Sensitivity analysis using Invest Sign

Given the uncertainty that is attached to parameters of the project, sensitivity analysis is a useful tool for the analysis of projects. Sensitivity analysis is used to help identify the key variables to which project is most sensitive and to take actions to ensure, that unfavorable shifts in these variables do not occur. It involves recalculating the project results for different values of major variables where they are varied one at a time. 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 NPV;

   interpreting the results.

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 or market price of a project item. The effect of the estimated ratios on the project worth is investigated through sensitivity analysis.

More about variables

Some of the variables entering into the project costs and benefits 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.

Quantities of outputs and inputs can also be affected by changes in technical or market conditions. Quantities should be broken down into their underlying components. 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.

Changes in the major values in the project statements the main outputs, inputs, and investment costs may 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. 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.

Results of the analysis

The results of the foregoing sensitivity analysis should be reviewed considering the following questions:

• Which are the variables with high sensitivity?

• 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. 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.

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, or sector 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;

• 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.

Sensitivity Analysis: An Example

Project example, listed below, is used here to illustrate the application of sensitivity analysis. For more information on running Sensitivity analysis on Invest Sign refer to article How Do I Run a Sensitivity Simulation. This example is for teaching purposes to use Invest Sign, so only a few key factors are selected.
The project involves a predicted increase of administrative wages, direct material costs and transportation expenses. The base case result, NPV is 43 104 euro at 10 percent discount and 5 percent reinvestment rate. The main variables to which the base case may be sensitive, together with the possible changes in those variables, are selected as follows:

   On the basis of previous projects, there is uncertainty on administration wages. Postevaluation studies indicate the possibility on wages increase or a little decrease and one more sales manager could be needed to reach the project goals, so the administrative wages can change from -3 to 4 percent.

   The forecast price of new technology network swichers to be key variable in the project analysis, as the project will increase the quantity of swichers output. In the sensitivity analysis, the forecast price of network swichers, which declines over the five years of the project anyway, is predicted to follow the same pattern but to be at the level of the lower range of the 30 percent distribution given together with the basic market price forecasts. This is equivalent to a price 4 percent lower than in the base case.

   Other variables are also included in the sensitivity analysis. The effect of 0 to 4 percent higher direct material cost is tested. The project benefits depend on ability to have good supply contracts. Finally, some combinations of variables are also tested.

Invest Sign allows to export these and other financial reports to selected format (MS word, Excell or others) to give better opportunity to analyse and use data. In this example, we exported Indexes of Sensitivity Analysis tables. The results of these sensitivity tests on underlying and specific benefit and cost factors are given in Tables 1, 2, 3.

Table 1. Indexes of Sensitivity Analysis by changing direct material costs

Table 2. Indexes of Sensitivity Analysis by changing Administrative Wages

Table 3. Indexes of Sensitivity Analysis by changing Selling Price

In each case you can look at percent change of NPV when variable changes by one percent:

User can use other combinations of key factors to see sensitivity by running simulation or only changing value of them by percent.