# Sensitivity Analysis Definition

## What Is Sensitivity Analysis?

Sensitivity analysis determines how different values of an independent variable affect a particular dependent variable under a given set of assumptions. In other words, sensitivity analyses study how various sources of uncertainty in a mathematical model contribute to the model's overall uncertainty. This technique is used within specific boundaries that depend on one or more input variables.

Sensitivity analysis is used in the business world and in the field of economics. It is commonly used by financial analysts and economists and is also known as a what-if analysis.

### Key Takeaways

• Sensitivity analysis determines how different values of an independent variable affect a particular dependent variable under a given set of assumptions.
• This model is also referred to as a what-if or simulation analysis.
• Sensitivity analysis can be used to help make predictions in the share prices of publicly traded companies or how interest rates affect bond prices.
• Sensitivity analysis allows for forecasting using historical, true data.
• While sensitivity analysis determines how variables impact a single event, scenario analysis is more useful to determine many different outcomes for more broad situations.
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## How Sensitivity Analysis Works

Sensitivity analysis is a financial model that determines how target variables are affected based on changes in other variables known as input variables. It is a way to predict the outcome of a decision given a certain range of variables. By creating a given set of variables, an analyst can determine how changes in one variable affect the outcome.

Both the target and input—or independent and dependent—variables are fully analyzed when sensitivity analysis is conducted. The person doing the analysis looks at how the variables move as well as how the target is affected by the input variable.

Sensitivity analysis can be used to help make predictions about the share prices of public companies. Some of the variables that affect stock prices include company earnings, the number of shares outstanding, the debt-to-equity ratios (D/E), and the number of competitors in the industry. The analysis can be refined about future stock prices by making different assumptions or adding different variables. This model can also be used to determine the effect that changes in interest rates have on bond prices. In this case, the interest rates are the independent variable, while bond prices are the dependent variable.

Sensitivity analysis allows for forecasting using historical, true data. By studying all the variables and the possible outcomes, important decisions can be made about businesses, the economy, and making investments.

Investors can also use sensitivity analysis to determine the effects different variables have on their investment returns.

## Usefulness of Sensitivity Analysis

Financial models that incorporate sensitivity analysis can provide management a range of feedback that is useful in many different scenarios. The breadth of the usefulness of sensitivity analysis includes but is not limited to:

• Understanding influencing factors. This includes what and how different external factors interact with a specific project or undertaking. This allows management to better understand what input variables may impact output variables.
• Reducing uncertainty. Complex sensitivity analysis models educate users on different elements impacting a project; this in turn informs members on the project what to be alert for or what to plan in advance for.
• Catching errors. The original assumptions for the baseline analysis may have had some uncaught errors. By performing different analytical iterations, management may catch mistakes in the original analysis.
• Simplifying the model. Overly complex models may make it hard to analyze the inputs. By performing sensitivity analysis, users can better understand what factors don't actually matter and can be removed from the model due to its lack of materiality.
• Communicating results. Upper management may already be defensive or inquisitive about an undertaking. Compiling analysis on different situations helps inform decision-makers of other outcomes they may be interested in knowing about.
• Achieving goals. Management may lay long-term strategic plans that must meet specific benchmarks. By performing sensitivity analysis, a company can better understand how a project may change and what conditions must be present for the team to meet its metric targets.

Because sensitivity analysis answers questions such as "What if XYZ happens?", this type of analysis is also called what-if analysis.

## Sensitivity vs. Scenario Analysis

In finance, a sensitivity analysis is created to understand the impact a range of variables has on a given outcome. It is important to note that a sensitivity analysis is not the same as a scenario analysis. As an example, assume an equity analyst wants to do a sensitivity analysis and a scenario analysis around the impact of earnings per share (EPS) on a company's relative valuation by using the price-to-earnings (P/E) multiple.

The sensitivity analysis is based on the variables that affect valuation, which a financial model can depict using the variables' price and EPS. The sensitivity analysis isolates these variables and then records the range of possible outcomes.

