when to use the different justified P/E formulas?

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poornewgrad

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sometimes I see the solution to justified P/E as using (1-b)/(r-g), but sometimes the answer tells me to use P0/E0. Am i confusing some concepts?
 
Justified means justified based on the fundamentals of the company.
Start with the mother of all formulas:
P0 = D1/(r-g).
Note that D1 = D0 (1+g) and that D1 = E1*(1-b)
if you want leading P/E, then
P0 = E1*(1-b)/(r-g), so
P0/E1 = (1-b)/(r-g)
That immediately tells you this is the formula for the leading P/E, i.e., looking at next year’s earnings.
Trailing uses P0/E0.
To get it from P0 = E1*(1-b)/(r-g), replace E1 by E0*(1+g), so
P0 = E0*(1+g)*(1-b)/(r-g), so
P0/E0 = (1+g)*(1-b)/(r-g). That’s trailing.
Do not try to memorize any of this…just derive as above…you will need that when you come to P/B, P/S, etc.
 
Justified P/E is the P/E it should be, like ‘theoretical’ P/E. You mentioned (1-b)/(r-g). That’s correct, more accurately, the justified leading P/E
Otherwise, like when they are asking what is the current trailing P/E. Then you could use P0/E0 that you have mentioned. This is simply trailing P/E.
Look out for the key word ‘justified’. =)
 
So that things don’t get confusing, as above correctly says.
Leading P/E = P0/E1 ……….. this is simply the observed price divided by expected earnings.
Justified Leading P/E = (1-b)/(r-g) ………… this is independent of the price, it is based on fundamentals.
 
Outstanding – if you get bored throw in the other ones… Otherwise tell me to stop being so lazy and figure it out myself! – Regardless ==> Great Example – lightbulb went on for me.
 
Looking at the thread title and OP, basically you use the justified P/E when the question specifies to do so. It’s always clear about it.
 
I’ve always been able to derive justified P/E ratios. But could you possibly do the same for P/B and P/S for us. Thanks!
 
P/B
Start with the mother of all formulas:
Po = D1/(r-g).
Note that D1 = D0 (1+g) and that D1 = E1*(1-b), so
Po = E1*(1-b)/(r-g), now you are looking for Po/Bo, so divide both sides by Bo:
P0/Bo = ( E1/Bo*(1-b) ) / (r-g), note that E1/Bo is ROE, b/c ROE=NI/Equity = EPS/Book value
P0/Bo = ( ROE*(1-b) ) / (r-g), note that g=b*ROE, so that b = g/ROE:
P0/Bo = ( ROE-g ) / (r-g)
P/S
Start with the mother of all formulas:
Po = D1/(r-g).
Note that D1 = D0 (1+g) and that D1 = E1*(1-b)
We want E0 because we want to have NI/S which is profit margin to show up, that’s same as Eo/S
Po = Eo*(1+g)*(1-b)/(r-g), now you are looking for Po/S, so divide both sides by S:
Po/S = Eo/S*(1+g)*(1-b)/(r-g)
This is usually enough. I don’t think you need to simplify it further, and you probably can.
 
Super useful! Thanks a bunch. I think i could’ve worked through it but just a bit lazy and busy working on other things.
 
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