# justified trailing vs. leading PE

When calculating justified trailing P/E why are we calculating the numerator by 1+g?

It seems, intuitively at least, that we would calculate leading P/E by the growth figure to obtain a future estimate and use previous figure for trailing.

Thanks,

John

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you always calculate the numerator with *(1+g), regardless of trailing, forward to justified ratio.

for a trailing PE ratio the thing trailing is the earnings. the reason we do this is there is no connection between the numerator (with 1+g in it) and the earnings. you see that because you use 1+g no matter what - justified, trailing or forward PE.

the (1+g) divided by (whatever) is how you get the PRICE, not the earnings. so again there is no relation there. it is Price = D(1+g)/r-g ; we divide by earnings to get our ratios (trailing, forward etc).

starbuck that’s not correct only trailing justified p/e is calculated by scaling up the numerator with (1+g). There’s no need to do that with the leading version because you’re dealing with earnings one period foward already. Pay close attention to the subscripts.

When the going gets weird, the weird turn pro.

Right you always have to make it 1 period out by scaling it up with (1+g).

Like I said the numerator and denominator in DDM or FCF models calculate the PRICE, it has nothing to do with the earnings. When you divide by earnings (to get trailing or forward PE) you just have to divide that value by an appropriate earnings number (trailing or forward). Again the (1+g) is not linked to the earnings only the Price.

When you are given leading earnings or trailing earnings that is the denominator of PE, which is separate from the numerator. The numerator always uses (1+g) to scale up dividends/FCF from today. But if you are given FCF or Dividends in 1 year then you do not have to scale them up.

starbuk Wrote:

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> you always calculate the numerator with *(1+g),

> regardless of trailing, forward to justified

> ratio.

Yeah so actually you didn’t say that at all. You’re still overdoing it again.

All that needs to be said is that you pay attention to the subscript and scale up in the case of lagging earnings with (1+g) or not with leading. No need to over complicate.

When the going gets weird, the weird turn pro.

Im not over doing anything. You have to get D(1) or FCF(1) no matter what so you do have to multiply by (1+g). If you have FCF(1) and you do it again then you are messing up. He is asking why you multiply by growth rate, not if we have FCF0 or FCF1, so my answer to multiply by (1+g) is correct since it is a part of every equation in order to get to FCF1 or D1.

Anyway his question was not about that at all, if you read 90% of my post you would see it focused on why earnings being trailing or leading has nothing to do with the (1+g) term which I explained.

P.S. you are not correct when you say that you do not scale up with (1+g) with trailing earnings. The 1+g gets you the price, what you do with the earnings (trailing or leading) is independent of how you calculate price.

I do not want to come off as rude, I just think that we are not understanding the question correctly since the formulas are pretty simple.

Andrew3032 Wrote:

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> starbuk Wrote:

> ————————————————–

> —–

> > you always calculate the numerator with *(1+g),

> > regardless of trailing, forward to justified

> > ratio.

>

> Yeah so actually you didn’t say that at all.

> You’re still overdoing it again.

>

> All that needs to be said is that you pay

> attention to the subscript and scale up in the

> case of lagging earnings with (1+g) or not with

> leading. No need to over complicate.

Dude… seriously… are you really this stupid? Your right the formulas are pretty simple. I think you just have an ego problem, and feel insecure about being wrong. Get over it.

When the going gets weird, the weird turn pro.

**** you Andrew

for those of us who want to get this right on exam day:

page 488 and 489 FSA book, show that you always use dividends one period out to calculate price. then you divide by the trailing or leading earnings.

Studying With

Thanks Starbuk. Can you find a concrete example/problem to prove your point and finish this thread off?

I can make one up.

D0 = 1.00

g (dividends and earnings) = 5%

r = 10%

E0 = 2.00

Trailing:

(D0*(1+g)/E0)/(r-g) = (1*(1.05)/2)/(0.1-0.05) = 10.5

Leading:

(D0*(1+g)/(E0*1+g))/(r-g) = (1*(1.05)/2.1)/(0.1-0.05) = 10.0

If you’re given D1 and/or E1, then use those instead of multiplying d0 and/or e0 by any given rates, but the objective is to get D1 and (if using leading) E1.

You can also colculate them out by using:

Trailing = payout ratio * (1+g) / (r-g)

Leading = payout ratio / (r-g)

This all assumes that dividends and earnings have a constant payout ratio over time (ie identical growth rates).

Studying With

nice grumble, you’re the man. So basically just make sure leading earnings are grossed up by 1+g since earnings will be growing in the future.

Yep, hence ‘leading’.

I have to say though, I kind of like it when people ask questions about things they’re confused about. Even if I don’t post, trying to figure out or just plain remember the answer is definitely keeping me on my game.

starbuk Wrote:

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> **** you Andrew

This is hilarious. He actually had to edit this post one time as well to type this. Brilliant. Simply Brilliant.

When the going gets weird, the weird turn pro.

Thanks for the feedback and example on this question

What I’m having a hard time grasping is why you’re dividing D1 by E0 for the trailing PE and not using the current/previous dividend, D0?

Utlizing D1 and E1, next period dvd and earnings, makes sense for leading PE, but using a future dvd amt for a historical figure is not sinking in.

John

John -

My posts replied to this question. The calculation of price is d(1+g)/(r-g) per the DDM. All we do to get leading or trailing is just divide that by E0 or E1.

So the calculation of price is independent of which earnings you are using. If you want an answer as to why the DDM uses (1+g), you will have to refer to the derivation of the DDM equation.

First let’s agree on the Gordon Growth Model,

P0(instinsic value)=D1(next years dividend)/(Ke(cost of equity)- Growth).It’s important to start here because we derive the Trailing and Leading P/Es from the GGM.

If we divide both sides of the above GGM equation by the last reported earings(TRAILING/HISTORICAL earnings) we get the TRAILING P/E ratio:

P0/

E0=D1/E0/(Ke-G).It’s just simply derived from GGM! And it’s simple; just divide both sides of the equation by E0.LEADING P/E is

next years estimate with regards to earnings and dividends. Dividends are expected to grow (D1) but in line with earnings. One of the underlying assumptions of the GGM from which these equations were derived is that dividends and earnings grow at the SAME rate. This allows for the dividend to be SUSTAINABLE.Moving on, to calculate the dividend payout ratio for a LEADING P/E, you use D1(next years estimated dividend) as you did before but you also divide by NEXT YEARS earnings. Because the growth rates are assumed to be the same, the increase in dividends and the increase in earnings cancel out within the dividend payout ratio.

Dividend payout ratio =D0(

~~1+G~~)/E0~~(1+G)~~I hope this helped you UNDERSTAND John! It’s much better to understand than to memorise parrot fashioned