Question

Gentleman Gym’s common stock just paid its annual dividend of $3 per share, and it is widely expected that the dividend will increase by 5 percent per year indefinitely. The risk-free rate is 3 percent and the market risk premium is 6 percent.

(a) What price should Gentleman Gym’s common stock sell for today if it has a βequity of 2.0?

(b) How would your answer change if Gentleman Gym’s βequity were 1.5?

Answer 1

a.

As per CAPM Model,

Required Rate = R_f = Beta(R_m - R_f)

Required Rate = 0.03 + 2(0.06) = 15%

As per Constant Dividend Growth Model

Stock Price = 3(1.05)/(0.15 - 0.05)

Stock Price = $31.50

b.

As per CAPM Model,

Required Rate = R_f = Beta(R_m - R_f)

Required Rate = 0.03 + 1.5(0.06) = 12%

As per Constant Dividend Growth Model

Stock Price = 3(1.05)/(0.12 - 0.05)

Stock Price = $45