## **Learning Outcomes**

After reading this article, you will be able to explain sensitivity analysis and its use in assessing how uncertainty in key assumptions affects management decisions. You will be able to identify critical variables in a decision, perform simple sensitivity calculations, and interpret the results to support risk-aware recommendations. This understanding is essential for the ACCA Performance Management (PM) exam.

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

For ACCA Performance Management (PM), you are required to understand how management accountants deal with risk and uncertainty during decision making. This article focuses on:

- Applying sensitivity analysis to quantify how changes in key variables affect outcomes
- Identifying which assumptions or estimates have the greatest impact on a decision
- Assessing how much a variable can change before a decision would be reversed
- Interpreting sensitivity results to guide risk management and communication in business cases

## **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. What does sensitivity analysis help management to determine?
   a) How likely an outcome is
   b) Which variable has the highest influence on a decision
   c) The probability that the budget will be achieved
   d) Whether results can be presented in graphical form

2. If a project is profitable, but a 6% reduction in price would cause it to break even, what is the sensitivity of the project profit to price changes?

3. True or false? Sensitivity analysis considers each variable in isolation to determine how far it must move before a decision reverses.

4. List two strengths and two limitations of using sensitivity analysis for management decisions.

## **Introduction**

In business decision making, assumptions are made about key factors such as selling prices, volumes, costs, and investment returns. Since these estimates are always uncertain, management needs tools to assess how changes in key assumptions could affect the chosen decision. Sensitivity analysis is a core technique for testing how robust a decision is to changes in important variables, and is a required skill in the ACCA PM exam.

> **Key Term: sensitivity analysis**
> A method to determine the extent to which the outcome of a decision changes as individual key variables are varied, assessing the impact of best and worst case scenarios.

## **THE PURPOSE AND PROCESS OF SENSITIVITY ANALYSIS**

Sensitivity analysis tests how the result of a decision (such as profit, NPV, or contribution) would change if a key assumption—such as unit price, demand, or cost—was either better or worse than expected.

This involves:

- Identifying the key assumptions on which the decision depends
- Changing one assumption at a time (e.g., price, cost, volume) while holding others constant
- Calculating the change needed in that variable for the decision outcome to reach zero (breakeven) or to switch from 'accept' to 'reject'
- Using the percentage change required as a measure of risk

The variable(s) requiring the smallest change to reverse the decision are the most critical and need the greatest management attention.

> **Key Term: key (critical) variable**
> A factor in a decision that, if it changes even slightly, can significantly alter the recommended course of action.

## **APPLYING SENSITIVITY ANALYSIS IN PRACTICE**

The steps in a typical sensitivity analysis are:

1. Calculate the base case result for the scenario, such as project NPV or profit.
2. For each key variable in turn (selling price, volume, costs), adjust its value until the decision (e.g., project NPV or profit) = 0.
3. Record the amount or percentage change required for each variable.
4. Variables with the least % change required are the most sensitive—meaning the decision is most exposed to changes in those parameters.

### **Worked Example 1.1**

**Scenario:** A proposed new product is forecast to generate a profit of \$40,000, based on:

- Unit selling price: \$50
- Unit variable cost: \$30
- Expected sales volume: 2,500 units
- Fixed costs: \$10,000

**Question:** What is the sensitivity of the project’s profit to changes in unit selling price?

> **Answer:**
>
> 1. Base profit is \$40,000.
> 2. To find the sensitivity to price, calculate the price at which project profit becomes zero:
>    Let revised price be P:
>    $$\text{Profit} = (P - 30) \times 2,500 - 10,000 = 0$$
>    $$(P - 30) \times 2,500 = 10,000$$
>    $$P - 30 = 4$$
>    $P = \$34$
> 3. Original price = \$50, break-even price = \$34, so the price can fall by \$16:
>    Sensitivity (%) = (\$16 / \$50) × 100 = 32%
>    Interpretation: Profit turns to zero if selling price drops by 32%. Management should consider how likely such a drop is.
>
> **Key Term: breakeven point (for a variable)**
> The value at which a particular variable causes the decision outcome (e.g., profit or NPV) to become zero.

## **INTERPRETING SENSITIVITY ANALYSIS RESULTS**

The variables with the smallest required percentage change to achieve breakeven are the most risky (critical). These are where management should focus forecasting accuracy, monitoring, and control. Sensitivity analysis does not provide the probability of such changes occurring, only the impact if they do.

> **Key Term: scenario analysis**
> A technique that examines the impact of changing two or more key variables together, constructing best- and worst-case outcomes for decision support.
>
> **Key Term: what-if analysis**
> An approach to exploring the effects on a decision outcome when assumptions are varied, commonly used for forecasting and risk assessment.

### **Worked Example 1.2**

Suppose a company's project NPV is \$20,000, based on:

- Discounted cash inflows \$120,000
- Discounted cash outflows \$100,000

Management identifies variable cost as a particularly uncertain input. At what level of variable cost would the project NPV be zero, if inflow and fixed costs remain unchanged?

> **Answer:**
>
> Let variable cost = X:
> NPV = \$120,000 – (Fixed costs + X) = 0
> Fixed costs (given by implication) = \$100,000 – Variable cost (assume all outflows are variable in this example)
> If variable costs, originally \$70,000 within the \$100,000 outflow, increase:
> \$120,000 – (Fixed costs + Variable cost) = 0
> Fixed costs = \$30,000 (since \$70,000 was variable originally)
> \$120,000 – (\$30,000 + X) = 0
> \$120,000 – \$30,000 – X = 0
> X = \$90,000
> So, variable costs can increase from \$70,000 to \$90,000 before project NPV falls to zero—a sensitivity of (\$20,000 / \$70,000) = 28.6%

### **Exam Warning**

> Sensitivity analysis examines one assumption at a time while keeping others constant. This fails to capture the real risks when multiple factors may shift together. For ACCA PM, always note that sensitivity does not say how likely a change is—just how big an impact it would have.

## **APPLICATIONS AND LIMITATIONS**

Sensitivity analysis is widely used for:

- Project appraisal, capital budgeting, and investment appraisal
- Cost-volume-profit (CVP) and break-even analysis
- Budget impact assessment for key inputs

Benefits:

- Simple computations
- Highlights where robust estimates are needed
- Supports management in identifying areas for risk monitoring

Limitations:

- Examines only one variable at a time
- Does not provide probabilities or likelihoods
- Ignores possible correlation between variables
- Relies on linear effects and may oversimplify in complex models

### **Revision Tip**

> When practicing for ACCA exam questions, always state which variable is most critical, briefly justify your conclusion, and comment on the management implications.

## **Summary**

Sensitivity analysis is a fundamental tool for assessing the reliability of management decisions in the face of uncertainty. By identifying the key variables that can most easily reverse a decision, finance professionals can guide managers in focusing planning, monitoring, and risk mitigation efforts in the right areas.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Explain the purpose of sensitivity analysis in risk and decision making
- Identify and define key variables for sensitivity assessment
- Calculate the percentage or amount of change required in a variable to reverse a managerial decision
- Judge which assumptions are most critical to decision robustness
- Recognize the benefits and limitations of sensitivity analysis for business cases

## **Key Terms and Concepts**

- sensitivity analysis
- key (critical) variable
- breakeven point (for a variable)
- scenario analysis
- what-if analysis


Sensitivity and scenario analysis - Sensitivity analysis on key assumptions