Principles of Managerial Finance

CHAPTER 7 Stock Valuation 325

5. Another assumption of the constant-growth model as presented is that earnings and dividends grow at the same
   rate. This assumption is true only in cases in which a firm pays out a fixed percentage of its earnings each year (has
   a fixed payout ratio). In the case of a declining industry, a negative growth rate (g< 0%) might exist. In such a case,
   the constant-growth model, as well as the variable-growth model presented in the next section, remains fully applic-
   able to the valuation process.

constant-growth model
A widely cited dividend
valuation approach that assumes
that dividends will grow at a
constant rate, but a rate that is
less than the required return.

zero-growth model
An approach to dividend
valuation that assumes a
constant, nongrowing dividend
stream.

The equation can be simplified somewhat by redefining each year’s dividend, Dt,

in terms of anticipated growth. We will consider three models here: zero-growth,

constant-growth, and variable-growth.

Zero-Growth Model

The simplest approach to dividend valuation, the zero-growth model,assumes a

constant, nongrowing dividend stream. In terms of the notation already introduced,

D 1 D 2 .. .D∞

When we let D 1 represent the amount of the annual dividend, Equation 7.2 under

zero growth reduces to

P 0 D 1


∞

t 1

D 1

 (PVIFAks,∞)D 1

 

k

1

s

 (7.3)

The equation shows that with zero growth, the value of a share of stock would

equal the present value of a perpetuity ofD 1 dollars discounted at a rateks. (Perpe-

tuities were introduced in Chapter 4; see Equation 4.19 and the related discussion.)

EXAMPLE The dividend of Denham Company, an established textile producer, is expected

to remain constant at $3 per share indefinitely. If the required return on its stock

is 15%, the stock’s value is $20 ($30.15) per share.

Preferred Stock Valuation Because preferred stock typically provides its

holders with a fixed annual dividend over its assumed infinite life, Equation 7.3

can be used to find the value of preferred stock.The value of preferred stock can

be estimated by substituting the stated dividend on the preferred stock for D 1 and

the required return for ksin Equation 7.3. For example, a preferred stock paying

a $5 stated annual dividend and having a required return of 13 percent would

have a value of $38.46 ($50.13) per share.

Constant-Growth Model

The most widely cited dividend valuation approach, the constant-growth model,

assumes that dividends will grow at a constant rate, but a rate that is less than the

required return. (The assumption that the constant rate of growth, g,is less than

the required return, ks,is a necessary mathematical condition for deriving this

model.^5 ) By letting D 0 represent the most recent dividend, we can rewrite Equa-

tion 7.2 as follows:

P 0 .. . (7.4)

D 0

 (1g)∞



(1ks)∞

D 0

 (1g)^2



(1ks)^2

D 0

 (1g)^1



(1ks)^1

D 1



ks

1



(1ks)t