Question

A share of stock with a beta of 0.72 now sells for $47. Investors expect the stock to pay a year-end dividend of $2. The T-bill rate is 3%, and the market risk premium is 6%. If the stock is perceived to be fairly priced today, what must be investors’ expectation of the price of the stock at the end of the year? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Required rate of return using CAPM model : Risk free rate+ [market risk premium * beta]

                                                    = 3 + [6 * .72]

                                                   = 3 + 4.32

                                                  = 7.32%

Now

current price =D1 /(Rs-g)

   47 = 2 /(.0732 -g)

(.0732 -g) = 2/47

(.0732- g) = .042553

g = .0732 -.042553

     = .03065 or 3.065%

Now D2: D1(1+g)

             = 2(11+.03065) = 2.0613

Price at end of year 1 =D2/(Rs-g)

                  = 2.0613 /(.0732-.03065)

                  = 2.0613 /.04255

                  = $ 48.44 per share

investors’ expectation of the price of the stock at the end of the year = $ 48.44 per share.