## **Learning Outcomes**

After reading this article, you will be able to explain how sensitivity and scenario analysis support risk management in decision-making. You will distinguish between one-variable sensitivity and combined scenario/what-if analysis, and interpret their results to advise on project viability. You will be equipped to apply these techniques and present findings effectively in the ACCA Performance Management exam.

## **ACCA Performance Management (PM) Syllabus**

For ACCA Performance Management (PM), you are required to understand the practical use of analytical techniques to manage uncertainty in decision-making. You need to be comfortable with:

- The use of sensitivity analysis to assess the impact of changes in key variables on decision outcomes
- How what-if and scenario analysis extend sensitivity analysis to consider multiple simultaneous changes
- Applying sensitivity and scenario analysis to investment, pricing, and budgeting problems
- Presenting clear interpretations and advice based on your analysis

## **Test Your Knowledge**

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision._

1. In a discounted cash flow appraisal, which variable is most commonly tested for sensitivity?
2. What is meant by a 'scenario analysis' in risk assessment?
3. Which of the following is not a benefit of sensitivity analysis?
   a) Identifies the most critical assumptions  
   b) Directly provides a recommended decision  
   c) Aids managerial judgement  
   d) Highlights risks for monitoring
4. If a decision's net present value is most sensitive to sales volume, how might a manager interpret this?

## **Introduction**

Business decisions inevitably involve uncertainty, whether due to market forces, cost estimates, or external change. Sensitivity and scenario analysis are practical tools used in Performance Management to address this uncertainty. By systematically varying key inputs, these techniques help managers and exam candidates understand which assumptions are most critical and how robust their recommendations are to different conditions.

> **Key Term: sensitivity analysis**
> The process of assessing how a decision outcome or key metric (such as profit or NPV) changes in response to a change in one variable, with all other variables held constant.
>
> **Key Term: what-if analysis**
> The examination of the effect on a decision's outcome when two or more variables are changed at the same time, often used to model credible alternative scenarios.
>
> **Key Term: combined scenario (“worst-case” or “best-case”)**
> An evaluation of the outcome when multiple adverse (worst-case) or favourable (best-case) variable changes are assumed simultaneously, representing extreme but plausible possibilities.

## **Sensitivity Analysis in Practice**

### Why Use Sensitivity Analysis?

For any management decision—such as investment appraisal, pricing, or budgeting—the result depends on estimates for key factors like sales price, volume, costs, or discount rates. If reality differs from these estimates, actual results may differ—possibly making a seemingly good decision unprofitable.

Sensitivity analysis directly answers: "How much can an assumption change before the decision outcome is reversed?" For example, "by what percentage could sales fall before a project's NPV becomes negative?"

This offers several benefits:

- Helps identify which assumptions are most critical
- Highlights areas to improve research or seek assurance
- Provides a clear focus for monitoring during implementation

### How to Perform Sensitivity Analysis

Typically, you vary one input at a time, keeping others constant, and recalculate the decision metric (e.g., NPV, profit, payback). The variable that requires the smallest change to switch the decision outcome (e.g., from positive to negative NPV) is the most 'sensitive'.

### **Worked Example 1.1**

A company considers launching a product with forecast annual sales of 10,000 units at \$12, variable cost \$7 per unit, and annual fixed costs of \$30,000. The investment is \$60,000 and the project's expected life is 4 years. What is the sensitivity of the project’s NPV to the sales volume estimate?

> **Answer:**
>
> 1. Calculate total contribution per year: (10,000 units × (\$12−\$7)) = \$50,000.
> 2. Subtract fixed costs: \$50,000−\$30,000 = \$20,000 per year cash flow.
> 3. Over 4 years: \$20,000 × 4 = \$80,000.
> 4. Less initial investment: NPV (ignoring discounting) = \$20,000 × 4 – \$60,000 = \$20,000.
> 5. To break even (NPV = 0): \$60,000 must equal the present value of all net annual cash inflows.
> 6. Calculate minimum sales volume required per year for NPV = 0:
>    - Let Q = required units.
>    - (\$12−\$7)Q − \$30,000 = \$15,000 per year cash flow.
>    - \$5Q − \$30,000 = \$15,000 → \$5Q = \$45,000 → Q = 9,000 units.
>    - Sensitivity: (10,000 − 9,000)/10,000 = 10%
>
> A 10% fall in sales volume would result in a zero NPV. Therefore, the investment is moderately sensitive to sales volume.

