A Glum Primer: How to Account for Risk with Uncertain Npvs

Abstract

This note describes a method for adjusting uncertain future cash flows into a present certain equivalent. The use of net present value (NPV) to adjust a stream of future known cash flows into a single-value equivalent adjusted for the time value of money is common practice. The use of simulation to produce a risk profile of NPV values is also now common. While the expected net present value (ENPV) is often used to convert a risk profile of uncertain NPVs into a single-value equivalent, this approach ignores risk and the decision maker's attitude toward risk. Simply put, a 50% probability of receiving an NPV of $1 million is not as attractive as a 100% chance of receiving an NPV of $500,000. The general logarithmic utility model (GLUM) constructs a single certain equivalent from a risk profile (i.e., a “risk-adjusted NPV”) which goes beyond ENPV to incorporate risk aversion into the decision-making criterion. The simplicity and many attractive properties of the GLUM prompt us to suggest it as more attractive than other ways to adjust an NPV risk profile for risk. Excerpt UVA-QA-0849 Rev. Nov. 26, 2018 A GLUM Primer: How to Account for Risk with Uncertain NPVs We use net present value (NPV) to convert a stream of future known cash flows into a single-value equivalent. The NPV tool uses a discount rate to correctly account for the time value of money. We often next use expected net present value (ENPV) to convert a risk profile of uncertain NPVs into a single-value equivalent. Although ENPV accounts for all possible NPVs and their relative likelihoods, it ignores risk and the decision-maker's attitude toward risk. Simply put, a 50% probability of receiving $ 1,000,000 is not as attractive as a 100% chance of receiving $ 500,000. This makes ENPV an incomplete decision-making criterion. The purpose of this note is to describe the general logarithmic utility model (GLUM), which constructs a single-value equivalent from a risk profile. The resulting single-value equivalent is called a “present certain equivalent,” or “risk-adjusted NPV,” which goes beyond ENPV to incorporate risk aversion into the decision-making criterion. The simplicity and many attractive properties of the GLUM prompt us to suggest it as more attractive than other ways to adjust an NPV risk profile for risk. How to Use the GLUM . . .