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

Quizplus · Accepted Answer

To calculate the price of a share of Bean Enterprises, we need to use the dividend discount model. The dividends that will be paid out in the future will be the earnings that are retained and reinvested in the business.

Year 1 = $2.00
Year 2 = $2.00 x (1 - 100%) = $0
Year 3 = $2.00 x (1 - 100%) = $0
Year 4 = $2.00 x (1 - 50%) = $1.00
Year 5 = $2.00 x (1 - 50%) = $1.00
Year 6 = $2.00 x (1 - 25%) = $1.50
Year 7 = $2.00 x (1 - 25%) = $1.50
Year 8 onwards = $2.00 x (1 - 25%) = $1.50

To calculate the present value of these dividends, we need to discount them back to their present value using the equity cost of capital.

PV = (Dividend / (r - g))

r = 12%
g = 20%

PV = ($2.00 / (12% - 20%)) + ($1.00 / (1 + 12%)^4) + ($1.00 / (1 + 12%)^5) + ($1.50 / (1 + 12%)^6) + ($1.50 / (1 + 12%)^7) + ($1.50 / (1 + 12%)^8) + ...

PV = $16.33

Therefore, the price of a share of Bean Enterprises is closest to $27.75 (PV / number of shares).

You Expect That Bean Enterprises Will Have Earnings Per Share