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Sensitivity analysis

223. Sensitivity analysis is the study of how sensitive the NPV, or the BCR, of a CBA is to the uncertainty in individual costs and benefits, and in the discount rate. The main purpose of a sensitivity analysis is to tell the analyst where to direct his or her efforts: further work may be warranted on estimating a particular cost or benefit if the degree of uncertainty around it is large and the NPV is particularly sensitive to it. The further work may enable the analyst to reduce the confidence interval around a cost or benefit.

224.One way of determining which costs or benefits most affect the NPV is to vary each one at a time, holding all other costs and benefits constant. If variables are correlated, they may need to be varied together.

225.If the confidence intervals have already been worked out, then they will give an immediate picture of the sensitivity of the NPV to a particular cost or benefit. The sensitivity analysis can be illustrated by way of a Tornado diagram which shows the 90% confidence intervals for the different costs and benefits, as well as for the discount rate. See the hypothetical transport example in figure 2. In that example, the 90% confidence interval for travel time savings is +/- $226 million in present value terms (the point estimate of travel time savings is $2,394 million NPV but this is not shown on the diagram)[16]. In other words, reasonable differences to the travel time savings estimate could change the project NPV by +/- $226 million. However, because the uncertainty in the travel time savings estimate is partly neutralised by uncertainty in some of the other estimates (see “Monte Carlo Simulation” below), the 90% confidence interval for the NPV of the project as a whole is less than the sum of the confidence intervals, only around +/- $309 million in this example.

226. In this example, the NPV is most sensitive to uncertainty in the cost of construction, followed by uncertainty in travel time savings. The NPV is not very sensitive to uncertainty in operations and maintenance costs, accident costs and CO2 emissions.

Figure 2
Figure 2 .
Source: The Treasury


  • [16]To produce the Tornado diagram for this hypothetical project, the following 90% confidence intervals were assumed:

    Travel time savings: +/- 20% initially, but the uncertainty grows by 8% each year.
    Construction costs, which are spread over three years, could vary by 10%, 12% and 14% in years 1, 2 and 3 respectively.
    The discount rate could be different by 12.5%, i.e. by one percentage point.
    Trip reliability benefits could vary by 20%.
    The deadweight cost of taxation could vary by 50%.
    Operations and maintenance costs could vary by 10%.
    Increased accident costs could vary by 10%.
    The value of CO2 emissions could vary by the same percentage as the travel time savings.
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