Consider Company A with a zero earnings retention ratio and a real growth rate in earnings of
$\gamma$ %. In an inflationary environment, the company can only pass inflation through its earnings
at a flow-through rate of $\lambda$%. So if I is the inflation rate, its earnings will grow at a rate of
g =$\gamma$+$\lambda$I. The real rate of return required for this company is $\rho$, so the nominal rate of return required is r==$\rho$+ I.
Use a simple dividend discount model (DDM) assuming that dividends will grow indefinitely at a constant compounded annual growth rate (CAGR), g = $\gamma$+ $\lambda$I.
a. Derive formulas equivalent of Equations (6.7) and (6.8), which assumed no real growth in earnings. Discuss the results.
b. Use these formulas to calculate P/E ratio on prospective earnings with the following data on Company A: $\gamma$= 2%, I = 4%, $\rho$ = 4%,$\lambda$ = 100%.
c. Same question for a Company B, whose inflation pass-through rate is only 80%.

Question

Quizplus · Accepted Answer

The Answer is a. Earnings will grow at a rate

\gamma

+

\lambda

I, assumed constant over time. For example, we have:

E _ { 1 } = E _ { 0 } imes ( 1 + y + \lambda I )

By discounting this perpetual stream of growing earnings at the required rate, r, we find that the intrinsic value of such a firm would then be:

P _ { 0 } = \frac { E _ { 1 } } { r - ( y + \lambda I ) } = E _ { 0 } imes \frac { 1 + \gamma + \lambda I } { r - ( \gamma + \lambda I ) }

(6.7a)
where P₀ is the intrinsic value
E₀ is the initial earnings level

\gamma

is the real growth rate in earnings
I is the annual inflation rate

\lambda

is the pass-through rate
r is the (nominal) required rate of return.
Of course, r is a nominal rate that includes the rate of inflation. If we introduce the real required rate of return

ho

= r- I, we get:
P₀ =E₀ *

\frac { 1 + \gamma + \lambda I } { ho + ( 1 - \lambda ) I - \gamma } = \frac { E _ { 1 } } { ho + ( 1 - \lambda ) I - \gamma }

The intrinsic P/E using prospective earnings is now equal to:
P₀/E₁ =

\frac { 1 } { ho + ( 1 - \lambda ) I - \gamma }

. (6.8a)
From Equation (6.8a) we can see that the higher the inflation flow-through rate, the higher the price of the company. Indeed, a company that cannot pass inflation through its earnings is penalized. The higher the inflation rate, the more negative the influence on the stock price if full inflation pass-through cannot be achieved. Irrespective of inflation, the higher the real growth rate, the higher the P/E.
b. Company A earnings will grow at a rate of

\gamma

+

\lambda

I = 2% +100% * 4% = 6%. The P/E will be
P/E =

\frac { 1 } { 4 \% + ( 0 \% ) imes 4 \% - 2 \% } = \frac { 1 } { 2 \% }

= 50.
c. Company B cannot fully pass inflation to its earnings. Its P/E is equal to:
P/E(B) =

\frac { 1 } { 4 \% + ( 20 \% ) imes 4 \% - 2 \% } = \frac { 1 } { 2.8 \% }

=35.7.
In the inflationary environment, Company B's earnings cannot grow as fast as inflation. Penalized by inflation and its inability to pass along inflation, Company B's price/earnings ratio is below that of Company A.

Consider Company a with a Zero Earnings Retention Ratio and a Real