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Unformatted text preview: The Assumptions and Math Behind WACC and APV Calculations Richard Stanton U.C. Berkeley Mark S. Seasholes U.C. Berkeley This Version October 27, 2005 * Abstract We outline the math and assumptions behind weighted average cost of capital (WACC) and adjusted present value (APV) calculations. We first derive a general formula for the discount rate of equity and beta of equity under minimal assumptions. We then take into consideration: i) The existence or non-existence of taxes; ii) Whether a firm has a constant amount of debt in dollar terms; iii) Whether a firm targets a constant proportion of debt in its capital structure; and iv) The frequency of debt rebalancing. These considerations give rise to well known results such as the Miles and Ezzell (1980) formula for WACC and differnt methods (formulae) for unlevering and re-levering betas. This document is intended for those who wish to understand the motivation behind valuing a firm with WACC and/or APV. Doctoral students and professors may find the document useful when teaching WACC and APV. In particular, this document helps answer questions like: Why does my firm use this formula to unlever beta, but you have taught us another formula? Understanding the assumptions behind both formulae turns out to be the key to answering such questions. Keywords: WACC, APV, Cost of Capital JEL Classification number: G32, A22, A23 * This document is based on work titled “WACC/APV—Mathematical Details” by Richard Stanton. Contact information: Mark S. Seasholes, U.C. Berkeley Haas School of Business, 545 Student Services Bldg., Berkeley CA 94720; Tel: 510-642-3421; Fax: 510-643-1420; email: [email protected] c 2005. 1 1 Introduction This document is intended for students who wish to delve into the math behind WACC and APV calculations. The derivations in this document highlight many of the assumptions behind these valuation methods. This document can be used by students ranging from advanced undergraduates to advanced MBAs. However, only the most curious students will find it interesting and benefit from it. Doctoral students and professors may find the document useful when teaching WACC and APV. In particular, this document helps answer questions like: Why does my firm use this formula to unlever beta, but you have taught us another formula? Understanding the assumptions behind both formulae turns out to be the key to answering such questions. 2 Definitions We lay out the notation used throughout the document. There are a myriad of possible ways to denote the same economic quantity. Many are self explanatory. 2.1 Unlevered Firms We use the following notation to denote the market value of a firm (and its equity) without leverage in its capital structure: V U = MV F,unlev = Market (enterprise) value of an unlevered firm E U = MV E,unlev = Market value of the equity of an unlevered firm Notice that V U = E U and we address this in Section 3. We also use the following definitions: FCF t = After-tax cashflow of the unlevered firm at time...
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This note was uploaded on 02/07/2011 for the course UGBA 103 taught by Professor Berk during the Fall '07 term at University of California, Berkeley.
- Fall '07