# Sensitivity Analysis

2 February 2017

Sensitivity analysis is a technique that indicates exactly how much a project’s profitability (NPV or IRR) will change in response to a given change in a single input variable, other things held constant. Sensitivity analysis begins with a base case developed using expected values (in the statistical sense) for all uncertain variables. Then, each uncertain variable is usually changed by a fixed percentage amount above and below its expected value, holding all other variables constant at their expected values. Thus, all input variables except one are held at their base case values.

The resulting NPVs (or IRRs) are recorded and plotted. Although sensitivity analysis is widely used in project risk analysis, it does have severe limitations. If an input variable is not expected to vary much (is relatively certain), a project would not be very risky even if a sensitivity analysis showed NPV to be highly sensitive to changes in that variable. In general, a project’s stand-alone risk, which is what is being measured by sensitivity analysis, depends on both the sensitivity of its profitability to changes in key input variables as well as the ranges of likely values of these variables.

## Sensitivity Analysis Essay Example

Because sensitivity analysis considers only the first factor, it can give misleading results. Furthermore, sensitivity analysis does not consider any interactions among the uncertain input variables; it considers each variable independently of the others. In spite of the shortcomings, sensitivity analysis does provide managers with valuable information. First, it provides profitability breakeven information for the project’s uncertain variables. Second, sensitivity analysis tells managers which input variables are most critical to the project’s profitability, and hence to the project’s financial success.

With such variables identified, managers can spend the most time forecasting the variables that “count,” so the resources expended in the analysis can be as productive as possible. Scenario analysis is a stand-alone risk analysis technique that considers the sensitivity of NPV to changes in key variables, the likely range of variable values, and the interactions among variables. To conduct a scenario analysis, managers pick a “bad” set of circumstances (i. e. , low volume, low salvage value, and so on), an average or “most likely” set, and a “good” set.

The resulting input values are then used to calculate NPVs for several “scenarios,” usually three. With NPVs for the worst, most likely, and best cases, managers can get a feel for the variability of the profitability of a project that results from uncertainty. Specifically, if probabilities are attached to the scenarios, a standard deviation of NPV can be calculated. While scenario analysis provides useful information about a project’s stand-alone risk, it is limited in two ways. First, it only considers a few discrete states of the economy, and hence provides information on only a few potential profitability outcomes for the project.

In reality, an almost infinite number of possibilities exist. Scenario analysis typically contains only three outcomes, but it could be expanded to include more states of the economy, say, five or seven. However, there is a practical limit on how many scenarios can be included in a scenario analysis. Second, scenario analysis—at least as normally conducted—implies a very definite relationship among the uncertain variables. That is, it assumes that all the worst case input values occur at the same time, because the worst case scenario is defined by combining the worst possible value of each uncertain variable.

Although this relationship (all worst values occurring together) may hold in some situations, in others it may not hold. The same circumstances occur in the best case. Thus, scenario analysis tends to create extreme profitability values for the worst and best cases because it automatically combines all worst and best input values, even if these values actually have only a remote chance of occurring together. Some projects are evaluated on the basis of minimizing the present value of future costs rather than on the basis of the projects’ NPVs.

This is done because it is often impossible to allocate revenues to a particular project; and it is easier to focus on comparative costs when two projects will produce the same revenue stream. In a conventional analysis, when inflows are being discounted, a higher discount rate leads to a lower present value, which penalizes an inflow for higher risk. However, to penalize an outflow for higher risk, the outflow must have a higher present value, not a lower one. Therefore, a cash outflow that has higher-than-average risk must be evaluated with a lower-than-average cost of capital. 15.

The corporate cost of capital is the opportunity cost rate that reflects the overall risk and debt utilization (capacity) of the business. Thus, the corporate cost of capital is the appropriate discount rate only for projects that have risk and debt capacity characteristics that match the business in the aggregate. The project cost of capital is the appropriate opportunity cost (discount rate) for a particular project. For projects with risk and debt capacity characteristics similar to the firm in the aggregate, the project cost of capital is the same as the corporate cost of capital.

However, projects with different characteristics will have a project cost of capital that differs from the corporate cost of capital. In general, projects with greater-than-average risk will have a project cost of capital that is greater than the corporate cost of capital, and projects with lower-than-average risk will have a project cost of capital that is less than the corporate cost of capital. Although debt capacity differences should be considered, in practice such differences are rarely recognized

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