## **Learning Outcomes**

After reading this article, you will be able to explain the role of sensitivity and scenario analysis as tools for assessing risk and uncertainty in management decisions for the ACCA Performance Management (PM) exam. You will know how to apply risk-adjusted decision rules such as maximax, maximin, and minimax regret, calculate expected values, and interpret the margin of safety in practical decision contexts.

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

For ACCA Performance Management (PM), you are required to understand techniques for handling risk and uncertainty in decision making. This article supports your revision of:

- The distinction between risk and uncertainty, and techniques to address each
- The use of sensitivity analysis to assess the impact of changes in key assumptions
- Scenario analysis, including the application of multiple changes and probabilities
- Calculation and interpretation of expected values for uncertain outcomes
- Application of risk-adjusted decision rules: maximax, maximin, minimax regret
- The concept of the margin of safety in decision making
- The use and limitations of these techniques in exam questions

## **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. By what percentage must a cost estimate increase before a project becomes unviable? Which analysis helps answer this question?
2. Which decision rule would a highly risk-averse manager most likely use: maximax, maximin, or minimax regret?
3. How is the expected value of a decision calculated, and why might it be inappropriate as a basis for a one-off project?
4. Define the margin of safety. What does it indicate about a business’s level of risk?

## **Introduction**

Business decisions are rarely made in the absence of uncertainty. Costs, sales, and external factors can change without warning, and managers must assess how such changes could affect their decisions and the performance of the business. The ACCA Performance Management (PM) exam expects you to both calculate and discuss the impact of uncertainty using sensitivity and scenario analysis, and to apply risk-adjusted decision rules.

This article explains how sensitivity and scenario analysis provide structured ways to test decision robustness. It also covers key risk-adjusted rules like maximax and maximin, the calculation and interpretation of expected values, and how analysing the margin of safety helps evaluate risk.

> **Key Term: sensitivity analysis**
> The process of assessing how sensitive a decision or outcome is to changes in key variables, such as costs, selling prices, or sales volumes.
>
> **Key Term: scenario analysis**
> Assessment of results when more than one parameter or key assumption is changed at the same time, often using different likely or possible scenarios.
>
> **Key Term: expected value (EV)**
> The weighted average of all possible outcomes for a decision, each weighted by its probability of occurrence.
>
> **Key Term: risk-adjusted decision rule**
> A decision criterion that incorporates the decision-maker’s attitude to risk, such as maximax, maximin, or minimax regret.
>
> **Key Term: margin of safety**
> The amount by which actual or budgeted sales can fall before a business reaches its break-even point.

## **SENSITIVITY ANALYSIS**

Sensitivity analysis examines how the result of a calculation or decision changes as a single input changes, while others remain constant. It helps identify which variables are most critical—often called "critical factors"—by working out the percentage or amount by which they must change to affect the decision.

Common applications for sensitivity analysis include:

- Investment appraisals (e.g., how much costs or sales can change before NPV becomes negative)
- Break-even and margin of safety calculations (how much sales can fall before a loss occurs)
- Special order or contract decisions

### **Worked Example 1.1**

A company is considering an investment which will generate annual cash inflows of \$40,000 for five years. The initial investment is \$150,000. The payback period is required to be within 4 years.

**Question:** Calculate by how much the annual cash inflow can fall before the project fails to meet the payback criterion.

> **Answer:**
>
> Required payback = \$150,000 ÷ 4 = \$37,500 per year.
> The current cash inflow is \$40,000, so it can fall by up to \$2,500 per year (\$40,000 – \$37,500) before payback exceeds four years.

Sensitivity analysis should be used to focus management attention where estimation errors are most costly.

### **Limitations**

- Only one variable is usually changed at a time, not reflecting realistic multi-factor changes
- Does not assess the probability of the change occurring, only the impact

## **SCENARIO ANALYSIS**

Scenario analysis involves changing multiple variables at once, representing different situations (“pessimistic”, “most likely”, “optimistic”, etc.). It is a better reflection of reality than sensitivity analysis, as adverse factors often occur together.

This approach is commonly used in budgeting and forecasting, where management produces “best case,” “worst case,” and “expected case” scenarios.

