Firm valuation: tax shields & discount rates

Ansay, Thomas (2009): Firm valuation: tax shields & discount rates.

Abstract

This paper proposes a new discounted cash flows’ valuation setup, and derives a general expression for the tax shields’ discount rate. This setup applies to any debt policy and any cash flow pattern. It only requires the equality at any time between the assets side and the liabilities side of the market value balance sheet, which has been introduced by Farber, Gillet and Szafarz (2006). This concept is extensively developed in the paper.

This model encompasses all the usual setups that consider a fixed discount rate for the tax shields and require a fixed level of debt or a fixed leverage ratio, in particular Modigliani & Miller (1963) and Harris & Pringle (1985). It proposes an endogenized and integrated approach and modelizes the different market value discount rates as functions of both their relevant leverage ratio and the operating profitability of the firm. Among these rates are the cost of debt and the tax shields’ discount rate, which are usually assume constant. In this model, all the discount rates are likely to vary as soon as perpetuity cases are not considered.

This setup introduces a new rate for the cost of levered equity without tax shields and develops the relation between the present value of tax shields and the market value of equity since debt tax shields entirely flow to equity. It only requires the risk free rate and the unlevered cost of capital as inputs but not the capital structure of the firm, as it tackles the circularity problem by considering an iterative approach.

This fully dynamic model yields both theoretical and economic sensible results, and allows straightforward applications. It apparently solves the discrepancies of the usual setups and hopefully paves the way for further research.

• Item Type: MPRA Paper
• Language: English
• Keywords: Discounted Cash Flow; Tax Shields; Discount Rates; Cost of Equity; Cost of Capital; Tax Shield Risk; Adjusted Present Value; Equity Cash Flow
• Subjects: O - Economic Development, Innovation, Technological Change, and Growth > O1 - Economic Development > O16 - Financial Markets ; Saving and Capital Investment ; Corporate Finance and Governance; G - Financial Economics > G3 - Corporate Finance and Governance

References

COPELAND T., KOLLER T. & MURRIN J. (2002), La stratégie de la valeur : l’évaluation d’entreprise en pratique, Editions d’Organisation, Paris.

DAMODARAN A. (2007), Valuation Approaches and Metrics : A Survey of the Theory and Evidence, Now Publishers Inc, New York.

DOSSOGNE S. (2003), Valorisation et cession d’entreprise : de l’intention à la finalisation, de la valeur au prix, Editions de la Chambre de Commerce et d’Industrie, Liège.

FERNANDEZ P. (2002), Valuation Methods and Shareholder Value Creation, Academic Press, Elsevier Science & Technology Books, San Diego.

KOLLER T., GOEDHART M. & WESSELS D. (2005), Valuation : Measuring and Managing the Value of Companies, 4e édition, John Wiley & Sons, Hoboken, New Jersey.

RAFFEGEAU J. & DUBOIS F. (2003), L’évaluation financière de l’entreprise, Presses universitaires de France, Paris. RAO K.S. & STEVENS E.C. (2007), A theory of the firm’s cost of capital, World Scientific Publishing Company, Singapore.

THAUVRON A. (2005), Evaluation d’entreprise, Economia, Paris.

ARZAC E. & GLOSTEN L. (2005), « A Reconsideration of Tax Shield Valuation », European Financial Management, Vol. 11, No. 4, pp. 453-461

BERTONECHE M. & FEDERICI F. (2006), « Valuation Methods and Discount Rate Issues : A Comprehensive Example », Harvard Business School, Boston (Teaching Note).

BOOTH, L. (2002), « Finding Value Where None Exists : Pitfalls in Using Adjusted Present Value », Journal of Applied Corporate Finance, Vol. 15, No. 1, pp.95-104

BOOTH, L. (2007), « Capital Cash Flows, APV and Valuation », European Financial Management, Vol. 13, No. 1, pp.29-48

COOPER I. & NYBORG K.G. (2004), « Discount Rates and Tax », Working Paper, London Business School

COOPER I. & NYBORG K.G. (2005), « The value of tax shields IS equal to the present value of tax shields », Journal of Financial Economics, Vol. 81, No. 1, pp.215-225

COOPER I. & NYBORG K.G. (2007), « Valuing the Debt Tax Shield », Working Paper, NHH – Department of Finance and Management Science

DAMODARAN A. (2005), « Dealing with Cash, Cross Holdings and Other Non-Operating Assets: Approaches and Implications », Research Paper N°196, Stern School of Business

DAMODARAN A. (2007), « Return on Capital (ROC), Return on Invested Capital (ROIC) and Return on Equity (ROE): Measurement and Implications», Working Paper, Stern School of Business

DE WET J.H. & HALL J.H. (2004), « The relationship between EVA, MVA and leverage », Meditari Accountancy Research, Vol. 12, No. 1, pp.39-59

ESTY, B.C. (1997), « Note on Value Drivers », Harvard Business School, Boston (Teaching Note).

