Question

Food Inc. just announced it is increasing its annual dividend to $5.0 next year and establishing a policy whereby the dividend will increase by 2.00 percent annually thereafter. Assuming the required rate of return is 9.00 percent. (1) What will the stock price per share be five years from now? (2) What will the stock price per share be ten years from now? (3) What will the stock price per share be twenty years from now

Answer 1

The stock price per share will be $78.8571, $87.0729, and $106.1394 in five, ten, and twenty years respectively.

Step-by-step explanation:

To find the stock price per share in the future, we can use the dividend discount model (DDM). The DDM calculates the present value of all the future dividends. The formula is: Stock Price = Dividend / (Required Rate of Return - Dividend Growth Rate). Using this formula, we can calculate the stock price per share five, ten, and twenty years from now.

(1) For the stock price per share five years from now:

1. Dividend = $5.00 x (1 + 0.02)^5 = $5.00 x 1.1040801 = $5.52
2. Stock Price = $5.52 / (0.09 - 0.02) = $5.52 / 0.07 = $78.8571

(2) For the stock price per share ten years from now:

1. Dividend = $5.00 x (1 + 0.02)^10 = $5.00 x 1.2190246 = $6.0951
2. Stock Price = $6.0951 / (0.09 - 0.02) = $6.0951 / 0.07 = $87.0729

(3) For the stock price per share twenty years from now:

1. Dividend = $5.00 x (1 + 0.02)^20 = $5.00 x 1.4859464 = $7.4297
2. Stock Price = $7.4297 / (0.09 - 0.02) = $7.4297 / 0.07 = $106.1394