Analytical solution to the circularity problem in the discounted cash flow valuation framework
In this paper we propose an analytical solution to the circularity problem between value and cost of capital. Our solution is derived starting from a central principle of finance that relates value today to value, cash flow, and the discount rate for next period. We present a general formulation wit...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2011
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/9107
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/9107
- Palabra clave:
- Capital cash flow
Cash flows
Circularity
Cost of capital
Firm valuation
Free cash flow
WACC
- Rights
- restrictedAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
| id |
UTB2_7abdea24386c31c589e8469193d3ab1c |
|---|---|
| oai_identifier_str |
oai:repositorio.utb.edu.co:20.500.12585/9107 |
| network_acronym_str |
UTB2 |
| network_name_str |
Repositorio Institucional UTB |
| repository_id_str |
|
| dc.title.none.fl_str_mv |
Analytical solution to the circularity problem in the discounted cash flow valuation framework |
| dc.title.alternative.none.fl_str_mv |
Solución analítica al problema de la circularidad usando flujos de caja descontados |
| title |
Analytical solution to the circularity problem in the discounted cash flow valuation framework |
| spellingShingle |
Analytical solution to the circularity problem in the discounted cash flow valuation framework Capital cash flow Cash flows Circularity Cost of capital Firm valuation Free cash flow WACC |
| title_short |
Analytical solution to the circularity problem in the discounted cash flow valuation framework |
| title_full |
Analytical solution to the circularity problem in the discounted cash flow valuation framework |
| title_fullStr |
Analytical solution to the circularity problem in the discounted cash flow valuation framework |
| title_full_unstemmed |
Analytical solution to the circularity problem in the discounted cash flow valuation framework |
| title_sort |
Analytical solution to the circularity problem in the discounted cash flow valuation framework |
| dc.subject.keywords.none.fl_str_mv |
Capital cash flow Cash flows Circularity Cost of capital Firm valuation Free cash flow WACC |
| topic |
Capital cash flow Cash flows Circularity Cost of capital Firm valuation Free cash flow WACC |
| description |
In this paper we propose an analytical solution to the circularity problem between value and cost of capital. Our solution is derived starting from a central principle of finance that relates value today to value, cash flow, and the discount rate for next period. We present a general formulation without circularity for the equity value (E), cost of levered equity (Ke), levered firm value (V), and the weighted average cost of capital (WACC). We furthermore compare the results obtained from these formulas with the results of the application of the Adjusted Present Value approach (no circularity) and the iterative solution of circularity based upon the iteration feature of a spreadsheet, concluding that all methods yield exactly the same answer. The advantage of this solution is that it avoids problems such as using manual methods (i.e., the popular "Rolling WACC") ignoring the circularity issue, setting a target leverage (usually constant) with the inconsistencies that result from it, the wrong use of book values, or attributing the discrepancies in values to rounding errors. |
| publishDate |
2011 |
| dc.date.issued.none.fl_str_mv |
2011 |
| dc.date.accessioned.none.fl_str_mv |
2020-03-26T16:32:58Z |
| dc.date.available.none.fl_str_mv |
2020-03-26T16:32:58Z |
| dc.type.coarversion.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
| dc.type.coar.fl_str_mv |
http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.type.driver.none.fl_str_mv |
