future operating

cash flows:

The PV of the residual value = £140 m  PVIF

14,6

= £140 m  0.4556 = £63.8

Shareholder Value = £59.50 m + £63.8 m

= £123.3 m

■ A note on taxation – two simplifications

You should appreciate how taxation is being handled in this example. All replacement

investment is treated as being fully tax-deductible in the year of expenditure. This is a

simplification adopted primarily for arithmetic convenience. In reality, the tax relief

will be spread out over time as the firm claims the 25 per cent writing down allowance

(WDA) each year. In addition, we have ignored the tax saving in relation to the 25 per

cent WDA on the incremental fixed capital expenditure.

Correction for the first factor would reduce the valuation simply because delay in

taking the tax relief would lower the PV of the stream of tax savings. On the other

hand, inclusion of the second set of tax savings would raise the SV figure. If you cal-

culate the ‘true’ valuation by allowing for these aspects, you will find a net increase in

the valuation, although the calculation is a little messy.

We now turn to discuss the actual valuation obtained.

■ Commentary

Looking at the figures as calculated, we find, rather alarmingly, that a large proportion

(52 per cent) of the SV is accounted for by the residual value. Moreover, the SV clearly

exceeds market value £95m, itself below the current book value of assets £120m. This

seems to imply that the company might be worth more if it were broken up (although

the resale value of the assets may not fetch book value). It is thus possible that the mar-

ket is valuing Safa for its break-up potential rather than as a going concern.

This raises the obvious question of why the market should place such an appar-

ently low value on Safa. We can consider some possible reasons for the market under-

valuation of Safa.

■ The market may currently apply a higher discount rate, for example, seeking a

higher reward for risk.

■ The growth estimate may be regarded as optimistic.

■ The flow of information provided to the market may be inadequate – for example,

if it does have plans for future investment, are these generally known and under-

stood, at least in outline?

■ Board control – presumably reflecting domination by members of the founding

family – may look excessive. Such enterprises rarely enjoy a good stock market rat-

ing, because there is often a suspicion that the interests of family members may be

allowed to dominate those of ‘outside’ shareholders.

■ The dividend policy may be thought ungenerous – a 20 per cent payout ratio is low

by UK standards, and there appears to be little scope for worthwhile strategic

investment. Retentions may simply be going into cash balances.

■ There may be doubts about whether Safa can recover some form of competitive

advantage.

■ The market may be unimpressed with its present cost advantage-based strategy.

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Chapter 11 The required rate of return on investment and Shareholder Value Analysis 283

ER =

+ b(ER

–

)

Company b

Required

return

Uniform

discount

rate

0 0.8 1.2 2.0

Activity b

Figure 11.1

Risk premiums for

activities of varying risk

11.6 USING ‘TAILORED’ DISCOUNT RATES

Applying the discount rates derived using the CAPM to investment projects assumes

that new projects fall into the same risk category as the company’s other operations.

This might be a reasonable assumption for minor projects in existing areas and perhaps

for replacements, but hardly seems justifiable for major new product developments or

acquisitions of companies in unrelated areas. If the expected return is positively relat-

ed to risk, firms that rely on a single discount rate may tend to over-invest in risky proj-

ects to the detriment of less risky, though still attractive projects. Many multi-divisional

companies are effectively portfolios of diverse activities of different degrees of risk. The

Beta of the firm as a whole is thus the weighted average of its component activity Betas.

Each division contributes to the firm’s overall business risk in a way similar to that in

which individual shares contribute to the systematic risk of a portfolio of securities. The

dangers of using a uniform discount rate are shown in Figure 11.1.

Figure 11.1 shows the relationship between the rate of return required on a particular

project and that expected on the market portfolio, linked by the Beta. The overall port-

folio of company activities may have a Beta of, say, 1.2, which is a weighted average of

the Betas of component activities. For example, activity A has a greater than average

degree of risk, with a Beta of 2.0, and thus a higher than average discount rate would be

applicable when appraising new projects in this area, while the reverse applies for activ-

ity B, which has a Beta of only 0.8. Clearly, to appraise all new projects using a discount

rate based on the overall company Beta of 1.2 would invite serious errors. For example,

in area X, application of the uniform discount rate would result in accepting some proj-

ects that should be rejected because they offer too low a return for their level of risk,

while in area Y, some worthwhile low-risk projects would be rejected. Firms should use

‘tailor-made’ cut-off rates for activities involving a degree of risk different from that of

the overall company.

■ Its gearing – currently, zero – may be thought to be too low. There is no tax shield

to exploit (see Chapter 19).

Whatever the reason(s), there is plenty for the board to consider!

Self-assessment activity 11.3

What are the discount rates applicable to the firm as a whole and activities A and B on Figure

11.1, assuming a risk-free rate of 5 per cent, and a market risk premium of 6 per cent?

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

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284 Part III Investment risk and return

Remove Impact

of Gearing?

b of

b of company

Asset b/Activity B

b = 1.2

b of Division B

= 0.8

b of Division A

b = 2.0

b of

project A

b of

project A

b of

project B

b of

project B

Figure 11.2

The Beta pyramid

Figure 11.2 shows the three levels, or tiers, of risk found in the multi-activity enter-

prise, each requiring a different rate of return.

In Chapter 19, we will find that there is a fourth tier of risk that uniquely applies to

ordinary shareholders. In a geared firm, that faces financial risk, the returns achieved

by shareholders are more volatile than the firm’s operating cash flows due to the inter-

est payments that must be paid on debt. In response to this higher risk, shareholders

demand a higher return. In other words, the Beta of the shares exceeds the Beta of the

firm’s business activities. To arrive at the activity Beta, we would need to ‘ungear’ the

Beta of the shares.

If the company is entirely equity-financed, the risks that shareholders incur coin-

cide with those incurred by the company as a whole, i.e. those related to trading and

operational factors. In this case, the Beta of the ordinary shares coincides with that of

the company itself.

Many companies are structured into separate strategic sub-units or divisions,

organised along product or geographical lines. In such companies, it is unlikely that

every activity faces identical systematic risk. So different discount rates should be

applied to evaluate ‘typical’ projects within each division.

However, even within divisions, rarely do two projects have identical risk. Hence,

different discount rates are required when new projects differ in risk from existing

divisional activities.

Segmental Betas

The company Beta is a weighted average of component divisional Betas. For a compa-

ny with two divisions, A and B, the overall Beta is a weighted average given by:

where the weights represent the proportion of company value accounted for by each seg-

ment. A similar expression would apply for each division, where the corresponding

weights would represent the contribution to divisional value accounted for by each com-

ponent activity. Figure 11.2 illustrates these concepts in the form of a ‘Beta pyramid.’

Company b  ¢b



 V

≤ ¢b



 V

≤

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