Question

Company Q’s current return on equity (ROE) is 14%. It pays out one half of earnings as cash dividends (payout ratio = 0.5). Current book value per share is $50. Book value per share will grow as Q reinvests earnings.

Assume that the ROE and payout ratio stay constant for the next four years. After that, competition forces ROE down to 11.5% and the payout ratio increases to 0.8. The cost of capital is 11.5%.

a. What are Q’s EPS and dividends in years 1, 2, 3, 4, and 5? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

b. What is Q’s stock worth per share?

Answer 1

a). g[Year (1 - 4)] = ROE * (1 - Payout Ratio) = 14% * (1 - 0.5) = 7%

ROE = Net Income / Equity

0.14 = Net Income / $50

Net Income = EPS = 0.14 * $50 = $7

Current Dividend(D0) = EPS * Payout Ratio

= $7 * 0.50 = $3.50

EPS(Year 1) = EPS(0) * (1 + g) = $7 * (1 + 0.07) = $7.49

D1 = D0 * (1 + g) = $3.50 * (1 + 0.07) = $3.75

EPS(Year 2) = EPS(1) * (1 + g) = $7.49 * (1 + 0.07) = $8.01

D2 = D1 * (1 + g) = $3.75 * (1 + 0.07) = $4.01

EPS(Year 3) = EPS(2) * (1 + g) = $8.01 * (1 + 0.07) = $8.58

D3 = D2 * (1 + g) = $4.01 * (1 + 0.07) = $4.29

EPS(Year 4) = EPS(3) * (1 + g) = $8.58 * (1 + 0.07) = $9.18

D4 = D3 * (1 + g) = $4.29 * (1 + 0.07) = $4.59

Constant Growth Rate(gC) = ROE * (1 - Payout Ratio) = 11.5% * (1 - 0.8) = 2.30%

EPS(Year 5) = EPS(4) * (1 + gC) = $9.18 * (1 + 0.023) = $9.39

D5 = EPS(Year 5) * Payout Ratio = $9.39 * 0.80 = $7.51

b). Stock Price = [D1 / (1 + r)] + [D2 / (1 + r)²] + [D3 / (1 + r)³] + [D4 / (1 + r)⁴] + [D5 / {(r - gC)(1 + r)⁴}]

= [$3.75 / (1 + 0.115)] + [$4.01 / (1 + 0.115)²] + [$4.29 / (1 + 0.115)] + [$4.59 / (1 + 0.115)⁴] + [$7.51 / {(0.115 - 0.023)(1 + 0.115)⁴}]

= $3.36 + $3.22 + $3.09 + $2.97 + $52.81 = $65.45