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 €40 per unit with a variable cost of €25 per unit. Fixed costs are €30 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €30 000p = €40v = €25profit = €6 000
Q = units
2.Break-even analysisHard
A product sells for €9 per unit, with a variable cost of €6 per unit and fixed costs of €12 000 per year. Budgeted sales are 4 800 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €12 000p = €9v = €6budget = 4 800
MS = %
3.Financial accountingMedium
Revenue is €200,000 and cost of sales is €140,000. What is the gross profit margin?
- A30%
- B70%
- C60%
- D43%
4.Financial accountingHard
Under IFRS 16, a lessee typically recognises a lease on the balance sheet as:
- AEquity and a provision
- BRevenue and inventory
- CAn operating expense only, spread evenly over the lease term
- DA right-of-use asset and a lease liability
3Solutions
1.Break-even analysis
Answer: Q = 2400 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 = 40 − 25 = €15
Units for the target profit
Q = (F + profit)/(p − v) = (30 000 + 6 000)/15 = 2 400
Answer
Q = 2 400 units
2.Break-even analysis
Answer: MS = 16.67 %
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).
Break-even quantity
Q = F/(p − v) = 12 000/3 = 4 000
Margin of safety
MS = (4 800 − 4 000)/4 800·100 = 16.67%
Answer
MS = 16.67%
3.Financial accounting
Answer: A · 30%
Why this is the answer
Gross profit = €60,000. Margin = €60,000 ÷ €200,000 = 30%.
Answer
A · 30%
4.Financial accounting
Answer: D · A right-of-use asset and a lease liability
Why this is the answer
IFRS 16 removed the operating lease distinction for lessees: they recognise a right-of-use asset and a liability for lease payments, except for short-term and low-value leases.
Answer
D · A right-of-use asset and a lease liability
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