The Assumptions and Math Behind Wacc and Apv Calculations

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 different 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