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Equivalence of the APV, WACC and flows to equity approaches to firm valuation


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  • Fernández, Pablo

    (IESE Business School)


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.

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Bibliographic Info

Paper provided by IESE Business School in its series IESE Research Papers with number D/292.

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Length: 35 pages
Date of creation: 12 Apr 1995
Date of revision:
Handle: RePEc:ebg:iesewp:d-0292

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Postal: IESE Business School, Av Pearson 21, 08034 Barcelona, SPAIN
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Keywords: Valuation methods; interest payments;

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  1. Fama, Eugene F., 1977. "Risk-adjusted discount rates and capital budgeting under uncertainty," Journal of Financial Economics, Elsevier, vol. 5(1), pages 3-24, August.
  2. Myers, Stewart C & Turnbull, Stuart M, 1977. "Capital Budgeting and the Capital Asset Pricing Model: Good News and Bad News," Journal of Finance, American Finance Association, vol. 32(2), pages 321-33, May.
  3. 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.
  4. 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.
  5. Isik Inselbag & Howard Kaufold, 1989. "How To Value Recapitalizations And Leveraged Buyouts," Journal of Applied Corporate Finance, Morgan Stanley, vol. 2(2), pages 87-96.
  6. Miles, James A & Ezzell, John R, 1985. " Reformulating Tax Shield Valuation: A Note," Journal of Finance, American Finance Association, vol. 40(5), pages 1485-92, December.
  7. Conine, Thomas E, Jr, 1980. " Corporate Debt and Corporate Taxes: An Extension," Journal of Finance, American Finance Association, vol. 35(4), pages 1033-37, September.
  8. 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 107-26, March.
  9. Rubinstein, Mark E, 1973. "A Mean-Variance Synthesis of Corporate Financial Theory," Journal of Finance, American Finance Association, vol. 28(1), pages 167-81, March.
  10. Miller, Merton H, 1977. "Debt and Taxes," Journal of Finance, American Finance Association, vol. 32(2), pages 261-75, May.
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