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 €45 per unit with a variable cost of €25 per unit. Fixed costs are €80 000 per month. How many units Q must be sold per month to make a profit of €12 000?
F = €80 000p = €45v = €25profit = €12 000
Q = units
2.Break-even analysisHard
A company sells 3 750 units per month at €26 each, with a variable cost of €18 per unit and fixed costs of €20 000 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 750p = €26v = €18 → €20F = €20 000
Q = units
3.Financial accountingMedium
Current assets are €300,000 and current liabilities are €150,000. What is the current ratio?
- A0.5
- B2.0
- C4.5
- D1.5
4.Financial accountingHard
Under IFRS 16, which lease may a lessee choose to expense on a straight-line basis instead of recognising a right-of-use asset?
- AAny lease with monthly payments
- BA ten-year lease of a large production machine
- CAny lease of land and buildings
- DA lease with a term of 12 months or less
3Solutions
1.Break-even analysis
Answer: Q = 4600 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 = 45 − 25 = €20
Units for the target profit
Q = (F + profit)/(p − v) = (80 000 + 12 000)/20 = 4 600
Answer
Q = 4 600 units
2.Break-even analysis
Answer: Q = 5000 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 = 3 750·(26 − 18) − 20 000 = €10 000
New contribution margin per unit
26 − 20 = €6
Units for the same profit
Q = (20 000 + 10 000)/6 = 5 000
Answer
Q = 5 000 units
3.Financial accounting
Answer: B · 2.0
Why this is the answer
€300,000 ÷ €150,000 = 2.0, so current assets cover short-term obligations twice.
Answer
B · 2.0
4.Financial accounting
Answer: D · A lease with a term of 12 months or less
Why this is the answer
Lessees may elect not to recognise short-term leases (12 months or less) and leases of low-value assets, expensing the payments instead.
Answer
D · A lease with a term of 12 months or less
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