Constant Leverage and Constant Cost of Capital: A Common Knowledge Half-Truth

Abstract

In this teaching note we show that using the findings of Tham and Velez-Pareja 2002, for finite cash flows, Ke and hence WACC depend on the discount rate that is used to value the tax shield, TS and as expected, Ke and WACC are not constant with Kd as the discount rate for the tax shield, even if the leverage is constant. We illustrate this situation with a simple example. We analyze five methods: DCF using APV, FCF and traditional and general formulation for WACC, present value of CFE plus debt and Capital Cash Flow, CCF.

In Tham and Velez-Pareja 2002, they derive a general expression for Ke, the cost of levered equity and for the Weighted Average Cost of Capital (WACC) applied to the Free Cash Flow (FCF) and Capital Cash Flow (CCF). For finite cash flows and perpetuities, the derivation presents the analysis for different levels of risk with respect to discounting the tax shields (TS). Taggart 1991 presents a revision of the set of formulations for the cost of levered Ke and WACC. He introduces the formulation with and without personal taxes and for different level of risk for discounting the TS, including the proposal by Miles and Ezzel 1980. However, Taggart does not include the case of Kd, the cost of debt as the level of risk for the TS and finite cash flows.

A typical approach for valuing finite cash flows is to assume that leverage is constant (usually as target leverage) and the Ke and WACC are also assumed to be constant. For cash flows in perpetuity, and with Kd as the discount rate for the tax shield, it is indeed the case that the Ke and WACC applied to the FCF are constant if the leverage is constant. However this does not hold true for finite cash flows. Though it might be convenient to perform calculations under such assumption, it is not in fact always true that Ke and WACC are constant under the constant leverage financing policy. As could be seen from the findings and example of Inselbag and Kaufold (1997), and as a general expression for Ke and WACC derived by Tham and Velez-Pareja (2002) shows, both the cost of levered equity and the Weighted Average Cost of Capital depend on the value of the interest tax shield (VTS), and in the case of finite cash flows valuation they could be changing from period to period if certain choice is made for the rate to discount for the expected tax shields.

The teaching note is organized as follows: An Introduction to state the problem; in Section Two we present the generalized formulation for the cost of capital for the finite cash flow valuation, and in particular formulae under the assumption that the discount rate for the tax shield (TS) is Kd. In Section Three we show a simple example. In Section Four we conclude.

Keywords: WACC, constant cost of capital, constant leverage, cash flows

JEL Classification: D61, G31, H43