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

APPENDIX H

Comparison of Volatility of Pretax and After-Tax Income

If x represents after-tax income, PTI represents pretax income, and t represents the effective corporate tax rate, this equation is true by definition:

(H.1)

For notational simplicity, let us redefine the term (1 − t) as A, the after-tax pull-through factor converting pretax into after-tax earnings.

(H.2)

By the operation of logarithms, we transform equation (H.2) into:

(H.3)

We can then take the first differences of the logarithms, since we are interested in volatility between periods. This gives us:

(H.4)

For the moderate changes we are likely to see from year to year, we can make the next approximation of the delta-logarithm operation:

(H.5)

We can then apply the basic identity formula for the variance of formula (H.5):

(H.6)

From inspection of this equation, it can be seen that the variance of percentage changes ...