Break-even analysis
- Contribution margin
- CM = p − v
- Break-even quantity
- QBE = FC/(p − v)
- Target profit
- Q = (FC + profit)/(p − v)
- Profit
- π = (p − v)·Q − FC
- Margin of safety
- (Q − QBE)/Q
Management Accounting: cram pack
Formula sheets, the key method steps for every topic and 4 practice problems, with full solutions at the back.
1Formulas and methods
2Practice problems
1.Break-even analysisMedium
A product sells for €20 with a variable cost of €18 per unit. Fixed costs are €2 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €1 000 after tax?
p = €20v = €18F = €2 000T = 20%after-tax profit = €1 000
Q = units
2.Break-even analysisHard
A company sells two products. Product A sells for €15 with a variable cost of €12; product B sells for €45 with a variable cost of €25. They sell in a fixed mix of 2 units of A for every 1 of B. Fixed costs are €5 200 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €15, vA = €12pB = €45, vB = €25A : B = 2 : 1F = €5 200
Q = units
3.Financial accountingMedium
Fixed costs are €20,000, the selling price is €50 and the variable cost is €30 per unit. What is the break-even point?
- A1,000 units
- B2,000 units
- C667 units
- D400 units
4.Financial accountingHard
Over three years a company reports rising profits while operating cash flow keeps falling. What should an analyst suspect?
- AThe company must have repaid all its loans
- BProfits may be driven by aggressive accruals, such as rising receivables or capitalised costs
- CThe company has very high earnings quality
- DDepreciation must have been too high
3Solutions
1.Break-even analysis
Answer: Q = 1625 units
Cost-volume-profit: each unit sold earns a contribution margin, price minus variable cost per unit. Profit = Q·(p − v) − F, where F is the fixed cost. At the break-even point profit is zero, so Q = F/(p − v).
Pre-tax profit needed
1 000/(1 − 0.2) = €1 250
Units needed
Q = (2 000 + 1 250)/2 = 1 625
Answer
Q = 1 625 units
2.Break-even analysis
Answer: Q = 600 units
Break-even with a sales mix: when products sell in a fixed ratio, use the weighted average contribution margin: weight each product's p − v by its share of units. Break-even units = F/(weighted contribution margin), split again in the mix ratio.
Contribution margins
cmA = €3, cmB = €20
Weighted contribution margin
(2·3 + 1·20)/3 = €8.67
Break-even units
Q = 5 200/8.667 = 600
A: 400, B: 200
Answer
Q = 600 units
3.Financial accounting
Answer: A · 1,000 units
Why this is the answer
Contribution per unit = €50 − €30 = €20. Break-even = €20,000 ÷ €20 = 1,000 units.
Answer
A · 1,000 units
4.Financial accounting
Answer: B · Profits may be driven by aggressive accruals, such as rising receivables or capitalised costs
Why this is the answer
A widening gap between profit and operating cash flow often signals working capital build-up or aggressive recognition, suggesting low earnings quality.
Answer
B · Profits may be driven by aggressive accruals, such as rising receivables or capitalised costs
ExamProblems · examproblems.com/courses/management-accounting