# P/E and Retention rate

All else equal, a firm will have a higher Price-to-Earnings (P/E) multiple if: A) return on equity (ROE) is lower. B) retention ratio is higher. C) the stock’s beta is lower. Your answer: The correct answer was C) the stock’s beta is lower. To increase P/E ratio, lower the retention ratio, lower k and or increase g. A lower beta would lead to a lower stock risk premium and a lower k. I thought increase in retention rate will increase g thus reducing k-g (denominator) and increasing dividnend (Nominator) of P/E (D1/E1(k-g)) Am I wrong?

Higher retention rate means less is paid out in dividends. Remember Rention Rate = 1-(Dividend Payout Ratio). So, the less that is paid out in dividends the higher EPS will be. Thus a higher retention rate means a lower P/E multiple.

definitely hear what your saying, but sounds like the lower beta (K) is going to outweigh effects of increased retention (g) sort of counter intuitive because most higher p/e stks have greater betas weird question

Patel, I’m willing to dispute that © is the only correct answer. Some equations first: g = ROE * retention ratio k= Rf + beta*(Rm - Rf) [CAPM Models] P/E1 = Div1/E1*(k-g) If ROE is lower, then g is lower as well. If g is lower, then P/E is lower! So (A) is incorrect. If the retention ratio is higher, then g is higher which causes P/E to be higher! So (B) is correct. If beta is low, then k (the required rate of return) is lower which causes P/E to be higher! So © is correct. In the end (B) and © are correct!!! If you got this question from Schweser, then this is a common misprint.

***CORRECTION to previous post*** We know that 1) Div1 = EPS * (1-retention ratio) 2) g = ROE * retention ratio Delta P/E = (1- retention ratio) / retention ratio So if the retention ratio increase and approaches 1, the P/E ratio decreases and approaches 0, therefore, answer (B) is incorrect. Just beware, if the retention ratio increases to the point where ROE * retention ratio is greater the k, then the DGM is no longer valid. In the end, © is the only correct answer!!