In the world of business, there are many variables, uncertainties, and risks. These factors affect the decision-making process in companies and sometimes make the procedure of doing business much more difficult.

A sensitivity analysis is a tool that businesses use to help them plan for the future. It’s a study of the effect that changes in an independent variable can have on a dependent variable, given certain assumptions. For example, how can changes in customer traffic in a bookstore affect sales revenue?

Let’s look at a few other examples where this can be a helpful tool. Maybe you want to know the effect that a 1% increase in the cost of raw materials will have on your profit.

Or maybe you have a business on Facebook, and want to run a promotional ad. You want to know how much to spend on the ad in order increase your customers and sales.

In all of these examples, a sensitivity analysis can help figure out the answer.

Usually, sensitivity analyses are used by financial analysts to create forecasting models. But this tool isn’t only applied in business. It can also be used in the social sciences, engineering and chemistry, as well as other fields and industries.

# Reasons for Using a Sensitivity Analysis

There are numerous benefits to running a sensitivity analysis. Some of the main reasons that a business will spend the time to apply this process are:

- Testing the robustness of a model given uncertainty.
- Studying the correlations between varying inputs and outputs.
- Communicating models to managers or clients effectively.
- Determining variables which have a large impact on outcome.
- Deciding if you can ignore the changing circumstances.
- Considering only the optimal scenario.
- Developing a hypothesis to test.
- Helping implement preventative actions to avoid harmful effects.

## Sensitivity Analysis vs Scenario Analysis

Sensitivity analysis and scenario analysis are both ways to assess the effect of variables on outcomes in cases of uncertainty. A sensitivity analysis separates all the variables and determines the changes in the outcomes, based on each individual input.

A scenario analysis, on the other hand, looks at the effects of an extreme situation, such as an industry disruption. In this analysis, variables are tailored according to the specific scenario.

So a sensitivity analysis provides a full range of possible outcomes based on a number of changing variables. A scenario analysis gives a thorough picture of what the outcome will be in the case a specific situation.

Each one of these two types of analyses serves their own. When combined together, an analyst can have an even better understanding of outcome variations in the future.

## Sensitivity Analysis in Decision-Making

Usually, decision-makers carry out a sensitivity analysis to better understand which variable will have a major effect on the outcome. It can be especially useful when assessing the risk of an investment. Since decision-making can be very difficult in the face of uncertainty, sensitivity analyses are extremely useful processes.

Sensitivity analyses provide a series of possible outcomes which help decision-makers understand the uncertainties. They can then understand the pros and cons of a decision model.

One method of conducting a sensitivity analysis is to replace uncertainties with expected values.This enables the decision-makers to determine how sensitive the outcome is to variations in inputs.

## Sensitivity Analysis in Financial Analysis

Sensitivity analysis is a tool that is widely used by investment bankers, since it has many uses, including:

- Assessing the impact on valuation as assumptions change.
- Determining macroeconomic impacts on the business value.
- Providing different valuations under changing scenarios.
- Testing the functionality of a financial model rate of customers
- Ensuring that assumptions are working as intended.

## What-if Analysis

In finance, a sensitivity analysis is often referred to as a what-if analysis or a simulation analysis. This is the technique used to make a decision based on a comparison to other potential decisions. Since this technique creates assumptions about a number of variables, such a comparison identifies the optimal outcome.

So a financial analyst can use a what-if analysis to make a business decision. It may be helpful to consider an example. Will posting an advertisement for a bookstore in a specific street location increase sales revenue?

The analyst can make assumptions about a range of variables. How many people will see the ad? How much traffic is on the street? What is the rate of customers entering the store from that location?

Analyzing these factors will all help to determine what impact the advertisement will have on sales revenue.

# Methods of Sensitivity Analysis

There are various methods and techniques of conducting a sensitivity analysis. Regarding methodology, sensitivity analyses can be done through model and simulation or scenario management tools.

In addition, different techniques are used. These include: differential analysis, factorial analysis, one at a time sensitivity measures, correlation analysis, and subjective sensitivity analysis.

You can also categorize the methods that the type of analysis conduct. This could be a mathematical, statistical, or graphical method. The industry and the purpose of the analysis will help you determine which method should be used.

A mathematical analysis involves calculating the outcome for different input values representing a possible range of inputs. It also determines the level of sensitivity of the output to variance in the input.

Mathematical analyses can include break-even analysis, nominal range sensitivity analysis, difference in log-odds ratio and automatic differentiation.

During statistical analysis, data is run in simulations. Inputs are assigned probability distributions, and the effect of variance on the output distribution is evaluated. Types of statistical analysis include: regression analysis, analysis of variance, response surface methods, among others.

Graphical analysis entails displaying the sensitivity in graphs and charts. This method provides a visual representation of the effect the variance in inputs has on the output. Graphical analysis can be used in combination with mathematical or statistical analysis.

This allow the data to be represented in a more visually attractive manner. It may also make it easier for decision-makers to understand.

# Steps for Conducting a Sensitivity Analysis

We will now walk you through the specific steps involved in this process.

### 1. Identify the Important Variables and Assumptions

Here, you pick which variables will likely affect the outcome. You should be careful not to include variables that will have a minimal or no effect on the outcome.

For example, you want to study the impact of population increase on the quality of education in a certain country. One of the most important variables would be the education budget. On the other hand, the public's political inclinations aren’t relevant to this outcome.

### 2. Choose the Correct Metric

The validity of your analysis depends on choosing the output metric from the beginning. You need to experiment and study the problem that you want to solve.

For example, you are analyzing data to decide if posting ads on Facebook will increase a product’s brand recognition. You will take different variables into consideration, such as how many people the ad will reach.

However, you might discover that brand recognition isn’t directly related to profit. In this case, you should have been looking at sales revenue in relation to ads, rather that brand recognition. Choosing the right output metric will save you time, so you don’t focus your analyses on the wrong measures.

### 3. Set up a Baseline

When you’re analyzing data and variance effects on outputs, you will need to measure percentage changes. This means you will need to establish baselines, and then measure changes against these.

Let’s use the example of measuring the effect of variance in customer traffic in a bookstore on sales revenue. The baseline may be the relationship between customer traffic and revenue at this time last year.

### 4. Identify Maximum and Minimum Value

For each variable, you will need to set a maximum value and a minimum value. This is sometimes known as the best case scenario and worst case scenario. The maximum value represents the optimal situation, the worst case value is the baseline. You can’t go below the baseline.

For example, your baseline for the sales revenue would be 5 million dollars if this was last year’s sales revenue. This number is the worst case value. On the other hand, 8 million dollars, for example, might be the best case value.

### 5. Data Analysis and Visualization

At this stage you start the actual work of analyzing the numbers. Whether you use Excel or any other statistical analysis software, you will either mathematically or statistically analyze data. As we mentioned earlier, it's a good idea to use graphs or charts for better representation of the data analysis.

# Summing Up

A sensitivity analysis can be a very useful tool in any field. While we often think of is as a business tool, it can be used in finance, engineering or any field of science. To make the best use out of it, you should learn all its approaches and methods.

Learning how to conduct a sensitivity analysis will help you understand the different possible outcomes, and make better decisions.