Question

The FI Corporation’s dividends per share are expected to grow indefinitely by 8% per year.

a. If this year’s year-end dividend is $4.00 and the market capitalization rate is 10% per year, what must the current stock price be according to the DDM?

b. If the expected earnings per share are $16.00, what is the implied value of the ROE on future investment opportunities? (Round your answer to 2 decimal places.)

c. How much is the market paying per share for growth opportunities (i.e., for an ROE on future investments that exceeds the market capitalization rate)? (Round your answer to 2 decimal places.)

Answer 1

Answer to Part a.

Current Price (P0) = ??
Expected Dividend (D1) = $4.00
Capitalization Rate (Ke) = 10%
Growth Rate (g) = 8%

P0 = D1 / (Ke – g)
P0 = $4.00 / (0.10 – 0.08)
P0 = $4.00 / 0.02
P0 = $200

Current Price of Stock is $200.

Answer to Part b.

Retention Ratio = 1 – Dividend Payout Ratio
Dividend Payout Ratio = DPS / EPS * 100
Dividend Payout Ratio = $4.00 /$16.00 * 100
Dividend Payout Ratio = 25%

Retention Ratio = 1 – 0.25 = 0.75 or 75%

g = ROE * b
0.08 = ROE * 0.75
ROE = 0.1067 or 10.67%

Answer to Part c.

PVGO = P – (EPS 1 / Ke)
PVGO = $200.00 – ($16.00 / 0.10)
PVGO = $40