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 $58. 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 .80. 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.)

Year	EPS	Dividends
1	$	$
2	$	$
3	$	$
4	$	$
5	$	$

b. What is Q’s stock worth per share? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Stock worth per share            $

Answer 1

For first 4 years:

ROE = 13%
Payout Ratio = 45%
Book Value per shares = $58

Growth Rate = ROE * (1 - Payout Ratio)
Growth Rate = 13% * (1 - 0.45)
Growth Rate = 7.15%

ROE = EPS0 / Book Value per shares
13% = EPS0 / $58
EPS0 = $7.54

After 4 years:

ROE = 11%
Payout Ratio = 80%

Growth Rate = ROE * (1 - Payout Ratio)
Growth Rate = 11% * (1 - 0.80)
Growth Rate = 2.20%

Answer a.

EPS0 = $7.54

D0 = EPS0 * Payout Ratio
D0 = $7.54 * 45%
D0 = $3.39

EPS1 = $7.54 * 1.0715 = $8.08
EPS2 = $8.08 * 1.0715 = $8.66
EPS3 = $8.66 * 1.0715 = $9.28
EPS4 = $9.28 * 1.0715 = $9.94
EPS5 = $9.94 * 1.0220 = $10.16

D1 = $3.39 * 1.0715 = $3.63
D2 = $3.63 * 1.0715 = $3.89
D3 = $3.89 * 1.0715 = $4.17
D4 = $4.17 * 1.0715 = $4.47
D5 = $4.47 * 1.0220 = $4.57

Answer b.

Cost of Capital, k = 11.0%

P4 = D5 / (k - g2)
P4 = $4.57 / (0.11 - 0.022)
P4 = $51.93

P0 = $3.63/1.11 + $3.89/1.11^2 + $4.17/1.11^3 + $4.47/1.11^4 + $51.93/1.11^4
P0 = $46.63

Stock worth per share is $46.63