Sensitivity analysis is a capital budgeting technique for computing measures of risk for a planned investment or action. It is a method for determining how sensitive a project’s value is relative to the changes in each of the variables in the analysis. It is done by changing each variable in turn and determining the effect on analysis results.

The purpose of sensitivity analysis is to identify the critical variables and to increase the understanding of the risks associated with a project. It is a way of assessing the relative importance of each variable with respect to the other variables.

## Why is Sensitivity Analysis needed?

To understand the need for sensitivity analysis, we first need to understand the impact of different variables on the net present value.

## What is Net Present Value

The net present value (NPV) is a measure of the present value of an investment. It is the present value of a future cash flow. In other words, it tells you how much money you can get today for a future cash flow. The future cash flow can be any amount, discounted back to the present.

The net present value is a part of investment appraisal and it, therefore, is based on forecasted figures. Forecasted figures are based on best estimates and these estimates can change in the future because as the time horizon increases, so does the uncertainty of forecasting. It is simply easier to forecast figures for the next year as compared to forecasting figures for the next six years because a lot of variables can change in the long term.

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Let us look at the NPV analysis of a project, to understand this with an example:

• Project outlay: \$1 million
• Cost of capital: 10%
• Period: 5 years
• Net receipts for each year: \$300,000
• Net present value: \$137,000

Here we can see that the net receipts figure has a lot of variables in it, such as

• Operational costs
• Inventory costs
• Taxation
• Depreciation
• Amortization
• Revenue

All of these variables can change because the forecast is for 5 years which is a long time period to predict anything with certainty. Even a slight change in any variable can increase or decrease the net present value, which can then have a significant impact on the decision-making.

For example, if the revenue is overestimated and in reality, the project can only generate 90% of the forecasted revenue, then it would reduce the net present value. Similarly, any variable can change and impact the net present value. This can create a lot of problems for the business, particularly if the business had to choose a project from a number of similar projects with similar net present values.

Let us continue the example by introducing multiple projects now.

• Project 1(Same as above)
• NPV: \$137,000
• Project 2
• NPV: \$150,000
• Project 3
• NPV: \$120,000

Based on these NPVs, the business would choose project 2 because it has got the highest NPV among the three projects being considered. Now let us assume that the sales revenue for these projects is subject to change due to uncertainties in forecasting.

As a result of this change, the new NPV for the three projects is

• Project 1
• NPV: \$130,000
• Project 2
• NPV: \$140,000
• Project 3
• NPV: \$145,000
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We can see that as a result of changes in sales revenue, in this scenario project 3 has the highest NPV and so if the business had chosen project 2 in the earlier scenario without carrying out sensitivity analysis, it would have made the wrong decision because project 2 is at a high risk of having its NPV reduced, or in other words project 2 is highly sensitive to negative changes in the sales revenue.

## Purpose of Sensitivity Analysis

The sensitivity analysis, therefore, tests the responsiveness or sensitivity of the NPV to critical factors that are linked with the project or proposal. Conducting a sensitivity analysis is

• A way of organizing analysis,
• A way of increasing understanding and insight into the situation.
• A way of determining the relative importance of each variable.
• A way of deciding which variables to concentrate on.
• A way of increasing the understanding of the situation

All of these benefits make the sensitivity analysis a good capital budgeting technique to understand the project or investment comprehensively. It is therefore a tool of helping the business in decision making, however, it is not a way of making or justifying a decision.

The sensitivity analysis takes the key assumptions that you have identified and tests them under different scenarios to see how they affect the final result. A typical sensitivity analysis will consider:

• Likelihood of an event occurring – high, medium or low.
• Magnitude of impact on the final result if your assumption changes.
• How likely that the impact will be in the positive or negative direction.
• How much change is required to make a significant impact.
• How much change is required to make a significant impact on the final result.
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There is a limitation to sensitivity analysis. The analysis, like the NPV calculation, is based on estimates and historical data. It analyzes what “may” or “may not” happen. It does not mean that the scenarios tested will definitely happen. This means that if we look at our earlier example if the sales revenue does not decrease then project 2 would be the best choice for the business.

So, what does sensitivity analysis tell us? It simply tells us about the risk that the business will be exposed to if the tested scenarios occur. It is up to the decision-makers to determine whether they are willing to take on the risk or not. Usually, businesses have risk thresholds and decisions are therefore made on the basis of sensitivity being within the threshold or not.