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

CFA Level II
#1

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

#2

I am not entirely sure, but my guess is that if markets are efficient the trailing P/E ratio should = Justified P/E?

#3

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?

#4

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 :frowning:

#5

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

#6

“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! :slight_smile: Does this help?

#7

Good explanation. Just to recap on the main point: Justified P/E’s are derived based upon the firm’s fundamentals.

#8

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.

#9

Yup, a firm’s P/E should be based on its fundamentals, and if its not, it is either overvalued or undervalued…

#10

y’all are awesome. I am much closer to understanding.

#11

thanks for your explanation ylager. You made it clearer for me also.

#12

I have a question on the trailing P/E, which can be calculated either by

  1. Trailing P/E = DPO (1+g) / r-g or

  2. Trailing P/E = market price per share / EPS over previous 12 months

If we are given information that could be used for both formulas, which inputs am I supposed to use?

Or will it be clear in the exam which formula to use?

Thank you!