Final answer:
The price of Miles Hardware's stock is calculated using the dividend growth model, discounting future dividends at the required return rate of 17%.
Step-by-step explanation:
When assessing the price of a stock, one method is to consider the value of future dividends. Miles Hardware has a policy of increasing its dividend by 12.5% annually. To determine the stock's price, we discount the future dividends back to present value using the required rate of return, which is 17% in this case. The dividend growth model formula, also known as the Gordon Growth Model, can be utilized here. However, when a company has a finite life, as in scenarios (a) through (e), the process involves calculating the present value of each year's dividend and summing these up. For the perpetual case in point (f), we use the formula P = D1 / (k - g), where P is the price, D1 is the dividend next year, k is the required rate of return, and g is the growth rate of the dividend.
For example, with a current dividend (Div0) of $1.65 and a growth rate of 12.5%, the next year's dividend (D1) would be $1.65 * 1.125 = $1.85625. In the perpetual case, the price of the stock would be calculated as P = $1.85625 / (0.17 - 0.125) = $1.85625 / 0.045 = $41.25. This is under the assumption that the company will continue paying dividends forever at the growing rate.
Calculating the price for the scenarios with 5, 15, 25, and 45 years remaining requires more detailed calculations to find the present value of dividends over each year until the end of the company's life. Each scenario involves larger computations, and each future dividend is discounted at the 17% rate of return investors desire.