Assume that CAPM is valid. A share of stock is now selling for $90. It will pay

Question

Assume that CAPM is valid. A share of stock is now selling for $90. It will pay a dividend of $10 per share at the end of the year. Its beta is 1. What do investors expect the stock to sell for at the end of the year? Assume the risk-free rate is 4% and the expected rate of return on the market portfolio is 18%. (Round your answer to 2 decimal places.)

Assume that CAPM is valid. A share of stock is now selling for $90. It will pay a dividend of $10 per share at the end of the year. Its beta is 1. What do investors expect the stock to sell for at the end of the year? Assume the risk-free rate is 4% and the expected rate of return on the market portfolio is 18%. (Round your answer to 2 decimal places.)

Explanation / Answer

According to CAPM

Required rate of Return (Ke) = Rf + Beta * (E(Rm) - Rf)

where Rf = Risk free rate

E(Rm) = Expected rate of return on market portfolio

Thus, Ke = 4% + 1 * (18% - 4%)

               = 4% + 14% = 18%

Now using Gordon Growth Model

Price of the stock = D1/(Ke- g)

where D1 = Next years dividend

g = Growth rate

90 = 10 /(18% - g)

g = 18% - 10/90 = 18% - 11.11% = 6.89%

Expected Price at the year end = D2/(Ke- g)

D2 = D1 * (1 + g) = 10 * (1 + 6.89%) = $10.689

Expected Price at the year end = 10.689/(18% - 6.89%) = 10.689/11.11% = $96.21

Thus, investors expect the stock to sell for $96.21 at the end of the year.

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