CP

In this form, we see that ˆrsis theexpected total returnand that it consists of anex-

pected dividend yield,D 1 /P 0 5.4%, plus anexpected growth rate or capital gains yield,

g8%.

Suppose this analysis had been conducted on January 1, 2003, so P 0 $23 is the

January 1, 2003, stock price, and D 1 $1.242 is the dividend expected at the end of

2003. What is the expected stock price at the end of 2003? We would again apply
      Equation 5-2, but this time we would use the year-end dividend, D 2 D 1 (1
      g) 
      $1.242(1.08) $1.3414:

Now, note that $24.84 is 8 percent larger than P 0 , the $23 price on January 1, 2003:

$23(1.08) $24.84.

Thus, we would expect to make a capital gain of $24.84 $23.00 $1.84 during

2003, which would provide a capital gains yield of 8 percent:

We could extend the analysis on out, and in each future year the expected capital gains

yield would always equal g, the expected dividend growth rate.

Continuing, the dividend yield in 2004 could be estimated as follows:

The dividend yield for 2005 could also be calculated, and again it would be 5.4 per-

cent. Thus, for a constant growth stock,the following conditions must hold:

1. The dividend is expected to grow forever at a constant rate, g.


2. The stock price is expected to grow at this same rate.


3. The expected dividend yield is a constant.


4. The expected capital gains yield is also a constant, and it is equal to g.


5. The expected total rate of return, ˆrs, is equal to the expected dividend yield plus the
   expected growth rate: ˆrsdividend yield
   g.

The term expectedshould be clarified—it means expected in a probabilistic sense, as

the “statistically expected” outcome. Thus, if we say the growth rate is expected to re-

main constant at 8 percent, we mean that the best prediction for the growth rate in

any future year is 8 percent, not that we literally expect the growth rate to be exactly 8

percent in each future year. In this sense, the constant growth assumption is a reason-

able one for many large, mature companies.

What conditions must hold if a stock is to be evaluated using the constant

growth model?

What does the term “expected” mean when we say expected growth rate?

Valuing Stocks That Have a Nonconstant Growth Rate

For many companies, it is inappropriate to assume that dividends will grow at a con-

stant rate. Firms typically go through life cycles.During the early part of their lives,

their growth is much faster than that of the economy as a whole; then they match the

Dividend yield 2003 

D 2004

Pˆ12/31/03



$1.3414

$24.84

0.0545.4%.

Capital gains yield 2003 

Capital gain

Beginning price



$1.84

$23.00

 0.08  8%.

Pˆ12/31/03D^2004

rsg



$1.3414

0.1340.08

$24.84.

Valuing Stocks That Have a Nonconstant Growth Rate 201

The popular Motley Fool
web site http://www.
fool.com/school/
introductiontovaluation.
htmprovides a good de-
scription of some of the
benefits and drawbacks of a
few of the more commonly
used valuation procedures.

Stocks and Their Valuation 197