# Question on calculating justified price earnings ratio

Question An analyst collects the following data on the return on equity (ROE) and the payout ratio for two companies, M and N. Using a required return of 12.4% for both companies, she computes the justified forward P/E ratios, which are also given below. Company | Return on Equity(%) | Payout Ratio (%) | Justified Forward P/E M 12 30 7.5 N 14 40 10 If Company M increases its dividend payout ratio to 40% and Company N decreases its dividend payout ratio to 30%, which of the following will most likely occur? The justified P/E ratio of: A. both companies would increase. B. both companies would decrease. C. Company M would increase but that of Company N would decrease. Answer given: Justified forward P/E: P0/E1 = p/(r – g). Using the new payout ratios, the justified forward P/Es, calculated below, of both firms would increase. Company M: New dividend growth rate = (1 – 0.4) x 12% = 7.2%; New Justified forward P/E = 0.4/(0.124 – 0.072) = 7.7x. Company N: New dividend growth rate = (1 – 0.3) x 14% = 9.8%; New Justified forward P/E = 0.3/(0.124 – 0.098) = 11.5x.

My question is where does the “0.124” , in the denominator of each of the new justified P/E ratios, come from? Isn’t it supposed to be r, the return on equity? so 12% for Company M and 14% for Company N?

required rate of return…