Equivalence Between the FCF Method, the CCF Method and the APV Approach

Abstract

In a recent paper, Ruback (2000) assumes that the discount rate for the tax shield in the Adjusted Present Value (APV) approach is the cost of debt and shows that the Capital Cash Flow (CCF) method and the Adjusted Present Value (APV) approach give different answers for the levered value. In this paper, using a simple numerical example with the Miles and Ezzell formulation for the tax shield, we show that the Free Cash Flow (FCF) method, the Capital Cash Flow (CCF) method and the APV approach give the same answers. The FCF method captures the benefit of the tax shield by lowering the cost of capital, the CCF method adds the tax shield directly to the FCF and the APV approach calculates the value of the tax shield separately. We organize the paper as follows. In Section One, we briefly review the assumptions underlying the three methods. In Section Two, we use a simple five-period binomial process to represent a finite stream of free cash flow and calculate the unlevered value with the risk-neutral method. In Section Three, we introduce risk-free debt financing with risk-free tax shields, and calculate the levered value with the three ways, the Free Cash Flow (FCF) method, the Capital Cash Flow (CCF) method and the APV approach. In addition, we verify that the APV approach is consistent with the answer from the risk-neutral method.