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 commonly used in business and economics by financial analysts and economists.
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 for broader situations.
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 and 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 ratio (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, 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 investments. Investors can also use sensitivity analysis to determine the effects different variables have on their investment returns.
The Lifeblood of Business Decisions: The Usefulness of Sensitivity Analysis
Financial models that incorporate sensitivity analysis can provide management with a range of feedback useful in various scenarios. The breadth of the usefulness of sensitivity analysis includes:
- Understanding influencing factors: This includes understanding how different external factors interact with a specific project or undertaking. Management can better understand which input variables may impact output variables.
- Reducing uncertainty: Complex sensitivity analysis models educate users about different elements impacting a project, informing team members about what to be alert to or plan for.
- Catching errors: Initial assumptions may contain errors. By performing various analytical iterations, management may catch mistakes in the initial analysis.
- Simplifying the model: Overly complex models may make input analysis difficult. Sensitivity analysis helps users identify insignificant factors that can be removed.
- Communicating results: Sensitivity analysis helps communicate different potential outcomes to upper management, aiding clarity and informed decision-making.
- Achieving goals: By performing sensitivity analysis, a company can better understand project changes and the conditions necessary to meet metric targets.
Sensitivity vs. Scenario Analysis: Diving Deeper into Outcomes
In finance, sensitivity analysis delivers insights into the impact of a range of variables on a given outcome. It’s crucial to distinguish this from scenario analysis. For example, suppose an equity analyst wants to perform a sensitivity analysis and a scenario analysis around the impact of earnings per share (EPS) on a company’s valuation using the price-to-earnings (P/E) multiple.
In sensitivity analysis, EPS and other valuation-affecting variables are isolated and assessed for their range of potential outcomes. Scenario analysis, in contrast, involves defining specific scenarios like a stock market crash or regulatory shift and adjusting the model to align with these scenarios. Taken together, analysts get a comprehensive understanding of outcomes, ranging from best to worst-case scenarios.
Pros and Cons: Balancing the Advantages and Limitations
Sensitivity analysis offers several advantages:
Pros:
- Provides management with different output situations based on risk or changing variables.
- Helps management target specific inputs to achieve more specific results.
- Communicates focus areas or the greatest risks to control.
- Identifies mistakes in the original benchmark.
- Reduces uncertainty and unpredictability in a given undertaking.
However, there are some limitations:
Cons:
- Heavily relies on assumptions that might not be accurate in the future.
- Can burden computer systems with complex, intensive models.
- May be overly complicated, distorting the analyst’s ability to evaluate influential variables.
- Might not accurately integrate independent variables since one variable might not reflect another’s impact.
Inspiring Confidence: An Example of Sensitivity Analysis
Imagine Sue, 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, resulting in total sales of $100,000.
Sue also found that a 10% increase in customer traffic results in a 5% increase in transaction volume. Using this information, she builds a financial model and sensitivity analysis based on these hypotheses. It tells her how sales change if customer traffic increases by 10%, 50%, or even 100%.
Comparing current transactions (100), an increase in customer traffic by 10%, 50%, or 100% leads to a rise in sales volume by 5%, 25%, or 50%, respectively. The sensitivity analysis shows that sales are highly responsive to customer traffic changes.
Applying Sensitivity Analysis to NPV
Sensitivity analysis in Net Present Value (NPV) assessment evaluates how changes in input variables influence a project’s profitability. Although companies estimate the project’s NPV, they may also want to understand how different conditions affect their returns.
How to Calculate Sensitivity Analysis for Clear, Reliable Outcomes
Sensitivity analysis is often performed using analysis software, and Excel has built-in functions compatible with this method. Generally, sensitivity analysis is calculated by using formulas referencing different input cells. For instance, in NPV analysis with a discount rate of 6%, one could perform sensitivity analysis by examining scenarios of 5%, 8%, and 10% discount rates.
Mastering The Two Types of Sensitivity Analysis
The two main types of sensitivity analysis are local sensitivity analysis and global sensitivity analysis:
- Local Sensitivity Analysis: It evaluates how one parameter affects predictions while keeping other parameters constant.
- Global Sensitivity Analysis: This broader analysis includes complex modeling scenarios, like Monte Carlo techniques, for a more comprehensive overview.
Sensitivity vs. Scenario Analysis: Not Just Split Ends
While sensitivity analysis focuses on predicting different outcomes for a single event, scenario analysis considers broader conditions where the precise outcome is unknown. For example, economists may use scenario analysis to project macroeconomic conditions 18 months into the future.
The Bottom Line: Empower Your Decisions
When a company wishes to predict varied outcomes for a project, it might consider sensitivity or scenario analysis. Exploring these techniques helps identify opportunities, mitigate risks, and guide decisions. In essence, sensitivity analysis offers a structured approach to making informed, strategic choices.
Related Terms: Scenario Analysis, Monte Carlo Techniques, Financial Forecasting, Strategic Planning.
References
- Stanford University, Department of Aeronautics and Astronautics. “Chapter 4, Sensitivity Analysis”, Pages 77.