### **Revision Tip**

Make sensitivity calculations for all key variables: sales price, variable cost per unit, fixed cost—whichever reversal requires the smallest change is the greatest risk.

## **Scenario and What-If Analysis**

While sensitivity analysis looks at one change at a time, management often needs to understand the combined effect of changes in several variables, especially in riskier projects. Scenario and what-if analysis address this need.

> **Key Term: scenario analysis**
> The assessment of decision outcomes under defined sets of simultaneous changes in several key variables, typically to model alternative future situations (e.g., best case, worst case, most likely).

### When Is Scenario Analysis Used?

Scenario analysis is used to assess how robust a decision is under more realistic or extreme conditions, where assumptions might go wrong together. For example, a company might test what happens if sales volumes fall and costs rise at the same time (a "worst-case" scenario).

### Typical Scenarios Modelled

- **Best-case:** All assumptions move favourably (e.g., higher sales, lower costs)
- **Worst-case:** Adverse combined changes (e.g., lower sales, higher costs)
- **Most likely:** Expected values for all variables

Unlike single-variable sensitivity, scenario analysis helps reveal if a project is sufficiently resilient, or if there are plausible risks that could undermine success.

### **Worked Example 1.2**

A company’s project appraisal is based on three uncertain inputs:

- Sales price per unit: \$10 (could fall to \$9 under pressure)
- Sales volume: 20,000 units/year (may drop to 16,000 in a downturn)
- Variable cost per unit: \$6 (could rise to \$7 if suppliers increase prices)

Calculate the NPV under best-case, likely-case, and worst-case combinations, with annual fixed costs of \$40,000 and 4-year life, investment of \$50,000.

> **Answer:**
>
> - **Most likely:** Total contribution = (\$10−\$6)×20,000 = \$80,000, less fixed = \$40,000 per year.
> - NPV = (\$40,000 × 4) - \$50,000 = \$110,000
> - **Worst-case:** (\$9−\$7)×16,000 = \$32,000; \$32,000−\$40,000 = (\$8,000) loss per year.
> - NPV = (−\$8,000 × 4) – \$50,000 = (\$82,000)
> - **Best-case:** (\$10−\$6)×20,000 = \$80,000; as above.
>
> This shows the project is viable in normal conditions, but highly vulnerable in a combined worst-case. Management may decide to seek risk reduction strategies or rethink the investment.

## **Interpreting and Presenting Results**

Sensitivity and scenario analyses are only effective if the results are clearly explained with management action in mind:

- Highlight the variable(s) the decision is most sensitive to—these are key risks.
- Present scenario outcomes to warn if severe conditions could quickly turn a positive NPV into a negative one.
- Suggest practical responses: further research, contract terms, contingency planning, insurance, or monitoring.

### **Exam Warning**

In the ACCA PM exam, always carry out both single-variable sensitivity and scenario ("what-if") analysis when required. Present results as clear, actionable advice—avoid simply listing percentages without interpretation.

## **Summary**

Sensitivity analysis tests the impact of changing one variable at a time, making it a key tool to identify critical assumptions. Scenario and what-if analysis test combinations of changes to reflect realistic situations. Both support decision-making under uncertainty, and clear reporting—including recommended actions—is essential for gaining full marks in the exam.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- The purposes and benefits of sensitivity and scenario analysis in performance management
- The difference between one-variable sensitivity and scenario analysis
- How to perform and interpret sensitivity calculations
- How to model best-case, worst-case, and most likely scenarios
- The importance of providing commentary and management advice alongside calculations

## **Key Terms and Concepts**

- sensitivity analysis
- what-if analysis
- combined scenario (“worst-case” or “best-case”)
- scenario analysis


Sensitivity and scenario analysis - Scenario and what-if analysis