Cost of Common Stock Using the Dividend Valuation Model In Chapter 9, we reviewed the dividend valuation method (DVM) for

Cost of Common Stock Using the Dividend Valuation Model In Chapter 9, we reviewed the dividend valuation method (DVM) for

valuing common stock. The DVM states that the price of a share of stock is the present value of all its future cash dividends, where the future divi- dends are discounted at the required rate of return on equity, r.

If these dividends are constant forever (similar to the dividends of per- petual preferred stock, as we just covered), the cost of common stock is derived from the value of a perpetuity. Let

D represent the constant divi- dend per share of common stock that is expected next period and each period after that forever; P 0 , the current price of a share of stock; and r e , the cost of common stock. The current price of a share of common stock is:

THE FUNDAMENTALS OF VALUATION

D P 0 = -----

We can solve for r e :

D r e = ------

However, common stock dividends do not usually remain constant. It’s typical for dividends to grow at a constant rate. Let D 0 indicate this period’s dividend. If dividends grow at a constant rate,

g, forever, the present value of the common stock is the present value of all future dividends:

0 = ---------------------------- … -----------------------------

0 + ---------------------------- 0 + + 0

Pulling today’s dividend D 0 from each term,

P = D --------------------- ( 1 + g ) + --------------------- ( 1 + g )

0 0 + … + 1 ---------------------- 2 ∞

( 1 + r e ) Expressing this in summation notation:

P 0 = D 0 ∑ --------------------

The summation term is approximately equal to (1 + g)/(r e – g), so we can rewrite the price of the common stock as:

( 1 + g ) P 0 = D 0 ------------------ ( r e – g )

If we refer to the next period’s dividend, D 1 , as this period’s divi- dend, D 0 , compounded one period at the rate g,

D 1 = D 0 (1 + g)

The Cost of Capital

then:

D P 0 = ------------------ 1

( r e – g ) Rearranging this equation to solve instead for r e ,

r e = ------- 1 + g (11-5)

we see that the cost of common stock is the sum of next period’s divi-

dend yield, D 1 / P 0 , plus the growth rate of dividends: Cost of common stock = Dividend yield + Growth rate of dividends

Consider a firm expected to pay a constant dividend of $2 per share per year, forever. If the firm issues stock at $20 a share, the firm’s cost of common stock is:

r = $2 e ---------- =

0.10 or 10% per year

But, if dividends are expected to be $2 in the next period and grow at a rate of 3% per year, and the required rate of return is 10% per year, the

expected price per share (with D 1 = $2 and g = 3%) is:

which is more than $8 above the price if there is no expected growth in dividends.

The DVM reflects two ideas that make some sense about the rela- tion between the cost of equity and the dividend payments:

■ The greater the current dividend yield, the greater the cost of equity. ■ The greater the growth in dividends, the greater the cost of equity.

However, the DVM has some drawbacks:

THE FUNDAMENTALS OF VALUATION

■ How do you deal with dividends that do not grow at a constant rate? This model does not accommodate nonconstant growth easily. ■ What if the firm does not pay dividends now? In that case, D 1 would

be zero and the expected price would be zero. But a zero price for stock does not make any sense! And if dividends are expected in the future, but there are no current dividends, what do you do?

■ What if the growth rate of dividends is greater than the required rate of return? This implies a negative stock price, which isn’t possible. ■ What if the stock price is not readily available, say in the case of a privately-held firm? This would require an estimate of the share price.

Therefore, the DVM may be appropriate to use to determine the cost of equity for companies with stable dividend policies, but it may not applicable for all firms.