4. Sensitivity analysis is undertaken to help identify the key variables that can influence the project cost and benefit streams. It involves recalculating the project results for different values of major variables where they are varied one at a time. Combinations of changes in values can also be investigated. Sensitivity analysis involves four steps:
selecting those variables to which the project decision may be sensitive;
determining the extent to which the value of such variables may differ from the base case;
calculating the effect of different values on the project results by recalculating the project NPV and EIRR; and
interpreting the results and designing mitigating actions.
5. Project statements are made up from underlying project data and assumptions. For example, vehicle operating cost savings are made up from traffic projections for different proportions of vehicle type, their division into without project and generated traffic, data on road quality and maintenance operations, and data on the vehicles and their operating costs. Sensitivity analysis of the project benefits for a road improvement project should be based on changes in such underlying variables rather than the aggregate benefit measure. Focusing on underlying rather than aggregate variables facilitates the design of actions to mitigate against uncertainty.
6. Some of the variables entering into the project cost and benefit streams will be predictable and small in value compared with total costs and benefits. It is not necessary to investigate the sensitivity of the project to such variables. Other variables may be larger and less predictable. Postevaluation studies and previous project experience may indicate both the type of variable that is uncertain and the likely extent of divergence from the base case value. There are some types of variable in every project that are likely to affect the project result and may be key variables for the project.
7. The quantities of inputs required to produce the expected quantity of outputs will be given in the corresponding technical feasibility study. However this is often subject to considerable uncertainty. Inadequate supplies or maintenance can change the ratio between inputs and outputs and reduce project outputs. In addition, the quantity of output produced for a given set of input supplies will depend upon the incentives created for producers. Changes in management, improved skills, and financial returns to the producer will all influence the output produced from the available inputs. Consideration should be given to both the technical and institutional characteristics of the project as a guide to sensitivity analysis.
8. Quantities of outputs and inputs can also be affected by changes in technical or market conditions. Quantities should be broken down into their underlying componentsfor example, agricultural outputs into areas and yields, or vehicle cost savings by type of vehicle, or construction costs into unit costs and quantitiesand the sensitivity of the project to each of the components considered. Output quantities will also depend upon demand forecasts and market analyses. The underlying assumptions of these forecasts and analyses should be subject to sensitivity analysis. 9. Changes in the major values in the project statementsthe main outputs, inputs, and investment costsmay occur because of changes in prices for any of these items. Changes can occur in the market prices or shadow prices used in calculating costs and benefits directly or used in the
estimation of opportunity costs. Commodity prices for major outputs and inputs can fluctuate considerably from year to year. The influence of the average annual forecast prices on the project worth should be tested by varying the forecasts, which should take into account the effect of possible changes in the quality of outputs over time on prices. The prices of labor and nontraded goods can also be subject to change although these might not have the same degree of impact on the project worth.
10. The timing and coordination of project activities may differ from the basecase. The timing of investment costs that occur early in the project life can affect the measure of project worth considerably. Alternative timings incorporating pessimistic assumptions about construction delays should be assessed. Different investment components need to be coordinated, for example, dam completion and resettlement in irrigation projects. The possible costs of delay in one investment component on the others should be investigated through alternative timing assumptions.
11. Project results can be seriously affected by the extent to which the investment assets are utilized. Lower utilization rates than in the basecase will be reflected in lower output levels and lower operational costs, but without any decline in investment costs. Utilization is commonly expressed as a percentage of feasible capacity use. The effects of a reduction in the rate of utilization should be investigated through adjustments to both benefit and cost streams, where possible distinguishing between fixed and variable costs.
12. Economic analyses of projects involve the estimation of opportunity costs for the outputs and inputs. In most calculations economic costs and benefits are calculated by using the ratio of the shadow price of a project item, or the resources that go into it, to its market price. The effect of the estimated ratios on the project worth should be investigated through sensitivity analysis. Except for the most labor intensive projects, it is rare that a project result would be significantly affected by a variation of the shadow wage rate for surplus labor; and for most projects, variation in the shadow wage rate for scarce labor is also unlikely to be significant. More significant will be the value assumed for the shadow exchange rate (SER) and therefore the shadow exchange rate factor (SERF), or the standard conversion factor (SCF), whichever numeraire is being used in the economic analysis. Alternative estimates of the SERF will affect both benefits and costs in the sensitivity analysis. Most simple estimates of the SERF (SCF) take account only of the tax and subsidy system and not of other factors separating financial and economic prices, such as monopoly rents; it is pertinent to include in the sensitivity analysis a higher value for the SERF (lower value for the SCF).
