Question

Assume that the risk-free rate is 5% and the expected rate of return on the market is 15%. Use the Security Market Line (SML) of the Capital Asset Pricing Model (CAPM) to answer the following questions and show all your calculations.

(a) A share of stock A is now selling for $150. It would pay a dividend of $12 per share at the end of the year. Its beta is 1.2. What must investors expect the stock A to sell for at the end of the year?

(b) Another stock B has an expected return of 8%. What is its beta?

(c) What is the expected return of a stock C with a beta of 1.5?

Answer 1

Part a

D1 = 12

Beta = 1.2

Price = 150

Expected rate = Risk free rate + (Beta * (Market return - Risk free rate))

Expected rate = 5% + (1.2 * (15% - 5%)

Expected rate = 17%

Price = D1 / (Rate - Growth rate)

150 = 12 / (15% - G)

(15% - G) * 150 = 12

(15% - G) = 8%

G = 15% - 8%

G = 7%

P1 = D1 * (1 + G) / (R -G)

P1 = (12 * (1 + 7%) ) / (15% - 7%)

P1 = (12 * (1 + 7%) ) / (15% - 7%)

P1 = 160.50

stock A to sell for at the end of the year for 160.50

Part b

Expected rate = Risk free rate + (Beta * (Market return - Risk free rate))

8% = 5% + (Beta * (15% - 5%)

8% = 5% + 10%Beta

Beta = (8% - 5%) / 10%

Beta = 0.30

Part c

Expected rate = Risk free rate + (Beta * (Market return - Risk free rate))

Expected rate = 5% + (1.5 * (15% - 5%)

Expected rate = 20%