Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

III. Valuation of Future

Cash Flows

(^282) 8. Stock Valuation © The McGraw−Hill
Companies, 2002
We can verify this answer by calculating the price in one year, P 1 , using 15 percent
as the required return. Based on the dividend growth model, this price is:
P 1 D 1 (1 g)/(R
g)
$1 1.10/(.15
.10)
$1.10/.05
$22
Notice that this $22 is $20 1.1, so the stock price has grown by 10 percent as it should.
If you pay $20 for the stock today, you will get a $1 dividend at the end of the year, and
you will have a $22
20 $2 gain. Your dividend yield is thus $1/20 5%. Your cap-
ital gains yield is $2/20 10%, so your total return would be 5% 10% 15%.
To get a feel for actual numbers in this context, consider that, according to the 2001
Value Line Investment Survey,Procter and Gamble’s dividends were expected to grow
by 8 percent over the next 5 or so years, compared to a historical growth rate of 13 per-
cent over the preceding 5 years and 11.5 percent over the preceding 10 years. In 2001,
the projected dividend for the coming year was given as $1.34. The stock price at that
time was about $75 per share. What is the return investors require on P&G? Here, the
dividend yield is 1.8 percent and the capital gains yield is 8 percent, giving a total re-
quired return of 9.8 percent on P&G stock.
Our discussion of stock valuation is summarized in Table 8.1.
252 PART THREE Valuation of Future Cash Flows

TABLE 8.1

Summary of Stock

Valuation

I. The general case

In general, the price today of a share of stock, P 0 , is the present value of all of its

future dividends, D 1 , D 2 , D 3 ,... :

P 0 ...

where Ris the required return.

II. Constant growth case

If the dividend grows at a steady rate, g,then the price can be written as:

P 0 

This result is called the dividend growth model.

III. Supernormal growth

If the dividend grows steadily after tperiods, then the price can be written as:

P 0 ... 

where

Pt

IV. The required return

The required return, R,can be written as the sum of two things:

RD 1 /P 0 g

where D 1 /P 0 is the dividend yieldand gis the capital gains yield(which is the

same thing as the growth rate in dividends for the steady growth case).

Dt(1 g)

(R
g)

Pt

(1 R)t

Dt

(1 R)t

D 2

(1 R)^2

D 1

(1 R)^1

D 1

R
g

D 3

(1 R)^3

D 2

(1 R)^2

D 1

(1 R)^1