11.14 Inflation and equity valuations

Proposition 11.11inflation pass-through and the P/E

Suppose real cash flows grow at $g_r$ , inflation is $\pi$ , and firms pass through a fraction $\lambda\in[0,1]$ of inflation to nominal dividend growth: $g = g_r + \lambda\pi$ . The nominal discount rate is $r = \rho + \pi$ , with $\rho$ the real required return. Under Gordon,

\frac{P}{D_1} = \frac{1}{\rho - g_r + (1-\lambda)\pi},\qquad \frac{\partial \ln(P/D_1)}{\partial\pi} = -\frac{1-\lambda}{\rho-g_r+(1-\lambda)\pi}. \tag{11.25}

Full pass-through ( $\lambda=1$ ) makes the valuation invariant to inflation. Incomplete pass-through ( $\lambda<1$ ) makes equity multiples fall as inflation rises.

Proof

Substitute $r-g = \rho+\pi-g_r-\lambda\pi$ into (11.10) and differentiate the log.∎

Why $\lambda<1$ in practice

Historical-cost depreciation and inventory accounting overstate real profits in inflation, so real taxes rise.
Input costs (energy) can rise faster than output prices. This is especially true for Indian oil marketing companies, whose retail prices are administered (M10).
Nominal debt gains are offset by higher refinancing rates.

Money illusion (Modigliani and Cohn, 1979) Investors may discount real cash flows at nominal rates, so inflation lowers prices mechanically even when $\lambda=1$ . This is a behavioural hypothesis, not an identity.

The "Fed model" This heuristic compares the equity earnings yield $E/P$ with the nominal 10-year yield. It is internally inconsistent by (11.25): with $\lambda=1$ , $E/P$ should track real yields, not nominal ones. Use real yields, or model $\lambda$ explicitly.

India Indian equity valuations have historically been higher than EM peers. In a supply-driven inflation with administered fuel prices, Indian sectors differ sharply in $\lambda$ . Upstream oil producers have $\lambda>1$ . Oil marketing companies, paints, airlines and tyres have $\lambda<1$ in the short run (M10). The relative performance of these sectors is therefore a market read on pass-through.