You have invested in a stock that has a dividend growth rate of 4%. It is expected to pay a dividend of $4 per share next year. You expect to sell the stock after 3 years, for a capital gain of about $6 per share. If your required rate of return is 8%, what price would you be ready to pay for the stock?
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A. B. C. D.Explanation
Be careful about the fact that $6 represents the capital gain on the stock, not the selling price. If you buy the stock for a price, P, then the problem has in effect told you that the cash flows from the stock are expected to be: $4 next year, $4 * 1.04 = $4.16 in year 2 and (P + $6 + $4 * 1.04^2) = $(P + 10.33) in year 3. The present value of these cash flows at a discount rate of 8% per year is equal to P and this equals
P = 4/1.08 + 4.16/1.08^2 + (P + 10.33)/1.08^3 = P/1.08^3 + 15.47. Solving for P gives P = 15.47/(1 - 1/1.08^3) = $75.04