# CHAPTER 33

# Probabilistic Approaches in Valuation: Scenario Analysis, Decision Trees, and Simulations

**T**hrough much of this book, we have focused on discounted cash flow and relative valuation approaches to valuation. Notwithstanding their popularity, these approaches share a common theme. The riskiness of an asset is encapsulated in one number—a higher discount rate, lower cash flows, or a discount to value—and the computation almost requires us to make assumptions (often unrealistic) about the nature of risk.

In this chapter, we consider a different and potentially more informative way of assessing the value of an investment. Rather than compute an expected value for an asset that tries to capture in one number all of the different possible outcomes, we could provide information on what the value of the asset will be under each outcome or at least a subset of outcomes. We will begin this section by looking at the simplest version, which is an analysis of an asset's value under three scenarios—a best case, the most likely case, and worst case—and then extend the discussion to look at scenario analysis more generally. We move on to examine the use of decision trees as a more complete approach to dealing with sequential risk. We will close the chapter by evaluating Monte Carlo simulations, the most complete approach to assessing risk across the spectrum.

## SCENARIO ANALYSIS

The expected cash flows that we use to value risky assets can be estimated in one of two ways. They can represent ...