 # Equities: Justified P/E based on inflation

I’m doing a CFAI questionbank on Equities and I’m confused about their answer to a justified P/E ratio as it relates to Inflation. They state, that all else equal, a company operating in an environment with higher inflation will have a lower justified P/E than one operating in an environment with lower inflation.

That intuitively makes sense at first glance (considering law of one price, Ex Ante PPP, etc.) . . . but then I looked at a formula I had jotted down that said Justified Forward P/E = 1 / [r - i + (1- y) * i)] where i is inflation rate, and y is the % of inflation that can be passed on to customers.

In this formula inflation serves to decrease the denomiator, the cap rate to \$1 earnings, which increases the justified multiple. I only studied out of the CFA material, except the live kaplan mock, so I don’t think I could have obtained this formula elsewhere but I can’t find it in the material now that I’m looking back through the book.

The only thing I can think is that I am taking them too literally in that I hold everything else constant, including r, but maybe I’m supposed to relax that assumption and let r rise with i as the risk free rate structure increases with the fisher effect.

Am I just overthinking this or did I write down a rogue formula?

Thanks for any input.

You wrote it down wrong:

P0/E1 = 1 / [ρ + (1 – λ)i]

where:

• ρ = required real rate of return
• λ = fraction of inflation costs passed along to customer
• i = inflation rate

Note that this formula assumes that growth arises solely from inflation.

I have not seen this in third party provider notes. Darn.

Then you didn’t look in Wiley’s notes.

its not there in Kaplan

It is there in CFA material (which is all that matters) and the formula listed by ‘S2000magician’ is the right one.

Sorry I don’t follow - the formulas look identical to me.

P/E = 1 / [r - i + (1- y) * i)] and P0/E1 = 1 / [ρ + (1 – λ)i].

Naturally the real rate of return can be expressed as the nominal rate less inflation or r-i

I think OP’s confusion lies in the fact that as inflation rises, r(nominal) in this case will rise as well… since rnominal is effectively rreal+inflation.

I prefer to use the r-i formula myself as it makes more sense to me.

You’re correct: I was too hasty in my criticism.

But your point is important: r changes with inflation, whereas ρ does not.