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 €12 per unit with a variable cost of €4 per unit. Fixed costs are €16 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €16 000p = €12v = €4profit = €5 000
Q = units
2.Break-even analysisHard
A product sells for €32 per unit, with a variable cost of €20 per unit and fixed costs of €18 000 per year. Budgeted sales are 1 950 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €18 000p = €32v = €20budget = 1 950
MS = %
3.Financial accountingMedium
Fixed costs are €20,000, the selling price is €50 and the variable cost is €30 per unit. What is the break-even point?
- A667 units
- B1,000 units
- C400 units
- D2,000 units
4.Financial accountingHard
An asset is impaired when its carrying amount is higher than its:
- AOriginal purchase price
- BResidual value only
- CDepreciation charge
- DRecoverable amount (the higher of fair value less costs of disposal and value in use)
3Solutions
1.Break-even analysis
Answer: Q = 2625 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 = 12 − 4 = €8
Units for the target profit
Q = (F + profit)/(p − v) = (16 000 + 5 000)/8 = 2 625
Answer
Q = 2 625 units
2.Break-even analysis
Answer: MS = 23.08 %
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) = 18 000/12 = 1 500
Margin of safety
MS = (1 950 − 1 500)/1 950·100 = 23.08%
Answer
MS = 23.08%
3.Financial accounting
Answer: B · 1,000 units
Why this is the answer
Contribution per unit = €50 − €30 = €20. Break-even = €20,000 ÷ €20 = 1,000 units.
Answer
B · 1,000 units
4.Financial accounting
Answer: D · Recoverable amount (the higher of fair value less costs of disposal and value in use)
Why this is the answer
If the carrying amount exceeds the recoverable amount, the difference is written off as an impairment loss.
Answer
D · Recoverable amount (the higher of fair value less costs of disposal and value in use)
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