A share of stock with a beta of .81 now sells for $56. Investors expect the stoc

Question

A share of stock with a beta of .81 now sells for $56. Investors expect the stock to pay a year-end dividend of $4. The T-bill rate is 4%, and the market risk premium is 7%. 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 3 decimal places.)

A share of stock with a beta of .81 now sells for $56. Investors expect the stock to pay a year-end dividend of $4. The T-bill rate is 4%, and the market risk premium is 7%. 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 3 decimal places.)

Explanation / Answer

Expected return =   Rf +[Beta *Market premium ]

                           = 4+ [.81 *7]

                            = 4 + 5.67

                          = 9.67%

P0 = D1/(Ke-g)

56 = 4 /(.0967 -g)

    .0967 -g = 4 /56

    .0967 -g = .0714

     g = .0967 -.0714 = .0253 or 2.53%

D2 = 4 (1+.0253 ) =4.1012

Stock price = 4.1012 /(.0967 -.0253)

              = 4.1012 / .0714

              = $ 57.440 per share

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