A Clarification on the Certainty Equivalence Approach in Capital Budgeting

Abstract:

Unlike the risk adjusted discount rate (RADR) approach, the (subjective) certainty equivalence (CEQ) approach can not results in objective valuation results. Moreover, (subjective) CEQ derived from popular utility functions such as CARA and CRRA normally can not satisfy the requirements of additivity and multiplicativity simultaneously, hence this approach could lead to contradictions during capital budgeting, even under the viewpoints of a given decision maker. Analysis based on the non-arbitrage axiom in a binomial model reveals the relationship among RADR, CEQ, and risk neutral probability (RNP) approach, which implies that CEQ used in capital budgeting should be the risk-neutral expectation in nature. (Objective) CEQ formulated in beta and market risk premium with absolute prices in the CAPM framework restores its objective nature and facilitates its application.

Key words:Capital Budgeting; Risk Adjusted Discount Rate (RADR); Certainty Equivalence (CEQ); Risk Neutral Probability (RNP)