Justified P/E, Trailing P/E, Leading P/E...Help Me P/E

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Are these formulas correct? I would be very grateful if someone could help me out on when to use which formula…
Trailing P/E = DPO (1+g) / r-g
Trailing P/E = stock price / eps
Leading P/E = DPO / r-g
Justified P/E = DPO (1+g) / r-g
**If Justified P/E and Trailing P/E both have the same formula, what is the difference between Justified and Trailing P/E?
Thanks in advance for any responses because I’m pretty confused on this subject
 
I am not entirely sure, but my guess is that if markets are efficient the trailing P/E ratio should = Justified P/E?
 
Leading just. P/E is = (D1/E1) / (r-g) = (1-b) / (r-g) => in other words, leading justified P/E is equal to the next year’s payout rate, divided by the cost of equity premium of sustainable growth
Trailing just. P/E is = (D1/ E0) / (r-g) = [(1-b)x(1+g)] / (r-g) => in other words, trailing justified P/E is equal to the payout rate that uses this year’s E as the base instead of next year’s E, divided by the cost of equity premium of the sustainable growth.
So there is a small but important difference in the formula – the use of trailing earnings for trailing P/E and forward earnings for leading P/E.
Does that makse sense?
 
Reading 43. Question 6a asks us to calculate a justified P/e. The answer is:
“The formula for calculating a P/E for a stable growth company is DPO/r-g” – does stable mean justified?
“If P/E is calculated on trailing earnings (year 0) the formula is DPO (1+g) / r-g”
that’s how I got my formulas for:
Justified P/E = DPO/r-g
Trailing P/E = DPO (1+g) / r-g
what is leading P/E?
what is unjustified P/E?
when do we use the formula Price / eps to compute P/E?
lots of P/E questions, but I’m short on answers :-(
 
ylager, am I reading you correctly:
basically there is leading justified p/e and there is trailing justified p/e…but I have seen questions that just ask for the justified P/E, which one do we use?
When do we use the formula price/eps?
Thanks in advance for any feedback
 
“justified” means if “intrinsic” or “fundamental” value. It is based on the Gordon Growth Model => Fundamental Value of Firm is = D1/(r-g). So “justified” P/E simply uses this “fundamental” value of firm calculation as the “P” in the P/E.
Based on my experience, CFAI will not play games with you and will tell you to use leading or trailing justified P/E to get your answer or will simply give you next year’s earnings implying the use of leading P/E.
So if a problem provides you with an earnings estimate for next year, a payout rate, cost of equity, and a constant growth rate, we can derive a “justified” leading P/E. For example:
EPS estimate for next year = $4.00, and stock is trading at $30 (this implies it is trading at 7.5x next year’s earnings).
Company pays out 60% in the form of dividend
Cost of equity is 14% (this is the required return)
Sustainable growth rate (g) is = 5% (by the way, g = ROE x b , where b is (1-payout rate)
So based on this info, leading justified P/E is = to the payout rate / difference between cost of equity and sustainable growth rate. Or (0.6) / (0.14 - 0.05) = 6.67x. As you can see, this firm’s “justified” or “intrinsic” P/E should be 6.67x, however, at $30 it is trading at 7.5x, therefore it is overvalued at current $30, and should be trading at $26.68 (6.67x$4) => short the stock! :)
Does this help?
 
Good explanation. Just to recap on the main point:
Justified P/E’s are derived based upon the firm’s fundamentals.
 
The equity section also provides another method for getting to the “intrinsic” P/E using the formula 1/r + [FF * G], whre FF is the Franchise Factor and is = to 1/r - 1/ROE, and G is the Growth Factor, and is = g/r-g. So on the exam, CFAI will use the appropriate name “justified” which means you use the (1-b)/(r-g) formula or the “intrinsic” which mean you use the 1/r + [FF*G] formula.
 
Yup, a firm’s P/E should be based on its fundamentals, and if its not, it is either overvalued or undervalued….
 
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