A company's earnings and dividends are growing at a constant rate of 8 percent. Last week it paid a dividend of $3.00. If the required rate of return is 15 percent, what is the price of the stock three years from now? (Do not round intermediate calculations. Round final answer to two decimal places.)
A) $58.31
B) $46.29
C) $51.02
D) $42.83

Question

Quizplus · Accepted Answer

The price of the stock three years from now can be calculated using the Dividend Discount Model for a stock with constant growth, which is given by the formula: P = D1 / (r - g), where P is the price of the stock, D1 is the dividend next year, r is the required rate of return, and g is the growth rate. First, we need to calculate the dividend three years from now (D4), since the question asks for the price three years from now, and then use D4 to find the price.The dividend three years from now (D4) can be calculated as: D4 = D0 * (1 + g)^4, where D0 is the last dividend paid.Given: D0 = $3.00, g = 8% or 0.08, r = 15% or 0.15.D4 = $3.00 * (1 + 0.08)^4 = $3.00 * 1.36049 = $4.08147.Now, to find the price three years from now, we actually need to calculate the price based on the dividend that will be paid in the fourth year, using D4 in the formula and calculating for P3 (since the dividend we've calculated is the one that will be paid at the end of the fourth year, the price we're calculating is effectively the price at the end of the third year, just before that dividend is paid).P3 = D4 / (r - g) = $4.08147 / (0.15 - 0.08) = $4.08147 / 0.07 = $58.31.Therefore, the price of the stock three years from now is $58.31.

A Company's Earnings and Dividends Are Growing at a Constant