APPENDIX F

Brief Recapitulation of the Miller 1977 Capital Structure Irrelevance Theorem

We will utilize the basic definitions from Chapter 4 and add a few more.

The definition of after-tax cash flow benefits from leverage is thus:

(F.1)

The bracketed term in equation (F.1) represents the after-tax income to common stock holders plus the after-tax income to debt holders. Subtracted from this amount is the after-tax income from the firm, assuming it is not leveraged.

ATBL is thus the net after-tax cash flow benefit to the security holders of the firm.

By subtracting out common terms, we are able to change equation (F.1) into:

(F.2)

Factoring our like terms allows us to distill this even further.

(F.3)

In order to value the cash flow stream in (F.3) to perpetuity, we discount the cash flow stream at the after-tax interest rate. More specifically, where GATBL denotes the capitalized value of the after-tax cash flow:

(F.4)

Substituting (F.4) into (F.3) gives us this expression:

(F.5)

We can make a basic cancellation and some slight rearranging to get:

(F.6)

Miller’s work implies that. At the macroeconomic level, the term in brackets must equal zero at the margin in equilibrium with the after-tax benefit to the corporation of the marginal dollar of debt issued being equal to the marginal cost of incremental taxes to the holder of the new debt. The marginal benefit to common shareholders is (1 − tC)(1 − tPS), and the marginal disadvantage of leverage to debt holders is (1 − tPD). (Hence, the ratio of these two terms must be one, and (F.6) becomes zero as the bracketed term vanishes.)

Since, in equilibrium, any debt-issuing firm can be considered the “marginal” debt issuer, relationship (F.6) is always perceived to hold from the perspective of such a firm. Consequently, the value of any individual firm should not be changed as a result of altering the amount of debt outstanding, once all portfolio rebalancing and tax minimization actions have been taken into account.