Justified leading and trailing P/E multiples

CFA Level II Equities
#1

Khan has identified two utilities (ABC and XYZ) for possible inclusion in Client 1’s portfolio. She uses a discount rate of 7% for both common stocks.

ABC is a publicly traded utility with an expected constant growth rate for earnings and dividends of 3.5%.

  • The most recent year’s dividend payout is 70%. The expected dividend payout in future years is 60%.
  • The common stock price is $14.49 per share.

Q. Based on the Gordon growth model, the justified leading P/E for ABC stock is closest to:

  1. 17.1.
  2. 17.7.
  3. 20.0.

A is correct. The justified leading P/E is calculated asP0E1=(1−b)/(r−g)

where b is the retention ratio, 1 – b is the dividend payout ratio, r is the discount rate, and g is the long-term growth rate.

ABC’s dividend payout rate, 1 – b, is given as 0.60. For Company ABC, the justified leading P/E isP0E1=(1−b)/(r−g)=(0.60)/(0.07−0.035)≈17.1

So if we had to find justified trailing multiple using the same formula, we would do
(1-60%)*(1+3.5%)/(7%-3.5%) right?

or would we use (1-70%)/(7%-3.5%)?

#2

You have to think that tha payout is also driving the growth rate estimate so you need to use forward looking payout.

Trailing PE = payout x (1 + g) / (Re - g)

Fwd PE formula comes from
P = D(yr1) / (Re - g)
P/E(yr1) = [ D(yr1) / E(yr1) ] / (Re - g)
P/E(yr1) = payout / (Re - g)

Adapting for trailing P/E

E (yr1) = E(yr 0) x (1+g)

P/ [ E(yr 0) x (1+g) ] = payout / (Re - g)
P/ E(yr 0) = [ payout x (1 +g) ]/ (Re - g)

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#3

okay…thanks a lot

#4

Yes. Consider this: Trailing P/E is calculated by current stock price and dividing it by the trailing EPS for the past 12 months. It based on the past information.

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#6

I understand. I think we say the same thing. But I found I made a mistake that the trailing p/e should be (1-70%)*(1+3.5%)/(7%-3.5%).

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#7

So you’re saying 1-70% is a mistake and that it should be 1-60%?

#8

YOu should be using the future payout number = 60%

For trailing P/E from your post is correct

So if we had to find justified trailing multiple using the same formula, we would do
(1-60%)(1+3.5%)/(7%-3.5%) right?*

1 Like
#9

okay