Selection of Variables and Depth of Analysis

When conducting sensitivity analysis, the analyst should normally consider

three specific areas:

• Aggregate costs and benefits. Simple sensitivity analysis of the effects of variations in total project costs and total project benefits often helps to indicate the joint influence of underlying variables. Except in special cases, however, this type of aggregate analysis alone does not assist judgments on the range of likely variation or on the specific measures that might  reduce project risks.

• Critical cost and benefit items. Sensitivity tests are usually most effective if costs and benefits are disaggregated in some detail. While the use of subaggregates—investment costs, operating costs, and the like—can be helpful, sensitivity analysis is best done in respect of individual parameters that are most critical to the project. On the benefit side, detailed sensitivity analysis typically includes such parameters as output prices or tariff levels, unit cost savings, and expected rate of growth in demand for project outputs. On the cost side, such analysis typically involves productivity coefficients and prices of major inputs. Shadow prices used in the economic analysis should normally be examined in sensitivity analysis.

• The effects of delays. Several types of delays can occur in projects: delays in starting the project, delays during the construction phase, or delays in reaching full capacity utilization (as in industrial projects) or in reaching full development  Analysts should include the relevant delay factors in sensitivity tests.1 The amount of detail desirable in sensitivity tests varies considerably from case to case. Analysts should analyze delays in terms of the effects on the NPV of delays of specified time intervals  although it may occasionally be useful to calculate the maximum permissible delay or switching value. The switching value method is, however, the preferred form of analysis for other variables, esp

The Expected Net Present Value Criterion

For projects with benefits measurable in monetary terms, the criterion for project acceptability should be the project’s expected NPV. This criterion requires that the project’s expected NPV must not be negative and must be at least as high as that of other mutually exclusive options. In most cases, this criterion is equivalent to requiring that the expected IRR exceed the opportunity cost of capital. The expected value, calculated by weighting all possible project outcomes with their corresponding relative frequencies or probabilities, takes account of the entire range of possible present values of net benefits from the project. For instance, the expected NPV of the following project is 3.6.

NPV versus Best Estimates

We often refer to the NPVs and IRRs reported in project appraisal documents as best estimates, sometimes meaning expected, and sometimes meaning most likely, values. The expected value, or mean, is not the same as the most likely value, or mode. The mode is the most frequently occurring value, or the most likely value, among all the possible values the NPV can take. Although for some statistical distributions the mode and the mean  coincide, often they do not. In the example, the mode—the value with the highest probability—is 7, whereas the mean is only 3.6.

Unfortunately, the use of modal values instead of means seems to be somewhat common. In many cases, analysts choose the most likely values for quantities, prices, and other uncertain variables. This approach may lead to wrong decisions, because the sum of most likely values is not always the most likely value of the sum.