6.4Equities: supply, demand and price

In this section we look at how a value can be arrived at for equities or ordinary

company shares. In doing this, we shall see that there are many similarities with the

valuation of bonds. The rst of these is that the market price must be the outcome

of the interaction between supply and demand: the current price of a share is that

price at which investors are just willing (in the aggregate) to hold the existing stock

of shares.

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6.4 Equities: supply, demand and price

Notice that this immediately introduces another major similarity with bonds; that

we treat supply as a stock. The current price represents the value that investors place

upon the existingquantity of shares and these shares may have come into existence

recently or long ago. If that valuation changes, then the price will rise but nothing

happens to the quantity of shares; likewise a fall in the value that investors place upon

them simply changes the market price without changing the quantity. Therefore, as

with bonds, we draw the supply curve vertically.

But remember the other points that we made in connection with the supply of

bonds. We said that the supply of bonds is not xed forever. So, if we think about

developments in the long run we would probably expect that the economy will grow

and with that growth existing rms will expand and new rms will be formed. In

both cases, new long-term funds will have to be raised and this will lead to new issues

of shares. The stock will expand and the supply curve will shift to the right.

Even in the shorter (let us call it the medium) term, the stock of shares may

expand if rms see that this is an attractive way to raise funds. This could happen

if other forms of nance become more expensive or if investors become more

enthusiastic about share ownership. In the latter case, there is an increase in demand

for all shares and so their prices will rise. Look again at Figure 6.2 and the discussion

that follows it. In that discussion, we said that if demand increases the price of the

bond will rise and, if nothing else changes, investors will earn a lower rate of return.

Furthermore, we went on to say, this lower rate of return that investors are prepared

to accept amounts to a lowering of the cost that a borrower has to pay if she chooses

to raise additional funds by issuing new bonds. So it is with shares. When share prices

are high (relative to the income they pay), then the cost of equity nance is low, and

vice versa. Thus, when stock markets are booming we tend to see more new issues

of shares and this will also increase the stock (and shift the supply curve).

Finally, in this comparison with bonds, recall that we said that when the price

is stable, the stock to which it belongs is willingly held. There may be people at

the margin willing to sell their holdings of the stock, but these are just matched by

people wishing to buy. In the aggregate, there is agreement that the current market

price represents the correct value for the share. But what does this mean? What leads

the market to agree that one particular price is appropriate?

As with bonds, the price of shares is determined by the value that the market

places upon a future stream of income. How is that value arrived at?

Like bonds, there is the size of the income payments. But now we start to meet

some differences between bonds and equities. With ordinary shares, the income

payments will vary depending upon the success of the rm and its dividend policy.

Thus the income payments are strictly speaking uncertain and so there is an element

of risk which is not present in the case of bonds. A further contrast with bonds is

that dividends might reasonably be expected to grow over time, as the rm expands

but also as the result of ination. If the dividend yield(dividend price) is to stay at

a normal level, the price of the share itself must be expected to rise. Thus the return

from ordinary shares comes from two distinct sources. The rst is the current dividend,

producing the current dividend yield; the second is the capital growth or capital

appreciation. We shall see shortly, in eqn 6.14, how we can disaggregate the total

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Chapter 6 • The capital markets

Box 6.4

The dividend irrelevance theorem

It seems intuitively obvious that an increase in a share’s dividend should make the share

more attractive to investors and should result in a rise in its price. Indeed, many nancial

managers and market analysts work on the basis that this is true and markets do often

respond to a cut in a rm’s dividend by reducing the price of the share. Furthermore, eqn

6.11 clearly says that if the next dividend is set to zero then P0.

But it is worth considering whether common sense might be leading us astray. Of

course, a rm may fail to pay a dividend because it cannot – its earnings are insufcient.

This is indeed bad news and it may well be that the share price should be very low or

even virtually zero. However, it is quite possible that a rm may reduce its dividend in

order to increase retained earnings so that it can expand its investment in a very pro-

ductive project. After all, if it did not use retained earnings (and maintained its dividend),

it would have to raise the funds in some other form, perhaps a new share issue, and thus

spread the wealth represented by the rm more thinly among a greater number of share-

holders or lenders. Existing shareholders would have their large dividend (adding to their

wealth) but there would be more shares in existence (diluting their wealth). By contrast,

accepting the lower dividend reduces shareholder wealth but this is offset because the

expansion of the rm raises the value of the shares of the existing shareholders.

What we have discovered here is a form of ‘trade-off’. Shareholders may add to their

wealth by having large dividends and small increases in the capital value of their shares

or small dividends and a rapid growth in capital value. Miller and Modigliani (1961) pointed

out that under certain assumptions, paying out earnings as dividends or retaining them

to nance new investment were strictly equivalent from the point of view of shareholder

wealth and therefore shareholders should be indifferent and the market price should not

depend upon dividend payments. What determined the value of a share was the value

of the rm and this was nothing more than the productivity of its real assets. As far as

share values were concerned it was earnings, or prots, that mattered and these in turn

depended upon the rm’s success in investing in productive assets.

A formal proof of the dividend irrelevance theoremis beyond the scope of this book,

though it can be found in almost any textbook on nancial management. If you look at

eqn 6.14, you can see that the return on a share is clearly split into two parts. Thus it

is obviously possible for the dividend to be very low indeed and the total return still to

be high provided that goffsets the low dividend yield. Formal proofs revolve around

showing that reductions in Das a proportion of earnings lead systematicallyto higher

values of g.

return into these two elements. This disaggregation is crucial to our understanding

of the dividend irrelevance theorem (see Box 6.4).

Secondly, the value of the future payments has to be discounted because they lie

in the future. Here again we are proceeding as we did with bonds, though we shall

see that our choice of an appropriate discount rate is different.

Mathematically, we can express the present value of a share as follows:

	DDDD
PV	012... n	(6.9)
	
	
	1 (1 K)2(1 K)3(1 K)n1
	K

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