### Uncertainty

Although benefit-cost analysis is intended to inform a decision-making process, it cannot eliminate uncertainty. Therefore, uncertainty should be explicitly taken into account as much as possible.

### Examples

• How many passengers will use a proposed transit system is uncertain.
• The costs of a new type of traveler information system may not be fully known because such a system has not been used before.

### One Simple Approach

1. Once the benefits and costs for each alternative have been identified, note those benefits and costs that are largest and that differ most between alternatives.

2. For these benefits and costs, establish a range within which each can reasonably be expected to fall. The highest valueand lowest value within the range might be characterized as "high" and "low" or "optimistic" and "pessimistic" to indicate their effect on the benefit-cost measure. A "most likely" value should also be included.

3. Develop a matrix of these values. As an example, for a proposed rail system it might be:
Values of variables
 Factor Optimistic Most likely Pessimistic Patrons/year 62,000 24,000 14,000 Operating costs/year \$50,000,000 \$75,000,000 \$100,000,000 Constructions costs \$250,000,000 \$500,000,000 \$800,000,000

4. Once the benefit-cost analysis model has been set up, conduct a sensitivity analysis. To do this, calculate the benefit-cost measures using the most likely values of all variables. Then, for each variable, calculate the benefit-cost measures for its highest and lowest value, using the most likely values for the other variables. This will show how sensitive the measure is to each variable.

Benefit-Cost Ratios
 Factor Optimistic Most likely Pessimistic Patrons/year 3.2 1.2 0.7 Operating costs/year 1.3 1.2 0.9 Constructions costs 1.4 1.2 1.0

In this case the ratio is most sensitive to the patronage estimate. In such a case, it might be worthwhile to do further study to refine the patronage estimate.
A worst-case scenario might also be investigated, using the lowest benefits and highest costs. If the worst-case scenario for a particular project yields a negative net present value, or a benefit-cost ratio less than one, then perhaps that project should be removed from consideration.
Of course, benefits and costs may not be independent of one another. For example, operating costs may be somewhat related to patronage. In such cases one can construct various likely scenarios such as:
• High construction cost, low patronage, low operating cost
• Most likely construction cost, low patronage, most likely operating cost
The benefit-cost measures can be graphed against the values of the different variables as shown below so that decision-makers can assess the outcomes based on their estimates of the likelihood of each.

The decision-maker can look at the graph and see that fewer than 20 million patrons per year are needed to achieve a benefit-cost ratio greater than 1, but that even the most likely patronage estimate yields a ratio of only 1.2. This graph might be compared to one for an alternative, such as a bus system. Then a decision could be based on likely patronage for the two alternatives.

### More Detailed Analysis

If there is consensus regarding the probability of different values of the variables, the probability of various possible outcomes can be calculated as well, along with the expected value of the benefit-cost measure.

Alternatively, statistical distributions can be assigned to the variables. From these, a distribution of benefit-cost measures can be found, instead of a specific value. The main problem with this approach is that these distributions are themselves uncertain, but such an approach may be useful as long as the underlying uncertainties are kept in mind. Both the STEAM and StratBENCOST models explicitly consider the uncertainty in key inputs, employing a Monte Carlo simulation approach.

### Uncertain Demand and Unusual Projects

Generally uncertainty is greater for services for which demand is uncertain, such as transit use, freight or air terminal use, or use of a new traveler information service. Costs for unusual, large public works, such as the Central Artery project in Boston, are likely to be even more uncertain because there is no experience to guide people in identifying all of the challenges that may be encountered.