6.4 Equities: supply, demand and price

where D...Dare the dividend payments in each year and Kis the chosen rate

0n

at which the future payments are discounted. In equilibrium, the price (P) will be

equal to the present value of the future income stream. If we rewrite this as

	n
	1
P	∑D	(6.10)
	t1K)t
	(1

then the expression is clearly identical to the one that we had for the valuation

of coupon payments from a bond (eqn. 6.3), except that D, the dividend, replaces

C, the coupon.

However, we cannot realistically act as though Dwere xed. In the rst of the two

expressions above we could imagine the series D...Dto be a series of variable

0n

dividends. The critical question of course is how we estimate their individual likely

values. One possibility might be to assume a steady rate of increase of dividends.

Doing this the value becomes

	00	Dg)2	n1
	DD(1 g)	(1	D(1 g)
P		0	... 0	(6.11)
			
			
	1 K(1 K)2	K)3	K)n
		(1	(1

where gis the growth rate of dividends. Simplifying, this gives

D(1 g)
P0	(6.12)

Kg

or

	D
P	1	(6.13)

	Kg

We can rearrange eqn 6.13 to yield some very useful information.

D
K1g	(6.14)

P

Equation 6.14 does two things. Firstly, it shows that K, the rate of discount as we

have so far called it, is equal to the dividend yield plus the rate of dividend growth.

With some additional assumptions and arithmetic, we could show that the rate of

dividend growth is equivalent to the rate of growth of the value of the rm. Provided

that the quantity of shares is xed, then the growth in rm value must be matched

by the growth in the value of the shares. What all this means is that K, the (total)

rate of return on this share, consists of a dividend yield and capital appreciation. We

shall see considerable signicance in this later.

Concentrating on the pricing of shares for the moment, eqn 6.13 identies three

variables which appear central to the determination of share values.

The rst is the dividend payment. This depends upon the size of the rm’s earnings

and the policy adopted by its directors towards the retention of earnings for further

investment and payments to shareholders.

Secondly, there is the term g. Failing any better information this might be taken

to approximate the long-run rate of growth of nominal national income, but it will

also be inuenced by the decisions and characteristics of the rm itself. It might be

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Chapter 6 • The capital markets

in a sector of the economy with high or low growth prospects. The rm might be

diversifying from a slow-growth into a high-growth market. It might have recently

acquired or lost a dynamic chairperson with a reputation for developing successful

rms. It might be a drug company rumoured to be about to make an important

breakthrough. All of these, and many more circumstances, will have a signicant impact

on the growth of future dividends.

Such things affect the projected earnings of individual rms and therefore the value

of their shares. Many events, however, can affect the projected earnings of companies

in general and if this changes the attractiveness of equities relative to other nancial

assets for which they are close substitutes, then share prices as a whole will change.

One obvious source of such circumstances is government policy. If it is expected that

in future the government is likely to restrain the growth in demand in the economy,

it will generally be expected that earnings will grow more slowly. The precise manner

of demand restraint may affect some classes of shares more than others. A rise in

direct taxes might cause shares in retail stores to fall more than shares in banks, for

example, but the general movement will be downwards. For this reason, a fall in

share prices can be sparked off by gures showing a balance of payments decit.

Alternatively, an anticipated increase in the rate of ination, foreshadowed by falling

unemployment and rising imports for example, may cause a fall if it is believed that

the government is bound to take deationary action.

Thirdly, there is the term K. We know that this is both the required rate of return on

the share and the rate at which we discount future dividend payments. In eqn 6.13 we

can see that a rise in Kwill lead to a bigger discounting of future earnings and there-

fore a lower value for the share. A fall in K, conversely, will produce a rise in price.

In Appendix I: Portfolio theory we explain that the capital asset pricing model

(CAPM) tells us that:

the required rate of return on an asset is equal to the risk-free rate plus a fraction (or

multiple) of the market risk premium where the fraction (or multiple) is represented by

the asset’s beta coefcient.

For an asset, A, we express this in eqn A1.6 as

AK(KK)	(A1.6)
Arfmrf

If we think of the required rate of return being made up in this way, we can look

systematically at some of the circumstances which will cause changes in its com-

position. Firstly, of course, interest rates, K, may rise or fall. Krises or falls accordingly

rf

and share prices move inversely, in a way which is similar to that of bonds. Notice

that Kis common to the determination of all share prices and so the change in

rf

price will be general. Alternatively, there could be a change in the market’s attitude

to risk and the market risk premium, KK, could rise or fall. Again, share prices

mrf

will move in the opposite direction and since the market price of risk enters into the

determination of all share values, the movement will be general.

In addition to both of these, however, circumstances may arise which lead to a

change in an individual rm’s -coefcient. For example, a rm’s diversication into

new activity, as we said earlier, might be successful in raising the growth of dividends.

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