Equivalence of the APV, WACC and flows to equity approaches to firm valuation
This paper shows that the three valuation methods (if used correctly) always yield the same result. The most striking result of this paper is that the Net Present Value of the tax shield due to interest payments (in the APV approach) should be calculated as follows in order to derive an accurate result: NPV OF INTEREST TAX SHIELDS = ƒ Dt-1 Kut T Â ------ t=1 t ' (1+Kut) t=1 T = Corporate tax rate / Kut = Cost of unlevered equity in period t / Dt1 = Value of debt in period t1 At first, it would appear that this formula implies that debt has a cost of Ku, and that the interest tax shields are discounted at Ku, but this is not the case. The Net Present Value of interest tax shields is not (and this is the main error in previous papers about this topic) the NPV of a single flow, but the difference of two NPVs of two flows with different risks: the NPV of the taxes paid in the unlevered firm and the NPV of taxes paid in the levered firm. Our formula is the difference of these two NPVs. Obviously, the flow of taxes paid in the levered firm is smaller but riskier than the flow of taxes paid in the unlevered firm. We show that, if used correctly, these three approaches to firm valuation will yield the same result. We apply these valuation procedures to perpetuities, to growing companies (at a constant rate g) and, finally, to any company. The main objective of this paper is to show that the three valuation methods always yield the same result. The paper also helps to think more about the meaning of the formulas and their relationships.
|Date of creation:||12 Apr 1995|
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- Miles, James A & Ezzell, John R, 1985. " Reformulating Tax Shield Valuation: A Note," Journal of Finance, American Finance Association, vol. 40(5), pages 1485-1492, December.
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- Masulis, Ronald W, 1983. " The Impact of Capital Structure Change on Firm Value: Some Estimates," Journal of Finance, American Finance Association, vol. 38(1), pages 107-126, March.
- Kaplan, Steven N. & Stein, Jeremy C., 1990. "How risky is the debt in highly leveraged transactions?," Journal of Financial Economics, Elsevier, vol. 27(1), pages 215-245, September.
- Lewellen, Wilbur G. & Emery, Douglas R., 1986. "Corporate Debt Management and the Value of the Firm," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(04), pages 415-426, December.
- Miller, Merton H, 1977. "Debt and Taxes," Journal of Finance, American Finance Association, vol. 32(2), pages 261-275, May.
- Conine, Thomas E, Jr, 1980. " Corporate Debt and Corporate Taxes: An Extension," Journal of Finance, American Finance Association, vol. 35(4), pages 1033-1037, September.
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