Justified Trailing PE vs Justified forward PE

CFA Level II Equities
#1

Justified Trailing PE = 1-b(1+g)/r-g

Justified Forward PE = 1-b/r-g

I am struggling to understand why we assume that the retention ratio for the Justified trailing PE ratio will grow at g, but we do not make the same assumption for the Justified forward PE ratio, can someone explain why?

#2

You’re not assuming that the retention ratio will grow at g; you’re assuming that earnings will grow at g:

E1 = E0 × (1 + g).

Thus, for trailing P/E you’re dividing by a number (E0) that is smaller by a factor of (1 + g), so the ratio is larger by a factor of (1 + g); for leading P/E you’re dividing by a number (E1) that is larger by a factor of (1 + g), so the ratio is smaller by a factor of (1 + g).

#3

Thanks S20000, It’s always good to have you around. I added the extra 0 to say thank you. :slight_smile:

#4

My pleasure!

I really appreciate it; thanks for your kind words.

That’s hilarious! I literally burst out laughing.

#5

Thanks a lot s2000 I wasted an entire day struggling at it

(and getting answers like “it’s just a formula”)

#6

Hi bloodline, S2000magician,

Speaking about retention (and dividend payout) ratios, could you please confirm whether D1/E1 = D0/E0 always needs to hold with a single constant long-term growth rate (g)? I recently ran into a problem where both a current and long term divident payout ratio were defined, along with only one assumed long-term growth rate. This seemed wrong to me, as in this case 1-b is not constant (D1/E1 is not equal to D0/E0) and the below equations do not hold:

Justified Trailing PE = 1-b(1+g)/r-g
Justified Forward PE = 1-b/r-g

Thanks a lot for your help in advance.