On the present-worth moments of serially correlated cash flows

The net present value (NPV) of a serially correlated cash-flow profile is examined. Given the expert estimates of end-of-period cash-flows, which are assumed to be beta variates, a methodology is developed to determine the first four moments of the profile’s NPV. The authors first determine the moments of the cash-flows, whereby the NPV expectation results readily. Then a correlative model based on time-series analysis is assumed in order to examine the cash-flow dependency; this is required for the determination of higher moments. Subsequently, it is shown that the higher moments of the NPV can be determined from the moments of period cash-flows and the time-series parameters. Although the beta-distributed assumption is used to illustrate the methodology, it is not a requirement in this analysis. Indeed, the approach presented in this paper is applicable to a finite cash-flow profile with arbitrarily distributed cash flows, as long as their individual moments can be determined.