info:eu-repo/semantics/article |
| dc.type.hasVersion.none.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
| dc.type.spa.none.fl_str_mv |
Artículo |
| status_str |
publishedVersion |
| dc.identifier.citation.none.fl_str_mv |
Innovar; Vol. 21, Núm. 42; pp. 55-68 |
| dc.identifier.issn.none.fl_str_mv |
01215051 |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/20.500.12585/9107 |
| dc.identifier.instname.none.fl_str_mv |
Universidad Tecnológica de Bolívar |
| dc.identifier.reponame.none.fl_str_mv |
Repositorio UTB |
| dc.identifier.orcid.none.fl_str_mv |
55215017700 6503847935 |
| identifier_str_mv |
Innovar; Vol. 21, Núm. 42; pp. 55-68 01215051 Universidad Tecnológica de Bolívar Repositorio UTB 55215017700 6503847935 |
| url |
https://hdl.handle.net/20.500.12585/9107 |
| dc.language.iso.none.fl_str_mv |
eng |
| language |
eng |
| dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_16ec |
| dc.rights.uri.none.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| dc.rights.accessRights.none.fl_str_mv |
info:eu-repo/semantics/restrictedAccess |
| dc.rights.cc.none.fl_str_mv |
Atribución-NoComercial 4.0 Internacional |
| rights_invalid_str_mv |
http://creativecommons.org/licenses/by-nc-nd/4.0/ Atribución-NoComercial 4.0 Internacional http://purl.org/coar/access_right/c_16ec |
| eu_rights_str_mv |
restrictedAccess |
| dc.format.medium.none.fl_str_mv |
Recurso electrónico |
| dc.format.mimetype.none.fl_str_mv |
application/pdf |
| dc.source.none.fl_str_mv |
https://www.scopus.com/inward/record.uri?eid=2-s2.0-84860895865&partnerID=40&md5=03d050942cb8fbb355bdc3f1bcc95454 |
| institution |
Universidad Tecnológica de Bolívar |
| bitstream.url.fl_str_mv |
https://repositorio.utb.edu.co/bitstream/20.500.12585/9107/1/MiniProdInv.png |
| bitstream.checksum.fl_str_mv |
0cb0f101a8d16897fb46fc914d3d7043 |
| bitstream.checksumAlgorithm.fl_str_mv |
MD5 |
| repository.name.fl_str_mv |
Repositorio Institucional UTB |
| repository.mail.fl_str_mv |
repositorioutb@utb.edu.co |
| _version_ |
1814021762836332544 |
| spelling |
2020-03-26T16:32:58Z2020-03-26T16:32:58Z2011Innovar; Vol. 21, Núm. 42; pp. 55-6801215051https://hdl.handle.net/20.500.12585/9107Universidad Tecnológica de BolívarRepositorio UTB552150177006503847935In this paper we propose an analytical solution to the circularity problem between value and cost of capital. Our solution is derived starting from a central principle of finance that relates value today to value, cash flow, and the discount rate for next period. We present a general formulation without circularity for the equity value (E), cost of levered equity (Ke), levered firm value (V), and the weighted average cost of capital (WACC). We furthermore compare the results obtained from these formulas with the results of the application of the Adjusted Present Value approach (no circularity) and the iterative solution of circularity based upon the iteration feature of a spreadsheet, concluding that all methods yield exactly the same answer. The advantage of this solution is that it avoids problems such as using manual methods (i.e., the popular "Rolling WACC") ignoring the circularity issue, setting a target leverage (usually constant) with the inconsistencies that result from it, the wrong use of book values, or attributing the discrepancies in values to rounding errors.Recurso electrónicoapplication/pdfenghttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/restrictedAccessAtribución-NoComercial 4.0 Internacionalhttp://purl.org/coar/access_right/c_16echttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84860895865&partnerID=40&md5=03d050942cb8fbb355bdc3f1bcc95454Analytical solution to the circularity problem in the discounted cash flow valuation frameworkSolución analítica al problema de la circularidad usando flujos de caja descontadosinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1Capital cash flowCash flowsCircularityCost of capitalFirm valuationFree cash flowWACCMejía-Peláez F.Vélez-Pareja I.Abarbanell, J., Valuing the gap using a discounted cash flow model (1999) Handout For the Purpose of Class Discussion, , http://www.haas.berkeley.edu, Hass Graduate School, University of Berkeley. Retrieved fromAbrams, J.B., (2001) Quantitative Business Valuation: A Mathematical Approach For Today's Professional, , New York: McGraw-HillAdserà, X., Vínolas, P., FEVA: A financial and economic approach to valuation (2003) Financial Analysts Journal, 59 (2), pp. 80-87Ansay, T., (2009) Firm Valuation: Tax Shields and Discount Rates, , Mémoire Présenté en vue de l'obtention du Master en Ingénieur de gestion, à finalité spécialiséeApreda, R., (2008) Cost of Capital Adjusted For Governance Risk Through a Multiplicative Model of Expected Returns, , http://ideas.repec.Org/p/cem/doctra/383.html, Working paper, downloadable fromBaginski, S.P., Wahlen, J.M., Residual income risk, intrinsic values, and share prices (2003) The Accounting Review, 7 S (1), pp. 327-351Benninga, S., (2006) Principles of Finance With Excel, , New York: OxfordBenninga, S., Sarig, O., (1997) Corporate Finance: A Valuation Approach, , New York: McGraw-HillBerk, J.B., Demarzo, P., (2009) Corporate Finance: The Core, , Boston: MA: PearsonBrealey, R.A., Myers, S.C., (2003) Principles of Corporate Finance, , New York: McGraw-HillCopeland, I., Koller, T., Murrin, J., (2000) Valuation. Measuring and Managing the Value of Companies, , 3rd ed. Hoboken, N.J.: John Wiley & Sons IncCrundwell, F.K., (2008) Finance For Engineers: Evaluation and Funding of Capital Projects Finance For Engineers, , London: Springer-Verlag London LimitedDamodaran, A., (2000) The Dark Side of Valuation, , http://pages.stern.nyu.edu/~adamodar/pd-files/papers/HighGrow.pdf, Hoboken, N.J.: John Wiley & Sons IncDamodaran, A., (2006) Valuation Approaches and Metrics: A Survey of the Theory and Evidence, pp. 30-31. , http://pages.stern.nyu.edu/~adamodar/pdfiles/papers/valuesurveypdfDamodaran, A., Valuation, (n. D.). Slide 46, , www.stern.nyu.edu/~adamodar/pptfiles/eq/dcfvegN.ppt, Available atDemario, M., Fazzone, A.P., The adjusted present value: An alternative approach to the effect of debt of business value (2006) Business Valuation Update, 72 (12). , http://www.bvresources.com/BVWireCentral/Material/WO112706/1206BVUDeManoFazzone.pdf, Available atFairchild, K., The Cost of Capital & Discount Rates, , http://faculty.business.utsa.edu/kfairchild/classes/5023/Lectures/5023Lectures.htm, (n. d.), Available atFama, E., French, K., Taxes, financing decisions, and firm value (1998) The Journal of Finance, 53 (3), pp. 819-843Froidevaux, P., (2004) Fundamental Equity Valuation: Stock Selection Based On Discounted Cash Flow, , Thesis presented to the Faculty of Economics and Social Sciences of the University of Fribourg (Switzerland) in fulfillment of the requirements for the degree of Doctor of Economics and Social Sciences, Accepted by the Faculty's Council on 1 July 2004Greenwald, B.C., Admissible Rate Bases, Fair Rates of Return and the Structure of Regulation (1980) The Journal of Finance, 35 (2), pp. 359-368Hess, D., Homburg, C., Lorenz, M., Sievers, S., (2009) Extended Dividend, Cash Flow and Residual Income Valuation Models- Accounting For Deviations From Ideal Conditions (April 9), , http://ssrn.com/abstract=1145201, Available at SSRNHitchner, J.R., (2003) Financial Valuation: Applications and Models Hoboken, , N.J.: John Wiley & Sons IncHua, N., Upneja, A., True market value of lodging stocks: A convergence approach (2005) Journal of Hospitality Financial Management, 13 (1). , http://scholarworks.umass.edu/jhfm/voll3/issl/14, Available at, Visited March 19, 2010Koller, T., Goedhart, M., Wessels, D., (2005) Valuation: