Cost of Capital and Value Without Circularity for Constant Growth Perpetuities

29 Pages Posted: 16 Aug 2010 Last revised: 24 Jan 2011

See all articles by Felipe Mejia-Pelaez

Felipe Mejia-Pelaez


Ignacio Velez-Pareja

Grupo Consultor CAV Capital Advisory & Valuation

Date Written: August 15, 2010


This paper presents the derivation of non-circular formulas for the calculation of the cost of equity, WACC, equity value (as a function either of initial debt or leverage), and levered firm value, using some previous results and showing their consistency with other well-known expressions. Relationships between growth, leverage, and debt level at instant zero (which must hold in all cases in order to assure consistency in the valuation process) are also deduced. In addition, a set of exact expressions to compute the impact on equity value of changes in the main variables which it depends on are shown, and conclusions regarding issues such as optimal capital structure that maximize equity value, or the nature of the interaction between cost of debt and equity value, are extracted. Finally, a set of detailed examples are presented that illustrate the proper application of the derived expressions and the steps involved in the process.

Keywords: Firm Valuation, Cost of Capital, Cost of Equity, Cash Flows, Free Cash Flow, Cash Flow to Equity, Capital Cash Flow, WACC, Perpetuities, Constant Growth, Circularity

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

Suggested Citation

Mejia-Pelaez, Felipe and Velez-Pareja, Ignacio, Cost of Capital and Value Without Circularity for Constant Growth Perpetuities (August 15, 2010). Available at SSRN: or

Felipe Mejia-Pelaez

Octum ( email )

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

Ignacio Velez-Pareja (Contact Author)

Grupo Consultor CAV Capital Advisory & Valuation ( email )

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


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