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.