Company Q’s current return on equity (ROE) is 14%. The firm pays out 50 percent

Question

Company Q’s current return on equity (ROE) is 14%. The firm pays out 50 percent of its earnings as cash dividends. (payout ratio = .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 .70. 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? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Stock worth per share            $

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

Explanation / Answer

a). Dividend growth rate = g = Plowback ratio × ROE = 0.5 × 0.14 = 0.07

ROE = EPS0 / Book equity per share

0.14 = EPS0 / $65

EPS0 = 0.14 x $65 = $9.10

DIV0 = payout ratio × EPS0 = 0.5 × $9.1 = $4.55

Growth Rates for EPS and dividends for year 5 and subsequent years is:

Dividend growth rate = g = Plowback ratio × ROE

= (1 – 0.07) × 0.115 = 0.0345, or 3.45%

b). P0 = D1/(1 + r)1 + D2/(1 + r)2 + D3/(1 + r)3 + D4/(1 + r)4 + D5/[(1 + r)4(r - g)]

= $4.55/1.1151 + $4.8685/1.1152 + $5.2093/1.1153 + $5.5739/1.1154 +

$8.6378/[1.1155 x (0.115 - 0.0345)]

= $4.0807 + $3.9160 + $3.7580 + $3.6063 + $62.2637 = $77.62

YEAR EPS DIVIDEND 0 $9.10 $4.55 1 $9.10 x 1.07 = $9.737 $9.737 x 0.5 = $4.8685 2 $9.10 x 1.072 = $10.4186 $10.4186 x 0.5 = $5.2093 3 $9.10 x 1.073 = $11.1479 $11.1479 x 0.5 = $5.5739 4 $9.10 x 1.074 = $11.9282 $11.9282 x 0.5 = $5.9641 5 $9.10 x 1.074 x 1.0345= $12.3398 $12.3398 x 0.7 = $8.6378

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