Question

A share of stock sells for $36 today. The beta of the stock is 1.1 and the expected return on the market is 15 percent. The stock is expected to pay a dividend of $0.90 in one year. If the risk-free rate is 3.5 percent, what should the share price be in one year?

Answer 1

Step-by-step explanation:

First, use CAPM formula to find the rate of return on this stock;

CAPM; r = risk free + beta(market return - risk free)

r = 0.035 + 1.1(0.15-0.035)

r =0.035 +0.115

r = 0.15 or 15%

Next, use dividend discount model to find growth rate of the dividends;

Price(yr0) = Div1/(r-g)

36 = 0.90/(0.15-g)

then cross-multiply to get;

5.4 - 36g = 0.90

5.4 -0.90 = 36g

4.5 = 36g

g = 4.5/36

g = 0.125 or 12.5%

Price next year (P1) = Current price (1+g)

P1 = 36*(1+0.125)

P1 = 40.5

Therefore in one year, this stock will be valued at $40.50