Capital Project Analysis When Cash Flows Evolve as a Continuous Time Branching Process

Optimal capital budgeting criteria now exist for a variety of applications when project cash flows (or present values) evolve in terms of the well‐known geometric Brownian motion. However, relatively little is known about the capital budgeting procedures that ought to be implemented when cash flows are generated by stochastic processes other than the geometric Brownian motion. Given this, our purpose here is to develop optimal investment criteria for capital projects with cash flows that evolve in terms of a continuous time branching process. Branching processes are compatible with an empirical phenomenon known as ‘volatility smile’. This occurs when there are systematic fluctuations in the implied volatility of a capital project's cash flows as the cash flow grows in magnitude. A number of studies have shown that this phenomenon characterizes the cash flow streams of the capital projects in which firms typically invest. We implement optimal capital budgeting procedures for both the continuous time branching process and the geometric Brownian motion using cost and revenue data for the Stuart oil shale project in central Queensland, Australia. This example shows that significant differences can arise between the optimal investment criteria for cash flows based on a branching process and those based on the geometric Brownian motion. This underscores the need for the geometric Brownian motion broadly to reflect the way a given capital project's cash flows actually evolve if serious errors in valuation and/or capital budgeting decisions are to be avoided.