Experts use sensitivity analysis to determine how different values in a set of independent variables will affect a particular dependent variable.

Economists and financial analysts use sensitivity analysis to predict a company’s stock price or to see the effect of interest rates. In this article, we cover what sensitivity analysis is and how it can be used, compare it to scenario analysis and give you an example of how you can use it.

**Contents**

**1**What is sensitivity analysis?

**2**Methods to apply sensitivity analysis

**2.1**Direct method

**2.2**Indirect method

**3**Differences between sensitivity analysis and scenario analysis

**4**Benefits of sensitivity analysis

**5**Uses of what-if analysis

**6**Examples of sensitivity analysis

**6.1**Example 1

**6.2**Example 2

**What is sensitivity analysis?**

Sensitivity analysis also referred to as *what-if analysis*, is a mathematical tool used in scientific and financial modeling to study how uncertainty in a model affects the overall uncertainty of that model.

It is a way of determining different values for an independent variable that can be done to influence a certain dependent variable, with a certain set of assumptions.

You can use sensitivity analysis when there are constraints depending on the input variable and when you want to answer questions like:

- Would the results of the study change if we used other assumptions?
- How sure are we of this assumption?

You can use sensitivity analysis to learn how certain changes will affect you. For example, if you want to know whether a change in the interest rate will affect the price of the bond if the interest rate increases by 2%. You can turn it into a “what if” statement:

“What happens to the cost of bonds if interest rates go up 2%?”

**Methods for applying sensitivity analysis**

The following two methods are used for sensitivity analysis:

**Direct method**

In the direct method, you will substitute different numbers into assumptions in the model. For example, assuming your revenue growth is 20% year over year, then the income formula would be:

**(Last year’s income) x (1 + 20%)**

Using the direct method, we substitute different numbers to substitute for the growth rate to see how much revenue is generated.

**Indirect method**

In the indirect method, you enter the percent change into the formula instead of changing the assumed value directly. For example, if your assumed revenue growth is 20% year over year and we know that the income formula is:

**(Last year’s income) x (1 + 20%)**

Instead of converting 20% to another number, we change the formula to:

**(Last year’s income) x (1 + (20% + X)), where X is the value in the model sensitivity analysis area.**

**Difference between sensitivity analysis and scenario analysis**

Sensitivity analysis can predict the outcome of an event given a given range of variables, and an analyst can use this information to understand how changes in one variable affect another variable or outcome. Sensitivity analysis can isolate certain variables and show a range of results.

However, scenario analysis determines what will happen during certain situations, such as a change in industry regulations or a stock market crash. An analyst can use information specific to a particular scenario to change the variables in the model, providing an understanding of the results for a particular real-life situation.

**Benefits of sensitivity analysis**

There are several benefits to using sensitivity analysis. It is important to remember that sensitivity analysis uses a set of results based on assumptions and later variables, based on historical data.

As such, *the what-if analysis* is a model with room for error and may not be completely accurate, but it is a valuable and widely used tool.

**The main benefits of using what-if analysis are:**

**Better decision making:**Sensitivity analysis provides decision-makers with a variety of results to help them make better business decisions.**More reliable predictions:**It provides an in-depth study of the variables that make predictions and models more reliable.**Highlight areas for improvement:**Sensitivity analysis helps decision-makers identify where to make improvements in the future.**Provides a higher degree of credibility:**Sensitivity analysis adds credibility to a financial model by testing it across multiple contingencies.

**Uses ***of what-if analysis*

*of what-if analysis*

There are multiple uses for *what-if analysis* across many careers and industries. Many situations require the use of sensitivity analysis to forecast, predict, identify areas of improvement or make adjustments. Following are some common applications of sensitivity analysis:

- Understand how input variables relate to output variables
- Generating hypotheses to test certain scenarios
- Make recommendations
- Communicating data and results
- Identifying break-even points, critical values, and optimal strategy changes
- Feasibility testing for ideal solutions
- Estimating the need for output and input variables
- Measuring parameters
- Making assumptions to enable decision making
- Assessing the amount of risk for a scenario or strategy
- Identify sensitive variables
- Develop recommendations

**Example of sensitivity analysis**

Here are two hypothetical examples of when *what-if analysis* could be used:

**Example 1**

Peter sells backpacks at a kiosk in the mall. He knew the back-to-school rush would begin in August, and he wanted to determine whether increased customer traffic at the mall would increase his sales revenue and, if so, by how much.

The average price of a backpack that Peter sells is 40,000. Last month, during his busy return to school, he sold 250 backpacks, making 10,000,000 sales. After using a spreadsheet software program, Peter found that when customer traffic at the mall increased by 20%, there was a 14% increase in his sales.

Now that Peter knows this information, he can use it to predict how much his sales revenue will increase or decrease. If customer traffic increases to 40%, his sales should increase by 28%. If customer traffic is down 10%, then sales should be down 7%.

**Example 2**

Jane is a sales manager and wants to better understand how an increase in holiday shoppers affects total sales for her department. Using data from last year’s holiday sales, Jane learns that total holiday sales is a function of transaction volume and price. He determined that when holiday shoppers increase 10%, then sales increase 5%.

Jane can build financial models and use *what-if analysis reports* using this information. Based on this, Jane now understands that if the increase in holiday shoppers is 50%, total sales must increase by 25%.