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.)

stock price?

I solved for r= 4% + .81 x 7%= 9.67%

Then i tried to solve for p but this is where I got stuck   DIV+capital gain/price= 4 + (p-56)/56. ??

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.)

stock price?

I solved for r= 4% + .81 x 7%= 9.67%

Then i tried to solve for p but this is where I got stuck   DIV+capital gain/price= 4 + (p-56)/56. ??

Explanation / Answer

The stock reach an “equilibrium” when is shall satisfy the CAPM return

As per CAPM equation:

Required rate of return is =Risk free rate + Beta * Market Risk premium

=4% + 0.81 *7%

=9.67 %

Hence the stock should earn 9.67% to be at equilibrium.

Stock Price = Dividend / Required rate

=4 /9.67%

= $41.37

Hence At $41.37 price the stock reach an “equilibrium” at which it is perceived as fairly priced today.

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