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 €40 with a variable cost of €20 per unit. Fixed costs are €16 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €8 000 after tax?
p = €40v = €20F = €16 000T = 20%after-tax profit = €8 000
Q = units
2.Break-even analysisHard
A company sells 12 500 units per month at €18 each, with a variable cost of €12 per unit and fixed costs of €30 000 per month. The variable cost rises by €3 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 12 500p = €18v = €12 → €15F = €30 000
Q = units
3.Financial accountingMedium
A product sells for €40 and has a variable cost of €30. What is its contribution-to-sales (C/S) ratio?
- A75%
- B10%
- C25%
- D33%
4.Financial accountingHard
A company records routine repair costs as additions to non-current assets instead of expenses. What is the effect this year?
- AProfit and assets are overstated
- BProfit and assets are understated
- CProfit is understated and assets are overstated
- DOnly cash is affected
3Solutions
1.Break-even analysis
Answer: Q = 1300 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).
Pre-tax profit needed
8 000/(1 − 0.2) = €10 000
Units needed
Q = (16 000 + 10 000)/20 = 1 300
Answer
Q = 1 300 units
2.Break-even analysis
Answer: Q = 25000 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).
Current profit
Π = 12 500·(18 − 12) − 30 000 = €45 000
New contribution margin per unit
18 − 15 = €3
Units for the same profit
Q = (30 000 + 45 000)/3 = 25 000
Answer
Q = 25 000 units
3.Financial accounting
Answer: C · 25%
Why this is the answer
Contribution = €10. C/S ratio = €10 ÷ €40 = 25%. Fixed costs ÷ C/S ratio gives break-even revenue.
Answer
C · 25%
4.Financial accounting
Answer: A · Profit and assets are overstated
Why this is the answer
Capitalising expenses moves cost out of profit into assets, so both are overstated now. Later depreciation spreads the cost over future years.
Answer
A · Profit and assets are overstated
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