You are considering the purchase of a common stock that paid a dividend of $2.00

Question

You are considering the purchase of a common stock that paid a dividend of $2.00 yesterday. You expect this stock to have a growth rate of 15 percent for the next 3 years, resulting in dividends of D1=$2.30, D2=$2.645, and D3=$3.04. The long-run normal growth rate after year 3 is expected to be 10 percent (that is, a constant growth rate after year 3 of 10% per year forever). If you require a 14 percent rate of return, how much should you be willing to pay for this stock? A. $56.46 B. $83.65 C. $89.75 D. $62.57

Explanation / Answer

Hi,

Please find the detailed answer as follows:

You need to calculate the present value of all future dividends and price of the stock at the end of Year 3 to calculate the current stock price.

Present Value of Future Dividends = 2.3/(1+.14)^1 + 2.645/(1+.14)^2 + 3.04/(1+.14)^3 = $6.104 or 6.10

Price at the End of Year 3 = D3*(1+g)/(ke - g) = 3.04*(1+.10)/(.14 - .10) = $83.60

Present Value of Price (Year 3) = 83.60/(1+.14)^3 = $56.43

Current Stock Price (PO) = Present Value of Future Dividends + Present Value of Price (Year 3) = 6.10 + 56.43 = $62.53 which is closest to $62.57

Option D ($62.57) is the correct answer.

Thanks.

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