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 €17 with a variable cost of €15 per unit. Fixed costs are €8 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €4 000 after tax?
p = €17v = €15F = €8 000T = 20%after-tax profit = €4 000
Q = units
2.Break-even analysisHard
A product sells for €24 per unit, with a variable cost of €18 per unit and fixed costs of €15 000 per year. Budgeted sales are 3 500 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €15 000p = €24v = €18budget = 3 500
MS = %
3.Financial accountingMedium
A machine with a carrying amount of €3,000 is sold for €4,000. What is recorded in the income statement?
- AA gain on disposal of €1,000
- BA loss on disposal of €1,000
- CA gain on disposal of €4,000
- DRevenue of €4,000
4.Financial accountingHard
When does activity-based costing (ABC) give the biggest improvement over traditional absorption costing?
- AWhen a firm makes only one standard product
- BWhen all costs are variable with labour hours
- CWhen overheads are large and driven by activities like set-ups rather than volume
- DWhen overheads are very small compared with direct costs
3Solutions
1.Break-even analysis
Answer: Q = 6500 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
4 000/(1 − 0.2) = €5 000
Units needed
Q = (8 000 + 5 000)/2 = 6 500
Answer
Q = 6 500 units
2.Break-even analysis
Answer: MS = 28.57 %
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) = 15 000/6 = 2 500
Margin of safety
MS = (3 500 − 2 500)/3 500·100 = 28.57%
Answer
MS = 28.57%
3.Financial accounting
Answer: A · A gain on disposal of €1,000
Why this is the answer
Gain or loss on disposal = proceeds − carrying amount = €4,000 − €3,000 = €1,000 gain. It is not part of normal revenue.
Answer
A · A gain on disposal of €1,000
4.Financial accounting
Answer: C · 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
C · When overheads are large and driven by activities like set-ups rather than volume
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