Justified Leading & Trailing P/E Ratio

Leading:

1-b/r-g or P0/E1

Trailing:

1-b(1+g)/r-g or P0/E0

Now, I understanding how the leading would use the forecasted earnings, E1, but what I don’t understand is why the growth rate is applied to the Trailing’s payout ratio and not to the leading. That seems backwards in my head. If you want the leading PE, ie projected PE wouldn’t you apply the growth rate to the leading?

Maybe I have my understanding of leading and trailing backwards?

E1 = E0(1 + g)

Because you’re dividing by earnings, P1/E1 < P1/E0 (assuming positive growth).

I wrote an article on justified ratios: http://financialexamhelp123.com/justified-ratios-price-multiples/

This makes sense from the derivation:

“The trailing P/E ratio is merely the leading P/E ratio multiplied by (1+g); this makes sense as E0 is smaller than E1 by a factor of (1+g).”

I guess my problem comes with the idea of linking it to using the GGM with getting D1 by doing D0(1+g) and discounting it back with r-g, but in this case the trailing P/E is looking 1 period forward, 1-b(1+g), but the leading isn’t, just 1-b. They are both being divided by the same r-g but missing the (1+g) on the top.

I may be confusing myself on something that shouldn’t be so closely examined or I should just take it for face value.