Sensitivity Analysis (Definition, Formula)

What is Sensitivity Analysis?

Sensitivity analysis is an analysis technique that works on the basis of what-if analysis like how independent factors can affect the dependent factor and is used to predict the outcome when analysis is performed under certain conditions. It is commonly used by investors who takes into consideration the conditions that affect their potential investment to test, predict and evaluate result.

Sensitivity Analysis Formula

The formula for sensitivity analysis is basically a financial model in excel where the analyst is required to identify the key variables for the output formula and then assess the output based on different combinations of the independent variables.

Mathematically, the dependent output formula is represented as,

Z = X² + Y²

Calculation of the Sensitivity Analysis (Step by Step)

Step 1: Firstly, the analyst is required to design the basic formula which will act as the output formula. For instance, say NPV formula can be taken as the output formula.
Step 2: Next, the analyst needs to identify which are the variables that are required to be sensitized as they are key to the output formula. In the NPV formula in excel, the cost of capital and the initial investment can be the independent variables.
Step 3: Next, determine the probable range of the independent variables.
Step 4: Next, open an excel sheet and then put the range of one of the independent variable along the rows and the other set along with the columns.

- Range of 1^st independent variable
- Range of 2^nd independent variable
Step 5: Next, go to the “Data” tab and click on the “What-if Analysis” button. Under that select the option of “Data Table”.
Step 6: Next, fill in the “Row input cell” with the reference to the 1^st independent variable and the “Column input cell” with the reference to the 2^nd independent variable.
Step 7: Finally, click enter for the table to take effect and present the probable outcomes. The table hence created is the sensitivity table.

Examples

You can download this Sensitivity Analysis Formula Excel Template here – Sensitivity Analysis Formula Excel Template

Example #1

Let us take the example of a simple output formula which is stated as the summation of the square of two independent variables X and Y.

In this case, let us assume the range of X as 2, 4, 6, 8, and 10, while that of Y as 1, 3, 5, 7, 9, 11, and 13. Based on the above-mentioned technique, all the combinations of the two independent variables will be calculated to assess the sensitivity of the output.

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For instance, if X = 3 (Cell B2) and Y = 7 (Cell B3), then Z = 3² + 7² = 58 (Cell B4)

Z = 58

For the calculation of Sensitivity Analysis go to the data tab in excel and then select What if analysis option. For the further procedure of sensitivity analysis calculation refer to the given article here – Two-Variable Data Table in Excel

Example #2

Let us take another example of bond pricing where the analyst has identified the coupon rate and the yield to maturity as the independent variables and the dependent output formula is the bond price. The coupon is paid half-yearly with a par value of $1,000 and the bond is expected to mature in five years. Determine the sensitivity of the bond price for different values of coupon rate and yield to maturity.

In this case, the analyst has taken the range of coupon rate as 5.00%, 5.50%, 6.00%, 6.50%, and 7.00%, while that of coupon rate as 5%, 6%, 7%, 8%, and 9%. Based on the above-mentioned technique, all the combinations of yield to maturity and coupon rate are taken to calculate the sensitivity of the bond price.

Therefore, the calculation of Bond Price is as follows

Bond Price =$102,160

For the calculation of Sensitivity Analysis go to the Data tab in excel and then select What if analysis option.

Relevance and Uses

A sensitivity analysis is a technique which uses data table and is one of the powerful excel tools which lets a financial user understand the result of the financial model under various conditions. It can also be seen as the perfect complement to another excel tool which is known as the scenario manager and as such it adds more flexibility to the valuation model during the process of analysis and finally in case of the presentation.

As such, it is very important for an analyst to appreciate the method of creation of a data table and then interpret its results to ensure that the analysis is heading in the desired direction. Further, a data table can be an effective and efficient way for presentation to the boss or client when it comes to expected financial performance under different circumstances.

Sensitivity Analysis