**Unformatted text preview: **der can earn capital gains by selling stock at a price above that originally paid,
what is really sold is the right to all future dividends. What about stocks that are
not expected to pay dividends in the foreseeable future? Such stocks have a value
attributable to a distant dividend expected to result from sale of the company or
liquidation of its assets. Therefore, from a valuation viewpoint, only dividends
are relevant.
By redefining terms, the basic valuation model in Equation 6.5 can be specified for common stock, as given in Equation 7.2:
P0 (1 D1
ks )1 (1 D2
ks )2 ... (1 D∞
ks )∞ (7.2) where
P0
Dt
ks value of common stock
per-share dividend expected at the end of year t
required return on common stock 4. The need to consider an infinite time horizon is not critical, because a sufficiently long period—say, 50 years—
will result in about the same present value as an infinite period for moderate-sized required returns. For example, at
15%, a dollar to be received 50 years from now, PVIF15%,50yrs , is worth only about $0.001 today. CHAPTER 7 Stock Valuation 325 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
zero-growth model
An approach to dividend
valuation that assumes a
constant, nongrowing dividend
stream. The simplest approach to dividend valuation, the zero-growth model, assumes a
constant, nongrowing dividend stream. In terms of the notation already introduced,
D1 D2 ... D∞ When we let D1 represent the amount of the annual dividend, Equation 7.2 under
zero growth reduces to
∞ P0 D1
t 1
ks )t
1 (1 D1 (PVIFAks ,∞) D1 1
ks D1
ks (7.3) The equation shows that with zero growth, the value of a share of stock would
equal the present value of a perpetuity of D1 dollars discounted at a rate ks. (Perpetuities 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 ($3 0.15) 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 D1 and
the required return for ks in 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 ($5 0.13) per share. Constant-Growth Model
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. The most widely cited dividend valuation approach, the constan...

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