S&P Enterprises will pay an annual dividend of $2.08 a share on its common stock next year. The firm just paid a dividend of $2.00 a share and adheres to a constant rate of growth dividend policy. What will one share of S&P common stock be worth ten years from now if the applicable discount rate is 8 percent?

The price of the stock will be $76.97

Explanation:

We first need to determine the constant growth rate on dividends.

Growth rate (g) = (D1 - D0) / D0  

Growth rate (g) = (2.08 - 2.00) / 2   =  0.04 or 4%

To calculate the price of a stock today whose dividends are growing at a constant rate, we use the constant growth model of DDM. The price of the stock today under this model is,

P0 = D1 / ( r - g )

Where,

Thus, to calculate the price of the stock today at t=10, we will use the dividend expected in Year 11 or D11.

D11 = D0 * (1+g)^11

Where P10 is the price 10 years from today.

P10 = 2 * (1+0.04)^11 / (0.08 - 0.04)

P10 = $76.97

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