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 €35 per unit with a variable cost of €20 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 = €35v = €20profit = €6 000
Q = units
2.Break-even analysisHard
A product sells for €29 per unit, with a variable cost of €25 per unit and fixed costs of €2 000 per year. Budgeted sales are 700 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €2 000p = €29v = €25budget = 700
MS = %
3.Financial accountingMedium
Which costs are relevant when making a business decision?
- AAllocated fixed overheads that do not change with the decision
- BFuture cash flows that differ between the alternatives
- CAll costs in last year's income statement
- DCosts already paid for the project
4.Financial accountingHard
Under IFRS 16, a lessee typically recognises a lease on the balance sheet as:
- ARevenue and inventory
- BEquity and a provision
- 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 = 4400 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 = 35 − 20 = €15
Units for the target profit
Q = (F + profit)/(p − v) = (60 000 + 6 000)/15 = 4 400
Answer
Q = 4 400 units
2.Break-even analysis
Answer: MS = 28.57 %
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) = 2 000/4 = 500
Margin of safety
MS = (700 − 500)/700·100 = 28.57%
Answer
MS = 28.57%
3.Financial accounting
Answer: B · Future cash flows that differ between the alternatives
Why this is the answer
Relevant costs are future, incremental cash flows. Sunk costs, committed costs and unchanged allocated overheads are ignored.
Answer
B · Future cash flows that differ between the alternatives
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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