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 €15 per unit with a variable cost of €12 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 = €15v = €12profit = €6 000
Q = units
2.Break-even analysisHard
A company sells 1 000 units at €19 each, with a variable cost of €4 per unit and fixed costs of €12 000. By what percentage %ΔΠ does operating profit change if sales volume falls by 20%?
Q = 1 000p = €19v = €4F = €12 000%ΔQ = −20%
%ΔΠ = %
3.Financial accountingMedium
A company is being sued. Its lawyers say losing is possible but not probable. How is this treated under IAS 37?
- AIgnored completely
- BDisclosed as a contingent liability in the notes
- CRecognised as a provision on the balance sheet
- DRecognised as an expense and paid into a reserve
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 lease with a term of 12 months or less
- CA ten-year lease of a large production machine
- DAny lease of land and buildings
3Solutions
1.Break-even analysis
Answer: Q = 6000 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 = 15 − 12 = €3
Units for the target profit
Q = (F + profit)/(p − v) = (12 000 + 6 000)/3 = 6 000
Answer
Q = 6 000 units
2.Break-even analysis
Answer: %ΔΠ = −100 %
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 = 1 000·15 = €15 000
Π = 15 000 − 12 000 = €3 000
DOL
DOL = 15 000/3 000 = 5
Change in profit
%ΔΠ = 5·(−20%) = −100%
Answer
%ΔΠ = −100%
Check: new profit = 800·15 − 12 000 = €0.00.
3.Financial accounting
Answer: B · Disclosed as a contingent liability in the notes
Why this is the answer
A possible obligation is not recognised but disclosed, unless the chance of outflow is remote. A probable, measurable outflow would require a provision.
Answer
B · Disclosed as a contingent liability in the notes
4.Financial accounting
Answer: B · 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
B · A lease with a term of 12 months or less
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