# P/S quickie..

A decrease in the earnings retention rate will cause a price-to-sales (P/S) multiple to: A) increase. B) decrease.

i think the ans is A and is related to the long disscusions we had last days

B

I can’t decide too, if it’s A or B

well the discussion is that less retention means higher dividend and probably higher price on the other hand more retention means higher growth therefore higher sales but thinking of it from today’s perspective I’d choose A

Formula is: Profit Margin*DPR*(1+g)/r-g Reduction in retention rate = increase in DPR Reduction in retention rate reduces g DPR increases in the numerator and g decreases in both the numerator and denominator. Which one dominates the other I have no clue.

let’s say E0/S0 = \$2 b = 75% g = 10% r = 15% g = roe x b (so here ROE is 13.333%) your p/s = 2 x .25 x 1.1/.05 = 11 take b to 25%, if ROE stayed at 13.333% then g = .033333 2 x .75 x 1.033333/.1166667 = 13.2857 not sure it’d always work, but P/S here goes up when you dropped the b if my basic math is ok (that assumes ROE stays same, not sure if that’s a brilliant assumption or not).

definitely it will B.Decrease only…lower retention results into lower growth…n lower figure of k-g has higher impact on valuation than increase in dividend…

I used justified P/S: PM*(1-b)(1+g) / r-g Some random numbers: PM = 10 ROE = .20 Retention high: .5 Retention low: .4 r = .15 so retention high: 10*.5*1.10 / .15-.1 = 110 p/s retention low: 10* .6 *1 .08 / .15-.08 = 92.5 It might just be the numbers I’ve chosen and the answer could be “not enough information.” Thoughts? T/G

this is the exact dillema as with does the price of share increase/decrease with increase/decrease of retention rate?

Definitely B. Using justified P/S and a quick bout with Excel, you can prove B. Just remember to keep (r-g) > 0.

dinesh you don’t have an answer for this?

The QBank answer to this is A The correct answer was A. A decrease in the earnings retention rate will increase the following expression for P/S due to the implied increase in the payout ratio, which is (1 b): P0 / S0 = [(E0 / S0)(1 b)(1 + g)] / (r g) Note that the reading does not allow for any interactive relationship between retention and growth. Thus, no explicit consideration is given to whether the increase in the payout ratio will cause an offsetting decrease in growth.

Answer is neither. It depend on whether the ROE is greater or smaller than the required return. Think of it this way, if ROE > k, the firm can create shareholder value § by reinvesting earnings. If ROE < k, the firm is better off paying its earnings out as dividends, since it doesn’t have investments that are good enough Look at a trailing P/E example: P(0)= 80 D(1)=2 E(1)=4 RR=.5 In first example, k=.12, g=.02, ROE= .04 If we decrease RR here, we create shareholder value since the ROE is less than the required return. We are paying more out to shareholders…this is good if ROE is low. lets make RR=.25…makes new g=.01 P(0)=3/(.12 - .01) *4 = 109.09 In second example, k=.22, g=.12, ROE= .24 If we decrease RR here, we destroy shareholder value, since ROE exceeds required return. ROE is large so we should be retaining earnings not paying dividends. Again change RR=.25…new g= .06 P(0)=3/(.22- .06) *4 = 75 So the price goes from 80 to 75 in one case, and 80 to 109 in the other case. Sales stay the same.

^ because they don’t provide info about roe and relation to RR they consider it constant

g=ROE x RR. You can’t hold them constant.

yes I know the formula I was refering to the note after the answer

Gotcha…my mistake