III.
P
ROCEDURE13. The following procedure should be followed when assessing the consequences of changes from base case values of major variables.
Variables to which the project is likely to be sensitive, such as those referred to above, and for which there is some uncertainty, should be listed. Alternative
values should be assumed, based on previous project data where available. The change in the value of the variable should be calculated and expressed as a percentage of the original value. The extent of change should be stated for those variables such as timing of activities where a percentage change is not meaningful. The project NPV and EIRR should be recalculated for stated changes in variables one at a time. Unless a different country estimate is available, the NPV should be calculated using an economic discount rate of 12 percent.
A sensitivity indicator (SI) summarizing the effect of change in a variable on the project NPV should be calculated. The SI is calculated as the ratio of the percentage change in the NPV to the percentage change in a variable (see Addendum). A high value for this indicator indicates project sensitivity to the variable. For variables where percentage changes are not meaningful, the percentage change in the NPV should be stated along with the stated change in the variable.
A switching value (SV) should also be calculated. Where the base case shows a positive NPV, the SV shows the percentage increase in a cost item (decline in a benefit item) required for the NPV to become zero (which is the same as the EIRR reducing to the cut-off level of 12 percent). The SV is itself a percentage, the percentage change in a variable for the project decision to change (see Addendum). It can be compared with the variation shown in postevaluation studies or in price forecasts. For many variables, the SV will be high, implying a very substantial change in the variable before the project decision is affected. For a few variables, the SV will be relatively low showing there may be a significant risk for the project outcome.
In deriving the economic costs and benefits of a project, a SERF (or SCF) will have been used along with other general conversion factors. Sensitivity analysis should include changes in the SERF (SCF) and other general conversion factors to see to what extent the project results are sensitive to the conversion factors used in the analysis.
The change in the NPV should be calculated for combinations of variables, for example, a lower level of demand and a delay in investment completion, or an increase in cost together with a lower output price. The rationale for any combination of variables should be stated, bearing in mind that changes in more than one variable may have a common cause.
The results of the sensitivity analysis should be presented in a table showing the base case results, the change in each variable considered, the sensitivity indicator, the switching value, and the changes in project worth for cases where these indicators cannot be calculated, or for combinations of variables. The table should include the consequences of alternative values relating to all technical, economic, environmental, and distributional aspects of the project.
14. The results of the foregoing sensitivity analysis should be reviewed considering the following questions:
Which are the variables with high SIs?
Have the calculations used the likely changes in these variables?
Do the likely changes come close to, or exceed, the switching values that will change the project decision?
How likely is it that the combinations of the variables investigated will occur? These questions will help identify the truly key variables for the project, those that have a substantial effect on the project results, where plausible changes come close to or exceed their switching values. For the key variables identified in this way, a statement should be made of the likelihood of the variation tested actually occurring, the switching values for the key variables that should provide a basis for project monitoring, and the measures that could be taken to mitigate or reduce the likelihood of such variations from the basecase.
15. Where projects are seen to be sensitive to specific variables, steps should be taken to reduce the extent of uncertainty surrounding those variables. This may require actions at the project, sector, or national level, for example:
At the project level
the agreement of long-term supply contracts at specified quality and prices to reduce uncertainty over operating costs;
the formulation of training activities to ensure technical ratios are achieved and maintained;
the development of information or publicity programs to increase access and use of new goods or services;
the incorporation of external effects into project costs through regulation or taxation to ensure they are taken into account; and
where there is considerable uncertainty in a large project or program, the implementation of a pilot project or phase to test technical assumptions and to observe users reactions.
At the sector level
tariff and price adjustments to ensure appropriate incentives for producers and the financial liquidity of implementing agencies;
technical assistance programs to develop project and operational management skills; and
At the national level
changes in tax and credit policy to influence incentives and simplify procedures; implementation of legislative reform and regulation to provide a more certain
framework for productive activities; and
changes in exchange rate and fiscal management to provide greater stability in prices and costs.