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

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

14 Pages Posted: 27 Apr 2010 Last revised: 8 Feb 2012

Felipe Mejia-Pelaez

Octum

Ignacio Velez-Pareja

Grupo Consultor CAV Capital Advisory & Valuation

Date Written: July 31, 2010

Abstract

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.

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

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: https://ssrn.com/abstract=1596426

Felipe Mejia-Pelaez

Octum ( email )

Carrera 35A 5A-170
Apt 1201 - Edificio Catay 8
Medellín, Antioquia
Colombia

Ignacio Velez-Pareja (Contact Author)

Grupo Consultor CAV Capital Advisory & Valuation ( email )

Ave Miramar # 18-93 Apt 6A
Cartagena
Colombia
+573112333074 (Phone)

HOME PAGE: http://cashflow88.com/decisiones/decisiones.html

Paper statistics

Downloads
635
Rank
32,578
Abstract Views
3,897