Sensitivity Analysis

What is Sensitivity Analysis?

Sensitivity analysis is a financial modeling technique used to determine how key input variables affect the outcome of a model or decision under certain assumptions. It helps in identifying which factors have the most significant impact on an outcome.

This technique is widely used in economics, finance, project management, and engineering to evaluate risk and uncertainty. Sensitivity analysis is also called “what if analysis”

Example of Sensitivity Analysis

For example, sensitivity analysis can be used to study the effect of a 1% increase in interest rates on bond prices. (What-If question). This question can be answered with sensitivity analysis.

So, sensitivity analysis answers the questions “if these variables deviate from expectations, what will be the effect, and which variable is causing the largest deviation?”

Other Examples:

• How will the profitability of a project change if raw material costs increase by 10%?
• What happens to GDP growth if inflation rises by 2%?

Why Sensitivity Analysis is Applied?

• Helps decision-makers understand how changes in key variables affect project success or financial performance.
• Identifies the most sensitive variables that can cause significant changes in the outcome.
• Used in capital budgeting, investment analysis, and financial forecasting.
• Helps in evaluating how fluctuations in costs, revenues, or interest rates impact profitability.
• Governments and organizations use sensitivity analysis to study the impact of policy changes on economic indicators.
• Helps in analyzing macroeconomic models and environmental policies.

How is Sensitivity Analysis Done?

To conduct a sensitivity analysis, follow these steps:

• Identify the key input variables that have the greatest impact on the output.
• Determine the likely range of values for those input variables.
• Systematically change the values of the input variables within their ranges and observe the resulting changes in the output.
• Analyze the sensitivity of the output to changes in each input variable.

An Example

A person wants to open a coffee shop and needs to estimate potential profit. The key variables affecting profit include Rent per month, Price of coffee per cup, Number of customers per day, Cost of coffee beans.

Procedure: Identify key input variables that affect profit

Assume that the coffee shop sells 200 cups per day at USD 5 per cup. The cost per cup (beans, milk, sugar, etc.) is USD2, and rent is USD 3,000 per month.

Profit=Revenue-Cost

π=(200×5×30)-{(200×2×30)+3000}

π=30,000-15,000-3,000=12,000

Perform sensitivity analysis:

• What if coffee price drops to USD 4.5? Profit decreases.
• What if cost of coffee beans rises to USD 2.5 per cup? Profit decreases.
• What if rent increases to USD 3,500? Profit decreases.

Types of Sensitivity Analysis

1. Partial Sensitivity Analysis

Partial Sensitivity analysis examines how the output of a model changes when only one input variable is varied while keeping all other variables constant. It is frequently used in discount rates such as to assess the impact of several discount rates on NPV.

Example: A company wants to analyze how price changes affect demand while keeping all other factors (income, advertisement, competitors’ prices) constant.

2. Scenario Analysis:

Scenario analysis evaluates the extreme possible outcomes of a model by considering the most favorable (best-case) and least favorable (worst-case) values of input variables.

Example: A business is planning to launch a new product. Three scenarios might be:

• Base Case Scenario: It is the benchmark scenario against which all scenarios are compared. It is based on historical data.
• Best-Case Scenario: Assume most favourable conditions, such as High demand, low production cost, and no supply chain issues → High Profits
• Worst-Case Scenario: Use the least favorable conditions such as: Low demand, high production cost, and supply chain disruptions → Losses

3. Local Sensitivity Analysis

Local Sensitivity analysis focuses on how small changes in an input variable (one at a time) affect the output around a specific value of the variable. It reflects how sensitive the outcome is to slight variations in inputs.

Examples:

• In a pharmaceutical study, increasing a drug dose by 1 mg and observing its effect on patients’ blood pressure.
• Analyzing the effect of a small change in interest rates on GDP growth.

4. Global Sensitivity Analysis

Global Sensitivity analysis examines how large variations in multiple input variables across their entire range impact the output.

Example:

• A car manufacturer tests a new engine by varying fuel type, engine size, and temperature to analyze their combined effect on fuel efficiency.
• Evaluating how multiple factors (inflation, interest rates, market trends) affect investment returns.

5. Break even analysis

Break-even analysis is a financial tool used to determine the point at which total revenue equals total cost, meaning there is no profit and no loss.

Example

A company produces smartphones with the following financial details:

• Fixed Costs = 200
• Selling Price per Unit = 450, the new break-even point is: 400 units. A price drop requires selling more units to break even.

  Uses/Applications of Sensitivity Analysis

  Use in Cost-Benefit Analysis

  Cost-Benefit Analysis (CBA) is widely used to evaluate investment projects, policies, and business decisions. Sensitivity analysis helps determine how changes in discount rates, expected revenues, or costs impact the net present value (NPV) of a project.

  Example: Suppose a government is considering building a highway with an estimated benefit of 300 million. If the discount rate changes from 5% to 7%, sensitivity analysis can show how this affects the project’s feasibility, helping policymakers make informed decisions.

  Use in Risk Management

  Risk management involves identifying, assessing, and mitigating potential risks in business operations, finance, and investments. Sensitivity analysis helps identify the most significant risk factors and their impact on outcomes.

  Example: In the stock market, investors use sensitivity analysis to assess how changes in interest rates or economic conditions impact the price of their assets. If inflation rises, the analysis can predict its effect on stock returns and guide investment decisions.

  Use in Regression Analysis and Econometrics

  In econometrics, sensitivity analysis is used to test the robustness of regression models. By slightly altering independent variables or assumptions, researchers can check whether their model’s results remain stable or vary significantly.

  Example: An economist studying the effect of education on wages may use sensitivity analysis by changing the definition of “education level” (e.g., years of schooling vs. degree earned) to see if the impact on wages remains consistent.

  Use in Break Even Analysis

  Break-even analysis helps businesses determine the minimum sales volume required to cover costs. Sensitivity analysis is applied to test how different cost structures, selling prices, and demand levels influence the break-even point.

  Example: A business launching a new product estimates that it needs to sell 10,000 units to break even. If raw material costs increase by 15%, sensitivity analysis can show how many additional units must be sold to maintain profitability.

  Benefits and Drawbacks

  Benefits

  • Helps assess how key variables impact outcomes.
  • Identifies risks and prepares for uncertainties.
  • Tests model robustness under different assumptions.
  • Helps organizations plan for multiple future scenario.
  • Focuses resources on the most influential factors.
  • Used in finance, economics, project management, engineering and more.

  Drawbacks:

  • Requires significant time, effort and computation.
  • Often assesses one factor at a time.
  • Does not predict the likelihood of different scenarios occurring.The
  • accuracy of sensitivity analysis depends on the correctness of initial assumptions.
  • Heavily relies on data.