Net Present Value Analysis of Projects Under Expected Utility

Abstract

The traditional decision-analytic approach to incorporate risk aversion into project evaluation is to calculate the expected utility of initial capital plus net present value. The choice of discount rate, and the convergence with the traditional finance approach, have always been a question. Our goal is to fill this gap. We adopt a standard continuous-time setup whereby the alternative to the project is the market for treasuries and stocks, and provide reasons to restrict preferences to generalized power or log utility. We find a convenient rate to discount portfolio capital (treasuries, stocks, and the project), which depends on market parameters and on the utility function. We also cater to practitioners, who discount the cash flows of the project, and ignore the market uncertainty. For them, we propose an adjusted discount rate that correctly compensate for the omission. The adjusted discount rate is lower than the beta-adjusted rate recommended in finance, and converges to the latter when the initial capital is large relative to the project, or the owner is risk neutral.