Measuring and Managing the Value of Companies- McKinsey & Co. Hoboken, , N.J.: John Wiley & Sons IncLazar, F., Prisman, E., (2006) Calculating the Cost of Capital For LDCs In Ontario, , http://www.oeb.gov.on.ca/documents/cases/EB-2006-0088/4cocJazarprisman_210606.pdf, Teaching slides available atLerner, E.M., Carleton, W.T., Financing decisions of the firm (1966) The Journal of Finance, 21 (2), pp. 202-214Liu, Y.C., The slicing approach to valuing tax shields (2009) Journal of Banking & Finance, 33, pp. 1069-1078Lobe, S., Caveat WACC: Pitfalls in the use of the weighted average cost of capital (2009) Corporate Ownership and Control, 6 (3), pp. 45-52Magni, C.A., Velez-Pareja, I., Potential dividends versus actual cash flows in firm valuation (2009) The ICFAI Journal of Applied Finance, 75 (7), pp. 51-66. , http://papers.ssrn.com/abstracts374070, Available at SSRNMathiesen, H., (2010) Presentation: Fundamental Value Analysis, , http://e.viaminvest.com/A2MonitorSystems/Ap-pA2MonitorSystems/Pres_FundamentalValueAnalysis.asp, Available atMcDaniel, W.R., (1994) Techniques For Including Flotation Costs In Capital Budgeting: Materiality, Generality and Circularity, pp. 139-148. , Financial Practice and Education, (Spring/SummerMello-e-Souza, C.A., Bee, S., (2005) Business Valuation Software: A Blueprint For Reliability, , http://ssrn.com/abstract=844543, (November 6). Available at SSRNMian, M.A., Velez-Pareja, I., Applicability of the classic WACC concept in practice (2008) Latin American Business Review, 8 (2), pp. 19-40. , http://ssrn.com/abstract=804764, Available at SSRNMiller, M.H., Debt and taxes (1977) Journal of Finance, 32 (2), pp. 261-276Modigliani, F., Miller, M.H., The cost of capital, corporation taxes and the theory of investment (1958) The American Economic Review, 48, pp. 261-297Mohanty, P., Solving the circularity problem in estimating the cost of capital: A practical approach (2007) The Icfai Journal of Applied Finance, 13 (2), pp. 29-38Myers, S.C., Interactions of corporate financing and investment decisions-implications for capital budgeting (1974) The Journal of Finance, 29 (1), pp. 1-25Penman, S.H., (2007) Financial Statement Analysis and Security Valuation, , 3rd ed. New York: McGraw-HillPfeiffer, T., Net present value-consistent investment criteria based on accruals: A generalisation of the residual income-identity (2004) Journal of Business Finance & Accounting, pp. 910-911. , (September/October)Pinteris, G., Notes on weighted-average cost of capital (WACC) Finance 422, , http://www.business.uiuc.edu/gpinteri/wacc.pdf, (n. d.), Department of Finance College of Business University of Illinois at Urbana-Champaign. Available atPratt, S.P., (2002) Cost of Capital: Estimation and Applications, , 2nd ed. Hoboken, New York: John Wiley & Sons IncPratt, S.P., (2008) Valuing a Business: The Analysis and Appraisal of Closely Held Companies, , 5th Ed. New York: McGraw-HillPratt, S., Grabowski, R., (2008) Cost of Capital: Applications and Examples, , 3rd Edition. Hoboken, N.J.: John Wiley & Sons IncRao, R.K.S., Stevens, E.C., (2007) A Theory of the Firm's Cost of Capital: How Debt Affects the Firm's Risk, Value, Tax Rate, and The Government Tax's Claim, , Singapore: World Scientific Publishing Co. Pte. LtdRosenberg, B., Guy, J., Prediction of beta from investment fundamentals. Part One, Prediction criteria (1976) Financial Analysts Journal, 32 (3), pp. 60-72Ruback, R.S., Capital cash flows: A simple approach to valuing risky cash flows (2002) Financial Management, 31 (2), pp. 85-103. , (Summer)Schiefner, L., Schmidt, R., (2003) Shareholder Value At Risk: Concept For Company Valuation, Implementation, and Simulation Example, , http://www2.wiwi.uni-halle.de/wiwi/lui/bwl/bank//schmidt/MLU-WIWI-WP47-2003.pdf, Available atSchultze, W., Valuation, tax shields and the cost of