Question

The required rate of return on the stock of Knight Titles is 8%. Its expected ROE is 10% and its expected earnings per share this year is $6.00. If the firm's plowback rate (b) is 40%, its P/E ratio will be _______.a.None of the aboveb.8.33c.15d.14.29

Answer 1

Answer:                   Ke = 8% = 0.08  

                              ROE = 10% = 0.10

             Expected EPS = $6

      Plowback rate ( b)  = 40% = 0.40

 Dividend per share (D) =  60%x $6 = $3.60

                                   Po =  D(1+g )/ke-g              

                                   Po = $3.6(1+0.04)/0.08-0.04

                                   Po = $3.744/0.04

                                   Po = $93.60

The current market price is $93.60

The price-earnings ratio = market price per share/Earnings per share

                                          = $93.6/$6

                                           = 15.6

The correct answer is C

Explanation: The price-earnings ratio is the ratio of market  price per share to earnings per share. In this scenario, it is important to obtain the market price per share using the above formula. Thereafter, the market price per share is divided by the earnings per share. There is need to calculate the dividend per share based on the retention rate of 40%. since the retention rate is 40%, the dividend pay-out rate will be 60%. Thus, dividend is 60% of the expected earnings per share. The estimation of growth rate (g) is based on Gordon's growth model, which is g = r x b. r represents return on equity while b denotes the plowback(retention rate).