Question

The stock of Nogro Corporation is currently selling for $13 per share. Earnings per share in the coming year are expected to be $2.30. The company has a policy of paying out 25% of its earnings each year in dividends. The rest is retained and invested in projects that earn a 17% rate of return per year. This situation is expected to continue indefinitely.

a. Assuming the current market price of the stock reflects its intrinsic value as computed using the constant-growth DDM, what rate of return do Nogro’s investors require? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. By how much does its value exceed what it would be if all earnings were paid as dividends and nothing were reinvested? (Do not round intermediate calculations. Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

Answer 1

a. D₁ = E₁ × (1 - b) = $2.30 × (1 - 0.25) = $1.725

g = b × ROE = 0.25 × 0.17 = 0.0425 or 4.25%

k = D₁ / P₀ + g = $1.725 / $13 + 0.0425 = 0.1752 or 17.52%

b. Since k = ROE, the NPV of future investment opportunities is zero:

PVGO = P₀ - E₁ / k = $13 - $2.30 / 0.1752 = -$0.13