6.4 Equities: supply, demand and price

But at the same time it may increase the variabilityof earnings. In this case both g

and Kincrease and the effect on the market valuation of the share will depend upon

the relative strength of the two developments. In a more straightforward case, a rm

with a steady record of dividends from activity overseas may nd that the country in

which it operates is sliding towards civil unrest. Its dividends may remain unchanged

but the market valuation will fall because of the increased risk thought to attach

to them. Much more commonly, rms will nd their share prices uctuating as a

result of changes in exchange rate risk. In the rst half of 2006, the US$ started to

fall in value against other major currencies and there was a widespread belief that

the trend might accelerate. Many large UK companies with interests in the US found

their share prices falling because of this possibility.

What can we now say about the demand for a share? According to the CAPM, the

demand for a share will be such that its price will produce the required rate of return,

which itself is given in Appendix I (eqn A1.6). Thus, in the expression:

D

K1g



P

for given expected values for Dand g, Pwill adjust to yield the appropriate value of K.

We can see this more clearly in eqn 6.13, where we can solve for P, given K, Dand g.

D

P1



Kg

Figure 6.4 shows all of these inuences schematically, for a share which we identify

as A. Reading from left to right, it says, rstly, that rational investors decide upon

the rate of return which they require. To do this, they take into account the rate they

could have on risk-free assets, K. They then consider the riskiness of investing in

rf

this particular company relative to a fully diversied portfolio of risky assets (shown

by ). Once they know its riskiness relative to the whole market portfolio, they

A

can then calculate the fraction (or multiple) of the whole market risk premium,

(KK), to add to the risk-free rate.

Amrf

Figure 6.4	The capital asset pricing model
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Chapter 6 • The capital markets

Once they know the rate of return they require, investors will then make a decision

about the price which they are prepared to pay for the share. Looking at its recent

record, they can see its track record of earnings growth and thus its rate of capital

appreciation, g. All that is then necessary is to ensure that the price they pay ensures

that the dividend yield, D/P, is sufcient when added to gto ensure that the actual

1

return, K, is equal to the return which they require, for this particular share, in these

A

particular circumstances.

Box 6.5 provides a numerical example.

Box 6.5

Imagine you are considering buying shares in XYZ plc. The rm pays out a constant fraction of earnings as dividends and the dividend payment last year was 25p per share. Earnings have grown at a steady 12 per cent for the last ten years and there is every reason to expect this growth to continue. The rm’s -coefcient is 1.1, the market risk premium is 15 per cent and the current risk-free rate is 5 per cent.

1	Find the equilibrium price of shares in XYZ.

Steps:

(a)Find the required rate of return as follows: K0.05 1.1(0.15) 0.215 or 21.5%.

(b)Find the expected nextdividend payment: D25p(1 0.12) 28p.

1

(c)Use eqn 6.13 to nd the price: P28p (0.215 0.12) 28p/0.095 £2.95.

2	What would be the likely effect on price if the rm issued a warning that future earnings growth was likely to be only 10 per cent p.a.?

Steps:

(a)In eqn 6.13, gwill take the value 0.10 instead of 0.12.

(b)However, if the rm continues its policy of paying a constant fraction of earnings

as dividends, dividends will grow only at 10 per cent p.a. and thus Dwill be

1

25p(1 0.10) 27.5p.

(c)The new price will therefore be 27.5p (0.215 0.10) 27.5/0.115 £2.39.

(d)The effect on price will be £2.95 £2.39, a fall of 56p.

Exercise 6.3Equity valuation

(a)

Calculate the market price of an ordinary share whose last dividend was 20p and whose earnings are expected to grow by 15 per cent p.a. for the foreseeable future. The current risk-free rate of interest is 8 per cent while the market risk premium is 10 per cent, and the share has a -coefcient estimated at 1.2.

(b)	Calculate the change in price that would result if the rate of interest rose to 9 per cent, everything else remaining as it was.

(c)	Keeping the rate of interest at 9 per cent, what would happen to the price of the share if the market risk premium fell to 9 per cent?

Answers at end of chapter

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