### Sensitivity Analysis

Sensitivity analysis is a systematic method for examining how the outcome of benefit-cost analysis changes with variations in inputs, assumptions, or the manner in which the analysis is set up.

### Examples

1. Estimates of patronage on a new light rail system vary from 4,000 to 10,000 passenger-trips per weekday. Would the system be viable with the lower patronage?
2. There are two design alternatives for constructing a bridge over an ice-prone river. The cost of one is lower unless there is a very cold winter, in which case it will be considerably higher. Is it worth taking a chance with this alternative?
3. There are differences of opinion regarding the lifetime of a pavement project. Are the benefit-cost rankings of the project alternatives different for different lifetime assumptions?

### Sensitivity to Uncertainty in the Magnitude of Benefits and Costs

See Dealing with Uncertainty for a discussion about using sensitivity analysis for uncertainty in model inputs, such as in examples 1 and 2 above, and for:

1. Determining the likely range of outcomes for the various alternatives
2. Examining the likelihood that a project will not have positive net benefits
3. Comparing risky with less risky projects

### Sensitivity to Different Assumptions Regarding the Value of Project Effects

The process described in Dealing with Uncertainty can be used when differences of opinion arise regarding values related to variables such as time. In decision-making, it is useful to know whether differences in these values affect project rankings.

### Sensitivity to Effects of Model Assumptions

Sensitivity analysis can also be used to assess the effects of model assumptions as in example 3.

### Approach

Consider the assumptions made in setting up the model and how they may affect the benefit-cost measure. These assumptions include:

• Project schedule
• Appropriate period of analysis
• Geographic scope
• Discount rate

### Sensitivity to the Type of Benefit-Cost Measure

The type of benefit-cost measure used can also affect the project ranking. Bigger projects will have a higher net present value than smaller projects with the same benefit-cost ratio. In the figure below, "b" has the highest benefit-cost ratio, indicated by the slope of the blue line through the origin and "b" being greater than the slopes for" a" and "c". However, "a" has a higher net present value, indicated by the intercept of a 45-degree line through the point on the vertical axis.

### Sources

Federal Highway Administration.Status of the Nation's Highways, Bridges, and Transit: 2002 Conditions and Performance Report. Available at: http://www.fhwa.dot.gov/policy/2002cpr/ch10.htm.