Question

ART Inc. has come out with a new and improved product. As a result, the firm projects an ROE of 25% a year until the end of year 3 and 15% a year afterwards, and it will maintain a plowback ratio of 20%. Its earnings in the coming year, i.e., E1, will be $3 per share. Investors expect a 12% rate of return on the stock. What would be its P0/E1 ratio?

Answer 1

Year 1 - Year 3:

ROE = 25%
Plowback Ratio = 20%

Growth Rate = ROE * Plowback Ratio
Growth Rate = 25% * 20%
Growth Rate = 5%

E1 = $3.00

D1 = E1 * Plowback Ratio
D1 = $3.00 * 20%
D1 = $0.60

D2 = $0.60 * 1.05 = $0.63
D3 = $0.63 * 1.05 = $0.6615

Year 4 and thereafter:

ROE = 15%
Plowback Ratio = 20%

Growth Rate = ROE * Plowback Ratio
Growth Rate = 15% * 20%
Growth Rate = 3%

D4 = $0.6615 * 1.03 = $0.681345

Required Return = 12%

P3 = D4 / (r - g), where r is required return and g is growth rate
P3 = $0.681345 / (0.12 - 0.03)
P3 = $7.5705

P0 = $0.60/1.12 + $0.63/1.12^2 + $0.6615/1.12^3 + $7.5705/1.12^3
P0 = $6.90

P0/E1 Ratio = P0 / E1
P0/E1 Ratio = $6.90 / $3.00
P0/E1 Ratio = 2.30