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Constant leverage and constant cost of capital: a common knowledge half-truth

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  • Ignacio Velez-Pareja
  • Rauf Ibragimov
  • Joseph Tham

Abstract

In this teaching note we show that using the findings of Tham and Velez-Pareja 2002, for finite cash flows, Ke and hence WACC depend on the discount rate that is used to value the tax shield, TS and as expected, Ke and WACC are not constant with Kd as the discount rate for the tax shield, even if the leverage is constant. We illustrate this situation with a simple example. We analyze five methods: DCF using APV, FCF and traditional and generalformulation for WACC, present value of CFE plus debt and Capital Cash Flow, CCF. In Tham and Velez-Pareja 2002, they derive a general expression for Ke, the cost oflevered equity and for the Weighted Average Cost of Capital (WACC) applied to the Free Cash Flow (FCF) and Capital Cash Flow (CCF). For finite cash flows and perpetuities, the derivation presents the analysis for different levels of risk with respect to discounting thetax shields (TS). Taggart 1991 presents a revision of the set of formulations for the cost of levered Ke and WACC. He introduces the formulation with and without personal taxes and for different level of risk for discounting the TS, including the proposal by Miles and Ezzel 1980. However, Taggart does not include the case of Kd, the cost of debt as the level of risk for the TS and finite cash flows. A typical approach for valuing finite cash flows is to assume that leverage is constant (usually as target leverage) and the Ke and WACC are also assumed to be constant. For cash flows in perpetuity, and with Kd as the discount rate for the tax shield, it is indeed thecase that the Ke and WACC applied to the FCF are constant if the leverage is constant. However this does not hold true for finite cash flows. Though it might be convenient to perform calculations under such assumption, it is not in fact always true that Ke and WACC are constant under the constant leverage financing policy. As could be seen from the findings and example of Inselbag and Kaufold (1997), and as a general expression for Ke and WACC derived by Tham and Velez-Pareja (2002) shows, both the cost of levered equity and the Weighted Average Cost of Capital depend on the value of the interest taxshield (VTS), and in the case of finite cash flows valuation they could be changing from period to period if certain choice is made for the rate to discount for the expected tax shields.

Suggested Citation

  • Ignacio Velez-Pareja & Rauf Ibragimov & Joseph Tham, 2007. "Constant leverage and constant cost of capital: a common knowledge half-truth," Proyecciones Financieras y Valoración 3939, Master Consultores.
    • Handle: RePEc:col:000463:003939
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    References listed on IDEAS

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    1. Ignacio Vélez-Pareja & Joseph Tham, 2004. "Consistency in Chocolate. A Fresh Look at Copeland’s Hershey Foods & Co Case," Proyecciones Financieras y Valoración 2191, Master Consultores.
    2. Ignacio Vélez-Pareja, 2007. "Cash Flow Valuation in an Inflactionary World. The Case of World Bank for Regulated Firms," Economic Analysis Working Papers (2002-2010). Atlantic Review of Economics (2011-2016), Colexio de Economistas de A Coruña, Spain and Fundación Una Galicia Moderna, vol. 6, pages 1-19, November.
    3. Hamada, Robert S, 1972. "The Effect of the Firm's Capital Structure on the Systematic Risk of Common Stocks," Journal of Finance, American Finance Association, vol. 27(2), pages 435-452, May.
    4. Robert A. Taggart & Jr., 1991. "Consistent valuation and Cost of Capital Expressions With Corporate and Personal Taxes," Financial Management, Financial Management Association, vol. 20(3), Fall.
    5. Ignacio Vélez-Pareja, 2004. "The Correct Definition for the Cash Flows to Value a Firm (Free Cash Flow and Cash Flow to Equity)," Proyecciones Financieras y Valoración 3577, Master Consultores.
    6. Benninga, Simon, 2006. "Principles of Finance with Excel," OUP Catalogue, Oxford University Press, number 9780195301502.
    7. Isik Inselbag & Howard Kaufold, 1997. "Two Dcf Approaches For Valuing Companies Under Alternative Financing Strategies (And How To Choose Between Them)," Journal of Applied Corporate Finance, Morgan Stanley, vol. 10(1), pages 114-122, March.
    8. Ignacio Vélez-Pareja & Joseph Tham, 2006. "An Embarrassment of Riches: Winning Ways to Value with the WACC," Economic Analysis Working Papers (2002-2010). Atlantic Review of Economics (2011-2016), Colexio de Economistas de A Coruña, Spain and Fundación Una Galicia Moderna, vol. 5, pages 1-23, February.
    9. Fernandez, Pablo, 2002. "Valuation Methods and Shareholder Value Creation," Elsevier Monographs, Elsevier, edition 1, number 9780122538414.
    10. Tham, Joseph & Velez-Pareja, Ignacio, 2004. "Principles of Cash Flow Valuation," Elsevier Monographs, Elsevier, edition 1, number 9780126860405.
    11. Miles, James A. & Ezzell, John R., 1980. "The Weighted Average Cost of Capital, Perfect Capital Markets, and Project Life: A Clarification," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(3), pages 719-730, September.
    12. Ignacio Velez-Pareja & Joseph Tham, 2008. "Constant leverage modeling: A reply to "A tutorial to the Mckinsey model for valuation of companies"," Proyecciones Financieras y Valoración 4574, Master Consultores.
    13. Ignacio Vélez-Pareja & Antonio Burbano, 2005. "Consistency in Valuation: A Practical Guide," Proyecciones Financieras y Valoración 2192, Master Consultores.
    14. Joseph Tham & Ignacio Velez-Pareja, 2005. "Modeling Cash Flows with Constant Leverage: A Note," Proyecciones Financieras y Valoración 1897, Master Consultores.
    15. Ignacio Velez-Pareja & Joseph Tham, 2000. "A Note on the Weighted Average Cost of Capital WACC," Proyecciones Financieras y Valoración 1926, Master Consultores.
    16. Ignacio Vélez-Pareja, 2004. "Modeling the Financial Impact of Regulatory Policy: Practical Recommendations and Suggestions. The Case of World Bank," Proyecciones Financieras y Valoración 3228, Master Consultores.
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    Cited by:

    1. Ignacio Vélez-Pareja, 2009. "Which Cost Of Debt Should Be Used In Forecasting Cash Flows?," Estudios Gerenciales, Universidad Icesi, June.

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    More about this item

    Keywords

    WACC; constant cost of capital; constant leverage; cash flows;
    All these keywords.

    JEL classification:

    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies
    • H43 - Public Economics - - Publicly Provided Goods - - - Project Evaluation; Social Discount Rate

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