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 $ 8.08 $ 3.64 2 $ 8.66 $ 3.90 3 $ 9.28 $ 4.18 4 $ 9.94 $ 4.47 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

a. Plowback ratio = 1 - Payut Ratio = 1-0.45 = 0.55

dividend growthrate = plowback ratio * ROE = 0.55*0.13 = 0.0715

Calculate EPS now,

ROE = EPS/Book value per share

13% = EPS/58

EPS = 58*13% = 7.54

hence div payout = 7.54*0.45 = 3.40

for 5th year 7.54*(1+0.0715)^4*(1+0.22)

We got 0.22 as the dividend growth for 5th year

for 5th year dividend growthrate = plowback ratio * ROE = 0.20*0.11 = 0.022

present value of stock = (div1/1.11^1)+ (div2/1.11^2)+(div3/1.11^3)+(div4/1.11^4)+[(Div5/(0.11-0.02))*(1/1.11^4)] = 46.65

Therefore , the Q's stock worth per share is $46.65

Please feel free to ask any question or if you require any explainations