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 €18 with a variable cost of €8 per unit. Fixed costs are €10 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €2 000 after tax?
p = €18v = €8F = €10 000T = 20%after-tax profit = €2 000
Q = units
2.Break-even analysisHard
A company sells 3 750 units per month at €13 each, with a variable cost of €8 per unit and fixed costs of €12 500 per month. The variable cost rises by €2 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 3 750p = €13v = €8 → €10F = €12 500
Q = units
3.Financial accountingMedium
Current assets are €300,000 and current liabilities are €150,000. What is the current ratio?
- A1.5
- B4.5
- C2.0
- D0.5
4.Financial accountingHard
When does activity-based costing (ABC) give the biggest improvement over traditional absorption costing?
- AWhen overheads are large and driven by activities like set-ups rather than volume
- BWhen a firm makes only one standard product
- CWhen all costs are variable with labour hours
- DWhen overheads are very small compared with direct costs
3Solutions
1.Break-even analysis
Answer: Q = 1250 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
2 000/(1 − 0.2) = €2 500
Units needed
Q = (10 000 + 2 500)/10 = 1 250
Answer
Q = 1 250 units
2.Break-even analysis
Answer: Q = 6250 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 = 3 750·(13 − 8) − 12 500 = €6 250
New contribution margin per unit
13 − 10 = €3
Units for the same profit
Q = (12 500 + 6 250)/3 = 6 250
Answer
Q = 6 250 units
3.Financial accounting
Answer: C · 2.0
Why this is the answer
€300,000 ÷ €150,000 = 2.0, so current assets cover short-term obligations twice.
Answer
C · 2.0
4.Financial accounting
Answer: A · When overheads are large and driven by activities like set-ups rather than volume
Why this is the answer
ABC assigns overheads using cost drivers for each activity. Where products use activities very differently, a single volume-based rate distorts product costs.
Answer
A · When overheads are large and driven by activities like set-ups rather than volume
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