Question

E A B The market price of a security is $40. Its expected rate of return is 13%. The risk-free rate is 7%, and the market risk premium is 8% . What will the market price of the security be if its beta doubles (and all other variables remain unchanged)? Assume the stock is expected to pay a constant dividend in perpetuity. Market price of security Security expected rate of return Risk free rate of return Market risk premium Change in beta (x) Solution Current security beta New security beta Current dividend New expected rate of return on security New price of security

Answer 1

According to the CAPM,

Expected Return = Risk-free Rate + [Beta*Market Risk Premium]

13% = 7% + [Beta*8%]

Beta*8% = 13% - 7%

Beta = 6% / 8% = 0.75

New Beta = Current Beta * 2 = 0.75 * 2 = 1.50

Current Dividend = Current Market Price * Current Expected Rate = $40 * 0.13 = $5.2

New Expected Return = 7% + [1.50 * 8%] = 7% + 12% = 19%

New Price = Dividend / New Expected Return = $5.20 / 0.19 = $27.37