You are considering buying shares of stock in the Steel Mill Corporation. The forecast for the firm is steady growth over the next decade. The firm just paid its annual dividend of $1.42 per share and has plans to increase that amount by 4 percent annually, indefinitely. You require a 12.5 percent return on this type of security. What is your estimate of the value of this stock ten years from now?

Question

Quizplus · Accepted Answer

To estimate the value of the stock ten years from now, we use the Gordon Growth Model (Dividend Discount Model for a perpetuity) formula: P = D / (r - g), where P is the price, D is the dividend, r is the required rate of return, and g is the growth rate. However, since we're calculating the value ten years from now, we first need to find the dividend in year 11 (D11), because the model calculates the present value of dividends from that point onwards indefinitely.The dividend in year 11 (D11) can be calculated as D0 * (1 + g)^11, where D0 is the current dividend and g is the growth rate. Given D0 = $1.42 and g = 4% or 0.04, we calculate D11 as follows:D11 = $1.42 * (1 + 0.04)^11 = $1.42 * 1.48024 ≈ $2.102Then, we use the Gordon Growth Model to find the price ten years from now, substituting D11 for D, r = 12.5% or 0.125, and g = 4% or 0.04:P = D11 / (r - g) = $2.102 / (0.125 - 0.04) = $2.102 / 0.085 ≈ $24.73Therefore, the estimate of the value of this stock ten years from now is approximately $24.73.

You Are Considering Buying Shares of Stock in the Steel