Justified Forward PE vs Trailing

A bit confused on something:

Justified forward P/E = D1/E1 / r-g

Trailing P/E = D1/E1 x (1+g) / r-g

Why does trailing include 1+g ? Surely if we are looking at the previous years P/E the payout ratio would have already included the growth rate? Why is Forward not including 1+g if we are looking at future rate?

Trailing P/E is based on trailing 12 months EPS thus dividend payout ratio should be adjusted for earnings growth.

Forward P/E is based on forward (forecasted) EPS so it shouldn’t be adjusted.

Last year’s earnings are less than next year’s earnings (by a factor of (1 + g)), so for the trailing P/E ratio we’re dividing by a smaller number; the ratio is larger by a factor of (1 + g).

I wrote an article on justified ratios that may be of some help here: http://financialexamhelp123.com/justified-ratios-price-multiples/

I know this is a counterintuitive concept; something that is trailing sounds like should be less but it isn’t as shown above. I meditated in a cave for 30 years and realized that trailing PE is greater than foward PE.

Trailing is (D0/E0)*(1+g)/r-g

We assume that the retention payout (b) will stay constant. D0/E0 = D1/E1 = 1 -b. We suppose that both D and E will grow at a rate of g.

Trailing PE ratio = D1/E0 = ( D0(1+g)/(r-g))/E0 = (D0/E0)(1+g)/(r-g) = (1-b)(1+g)/(r-g)

Leading PE ratio = D1/E1 = (D0(1+g)/(r-g))/(E0(1+g)) = (D0/E0)/(r - g) = (1-b)/(r-g)

Leading PE is less than trailing PE because we assume that the denominator (Earnings) has grown at a rate of g while the numerator is D1 in both cases.

what if D0/E0 (current payout ratio) is not equal to D1/E1 (expected, long-term payout ratio)? Does that mean we have to use different (1-b) values in the Trailing / Leading PE formulae, and wouldn’t that violate the assumption of a constant dividend + earnings growth rate (g)?

Then the Gordon growth model doesn’t apply, so the formula will likely give the wrong value.

Makes sense @S2000magician.

As always, thanks a lot for your insights and support provided to this community!

My pleasure.