Question

**Expected returns, dividends, and growth**

The constant growth valuation formula has dividends in the numerator. Dividends are divided by the difference between the required return and dividend growth rate as follows:

P̂0 | = | D1/(rs − gL) |

Which of the following statements best describes how a change in a firm’s stock price would affect a stock’s capital gains yield?

a.The capital gains yield on a stock that the investor already owns has an inverse relationship with the firm’s expected future stock price.

b.The capital gains yield on a stock that the investor already owns has a direct relationship with the firm’s expected future stock price.

Walter Utilities is a dividend-paying company and is expected to pay an annual dividend of $2.25 at the end of the year. Its dividend is expected to grow at a constant rate of 7.50% per year. If Walter’s stock currently trades for $16.00 per share, what is the expected rate of return?

8.70%

7.63%

21.56%

17.06%

Which of the following conditions must hold true for the constant growth valuation formula to be useful and give meaningful results?

a. The company’s stock cannot be a zero growth stock.

b. The required rate of return, rss, must be greater than the long-run growth rate.

c. The company’s growth rate needs to change as the company matures.

Answer #1

The answer is

b.The capital gains yield on a stock that the investor already owns has a direct relationship with the firm’s expected future stock price.

As Capital Gains Yield = (Future Price – Current price)/Current Price

Stock Price = Expected Dividend/(Expected Rate of return – growth rate)

16 = 2.25/(Expected Rate of return – 7.50%)

Expected rate of return = 21.5625%

i.e. 21.56%

b. The required rate of return, rss, must be greater than the long-run growth rate.

as the formula does not work when the growth rate is higher than the required return

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numerator. Dividends are divided by the difference between the
required return and dividend growth rate as follows:
Pˆ0P̂0
= =
D1(rs – g)D1(rs – g)
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