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 €30 per unit with a variable cost of €18 per unit. Fixed costs are €60 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €60 000p = €30v = €18profit = €6 000
Q = units
2.Break-even analysisHard
A company sells 3 130 units per month at €12 each, with a variable cost of €6 per unit and fixed costs of €15 000 per month. The variable cost rises by €3 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 130p = €12v = €6 → €9F = €15 000
Q = units
3.Financial accountingMedium
What is the key difference between absorption costing and marginal costing?
- AAbsorption costing includes fixed production overheads in inventory; marginal costing treats them as period costs
- BMarginal costing is required by IFRS for external reporting
- CMarginal costing includes all overheads in inventory; absorption costing excludes them
- DAbsorption costing ignores variable costs
4.Financial accountingHard
Inventory days are 60, receivable days 45 and payable days 30. What is the cash conversion (operating) cycle?
- A15 days
- B75 days
- C135 days
- D105 days
3Solutions
1.Break-even analysis
Answer: Q = 5500 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 = 30 − 18 = €12
Units for the target profit
Q = (F + profit)/(p − v) = (60 000 + 6 000)/12 = 5 500
Answer
Q = 5 500 units
2.Break-even analysis
Answer: Q = 6260 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 = 3 130·(12 − 6) − 15 000 = €3 780
New contribution margin per unit
12 − 9 = €3
Units for the same profit
Q = (15 000 + 3 780)/3 = 6 260
Answer
Q = 6 260 units
3.Financial accounting
Answer: A · 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
A · Absorption costing includes fixed production overheads in inventory; marginal costing treats them as period costs
4.Financial accounting
Answer: B · 75 days
Why this is the answer
60 + 45 − 30 = 75 days between paying suppliers and collecting cash from customers. A shorter cycle needs less working capital finance.
Answer
B · 75 days
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