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11.2 Expected Values, Expected Value Tables and Their Limitations
CIMA BA2: Fundamentals of Management Accounting Exam
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1 Chapter 1: The Context of Management Accounting
1.1 The Need for Management Accounting, the GMAP Definition & Comparison with Financial Accounting 1.2 Qualities of Good Management Information: From Data to Decisions 1.3 Information for Operational, Managerial and Strategic Levels 1.4 The Role of the Management Accountant: CIMA's View, IFAC's Domain & Position in the Organisation 1.5 CIMA as a Professional Body: Members, Candidates, the Profession & Society
2 Chapter 2: Cost Identification, Classification and Behaviour
2.1 Cost Classification by Nature, Function, and Element 2.2 Cost Behaviour Patterns and Relevant Range 2.3 The High-Low Method and Cost Prediction 2.4 Scattergraph and Least-Squares Regression for Cost Estimation
3 Chapter 3: Overheads and Absorption Costing
3.1 Production Overheads: Allocation and Apportionment 3.2 Overhead Absorption Rates (OAR) & Under/Over-Absorption
4 Chapter 4: Marginal Costing, Profit Reconciliation and Cost-Based Pricing
4.1 Marginal Costing vs Absorption Costing Principles 4.2 Reconciling Marginal and Absorption Costing Operating Profits 4.3 Pricing with Cost Information: Full-Cost-Plus, Marginal-Cost-Plus, Mark-Ups, Margins and Return Targets
5 Chapter 5: Budget Preparation: Functional, Master and Cash Budgets
5.1 Purposes of Budgeting & The Budgeting Process 5.2 The Principal Budget Factor & Functional Budgets 5.3 The Master Budget: Budgeted Profit or Loss, Financial Position and Cash Flow 5.4 Cash Budgets & Cash Flow Forecasting
6 Chapter 6: Budgetary Control: Flexible Budgets, Behaviour and Budgeting Approaches
6.1 Fixed vs Flexible Budgeting and Budget Flexing 6.2 Budgetary Control Systems, Participation & Behavioural Aspects 6.3 Alternative Budgeting Approaches: Incremental, ZBB & Rolling Budgets
7 Chapter 7: Standard Costing and Cost Variances
7.1 Standard Costing Principles and Types of Standards 7.2 Direct Material Price and Usage Variances 7.3 Direct Labour Rate, Efficiency, and Idle Time Variances 7.4 Variable and Fixed Overhead Variances
8 Chapter 8: Sales Variances, Operating Statements and Interpreting Variances
8.1 Sales Variances and Operating Statements (Marginal and Absorption Formats) 8.2 Interpreting Variances: Causes, Interrelationships and Deciding What to Investigate
9 Chapter 9: Performance Measurement
9.1 The Need for Performance Measures: Responsibility Accounting, Controllability and Service Industries 9.2 Financial and Non-Financial Performance Measures in Manufacturing and Service Organisations
10 Chapter 10: Integrated Accounts, Job and Batch Costing and Management Reports
10.1 Integrating Cost and Financial Accounts: Control Accounts and the Manufacturing Account 10.2 Integrated Ledgers with Under- and Over-Absorption and Standard Cost Variances 10.3 Job and Batch Costing: Job Cost Cards, Job Accounts and Pricing a Job 10.4 Cost Reports for Manufacturing, Service and Not-for-Profit Organisations
11 Chapter 11: Risk, Probability and Statistics for Decision-Making
11.1 Risk, Uncertainty and Probability: Rules and Joint Probabilities for Decisions 11.2 Expected Values, Expected Value Tables and Their Limitations 11.3 Averages and Dispersion: Mean, Median, Mode, Range, Variance, Standard Deviation and Coefficient of Variation 11.4 The Normal Distribution: Z-Scores, Normal Distribution Tables and Business Probabilities
12 Chapter 12: Relevant Costing and Short-Term Decisions
12.1 Relevant Cost Concepts: Future, Incremental, and Opportunity Costs 12.2 Relevant Costs of Materials, Labour, and Overheads 12.3 Short-Term Operational Decisions: Make-or-Buy, Shutdowns, Special Orders
13 Chapter 13: Breakeven Analysis and Limiting Factor Analysis
13.1 Single-Product Break-Even Analysis & Margin of Safety 13.2 Target Profit Calculations, Operating Gearing & CVP Assumptions 13.3 Multi-Product CVP Analysis & Break-Even Charts 13.4 Limiting Factor Analysis (Key Factor Analysis)
14 Chapter 14: Long-Term Decisions: Time Value of Money, Payback, NPV and IRR
14.1 Time Value of Money: Compounding, Discounting, Annuities & Perpetuities 14.2 Payback Period Method: Constant and Uneven Cash Flows 14.3 Net Present Value (NPV): Methodology and Decision Rules 14.4 Internal Rate of Return (IRR) and Interpolation
11.2 Expected Values, Expected Value Tables and Their Limitations
Key Takeaways Explain This Topic AI
The expected value is EV = Σ(outcome × probability), the long-run average result if the same decision were repeated many times.
An expected value table lists each possible decision against each possible outcome, calculates the payoff in every cell, and selects the decision with the highest expected value.