FARBER A., GILLET R. & SZAFARZ A. (2006), « A General Formula for the WACC », International Journal of Business, Vol. 11, No. 2, pp.211-218

FARBER A., GILLET R. & SZAFARZ A. (2007), « A General Formula for the WACC: a Reply », International Journal of Business, Vol. 12, No. 3, pp.405-411

FERNANDEZ P. (1995), « Equivalence of the APV, WACC and Flows-to-Equity approaches to firm valuation », Research Paper No. 292, IESE Business School - University of Navarra

FERNANDEZ P. (2004), « The Value of Tax Shields is not equal to the Present Value of Tax Shields », Journal of Financial Economics, No. 73, pp.145-165

FERNANDEZ P. (2006), « Company Valuation Methods: the most common errors in valuations », Working Paper No. 449, IESE Business School - University of Navarra

FERNANDEZ P. (2007), « A General Formula for the WACC: a Comment », International Journal of Business, Vol. 12, No. 3, pp.399-403

FERNANDEZ P. (2008a), « Valuing Companies by Cash Flow Discounting: Ten Methods and Nine Theories », Working Paper, IESE Business School - University of Navarra

FERNANDEZ P. (2008b), « Equivalence of the different discounted cash flow valuation methods : Different alternatives for determining the discounted value of tax shields and their implications for the valuation », Working Paper, IESE Business School - University of Navarra

GRAHAM J.R. (1996a), « Debt and the marginal tax rate », Journal of Financial Economics, No. 41, pp.41-73

GRAHAM J.R. (1996b), « Proxies for the corporate marginal tax rate », Journal of Financial Economics, No. 42, pp.187-221

GRAHAM J.R. & LEMMON M.L. (1998), « Measuring Corporate Tax Rates and Tax Incentives : A New Approach », Journal of Applied Corporate Finance, Vol. 11, No. 1, pp.54-65

GRAHAM J.R. (2000), « How big are the Tax Benefits of Debt ? », The Journal of Finance, Vol. 55, No. 5, pp.1901-1941

GRINBLATT M. & LIU J. (2008), « Debt Policy, corporate taxes and discount rates », Journal of Economic Theory, No. 141, pp.225-254

HARRIS R.S. & PRINGLE J.J. (1985), « Risk-Adjusted Discount Rates – Extensions from the Average-Risk case », The journal of Financial Research, Vol. 8, No. 3, pp.237-244

LIU Y.-C. (2009), « The slicing approach to valuing tax shields », Journal of Banking & Finance, Vol. 33, No. 6, pp. 1069-1078

MODIGLIANI F. & MILLER M. (1958), « The Cost of Capital, Corporation Finance and the Theory of Invesment », American Economic Review, Vol. 48, No. 3, pp. 261-297.

MODIGLIANI F. & MILLER M. (1963), « Corporate income taxes and the cost of capital : a correction », American Economic Review, Vol. 53, No. 3, pp. 433-443.

MILES J. & EZZEL J. (1980), « The Weighted Average Cost of Capital, Perfect Capital Markets, and Project Life : A Clarification », The Journal of Financial and Quantitative Analysis, Vol. 15, No. 3, pp. 719-730.

PENMAN, S.H. (2006), « Handling Valuation Models », Journal of Applied Corporate Finance, Vol. 18, No. 2, pp.48-55

RUBACK, R.S. (2002), « Capital Cash Flows : A Simple Approach to Valuing Risky Cash Flows », Financial Management, Vol. 31, No. 2, pp.85-103

SABAL, J. (2007), « WACC or APV ? », Journal of Business Valuation and Economic Loss Analysis, Vol. 2, No. 2, pp.1-15

SCHMIDLE, S. (2006), « Deriving the Capital Cash Flow Method as a Rational Return Expectation », Working Paper

SHEVLIN, T. (1990), « Estimating corporate marginal tax rates with asymmetric tax treatment of gains and losses », Journal of the American Taxation Association, Vol. 11, pp.51-67

UDAY C. & BYUNG T.R. (2008), « The Role of Revenue in Firm Valuation », Accounting Horizons, Vol. 22, No. 2, pp. 199-222

VÉLEZ-PAREJA I. & THAM J. (2005), « Proper Solution of Circularity in the Interacting of Corporate Financing and Investment Decisions: a Reply to the Financing Present Value Approach », Management Research News, Vol. 28, No. 10, pp. 65-92

VÉLEZ-PAREJA I. & MIAN M. (2008), « Applicability of the Classic WACC Concept in Practice», Latin American Business Review, Vol. 8, No. 2, pp. 19-40

WOOD J.S. & LEITCH G. (2004), « Interactions of Corporate Financing and Investment Decisions: the Financing Present Value Approach to Evaluating Investment Projects that Change Capital Structure », Managerial Finance, Vol. 30, No. 2, pp. 16-37