Do the RIM (Residual Income Model), EVA® and DCF (Discounted Cash Flow) Really Match?

In Velez-Pareja and Tham (2001), we presented several different ways to value cash flows. First, we apply the standard after-tax Weighted Average Cost of Capital, WACC to the free cash flow (FCF). Second, we apply the adjusted WACC to the FCF, and third we apply the WACC to the capital cash flow. In addition, we discount the cash flow to equity (CFE) with the appropriate returns to levered equity. We refer to these four ways as the "discounted cash flow (DCF)" methods. In recent years, two new approaches, the Residual Income Method (RIM) and the Economic Value Added (EVA) have become very popular. Supporters claim the RIM and EVA are superior to the DCF methods. It may be case that the RIM and EVA approaches are useful tools for assessing managerial performance and providing proper incentives. However, from a valuation point of view, the RIM and EVA are problematic because they use book values from the balance sheet. It is easy to show that under certain conditions, the results from the RIM and EVA exactly match the results from the DCF methods. Velez-Pareja 1999 reported that when using relatively complex examples and book values to calculate Economic Value Added (EVA), the results were inconsistent with Net Present Value (NPV). Tham 2001, reported consistency between the Residual Income Model (RIM) and the Discounted Cash Flow model (DCF) with a very simple example. Fernandez 2002 shows examples where there is consistency between DCF, RIM and EVA. He uses a constant value for the cost of levered equity capital and in another example constant debt. Young and O'Byrne, 2001, show simple examples for EVA but do not show the equivalence between DCF and EVA. Ehrbar (1998) uses a very simple example with perpetuities and shows the equivalence between EVA and DCF. Lundholm and O'Keefe, 2001, show this equivalence with an example with constant Ke. Tham 2001, commented on their paper. Stewart, 1999, shows the equivalence between DCF and EVA with an example using a constant discount rate. Copeland, et al, show an example with constant WACC and constant cost of equity even with varying debt and assuming a target leverage that is different to the actual leverage. In general, textbooks do not specify clearly how EVA should be used to give consistent results. In this teaching note using a complex example with varying debt, varying leverage and terminal (or continuing value), we show the consistency between DCF, RIM and EVA. We stress what Velez-Pareja 1999 and Fernandez 2002 said: for a single period, RI or EVA does not measure value. We have to include expectations and market values in the calculation of discount rates and hence values.