# Probabilistic Approaches: Scenario Analysis, Decision Trees and Simulations

PROBABILISTIC APPROACHES: SCENARIO ANALYSIS, DECISION TREES AND SIMULATIONS In the last chapter, we examined ways in which we can adjust the value of a risky asset for its risk. Notwithstanding their popularity, all of the 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 the value – and the computation almost always 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 and presenting the risk in an investment. Rather than compute an expected value for an asset that that tries to reflect 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, most likely case and worse case – and then extend the discussion to look at scenario analysis more generally. We will move on to examine the use of decision trees, a more complete approach to dealing with discrete risk. We will close the chapter by evaluating Monte Carlo simulations, the most complete approach of assessing risk across the spectrum.

Scenario Analysis The expected cash flows that we use to value risky assets can be estimated in one or two ways. They can represent a probability-weighted average of cash flows under all possible scenarios or they can be the cash flows under the most likely scenario. While the former is the more precise measure, it is seldom used simply because it requires far more information to compile. In both cases, there are other scenarios where the cash flows will be different from expectations; higher than expected in some and lower than expected in others. In scenario analysis, we estimate expected cash flows and asset value under various scenarios, with the intent of getting a better sense of the effect of risk on value. In this section, we first consider an extreme version of scenario analysis where we consider the value in the best and the worst case scenarios, and then a more generalized version of scenario analysis.

2 Best Case/ Worse Case With risky assets, the actual cash flows can be very different from expectations. At the minimum, we can estimate the cash flows if everything works to perfection – a best case scenario – and if nothing does – a worst case scenario. In practice, there are two ways in which this analysis can be structured. In the first, each input into asset value is set to its best (or worst) possible outcome and the cash flows estimated with those values. Thus, when valuing a firm, you may set the revenue growth rate and operating margin at the highest possible level while setting the discount rate at its lowest level, and compute the value as the best-case scenario. The problem with this approach is that it may not be feasible; after all, to get the high revenue growth, the firm may have to lower prices and accept lower margins. In the second, the best possible scenario is defined in terms of what is feasible while allowing for the relationship between the inputs. Thus, instead of assuming that revenue growth and margins will both be maximized, we will choose that combination of growth and margin that is feasible and yields the best outcome. While this approach is more realistic, it does require more work to put into practice. How useful is a best case/worse case analysis? There are two ways in which the results from this analysis can be utilized by decision makers. First, the difference between the best-case and worst-case value can be used as a measure of risk on an asset; the range in value (scaled to size) should be higher for riskier investments. Second, firms that are concerned about the potential spill over effects on their operations of an investment going bad...

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