capital with personal taxes: A framework for incorporating taxes (2004) International Journal of Theoretical and Applied Finance, 7 (6), pp. 769-804Schuster, P., Jameson, M., The past performance and future value of companies (2003) Management Accounting Quarterly, 4 (4). , http://www.imanet.org/pdf/1836.pdf, Available atStrategy @ Risk, the Weighted Average Cost of Capital, , http://www.strategy-at-risk.com/2008/09/08/the-weighted-average-cost-of-capital, Available atTaggart, R.A., Consistent valuation cost of capital expressions with corporate and personal taxes (1991) Financial Management (Autumn), pp. 8-20Tham, J., Velez-Pareja, I., (2004) Principles of Cash Flow Valuation, An Integrated Market-based Approach, , Boston: Academic PressTijdhof, L., Practical Guide For Strategic Decision-making- Part 1: Is Estimating the WACC Like Interpreting a Piece of Art?, , http://www.zanders.nl/publicaties/documents/WACC_partl.pdf, (n. d.) WACO, (Visited March 20, 2010)Truong, C., Partington, C., Peat, M., Cost-of-capital estimation and capital-budgeting practice in Australia (2008) Australian Journal of Management, 33 (1), pp. 95-121. , (June)Turner, J., (2008) The Circularity Problem With Free Cash Flow, , http://ssrn.com/abstract=1095227, Available at SSRNVelez-Pareja, I., Valuating cash flows in an inflationary environment. The case of World Bank (2006) Trends In Inflation Research, pp. 87-141. , In B. T. Credan (éd.), New York: Nova PublishersVelez-Pareja, I., Constructing consistent financial planning models for valuation (August 15) (2009) IIMS Journal of Management of Science, 1, pp. 1-26. , http://ssrn.com/abstract=1455304, (January-June 2010), Inaugural Issue, Available at SSRNVelez-Pareja, I., Risky tax shields and risky debt: An exploratory study (2010) Cuadernos De Administración, 23 (41), pp. 213-235Velez-Pareja, I., Benavides, J., There exists circularity between WACC and Value? (2006) Another solution. Estudios Gerenciales, 98, pp. 13-23. , January-MarchVelez-Pareja, I., Burbano-Perez, A., Consistency in valuation: A practical guide (2010) Academia, Revista Latinoamericana De Administración, 44, pp. 21-43. , MayVelez-Pareja, I., Tham, J., Proper solution of circularity in the interactions of corporate financing and investment decisions: A reply to the financing present value approach (2005) Management Research News, 28 (10), pp. 65-92Velez-Pareja, I., Tham, J., Market value calculation and the solution of circularity between value and the weighted average cost of capital WACC (2009) RAM-Revista De Administraçâo Mackenzie, 10 (6). , http://www3.mackenzie.br/editora/indexphp/RAM/issue/view/38, Retrieved fromVelez-Pareja, I., Tham, J., Company's valuation in an emerging economy- Case Study TIMANCO S. A (2010) The Valuation Journal, 5 (2), pp. 4-45Velez-Pareja, I., Ibragimov, R., Tham, J., Constant leverage and constant cost of capital: A common knowledge half-truth (June 29) (2008) Estudios Gerenciales, 24 (107), pp. 13-34. , http://ssrn.com/abstract=997435, Available at SSRNVishwanath, S.R., (2007) Corporate Finance: Theory and Practice, , 2nc ed. New Delhi: Response BooksWood, J.S., Leitch, C., Interactions of corporate financing and investment decisions: The financing present value (""FPV"") approach to evaluating investment projects that change capital structure (2004) Managerial Finance, 30 (7), pp. 16-37Woolley, S., (2009) Sources of Value: A Practical Guide to The Art and Science of Valuation, , Cambridge: Cambridge University Presshttp://purl.org/coar/resource_type/c_6501THUMBNAILMiniProdInv.pngMiniProdInv.pngimage/png23941https://repositorio.utb.edu.co/bitstream/20.500.12585/9107/1/MiniProdInv.png0cb0f101a8d16897fb46fc914d3d7043MD5120.500.12585/9107oai:repositorio.utb.edu.co:20.500.12585/91072021-02-02 14:08:10.5Repositorio Institucional UTBrepositorioutb@utb.edu.co |