CAPM and Capital Budgeting: Present/Future, Equilibrium/Disequilibrium, Decision/Valuation

This paper expands on the results obtained in Magni (2009) regarding investment decisions with the Capital Asset Pricing Model (CAPM). It is shown that four different decision criteria are deductively drawn from this model: the disequilibrium Net Present Value (NPV), the equilibrium NPV, the disequilibrium Net Future Value (NFV), and the equilibrium NFV. It is shown that all of them may be used for accept-reject decisions, but only the equilibrium NPV and the disequilibrium NFV may be used for valuation, given that they have the additivity property. However, it is possible to deductively dismiss the two nonadditive indexes if the ‘accept/reject’ problem is reframed as a choice among mutually exclusive alternatives. As for the remaining (additive) measures, the equilibrium NPV and the disequilibrium NFV are unreliable for both valuation and decision, because despite their additivity, they do not signal arbitrage opportunities whenever there is some state of nature for which they are decreasing functions with respect to the end-of-period cash flow. In this case, the equilibrium value of a project is not the price it would have if it was traded in the security market. This result is the capital-budgeting counterpart of Dybvig and Ingersoll’s (1982) result.