P7-9: Common stock value: Constant growth McCracken Roofing Inc. common stock paid a dividend of $1.20 per share last year. The company expects earnings and dividends to grow at a rate of 5% per year for the foreseeable future. a. What required rate of return for this stock would result in a price per share of $28? b. If McCracken expects both earnings and dividends to grow at an annual rate of 10%, what required rate of return would result in a price per share of $28?

Respuesta :

Answer:

a) rate of return = 0.095 = 9.5%

b) rate of return = 0.147143 = 14.7143%

Explanation:

a) using the constant growth model:

[tex]P = \frac{D0 (1+g)}{ke - g)}[/tex]

[tex]28=\frac{1.2(1.05)}{ke-0.05} \\[/tex]

therefore[tex]ke =\frac{1.2(1.05)}{28} +0.05[/tex]

[tex]ke = 0.095 =9.5%[/tex]

b) using the working from above, we showed that

[tex]ke=\frac{Do(1+g)}{P0} + g[/tex]

given g= 10%, P0=28 and D0=1.2

[tex]ke = \frac{1.20(1+0.1)}{28} + 0.1 = 0.147142857 = 14.7143%[/tex]