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 €55 per unit with a variable cost of €45 per unit. Fixed costs are €20 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €20 000p = €55v = €45profit = €6 000
Q = units
2.Break-even analysisHard
A product sells for €18 per unit, with a variable cost of €6 per unit and fixed costs of €9 600 per year. Budgeted sales are 1 000 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €9 600p = €18v = €6budget = 1 000
MS = %
3.Financial accountingMedium
Budgeted sales are 1,500 units and the break-even point is 1,000 units. What is the margin of safety?
- A1,000 units
- B500 units
- C1,500 units
- D2,500 units
4.Financial accountingHard
Under IFRS 16, a lessee typically recognises a lease on the balance sheet as:
- AAn operating expense only, spread evenly over the lease term
- BEquity and a provision
- CA right-of-use asset and a lease liability
- DRevenue and inventory
3Solutions
1.Break-even analysis
Answer: Q = 2600 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 = 55 − 45 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (20 000 + 6 000)/10 = 2 600
Answer
Q = 2 600 units
2.Break-even analysis
Answer: MS = 20 %
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) = 9 600/12 = 800
Margin of safety
MS = (1 000 − 800)/1 000·100 = 20%
Answer
MS = 20%
3.Financial accounting
Answer: B · 500 units
Why this is the answer
Margin of safety = budgeted sales − break-even sales = 500 units, or one third of budgeted sales.
Answer
B · 500 units
4.Financial accounting
Answer: C · 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
C · A right-of-use asset and a lease liability
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