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 €14 per unit with a variable cost of €8 per unit. Fixed costs are €12 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €12 000p = €14v = €8profit = €6 000
Q = units
2.Break-even analysisHard
A company sells 2 500 units at €24 each, with a variable cost of €18 per unit and fixed costs of €6 000. By what percentage %ΔΠ does operating profit change if sales volume falls by 12%?
Q = 2 500p = €24v = €18F = €6 000%ΔQ = −12%
%ΔΠ = %
3.Financial accountingMedium
A machine costs €10,000 and is depreciated at 20% a year on the reducing balance. What is the depreciation charge in year 2?
- A€4,000
- B€1,600
- C€1,800
- D€2,000
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 = 3000 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 = 14 − 8 = €6
Units for the target profit
Q = (F + profit)/(p − v) = (12 000 + 6 000)/6 = 3 000
Answer
Q = 3 000 units
2.Break-even analysis
Answer: %ΔΠ = −20 %
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Contribution margin and profit
CM = 2 500·6 = €15 000
Π = 15 000 − 6 000 = €9 000
DOL
DOL = 15 000/9 000 = 1.667
Change in profit
%ΔΠ = 1.667·(−12%) = −20%
Answer
%ΔΠ = −20%
Check: new profit = 2 200·6 − 6 000 = €7 200.00.
3.Financial accounting
Answer: B · €1,600
Why this is the answer
Year 1: 20% × €10,000 = €2,000, leaving €8,000. Year 2: 20% × €8,000 = €1,600. Reducing balance charges less each year.
Answer
B · €1,600
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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