Executive Summary
The article uses a simple numerical example to illustrate that:

Weighted average cost of capital (WACC) and adjusted present value (APV) valuation yield identical results in the (hypothetical) situation when expected cash flows are constant over time;

The equivalence depends crucially on using the right discount rates;

Such discount rates are different when the debt is constant over time, or when it is only expected to be constant over time;

The equivalence between WACC and APV disappears in the more realistic situation when expected cash flows are nonconstant, unless the financial structure remains stable;

The formula most often used by practitioners to relate the beta of equity and the beta of the assets of a corporation is inconsistent with WACC valuation.
Introduction
Franco Modigliani and Merton Miller’s (1958) Propositions I and II have generated two valuation methodologies, hereafter referred to as WACC (weighted average cost of capital) and APV (adjusted present value) valuation. Briefly, Proposition I states that the value of a firm does not depend on its capital structure, and Proposition II states that a firm’s value depends on three things: the required rate of return on its assets; its cost of debt; and its debt/equity ratio. Both valuation methodologies are equivalent provided that the discount rates are chosen appropriately and consistent assumptions are made regarding the corporation’s financial policy. They are not equivalent otherwise, and both may lead to inappropriate valuation if used with insufficient care.
Modigliani and Miller’s (MM) Proposition II addresses the relationship between the cost of equity of a levered firm and the cost of equity of its unlevered equivalent. Whenever financial markets are frictionless, such a relationship reflects an equilibrium generated by investors’ arbitrage activities. A consequence is that, in the absence of market imperfections, neither the value nor the cost of capital of a corporation vary with its financial structure: the value of the firm is equal to the present value of the free cash flows, discounted at a constant weighted average cost of capital.
Conversely, as emphasized in many ways by contemporary corporate finance, when imperfections exist a firm’s financial structure may impact its valuation. The most familiar imperfection is the tax advantage of debt implied by the tax deductibility of interest. MM Proposition I shows that the value of a levered firm is equal to the present value of the free cash flows discounted at the unlevered cost of capital, plus the present value of the tax savings. This is the basis for APV valuation. WACC valuation remains valid if an adjustment is made for a world where borrowing has a tax advantage; the value is equal to the present value of the free cash flows discounted at a weighted average cost of capital, with the latter now incorporating the impact of the tax shield:
WACC = Cost of debt × w(1 − t) + Cost of equity × (1 − w)
where w is the ratio, D/EV, of debt to enterprise value, and t is the tax rate.
The WACC and the APV approaches are equivalent to the extent that the return requirements used for discounting reflect the arbitrageimplied structure of return requirements. However, practitioners using both methodologies usually arrive at different valuations. This article shows that such differences are the consequence of different implicit assumptions regarding the firm’s debt policy, and it attempts to draw conclusions on the methodological precautions that must be taken. An example will illustrate this.
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