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 €50 per unit with a variable cost of €45 per unit. Fixed costs are €5 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €5 000p = €50v = €45profit = €5 000
Q = units
2.Break-even analysisHard
A product sells for €24 per unit, with a variable cost of €12 per unit and fixed costs of €30 000 per year. Budgeted sales are 2 880 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €30 000p = €24v = €12budget = 2 880
MS = %
3.Financial accountingMedium
A product sells for €40 and has a variable cost of €30. What is its contribution-to-sales (C/S) ratio?
- A10%
- B25%
- C33%
- D75%
4.Financial accountingHard
Goodwill arises in a business combination when:
- AA company has a good reputation
- BThe acquired company makes a loss
- CThe consideration paid exceeds the fair value of identifiable net assets acquired
- DAssets are revalued upwards
3Solutions
1.Break-even analysis
Answer: Q = 2000 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 = 50 − 45 = €5
Units for the target profit
Q = (F + profit)/(p − v) = (5 000 + 5 000)/5 = 2 000
Answer
Q = 2 000 units
2.Break-even analysis
Answer: MS = 13.19 %
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) = 30 000/12 = 2 500
Margin of safety
MS = (2 880 − 2 500)/2 880·100 = 13.19%
Answer
MS = 13.19%
3.Financial accounting
Answer: B · 25%
Why this is the answer
Contribution = €10. C/S ratio = €10 ÷ €40 = 25%. Fixed costs ÷ C/S ratio gives break-even revenue.
Answer
B · 25%
4.Financial accounting
Answer: C · The consideration paid exceeds the fair value of identifiable net assets acquired
Why this is the answer
Goodwill = consideration − fair value of identifiable net assets. Under IFRS it is not amortised but tested for impairment annually.
Answer
C · The consideration paid exceeds the fair value of identifiable net assets acquired
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