Question

The FI Corporation’s dividends per share are expected to grow indefinitely by 5% per year. a. If this year’s year-end dividend is $8 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 $12, what is the implied value of the ROE on future investment opportunities? 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)?

Answer 1

a)

P₀ = Div₁ / (Re - g)

• P₀ = current stock price = ?
• Div₁ = next dividend = $8
• Re = equity cost = 10%
• g = constant growth rate = 5%

P₀ = $8 / (10% - 5%) = $8 / 5% = $160

b)

EPS = $12

Return on equity (ROE) = g / b

b = retention rate = 1 - payout ratio = 1 - ($8/$12) = 0.333

g = 5%

ROE = 5% / 0.333 = 15%

c)

Present value of growth opportunity (PVGO) = P₀ - EPS/Re

• P₀ = $160
• EPS = $12
• Re = 10%

PVGO = $160 - $12/10% = $160 - $120 = $40 per share