Equity Valuation, Risk, and Investment: A Practitioner's Roadmap

APPENDIX E

Adjustments Required to the Traditional Growth/Equity Valuation Formula to Preserve Inflation Neutrality

Beginning with equation (D.12), we are interested in the relationship between the valuation ratio and changes in the inflation rate. In mathematical terms, this is the definition of the first derivative of (D.12) with respect to π:

(E.1)

Factoring out like terms gives us the next step:

(E.2)

The derivative dW/dπ can be zero if, and only if, the bracketed term in (E.2) equals zero. More formally,

(E.3)

We can then carry out operations on the bracketed term. It should be easy to see that

(E.4)

We need to examine each of the derivative terms in turn, first recalling that

(E.5)

where ρE = inflation-adjusted discount rate

The next step is to apply the product rule for differentiation to obtain:

(E.6)

Expanding this out a little further gives us:

(E.7)

where z = inflation-adjusted ...