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 €32 per unit with a variable cost of €30 per unit. Fixed costs are €10 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €10 000p = €32v = €30profit = €6 000
Q = units
2.Break-even analysisHard
A product sells for €17 per unit, with a variable cost of €15 per unit and fixed costs of €8 000 per year. Budgeted sales are 5 000 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €8 000p = €17v = €15budget = 5 000
MS = %
3.Financial accountingMedium
An asset costs €50,000, has a residual value of €5,000 and a useful life of 5 years. What is the annual straight-line depreciation?
- A€9,000
- B€11,000
- C€5,000
- D€10,000
4.Financial accountingHard
Under the matching principle, the cost of a product warranty sold with goods this year should be:
- ARecorded as revenue
- BRecognised only when a customer actually makes a warranty claim
- CIgnored until the warranty expires
- DEstimated and recognised as an expense in the year of sale
3Solutions
1.Break-even analysis
Answer: Q = 8000 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 = 32 − 30 = €2
Units for the target profit
Q = (F + profit)/(p − v) = (10 000 + 6 000)/2 = 8 000
Answer
Q = 8 000 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) = 8 000/2 = 4 000
Margin of safety
MS = (5 000 − 4 000)/5 000·100 = 20%
Answer
MS = 20%
3.Financial accounting
Answer: A · €9,000
Why this is the answer
(Cost − residual value) ÷ useful life = (€50,000 − €5,000) ÷ 5 = €9,000 per year.
Answer
A · €9,000
4.Financial accounting
Answer: D · Estimated and recognised as an expense in the year of sale
Why this is the answer
A provision for expected warranty costs is recognised when the goods are sold, matching the expense with the related revenue (IAS 37).
Answer
D · Estimated and recognised as an expense in the year of sale
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