The expected value may not be a possible outcome of a single decision, so it is most reliable for decisions that are repeated many times.
Expected values ignore the spread of outcomes and assume the decision-maker is risk-neutral, so two options with equal EVs can carry very different risks.
Last updated: September 2026
Why this topic is examined
Syllabus area D1(b) asks you to demonstrate the use of expected values and joint probabilities in decision-making , including expected values and expected value tables and the limitations of expected values . Expect number-entry questions (calculate an EV or the best option from a payoff table) and conceptual questions about when an EV is a sensible basis for a decision. Section 11.1 covered the probability rules this section uses.
The expected value EV = ∑ ( x × p ) \text{EV} = \sum (x \times p) EV = ∑ ( x × p )
where x x x is each possible outcome and p p p its probability. The probabilities must sum to 1.
Worked example
A company is considering a new subscription service. Its estimates of net present value (NPV) under three demand scenarios are:
- Demand Probability NPV $ NPV × probability $
- Weak 0.25 (40,000) (10,000)
- Moderate 0.50 50,000 25,000
- Strong 0.25 120,000 30,000
- Expected value 1.00 45,000
The expected NPV is positive ($45,000), so on an expected value basis the project is worthwhile. Note that $45,000 is not one of the possible outcomes: the actual result will be a $40,000 loss, a $50,000 gain or a $120,000 gain.
Expected values from joint probabilities
In Section 11.1, sales volume and contribution per unit were combined into four joint outcomes. The expected contribution is:
- Joint outcome Joint probability Contribution $ Weighted $
- 10,000 units at $5 0.42 50,000 21,000
- 10,000 units at $4 0.18 40,000 7,200
- 8,000 units at $5 0.28 40,000 11,200
- 8,000 units at $4 0.12 32,000 3,840
- Expected contribution 1.00 43,240
Because the two variables are independent, the same answer comes from expected volume × expected contribution per unit: (0.6 × 10,000 + 0.4 × 8,000) × (0.7 × $5 + 0.3 × $4) = 9,200 × $4.70 = $43,240. After fixed costs of $41,000, the expected profit is $2,240, even though the probability of a loss is 0.58. This shows why expected values should not be read in isolation.
Expected value tables (payoff tables)
An expected value table sets out the payoff for every combination of decision (what management chooses) and outcome (what actually happens), then calculates the expected value of each decision.
Worked example: how many cakes to bake
A bakery buys cakes for $4 each and sells them for $10. Unsold cakes are thrown away at the end of the day. Daily demand is either 100, 200 or 300 cakes, with probabilities 0.3, 0.5 and 0.2. The bakery must decide in the morning whether to buy 100, 200 or 300 cakes.
Step 1: calculate each payoff. Payoff = $10 × cakes sold − $4 × cakes bought, where cakes sold is the lower of demand and cakes bought.
- Cakes bought Demand 100 (p = 0.3) Demand 200 (p = 0.5) Demand 300 (p = 0.2)
- Buy 100 1,000 − 400 = 600 600 600
- Buy 200 1,000 − 800 = 200 2,000 − 800 = 1,200 1,200
- Buy 300 1,000 − 1,200 = (200) 2,000 − 1,200 = 800 3,000 − 1,200 = 1,800
Step 2: calculate the expected value of each decision.
- Decision Calculation Expected payoff $
- Buy 100 (0.3 × 600) + (0.5 × 600) + (0.2 × 600) 600
- Buy 200 (0.3 × 200) + (0.5 × 1,200) + (0.2 × 1,200) 900
- Buy 300 (0.3 × −200) + (0.5 × 800) + (0.2 × 1,800) 700
Step 3: choose. On an expected value basis the bakery should buy 200 cakes , giving an expected daily profit of $900.
Tip
Work down each row (decision) of the payoff table to find its EV, and compare the EVs. A common error is to average across a column (an outcome), which mixes different decisions together.
Because the bakery makes the same decision every day, the expected value is a sensible guide: over many days, the average daily profit from buying 200 cakes should be close to $900.
Limitations of expected values
Limitation Explanation
Long-run average The EV is the average result over many repetitions. For a one-off decision the EV may never actually occur, as in the subscription example.
Ignores risk (spread) Two options can have the same EV but very different ranges of outcomes. The EV says nothing about the chance of a large loss.
Assumes risk neutrality Using EV alone treats a decision-maker as indifferent to risk. A risk-averse manager might prefer a lower but safer outcome.
Depends on probability estimates Probabilities are often estimates or based on past data that may not hold in future.
Simplified outcomes Real outcomes usually form a continuous range, not the two or three values in a table.
Same EV, different risk
- Option Outcomes $ Probabilities EV $
- A 50,000 or 70,000 0.5 / 0.5 60,000
- B (40,000) or 160,000 0.5 / 0.5 60,000
Both options have an EV of $60,000, but Option B has a 50% chance of a $40,000 loss. A small company might not survive that loss. The standard deviation (Section 11.3) measures this spread.
Note
Techniques for decisions under uncertainty , where probabilities cannot be estimated (such as maximin, maximax and minimax regret), are not examined in BA2: the syllabus states that candidates will not be asked to apply techniques to deal with uncertainty. Focus on expected values, joint probabilities, measures of dispersion and the normal distribution.