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