Example of Probabilistic Results Interpretation

Interpretation of risk analysis results goes beyond a simple comparison of which alternative on average costs less by including an analysis of the likelihood that any particular outcome will occur. There is no presumption that any particular alternative is better. Figure 12.11 shows the risk profile of the NPV for Alternatives 1 and 2 in histogram form, where the probability is the area under the curve. As figure 12.11 shows, the entire range of conceivable outcomes is arrayed with the estimated probability of each outcome actually occurring. The main advantage of the histogram is that it readily shows the variability about the mean. If the distribution is wider, the variability is greater. As shown, the outcome for Alternative 2 is more uncertain than Alternative 1.

In interpreting the risk profile in figure 12.11, it is important to distinguish between upside risk and downside risk. Downside risk for project cost implies cost overrun — chance of financial failure. Upside risk for project costs implies cost underrun — opportunity for low cost. As figure 12.11 shows, Alternative 2 has greater upside risk compared to Alternative 1. However, as discussed below, it is important to quantify the probability of cost overrun for Alternative 2. Figure 12.12 shows the risk profiles for Alternatives 1 and 2 in cumulative probability form. As shown, there is a 30 percent probability that project costs for Alternative 2 will be less than $40.21 thousands. This means that for the 100,000 iterations that were processed, 30 percent of the calculated values for NPV were less than $40.21 thousands. The variability for the proposed alternative is inversely proportional to the slope of the cumulative curve. In other words, if the slope is steeper, the variability is less. If the slope is flatter, the variability is greater. As shown, the slope for Alternative 2 is flatter than that for Alternative 1, and is therefore more variable.

Figure 12.11 –Relative probability distribution- NPV for Alternatives 1 and 2

Figure 12.12 –Cumulative probability distribution of NPV for Alternatives 1 and 2

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