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 €16 per unit with a variable cost of €12 per unit. Fixed costs are €8 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €8 000p = €16v = €12profit = €6 000
Q = units
2.Break-even analysisHard
A company sells 3 000 units per month at €19 each, with a variable cost of €15 per unit and fixed costs of €4 800 per month. The variable cost rises by €2 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 3 000p = €19v = €15 → €17F = €4 800
Q = units
3.Financial accountingMedium
What is the key difference between absorption costing and marginal costing?
- AAbsorption costing ignores variable costs
- BMarginal costing is required by IFRS for external reporting
- CAbsorption costing includes fixed production overheads in inventory; marginal costing treats them as period costs
- DMarginal costing includes all overheads in inventory; absorption costing excludes them
4.Financial accountingHard
Under the matching principle, the cost of a product warranty sold with goods this year should be:
- AEstimated and recognised as an expense in the year of sale
- BIgnored until the warranty expires
- CRecognised only when a customer actually makes a warranty claim
- DRecorded as revenue
3Solutions
1.Break-even analysis
Answer: Q = 3500 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).
Contribution margin per unit
p − v = 16 − 12 = €4
Units for the target profit
Q = (F + profit)/(p − v) = (8 000 + 6 000)/4 = 3 500
Answer
Q = 3 500 units
2.Break-even analysis
Answer: Q = 6000 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).
Current profit
Π = 3 000·(19 − 15) − 4 800 = €7 200
New contribution margin per unit
19 − 17 = €2
Units for the same profit
Q = (4 800 + 7 200)/2 = 6 000
Answer
Q = 6 000 units
3.Financial accounting
Answer: C · Absorption costing includes fixed production overheads in inventory; marginal costing treats them as period costs
Why this is the answer
Under absorption costing each unit carries a share of fixed production overhead. Marginal costing values inventory at variable cost only and expenses fixed costs in the period.
Answer
C · Absorption costing includes fixed production overheads in inventory; marginal costing treats them as period costs
4.Financial accounting
Answer: A · Estimated and recognised as an expense in the year of sale
Why this is the answer
A provision for expected warranty costs is recognised when the goods are sold, matching the expense with the related revenue (IAS 37).
Answer
A · Estimated and recognised as an expense in the year of sale
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