# Equity Val

A company currently has a required return on equity of 14 percent and an ROE of 12 percent. All else equal, if there is an increase in a firm’s dividend payout ratio, the stock’s value will most likely: A) increase. B) decrease. C) not change. D) either increase or decrease. Apparently the answer is A. In the explanation they keep referring to the P/E ratio. My reasoning was that if the firm’s payout ratio increases, g goes down, and the demonimator in the DDM model goes down, therefore the value of the stock should increase. On the flip side, the numerator will be smaller (because dividends increase by a smaller amout now), so why would the numerator effect dominate? Is it because the company is earning a lower rate on new projects than the rate required by the market (ROE < ke), I don’t get this.

Kce = Divident Payout + g Kce = D1/P0 + g Divident Payout increases --> required return on equity should increase - Dinesh S EDIT: nahh… this doesn’t sound correct …

g = ROE ( 1-k ) where k - dividend payout. as Dividend Payout increases – g decreases so (rce-g) would increase so Price should decrease.

that’s what I thought, but the answer is A) increase.

lets make an example: P/E = earnings multiplier : (1-rr) / (k-g) = (1-rr) / (k-rr*roe) = (1-rr) / ( 0.14 - rr*0.12) Increase in div.payout ratio means decrease in rr both in the numerator & denominator. Assume rr=0.5 then 0.5 / (0.14 - 0.06) = 6.25 now increase in div. payout means rr decreases rr=0.3 then 0.7 / ( 0.14 - 0.3 * 0.12 ) = 6.73 indeed the P/E ratio went up. Price of a stock = earnings * P/E … if P/E increases then P increases. Hope this helps a little.

Just for an example: K=14 RR=50% and Div Payout = 50%. Suppose div payout is .50 Cents. G will be 50% X 12% = 6 By forumula, .50/14-6 = .50/8% = 6.25 If diV payout increases to .60. RR would decrease to .40 G would be 40% * 12% = 4.8% By formula: .6/14-4.8 = .6/9.2% = 6.52 Hence stock price increased

Thanks barthezz, but why did you think to rationalize this using P/E is what I don’t get. If I see a question like that on the exam, I’ll start thinking DDM and go through the steps cpk went through. I think it has something to do with whether the company is earning a lower rate on new projects than the rate required by the market

Original: Kce = 14% ROE = 12% RR (my choice) = 50% Original Dividend (my choice) = \$1 g = 50%*12% = 6% \$1(1.06) = \$1.06 = next year div \$1.06/(14%-6%) = \$13.25 New: Kce = 14% ROE = 12% RR = 25% New Dividend = \$1.50 g = 25%*12% = 3% \$1.50(1.03) = \$1.545 = next year div \$1.545/(14%-3%) = \$14.05 Therefore, answer is A. Magnitude of change in numerator is greater than magnitude of change in denominator, which makes the price greater. Lola, you said “my reasoning was that if the firm’s payout ratio increases, g goes down, and the demonimator in the DDM model goes down, therefore the value of the stock should increase.” I believe that if g goes down, the denominator should go up (to a greater percentage) if Kce stays the same (because it is Kce - g). I think the key is that since the dividend payout ratio is increasing, you need to increase the base value of the dividend, since you are paying a higher dividend as a percentage of earnings. Anyone that gets a different answer or reasoning, please let me know!!!

I think you are right lola…the reasoning has to be on the lines that since required return > ROE, price would increase if the company pays out more. On the flip side if ROE>Required return, company is expected to retain more and plough that through its more prifitable projects. Maybe someone else can confirm that Good question…

cpk- What about the respective increase in the dividend as a result of increasing the dividend payout ratio? I understand the denominator decreases, but the numerator will increase, and by my calculations, I believe it increases by a larger amount in proportion to the denominator. Please let me know if my reasoning here is incorrect!?!? Thanks.

finance03 Wrote: > I believe that if g goes down, the denominator > should go up of course you’re right. That’s a typo. If I couldn’t see this, then this asset valuation prob would be the least of my worries on dec 1. lol thanks to all for the discussion.

lola, Dividend payout ratio means 2 things in the numerator: I. (1-rr) II. D/E (Dividends / Earnings) the text states “increase in a firm’s dividend payout ratio”. Since ROE is a component of g and multiplied by rr you have to go with I. They point you in the direction of rr. Sorry that I do not have a better explication for that.

I encountered a somewhat simmilar question. A Company’s ROE is greater than its required return on equity. The earnings multiplier (P/E) for that company’s common stock is most likely to be positively related to the A) Market Risk Premium B) Risk free rate of return C) Company’s earnings retention ratio D) Stock’s Beta Correct Answer: C This is an opposite scenario from the 1st question where the ROE> Required return.

Yes, finance03 – you are right. That got missed in all our calculations. using the P/E ratio seems to bring it out straight. because P/E = k/(rce-g) and K increased g decreased, rce-g increased but in net effect k increase overshadows the increase in the denominator Nice to know intuitively… CP

Ok perfect, wanted to make sure I had this right. Thanks.

How about replacing your calculation with the first rr=0.99, then reduce it to rr=0.98 Before the increase in payout ratio (or decrease in retention ratio): 0.01/(0.14-0.12*0.99)=2.12 After the increase in payout ratio: 0.02/(0.14-0.12*0.98)=0.89 So in this case, P/E multiply goes down. What can we conclude the effect on stock price of an increase in payout ratio?

Could it be that the price decreases less than earnings, thus increasing net value? The price will drop by the amount of the dividend increase. Earnings will decrease more as the dividend is paid out (cash out) and the return the company can make in its retained earnings is lost (opportunity cost). P/E = earnings multiplier : (1-RR) / (k-g) = (1-RR) / (k-RR*ROE) The change in RR is constant, but since the change is multiplied in the denominator the total effect is an increase in value.

Sondin, I think your math is incorrect: 0.01/(0.14-0.12*0.99)=0.4716

Ops, forget it, I forgot to get the inverse of 2.12 which is 0.4716.

lola Wrote: I think it has something to do with > whether the company is earning a lower rate on new > projects than the rate required by the market lola is absolutely right. let’s denote k - required rate by the market, ke - return on equity, rr - retention ratio P/E = (1-rr)/(k-r*ke) = [(k-r*ke)/k3 - (k-ke)/ke]/(k-r*ke)=1/ke-(k-ke)/[ke*(k-r*ke)] if rr goes up, the denominator goes down, the ratio goes up, P/E goes down (because k>ke) so if rr goes down (or payout ratio goes up) then P/E goes up