You expect that Bean Enterprises will have earnings per share of $2 for the coming year. Bean plans to retain all of its earnings for the next three years. For the subsequent two years, the firm plans on retaining 50% of its earnings. It will then retain only 25% of its earnings from that point forward. Retained earnings will be invested in projects with an expected return of 20% per year. If Bean's equity cost of capital is 12%, then the price of a share of Bean Enterprises is closest to:

Question

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The price of a share of Bean Enterprises can be calculated using the dividend discount model (DDM), adjusted for the retention ratio and the return on retained earnings. For the first three years, Bean retains all earnings, so the growth rate is 20% (the return on retained earnings). For the next two years, the growth rate is 10% (50% of 20%), and afterward, it's 5% (25% of 20%). The terminal value at the end of year 5 can be calculated using the Gordon Growth Model, considering the perpetual growth rate of 5% from year 5 onwards. The dividends paid out from year 4 onwards are calculated based on the retention ratio and the earnings growth. The present value of these dividends and the terminal value, discounted back at the equity cost of capital of 12%, gives the price of the share. The correct calculation involves projecting the earnings growth, calculating dividends from year 4, and discounting these cash flows back to the present value. Given the options, the closest value to the correct calculation methodology is $27.75, indicating a complex calculation that accounts for the changing retention ratios and the impact on growth and dividends.

You Expect That Bean Enterprises Will Have Earnings Per Share