Question

Company Q’s current return on equity (ROE) is 13%. The firm pays out 45 percent of its earnings as cash dividends. (payout ratio = .45). Current book value per share is $53. 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 11.0% and the payout ratio increases to .70. The cost of capital is 11.0%.

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.)

Answer 1

Plowback ratio = 1 –payout ratio = 1.0 –0.45 = 0.55

Dividend growth rate = g= Plowback ratio × ROE = 0.55 × 0.13 = 0.0715

ROE = EPS₀/Book equity per share

EPS₀ = 0.13*53 = $6.89

DIV₀= payout ratio × EPS₀= 0.55× $ = $3.50

after 4 year g = Plowback ratio × ROE = (1 –0.7) × 0.11 = 0.033

Year	EPS	DIVIDENDS
1	6.89*1.0715=7.38	7.38*0.45= 3.321
2	6.89*1.07152=7.91	3.55
3	6.89*1.07153=8.47	3.811
4	6.89*1.07154=9.08	4.086
5	6.89*1.033*1.07154=9.38	9.38*0.7= 6.56

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