On the other hand, for a scenario analysis, an analyst determines a certain scenario such as a stock market crash or change in industry regulation. The analyst then changes the variables within the model to align with that scenario. Put together, the analyst has a comprehensive picture and now knows the full range of outcomes, given all extremes, and has an understanding of what the outcomes would be, given a specific set of variables defined by real-life scenarios.

## Advantages and Limitations of Sensitivity Analysis

Conducting sensitivity analysis provides a number of benefits for decision-makers. First, it acts as an in-depth study of all the variables. Because it's more in-depth, the predictions may be far more reliable. Secondly, It allows decision-makers to identify where they can make improvements in the future. Finally, it allows for the ability to make sound decisions about companies, the economy, or their investments.

There are some disadvantages to using a model such as this. The outcomes are all based on assumptions because the variables are all based on historical data. Very complex models may be system-intensive, and models with too many variables may distort a user's ability to analyze influential variables.

Pros
• Provides management different output situations based on risk or changing variables

• May help management target specific inputs to achieve more specific results

• May easily communicate areas to focus on or greatest risks to control

• May identify mistakes in the original benchmark

• Generally reduces the uncertainty and unpredictability of a given undertaking

Cons
• Heavily relies on assumptions that may not become true in the future

• May burden computer systems with complex, intensive models

• May become overly complicated which distorts an analysts ability to

• May not accurately integrate independent variables (as one variable may not accurately the impact of another variable)

## Example of Sensitivity Analysis

Assume Sue is a sales manager who wants to understand the impact of customer traffic on total sales. She determines that sales are a function of price and transaction volume. The price of a widget is $1,000, and Sue sold 100 last year for total sales of$100,000.

Sue also determines that a 10% increase in customer traffic increases transaction volume by 5%. This allows her to build a financial model and sensitivity analysis around this equation based on what-if statements. It can tell her what happens to sales if customer traffic increases by 10%, 50%, or 100%.

Based on 100 transactions today, a 10%, 50%, or 100% increase in customer traffic equates to an increase in transactions by 5%, 25%, or 50% respectively. The sensitivity analysis demonstrates that sales are highly sensitive to changes in customer traffic.

## What Is Sensitivity Analysis in NPV?

Sensitivity analysis in NPV analysis is a technique to evaluate how the profitability of a specific project will change based on changes to underlying input variables. Though a company may have calculated the anticipated NPV of a project, it may want to better understand how better or worse conditions will impact the return the company receives.

## How Do You Calculate Sensitivity Analysis?

Sensitivity analysis is often performed in analysis software, and Excel has built in functions to help perform the analysis. In general, sensitivity analysis is calculated by leveraging formulas that reference different input cells. For example, a company may perform NPV analysis using a discount rate of 6%. Sensitivity analysis can be performed by analyzing scenarios of 5%, 8%, and 10% discount rates as well by simply maintaining the formula but referencing the different variable values.

## What Are the Two Main Types of Sensitivity Analysis?

The two main types of sensitivity analysis are local sensitivity analysis and global sensitivity analysis. Local sensitivity analysis assesses the effect of a single parameter at a time while holding all other parameters constant, while global sensitivity analysis is a more broad analysis used in more complex modeling scenarios such as Monte Carlo techniques.

## What Is the Difference Between Sensitivity Analysis and Scenario Analysis?

Sensitivity analysis is the technique of taking a single event and determining different outcomes of that event. For example, a company may analyze its valuation based on several factors that may influence the calculation. On the other hand, scenario analysis relates to more broad conditions where the outcome is not known. For this example, imagine economists trying to project macroeconomic conditions 18 months from now.

## The Bottom Line

When a company wants to determine different potential outcomes for a given project, it may consider performing a scenario analysis. Scenario analysis entails manipulating independent variables to see the resulting financial impacts. Companies perform scenario analysis to identify opportunities, mitigate risk, and communicate decisions to upper management.

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1. Stanford University, Department of Aeronautics and Astronautics. "Chapter 4, Sensitivity Analysis," Pages 77.

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