Assume that the expected dividend growth rate (g) for a firm decreased from 5% to zero. Further, assume that the firm’s cost of equity (k) and dividend payout ratio will maintain their historic levels. The firm’s P/E ratio will most likely:
A) decrease. B) become undefined. C) increase.
Their answer is A with the explanation: The P/E ratio may be defined as: Payout ratio / (k - g), so if k is constant and g goes to zero, the P/E will decrease.
My answer is B with the explanation: g= ROE * (1-dividend payout). Dividend payout # 1, g=0 => ROE = 0 => earnings =0 => P/E is undefined.
Dividend growth rate keeps historic levels => it differs from 1 (otherwise, the previous year growth rate will be 0 also). In order to g = 0, ROE = 0 => earning = 0 ???
It is plausible to say the company isn’t retaining earnings, that is, they are paying out all their earning as dividends, hence, zero growth. When there is zero growth,expected dividends doesn’t increase, but the denominator (Ke-g) remains the same, so, Price reduces, and earnings remain the same, so P/E ratio reduces. Hope it helps.
I guess the confusion happen primarily due to the equation.
I think this question is based on “Price mutiples based on fundamental”
This means: (Po/E1) = (D1/E1) / (r-g) -----------(1)
From equation 1, if the divdend payout rate (D1/E1) remain constant ; and g decreases which result in a larger denominator (r-g), LHS of (1) ie the P/E ratio will decrease. That’s the reason why answer is A.
If however, the question did not state that dividend payout rate remain constant (i.e. divdend payout rate increases), then the answer will have been B i.e. undefined. This can been seen from RHS of equation (1) where we can see ambigious net effect- Numerator (D1/E1) increases and denominator (r-g) increases. This is known as the dividend displacement of earnings.
I though i understood the " dividends displacement of earnings" as it is explained in the CFAI curiculum : page 268 book 4 "the P/E & payout ratio appears to be positively related. This relationship may not be true, however, because a higher payout ratio may imply a slower growth rate.
Because the payout ratio is in the numerator AND the denominator, the relation of payout ratio on P/E is undetermined. Howerver, in the exercice of the next page of the book 4; it is written as follows : “The equation implies a positive relationship between he payout ration and the P/E multiple. A higher payout ratio supports a higher P/E.” no nuance after… I really do not understand
The payout ratio is only in the numerator for calculating P/E.
A higher payout ratio essentially means a bigger return on your stock investment, since a higher payout ratio means more dividends as a proportion of earnings, thus the value (or price) of the stock increases. Of course, all other things constant.
But in reality, a higher payout ratio is a management decision, and is usually done after a period of slower growth, or less opportunity for profitable reinvestment.
Maybe im wrong but i think that : P / EPS = (D / EPS) / r - g with g = constant growth rate = ROE * (1 - (D / EPS)) with (1 - (D / EPS)) = retention rate
with D / EPS = payout ratio So P / EPS = (D / EPS) / r - (ROE * (1 - (D / EPS))) D/EPS has a positive and negative impact on P/EPS. If “everything else equal”, a change in payout ratio in the numerator may theorically impact positivelly the P/EPS but if it is not precised, then the change is “undetermined”…
By holding all else equal, we are assuming that ONLY the payout ratio changes in the P/E equation.
But since an increase in the PR modifies the growth variable of the constant growth model, then we adjust the components of ROE accordingly to keep the g consant.
In other words, if only the PR ratio changes, or if we look at an exact copy of this company that pays a higher PR for the same charectristics of growth and risk, then the P/E ratio would always be higher.
Higher PR implies higher P/E ratios all else the same.