Question

The market price of a security is $60. Its expected rate of return is 10%. The risk-free rate is 6%, 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. (Round your answer to 2 decimal places.) Market price $

Answer 1

Risk free rate = 6%

market risk premium = 8%

expected rate of return from security = 10% = R

using CAPM model

expected return = risk free rate + beta* market risk premium

let beta = x

10 = 6 +x*8

x= 0.5

beta = 0.5

Using dividend discount model to caluclate amount of dividend that company is paying

since dividend is constant so growth = 0

cost of equity = Dividend/ Market price

cost of equity = 10%

market price = 60$

dividend = (10/100)*60 = $6

since this dividend is constant in perpetuity.

now beta doubles

new beta = 0.5*2= 1

expected return using CAPM model

expected return = risk free rate + beta* market risk premium

= 6% + 1* 8%

= 14%

using dividend discount model

14%= dividend / market price

0.14= 6/ market price

new market price= $42.86