Question

The stock of Nogro Corporation is currently selling for \(10 per share. Earnings per share in the coming year are expected to be \)2. The company has a policy of paying out 50% of its earnings each year in dividends. The rest is retained and invested in projects that earn a 20% 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?

b. By how much does its value exceed what it would be if all earnings were paid as dividends and nothing were reinvested?

c. If Nogro were to cut its dividend payout ratio to 25%, what would happen to its stock price? What if Nogro eliminated the dividend?

Short answer

a.20%

b. $0

c. $40

Step-by-step solution

Step by Step SolutionStep 1: Given information

E₁= $2

b = 5% = 0.5

ROE = 20% = 0.20

g = b x ROE = 0.5 x 0.20 = 0.10 = 10%

D₁= E₁x (1 – b) = $2 x 0.5 = $1.0

Calculation of rate of return ‘a’

P₀= D₁/ k – g

k = D₁/ P₀+ g

= $1 / $10 + 0.10

= 0.20 or 20%

Calculation of PVGO ‘b’

Since k = ROE)

PVGO = P₀– E₁/ k

$10 - $2 / 0.20

= $0

This implies that NPV of future investment opportunities = 0

Calculation of Present value of growth opportunities ‘c’

PVGO = P₀– E₁/ k

= $160 - $12 / 0.10

=$40