Question

You are considering buying a stock that you believe pays $5 in dividends a year forever. a. Suppose you believe that the beta of the stock is 0.4. How much is the stock worth if the risk free rate is 4% and the expected rate of return on the market portfolio is 11%? b. By how much will you overvalue the stock if its beta is actually 0.6?

Answer 1

Given about a stock,

Dividend D = $5

Beta = 0.4

Risk free rate Rf = 4%

expected rate of return on the market portfolio Rm = 11%

=> using CAPM, expected return on stock = Rf + beta*(Rm - Rf)

=> rs = 4 + 0.4*(11 - 4) = 6.8%

So, stock price today using perpetuity model is dividend/required return

=> P0 = 5/0.068 = $73.53

If actual beta of stock is 0.6

So, required return R = 4 + 0.6*(11-4) = 8.2%

So, stock price today P = 5/0.082 = $60.98

using beta of 0.4, stock is overvalues by (73.53 - 60.98) = $12.55