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Analytical Solution to the Circularity Problem in the Discounted Cash Flow Valuation Framework

Felipe Mejia-Pelaez

Internexa S.A. E.S.P.

Ignacio Velez-Pareja

Master Consultores

July 31, 2010

Innovar, Vol. 21, No. 42, pp. 55-68, 2011

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 derive a general formulation for the equity value, E, for the cost of unlevered equity, firm value and the weighted average cost of capital, WACC, without circularity. We furthermore compare the results obtained using these formulas with the results using the Adjusted Present Value approach (no circularity) and the iterative solution of circularity based upon the iteration feature of a spreadsheet. We conclude that all methods produce the same answer.

Number of Pages in PDF File: 14

Keywords: Firm valuation, cost of capital, cash flows, free cash flow, capital cash flow, WACC, circularity

JEL Classification: M21, M40, M46, M41, G12, G31, J33

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Date posted: April 27, 2010 ; Last revised: February 8, 2012

Suggested Citation

Mejia-Pelaez, Felipe and Velez-Pareja, Ignacio, Analytical Solution to the Circularity Problem in the Discounted Cash Flow Valuation Framework (July 31, 2010). Innovar, Vol. 21, No. 42, pp. 55-68, 2011. Available at SSRN: http://ssrn.com/abstract=1596426

Contact Information

Felipe Mejia-Pelaez
Internexa S.A. E.S.P. ( email )
Calle 12 sur N° 18
168, Bloque 5
Ignacio Velez-Pareja (Contact Author)
Master Consultores ( email )
Ave Miramar # 18-93 Apt 6A
+575 690 9972 (Phone)
HOME PAGE: http://cashflow88.com/decisiones/decisiones.html
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