## Expected Rate of Return on a Constant Growth Stock

We can solve Equation 5-2 for rs, again using the hat to indicate that we are dealing with an expected rate of return:10

Self-Test Questions

We can solve Equation 5-2 for rs, again using the hat to indicate that we are dealing with an expected rate of return:10

 Expected rate Expected Expected growth of return l- rate, or capital gains yield rs = - -Po g. (5-4)

Thus, if you buy a stock for a price P0 = \$23, and if you expect the stock to pay a dividend D1 = \$1.242 one year from now and to grow at a constant rate g = 8% in the future, then your expected rate of return will be 13.4 percent:

9Many apparent puzzles in finance can be explained either by managerial compensation systems or by peculiar features of the Tax Code. So, if you can't explain a firm's behavior in terms of economic logic, look to bonuses or taxes as possible explanations.

10The rs value in Equation 5-2 is a required rate of return, but when we transform to obtain Equation 5-4, we are finding an expected rate of return. Obviously, the transformation requires that rs = rs. This equality holds if the stock market is in equilibrium, a condition that will be discussed later in the chapter.

The popular Motley Fool web site http://www. fool.com/school/ introductiontovaluation.

htm provides a good description of some of the benefits and drawbacks of a few of the more commonly used valuation procedures.

In this form, we see that rs is the expected total return and that it consists of an expected dividend yield, D1/P0 = 5.4%, plus an expected growth rate or capital gains yield, g = 8%.

Suppose this analysis had been conducted on January 1, 2003, so P0 = \$23 is the January 1, 2003, stock price, and D1 = \$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, D2 = D1 (1 + g) = \$1.242(1.08) = \$1.3414:

2004

\$1.3414

12/31/03

Now, note that \$24.84 is 8 percent larger than P0, the \$23 price on January 1, 2003:

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:

Capital gains yield2003

Capital gain _ \$1.84 Beginning price \$23.00

0.08

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:

Dividend yield2003

D2004 P12/31/03

The dividend yield for 2005 could also be calculated, and again it would be 5.4 percent. 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, rs, is equal to the expected dividend yield plus the expected growth rate: rs = dividend yield + g.

The term expected should be clarified—it means expected in a probabilistic sense, as the "statistically expected" outcome. Thus, if we say the growth rate is expected to remain 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 reasonable one for many large, mature companies.

r ii j . t. What conditions must hold if a stock is to be evaluated using the constant jeu- iesi growth model?

Questions

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

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### Responses

• mezan aman
Is expected growth rate also the expected capital gains yield?
8 years ago
• Kenneth
What decisions must hold in order to for a stock to be evaluated using the constant growth model?
8 years ago
• Eleanor Findlay
What conditions must hold if a stock is to be evaluated using the constant growth model?
8 years ago
• karl
What conditions must hold if a stock is to be evaluated using the constant growth mode?
8 years ago
• Marjo
What happens to constant growth stocks if the yield drops?
8 years ago
• Claudia Piccio
What is the expected return on corporation stock in the future?
7 years ago
• gigliola
Is the capital gain rate and the constant growth rate of dividends?
7 years ago
• isumbras
What is meant by expected constant growth rate?
7 years ago
• ISAIA
What would your firm’s stock value be if the dividend was expected to grow at a constant:?
6 years ago
• Aran
What happens when stock's dividend grows at a constant rate?
6 years ago
• Zak
What is the stock’s total expected yield or rs?
5 years ago