Utility functions based on net present worth

In order to help a decision maker, an analyst often seeks to represent the decision maker’s preferences in a value function, if the decision is under certainty, or in a utility function, if the decision is under uncertainty. When the alternatives involve outcomes that are different streams of future cash flows net present worth can be justified as an appropriate value function, but it may not be an appropriate utility function since net present worth requires the decision maker to be univariate and multivariate risk neutral. This paper describes which risk attitudes can be represented by various functions of net present worth. Furthermore, it is shown that the preferences implied by comparing alternatives on the basis of discounted certainty equivalently can be expressed as a utility function only if that utility function is equivalent to net present worth.