Three Residual Income Valuation Methods and Discounted Cash Flow Valuation

Abstract

In this paper we show that the Residual Income models for equity valuation always yield the same value as the Discounted Cash Flow Valuation models. We use three residual income measures: Economic Profit, Economic Value Added (EVA) and Cash Value Added. We also show that economic profit and EVA are different, although Copeland, Koller and Murrin (2000, page 55) say that economic profit is a synonym of EVA. Specifically, we first show that the present value of the Economic Profit discounted at the required return to equity plus the equity book value equals the value of equity. The value of equity is the present value of the Equity cash flow discounted at the required return to equity. Then, we show that the present value of the EVA discounted at the WACC plus the enterprise book value (equity plus debt) equals is the enterprise market value. The enterprise market value is the present value of the Free cash flow discounted at the WACC. Then, we show that the present value of the Cash Value Added discounted at the WACC plus the enterprise book value (equity plus debt) equals is the enterprise market value. The enterprise market value is the present value of the Free cash flow discounted at the WACC.