Stochastic internal rate of return on investments in sustainable assets generating carbon credits

Internal rate of return (IRR) is a widely used tool in ranking capital budgeting projects and eventual accept or reject decisions. In this paper, we consider an investment decision involving a sustainable, energy efficient, greenhouse gases (GHG) reducing asset and incorporate the value of carbon emission allowances for the investing company. These allowances create cash flows that may be characterized by significant volatility and uncertainty. The methodology developed in this paper allows decision makers to integrate their knowledge of carbon trading markets and the cash flows that result from sale of emissions credits. The novel methodology utilizes a Bayesian model for IRR that uses Gibbs sampler. Analysis of the results shows that IRR is influenced by volatility and uncertainty of carbon credit cash flows. Ignoring those uncertainty characteristics and simply using the expected values of cash flows can result in significantly inaccurate investment rate of returns. When compared to deterministic IRR calculations, the results show that the occurrence of very high and very low cash flows affects IRR positively, whereas higher variability of cash flow distribution affects IRR of GHG-reducing asset negatively. In other words, frequent large or small cash flows are preferred over fluctuating cash flows. The results may also provide a rationale for the existence of an anomalous consumer behavior known as the energy efficiency gap.