Question

ART has come out with a new and improved product. As a result, the firm projects an ROE of 30%, and it will maintain a plowback ratio of 0.3. Its earnings this year will be $5 per share. Investors expect a 12% rate of return on the stock.

a) At what price would you expect ART to sell?

b) At what P/E ratio would you expect ART to sell?

c) What is the present value of growth opportunities for ART?

d) What price do you expect ART shares to sell for in 4 years?

Answer 1

ROE = 30%
Plowback Ratio, b = 0.30

Growth Rate, g = ROE * b
Growth Rate, g = 30% * 0.30
Growth Rate, g = 9%

Expected EPS, EPS1 = $5.00

Expected Dividend, D1 = EPS1 * (1 - b)
Expected Dividend, D1 = $5.00 * (1 - 0.30)
Expected Dividend, D1 = $3.50

Required Return, rs = 12%

Answer a.

Current Price, P0 = D1 / (rs - g)
Current Price, P0 = $3.50 / (0.12 - 0.09)
Current Price, P0 = $116.67

Answer b.

P/E Ratio = P0 / EPS1
P/E Ratio = $116.67 / $5.00
P/E Ratio = 23.33

Answer c.

Present Value of Growth Opportunities, PVGO = P0 - EPS1 / rs
Present Value of Growth Opportunities, PVGO = $116.67 - $5.00 / 0.12
Present Value of Growth Opportunities, PVGO = $116.67 - $41.67
Present Value of Growth Opportunities, PVGO = $75.00

Answer d.

Expected Price in 4 years, P4 = P0 * (1 + g)^4
Expected Price in 4 years, P4 = $116.67 * 1.09^4
Expected Price in 4 years, P4 = $164.69