### **Worked Example 1.2**

A business has the following three scenarios for next year’s contribution:

- Best case: \$200,000 profit (probability 20%)
- Most likely: \$100,000 profit (probability 60%)
- Worst case: \$30,000 loss (probability 20%)

**Question:** What is the expected value (EV) for next year's profit?

> **Answer:**
>
> EV = (0.2 × \$200,000) + (0.6 × \$100,000) + (0.2 × -\$30,000)
> = \$40,000 + \$60,000 - \$6,000 = \$94,000

Scenario analysis can also be done without probabilities, by presenting different possible results side by side.

## **RISK-ADJUSTED DECISION RULES**

Decision makers have different attitudes to risk, which affects how they choose among uncertain outcomes. The most common rules are:

- **Maximax:** The optimistic rule—choose the alternative with the highest possible payoff.
- **Maximin:** The pessimistic rule—choose the alternative with the best of the worst possible outcomes.
- **Minimax Regret:** Choose the alternative that minimises the maximum regret (the opportunity loss of not having made the best possible decision in hindsight).

These rules are typically assessed using payoff tables, summarising all possible outcomes for each option.

### **Worked Example 1.3**

A company can launch Product X or Product Y.

| Scenario    | X profit | Y profit |
| ----------- | -------- | -------- |
| High demand | \$100k   | \$80k    |
| Low demand  | \$30k    | \$55k    |

**Question:** Using maximax, maximin, and minimax regret, what decision does each rule favour?

> **Answer:**
>
> - **Maximax:** Take the best possible profit: X (\$100k) vs Y (\$80k). Choose X.
> - **Maximin:** Take the best of the worsts: X (\$30k) vs Y (\$55k). Choose Y.
> - **Minimax Regret:** Regret table:
>   - For high demand:
>     - X regret = \$0; Y = \$20k (100–80)
>   - For low demand:
>     - X regret = \$25k (55–30); Y = \$0
>       Max regret: X = \$25k; Y = \$20k. Choose Y (lower max regret).

These decision rules reflect different attitudes to risk, which should be matched to organisational preference.

### **Exam Warning**

> Payoff tables must account for all outcome and decision combinations. Errors in the structure of tables often lead to incorrect decision recommendations in the exam.

## **EXPECTED VALUES IN DECISION MAKING**

The expected value (EV) takes the average outcome, weighted by probability, as shown in the earlier example. In practice, EV is useful if a decision is repeated many times, but may not be helpful for one-off major projects due to outcome variability.

- **Advantages:**
  - Incorporates probabilities into quantitative decision making
  - Reduces complex scenarios to a single figure for easier comparison

- **Drawbacks:**
  - May not reflect actual possible results—EV is an average, which may never occur
  - Ignores dispersion or spread of possible outcomes (risk)
  - Often relies on subjective or uncertain probabilities
  - Not always suitable for one-off or high-stakes decisions

## **THE MARGIN OF SAFETY**

The margin of safety is a key output of break-even analysis. It measures how far expected sales can fall before losses occur, indicating the riskiness of operations or a project.

Margin of safety (units) = Budgeted sales – Breakeven sales

Margin of safety (%) = (Budgeted sales – Breakeven sales) ÷ Budgeted sales × 100

A low margin of safety means higher risk of losses if sales decline unexpectedly.

### **Worked Example 1.4**

A company expects to sell 12,000 units. Break-even is at 10,000 units.

**Question:** What is the margin of safety?

> **Answer:**
>
> Margin of safety = 12,000 – 10,000 = 2,000 units
> Margin of safety (%) = 2,000 ÷ 12,000 × 100 = 16.7%

## **Summary**

Sensitivity and scenario analysis are fundamental tools for testing the robustness of business decisions, particularly where uncertainty is present. Sensitivity focuses on the effect of changes in one variable, while scenario analysis looks at combined possible shifts. Risk-adjusted decision rules (maximax, maximin, minimax regret) capture different managerial attitudes to risk. The expected value approach, though commonly used, has limitations. The margin of safety provides a practical measure of buffer against losses.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Risk and uncertainty require structured analysis in decision making
- Sensitivity analysis assesses impact of single variable changes
- Scenario analysis examines combined changes and possible outcomes
- Key risk-based decision rules: maximax, maximin, minimax regret—applied through payoff tables
- Calculation and interpretation of expected values, with advantages and drawbacks
- How margin of safety signals the risk inherent in plans

## **Key Terms and Concepts**

- sensitivity analysis
- scenario analysis
- expected value (EV)
- risk-adjusted decision rule
- margin of safety


Sensitivity and scenario analysis - Risk-adjusted decision rules and margins of safety