The derivation of the NPV variance of a risky capital investment project with first-order autoregressive cash flows and autoregressive conditional heteroscedastic variances

Abstract

In this article, the authors develop a closed-form solution for assessing the capital investment project NPV variance when cash flows obey a first-order autoregressive process. A distinction is established between static and dynamic solutions as the authors focus on the case involving partial positive dependence between cash flows. Under a Markovian process, the NPV solution is stationary in mean but not strictly in variance. Constraining the process to become fully stationary will overestimate the NPV variance. Finally, the authors show that the Markovian NPV variance closed-form solution is robust to the introduction of autoregressive conditional heteroscedastic variances complying with a GARCH(1,1) process; it will, however, have its value increased and consequently the riskiness of the capital investment project.