 # Justfied Trailing P/E Ratio

Hi guys, I am a bit confused as to why the justfied trailing P/E ratio is calculated as ((1-b)* (1+g))/r-g my confusion is on the (1+g) term which i thought refelects an analyst’s forecast. I noticed even the 2006 actual exam (in the book) gave the answer using the same method. Isnt trailing P/E a historical ratio (i.e for the psat 4 quarters). Where is the (1+g) coming from? Thank u for your help.

Mukaranga, you’ve basically got this figured out already. So at LI, you learned the Gordon Growth Model (i.e. single-stage DDM) and further, how to translate it into a justified P/E model. You started with: P0 = D1 / r-g Then divided both sides by E0, producing: P0/E0 = (D1/E0) / r-g What may not have been made clear is that this is trailing P/E, i.e. P0/E0. And E0, as you’ve pointed out, is earnings trailing twelve months. So but where did D1 come from? All this formula is doing is breaking D1 into two component steps: specifically, it’s starting with the current dividend, D0, and growing it by the forecast rate to produce D1. D1 = D0*(1+g) = (1-b)(1+g) Recall that “b” is the earnings retention rate, so that 1-b is the dividend payout rate, and growing this figure by g produces D1, whether in the aggregate or on a per-share basis. And you follow a similar approach to reach the justified leading P/E. Begin again with the Gordon Growth Model: P0 = D1 / r-g Now divide both sides by forecast earnings, i.e. E1 P0/E1 = (D1/E1) / r-g = (1-b)/(r-g) Now where’d “g” come from? It’s your same old friend from LI: the firm’s sustainable growth rate: earnings retention rate * return on equity. We’re working with the single-stage DDM here, so there’s no abnormal super-growth periods or other such complications to contend with. Notice that if earnings are expected to grow, the justified leading P/E will be less than the justified trailing P/E. Anyway, I think you’re mostly on track here and hopefully this’ll click after a good night’s rest. Let me know though if this explanation isn’t quite on target. Cheers. edit: typos.

Thanks for the explanation hiredgun. Thanks a lot