Question

The Clipper Sailboat Company is expected to earn $4 per share next year. The company will have a return on equity of 15 percent and the company will grow 6 percent in the future. The company has a cost of equity of 13 percent. Given that information, answer the following questions.

1. What is the value of the company's stock? Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

2. What is the present value of the growth opportunity? Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

3. Assume that the growth rate is only 4 percent. What would the appropriate P/E multiple be for this stock? Do not round intermediate calculations. Round your answer to two decimal places.

      ×

Answer 1

a)

Growth rate = (1 - Dividend payout ratio) * Return on equity

6% = (1 - Dividend payout ratio) * 15%

(1 - Dividend payout ratio) = 6% / 15%

(1 - Dividend payout ratio) = 40%

Dividend payout ratio = 60%

Expected Dividend = Expected Earnings per share * Dividend payout ratio

Expected Dividend = $4 * 60%

Expected Dividend = $2.4

Stock Price (P₀) = Expected Dividend / (Cost of Equity - Growth rate)

Stock Price (P₀) = $2.4 / (13% - 6%)

Stock Price (P₀) = $34.29

b)

Stock Price (P₀) = (Expected Earnings per share / Cost of Equity) + Present value of growth opportunity (PVGO)

$34.29 = ($4 / 13%) + Present value of growth opportunity (PVGO)

Present value of growth opportunity (PVGO) = $34.29 - ($4 / 13%)

Present value of growth opportunity (PVGO) = $3.52

c)

Growth rate = (1 - Dividend payout ratio) * Return on equity

4% = (1 - Dividend payout ratio) * 15%

(1 - Dividend payout ratio) = 4% / 15%

(1 - Dividend payout ratio) = 26.67%

Dividend payout ratio = 73.33%

Stock Price (P₀) = Current Dividend (D₀) * (1 + Growth rate) / (Cost of Equity - Growth rate)

Divide both Sides by Current Earnings (E₀)

Stock Price (P₀) / Current Earnings (E₀) = (Current Dividend (D₀) / Current Earnings (E₀)) * (1 + Growth rate) / (Cost of Equity - Growth rate)

Dividend payout ratio = Dividend (D₀) / Earnings (E₀)

Stock Price (P₀) / Current Earnings (E₀) = 73.33% * (1 + 4%) / (13% - 4%)

Stock Price (P₀) / Current Earnings (E₀) = 8.47

Trailing P/E = 8.47

Stock Price (P₀) = Expected Dividend (D₁) / (Cost of Equity - Growth rate)

Divide both Sides by Expected Earnings (E₁)

Stock Price (P₀) / Expected Earnings (E₁) = (Expected Dividend (D₁) / Expected Earnings (E₁)) * (1 + Growth rate) / (Cost of Equity - Growth rate)

Dividend payout ratio = Expected Dividend (D₁) / Expected Earnings (E₁)

Stock Price (P₀) / Expected Earnings (E₁) = 73.33% / (13% - 4%)

Stock Price (P₀) / Expected Earnings (E₁) = 8.15

Leading P/E = 8.15