Question

Company Q’s current return on equity (ROE) is 14%. It pays out 50 percent of earnings as cash dividends (payout ratio = 0.50). Current book value per share is $65. 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 0.70. The cost of capital is 11.5%.

a. What are Q’s EPS and dividends in years 1, 2, 3, 4, and 5?

b. What is Q’s stock worth per share?

Answer 1

Part A

Plowback ratio = 1 - payout ratio = 1 - 0.50 = .50

Dividend growth rate =g = Plowback ratio x ROE = .50 x 14% = 7%

ROE = EPSo / Book value per share

14% = EPSo/65

EPSo = 65 x 14% = $9.10

DIVo = Payout Ratio x EPSo = .50 x 9.10 = $4.55

Growth after 4 year = Plowback ratio x ROE = (1-0.7) x 11.50% = $ 0.0345

Year	EPS	Dividend
1	=9.1*1.07	=9.74*0.5
2	=9.1*(1.07^2)	=10.42*0.5
3	=9.1*(1.07^3)	=11.15*0.5
4	=9.1*(1.07^4)	=11.93*0.5
5	=9.1*1.0345*(1.07^4)	=12.34*0.7

Year	EPS	Dividend
1	9.74	4.87
2	10.42	5.21
3	11.15	5.57
4	11.93	5.96
5	12.34	8.64

Part B

P0 = D1/(1+r)1 + D2/(1+r)2 + D3/(1+r)3 + D4/(1+r)4+ P4/(1+R)4

Where, P4 = D5 / r- g = 8.64 / (11.50% - 3.45%) = 107.3292

P0 = 4.87/ (1.115)1 + 5.21/ (1.115)2+5.57/ (1.115)3+5.96/ (1.115)4+ 107.292/ (1.115)4

P0= $85.86 (rounded off)

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