Trailing P/E

CFA Level I
#1

Hey guys.

I just found out something’s wrong with calculating trailing P/E(just for me, maybe).

Trailing P/E is P0/E0, compared to P0/E1, which is leading P/E, so I know that traling P/E would be higher, assuming that earnings would grow.

So Trailing P/E would be

P0/E0 = (D1/E0)/(k-g) = {D0x(1+g)/E0}/(k-g), right?(where E0 = EPS0)

but I keep getting different numbers for P0/E0 and {D0x(1+g)/E0}/(k-g), given the same values to fill in.

For example, if

P0 = 35

E0 = 6

D0 = 2.4

k = 15%

g = 8%

If I solve for P0/E0, I get 35/6 = 5.83

If I solve for {D0x(1+g)/E0}(k-g), I get {2.4x(1.08)/6}/(.15-.08) = 6.17

I don’t get what’s going on… Maybe it’s because the values given aren’t correlated accordingly?

I mean, (growth rate) = (retention rate) x ROE, and there is some relation with the ROE and the given figures, but the figures given are not in compliance with the formula?

If there is something wrong, what formula should I use to calculate trailing P/E if it asks?

P0/E0? or {D0x(1+g)/E0}/(k-g)?

thanks, guys

#2

Oh, and just one more other thing.

When calculating the value of a non-convertible, non-callable preferred stock, you don’t consider the growth rate at all, right? I would be must thankful if someone confirmed this.

Again, thanks guys!

#3

D1 = 2.4(1.08) = 2.592 E1 = 6 (1.08) = 6.48 (D1/E1) / (r-g) 2.592/ 6.48 /(0.15-0.08) = 5.714

5.71 (leading)< 5.83 (trailing)

#4

Trailing P/E = Leading P/E × (1 + g)

I wrote an article about justified ratios that covers this: http://financialexamhelp123.com/justified-ratios-price-multiples/

#5

I don’t understand this calculation at all.

Leading P/E = 35 / 6.48 = 5.40

#6

Leading P/E is suppose to be higher than Trailing P/E ratio due to the growth potential. So I don’t get how come ur leading is lower than the trailing.

#7

Trailing: same price, lower earnings, higher ratio.

Leading: same price, higher earnings, lower ratio.

#8

Here is my understanding of the question:

Given info are:

E0 = 6

P0 = 35

g = 8% (Assuming it’s for both Earnings and Dividends)

Therefore, my cals are:

Trailing P/E = P0/E0 = 35/6 = 5.833

As for the leading P/E = P0/E1

P0/E1 = (D1/E1) (r-g)

D1 = D0 (1+g) = 2.4(1.08) = 2.592

E1 = E0(1+g) = 6 (1.08) = 6.48

P0/E1 = (D1/E1) / (r-g) = 2.592/ 6.48 /(0.15-0.08) = 5.714

Hence I got:

5.71 (leading)< 5.83 (trailing)

#9

I believe

Trailing = P0/E0

And Leading = P0/E1

Since E1=E0 (1+g)

Leading = P0/E1 = P0/[E0(1+g)]

= Trailing / (1+g)

So Leading * (1+g) = Trailing ratio - same as what S2000 has stated above.

====

Hilda

please realize - since D1=D0(1+g) and E1=E0(1+g) -> d1/e1 = d0/e0

so if D1/E1 is a different value from D0/E0 -> you are obviously doing something wrong.

#10

Very interesting indeed.

I follow both cpk123 and S2000magician’s logic however based on the curriculum. However i was following the curriculum’s gordon growth formula (see formula 14 specified in the CFA book). I was using that formula. So am I not using the right formula?

This is from the curriculum (Reading 50 Equity Valuation: Concepts and Basic Tools, Section 5.1)

5.1. Relationships among Price Multiples, Present Value Models, and Fundamentals Price multiples are frequently used independently of present value models. One price multiple valuation approach, the method of comparables, does not involve cash flow forecasts or discounting to present value. A price multiple is often related to fundamentals through a discounted cash flow model, however, such as the Gordon growth model. Understanding such connections can deepen the analyst’s appreciation of the factors that affect the value of a multiple and often can help explain reasons for differences in multiples that do not involve mispricing. The expressions that are developed can be interpreted as the justified value of a multiple—that is, the value justified by (based on) fundamentals or a set of cash flow predictions. These expressions are an alternative way of presenting intrinsic-value estimates. As an example, using the Gordon growth model identified previously in Equation 9 and assuming that price equals intrinsic value (P0 = V0), we can restate Equation 9 as follows: Equation (9.1) P0=D1/r−g To arrive at the model for the justified forward P/E given in Equation 14, we divide both sides of Equation 9.1 by a forecast for next year’s earnings, E1. In Equation 14, the dividend payout ratio, p, is the ratio of dividends to earnings: Equation (14) P0/E1=D1/E1/r−g = p/(r-g)

#11

the formula is fine, but your interpretation is not.

P0 = 35, E0 = 6, D0 = 2.4, k = 15%, g = 8%

E1 = E0 * 1+g) = 6 * 1.08 = 6.48

P0/E1 = 35/6.48 = 5.40

===

Or P0/E0 = 35/6 = 5.83

=========

LEADING P/E * (1+G) = 5.40 * 1.08 = 5.832

Check -> D0 (1+g) / (r - g) = 2.4 * 1.08 / (0.15 - 0.08) = 37.03

So P0 provided is underpriced when compared to the dividends and the growth rate provided here.

#12

Thanks cpk123. Appreciate your effort in explaining this to me.

#13

Thanks guys.

#14

My pleasure.

#15

wow guys, thanks for all this

I just found out what was wrong with my interpretation

when I said

P0/E0 = (D1/E0)/(k-g) = {D0x(1+g)/E0}/(k-g)

it was WRONG

the formula on the right should be {D0x(1+g)/E0x(1+g)}/(k-g)

I guess the assumption is that dividends don’t grow by themselves; they grow WITH earnings, so you have to take into account that part in the equation.

Again, much thanks!