Uncertainty is a factor in the analysis of transportation projects just as it is in any other enterprise. Fortunately, much of the uncertainty associated with transportation investments can be evaluated and managed.

Typically, the analyst is faced with a number of uncertainties when evaluating a highway investment. Many of these uncertainties can be measured by quantifying the probability of an event and its impact if it occurs. Measured uncertainty is known as "risk." Risk can be identified and understood by answering three questions:

*What can happen?*The following are examples of things that can happen that would change BCA results: there are initial construction or future rehabilitation cost overruns, facility service life is less or more than expected, or traffic volumes vary significantly from projections.*How likely is it to happen?*Some things are more likely to occur than are others. For instance, it may be that the project in question is well understood and unlikely to have construction cost overruns.*What are the consequences of an event occurring?*In some cases, an input variable may be subject to significant variability, but any given occurrence (within a realistic range) would not substantially affect the economic justification for the project. For instance, the price of a paving material may be subject to large swings, but the benefits of a particular alternative using that material may be sufficiently large to maintain the alternative as the preferred one even if the paving material price doubles. In other cases, there may be little likelihood that an event will occur (such as an earthquake), but its occurrence would have major consequences unless certain precautions are taken in the project's design.

Risk analysis will help the analyst answer these questions and determine if efforts to mitigate some or all of the risk would be cost-effective.

The traditional means by which analysts have evaluated risk is through sensitivity analysis. In a typical sensitivity analysis, the value of an input variable identified as a significant potential source of uncertainty is changed (either within some percentage of the initial value or over a range of reasonable values) while all other input values are held constant, and the amount of change in analysis results is noted. This sensitivity process is repeated for other input variables for which risk has been identified. The input variables may then be ranked according to the effect of their variability on BCA results.

Sensitivity analysis allows the analyst to get a feel for the impact of the variability of individual inputs on overall economic results. In general, if the sensitivity analysis reveals that reasonable changes in an uncertain input variable will not change the relative economic ranking of project alternatives or undermine the project's economic justification, then the analyst can have reasonable comfort that the results are robust. Alternatively, a reasonable change in an uncertain input value could severely undermine the project's economic justification. If so, the analyst would investigate methods to reduce the risk of a change in that input value and analyze steps to minimize consequences if the adverse event occurs. If the risk cannot be mitigated, the analyst may recommend against undertaking that particular project design.

There is usually some uncertainty associated with several variables in an economic analysis, and these variables may vary simultaneously. Sensitivity analysis as traditionally practiced can measure the effect of a change in more than one variable at a time, but the results of analysis involving many different scenarios can become confusing to interpret. Fortunately, continuing advances in computing power available through microcomputers permit the practice of probabilistic-based risk analysis, most often through a method known as Monte Carlo simulation.

In Monte Carlo simulation, the analyst assigns an appropriate probability distribution (based on expert opinion, historical data, and other information) to each of the input variables subject to uncertainty in the economic analysis. The Monte Carlo simulation samples randomly from the probability distributions for each input, runs the selected input values through the BCA formula to calculate a discrete economic result, and then repeats this process over and over again. The results, which are based on the randomly selected input values, are arrayed in the form of an average BCA result and a probability distribution covering all potential outcomes of the BCA.

Figure 2 illustrates the NPV outcomes of two competing project alternatives analyzed using the Monte Carlo simulation method. This particular analysis is relatively easy to interpret. Assume that these are two alternatives to accomplish a particular project, or two projects competing for the same funding. Alternative B has a higher mean NPV (represented by the value under the peak) than does alternative A. The NPV for alternative A, however, has a tighter range of potential values than does alternative B, and, unlike alternative B, is not at significant risk of having a negative NPV. If the decision maker were risk neutral (or a risk taker), alternative B would be preferred. If the decision maker were risk averse, alternative A, with its somewhat lower NPV but lower range of downside outcomes, might be preferred.

**FIGURE 2. Probabilistic Outcome Distributions**

Once risks have been identified and quantified, the next step is to evaluate potential actions to mitigate them. Many actions may be taken to reduce risk, including increased engineering, additional quality testing, application of value engineering, and various contractual methods such as design/build. In some cases, the object of risk mitigation may be to shift risk to the party that is most able to control it, such as through the use of construction warranties.

The reduction of risk to the agency and the traveling public associated with a potential risk mitigation action must be weighed against the cost of the action. Accordingly, the range of potential economic outcomes for the project should be calculated with and without the risk mitigation action in place. If a highway agency were risk neutral, it would pursue risk mitigation to the extent that the cost of the action(s) is at least compensated by the higher expected value of the mean BCA outcome (e.g., due to a reduction in the number of potential downside NPV outcomes). If the agency is risk averse, it may decide to accept a lower expected NPV in exchange for reduced downside risk.

More information on risk analysis, particularly as applied in LCCA, is available in "Life-Cycle Cost Analysis in Pavement Design," an FHWA interim technical bulletin (FHWA-SA-98-079, 1998). This document is available on the Office of Asset Management Web site at http://www.fhwa.dot.gov/infrastructure/asstmgmt/lcca.htm.

Updated: 10/23/2013