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 company sells 8 000 units at €18 each. The variable cost is €12 per unit and fixed costs are €30 000. Find the degree of operating leverage DOL at this sales level.
Q = 8 000p = €18v = €12F = €30 000
DOL =
2.Break-even analysisHard
A product sells for €40 per unit, with a variable cost of €20 per unit and fixed costs of €50 000 per year. Budgeted sales are 3 130 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €50 000p = €40v = €20budget = 3 130
MS = %
3.Financial accountingMedium
What is the key difference between absorption costing and marginal costing?
- AAbsorption costing includes fixed production overheads in inventory; marginal costing treats them as period costs
- BMarginal costing is required by IFRS for external reporting
- CMarginal costing includes all overheads in inventory; absorption costing excludes them
- DAbsorption costing ignores variable costs
4.Financial accountingHard
When does activity-based costing (ABC) give the biggest improvement over traditional absorption costing?
- AWhen overheads are very small compared with direct costs
- BWhen overheads are large and driven by activities like set-ups rather than volume
- CWhen all costs are variable with labour hours
- DWhen a firm makes only one standard product
3Solutions
1.Break-even analysis
Answer: DOL = 2.667
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Total contribution margin
CM = 8 000·(18 − 12) = €48 000
Operating profit
Π = 48 000 − 30 000 = €18 000
DOL
DOL = 48 000/18 000 = 2.667
Answer
DOL = 2.667
2.Break-even analysis
Answer: MS = 20.13 %
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) = 50 000/20 = 2 500
Margin of safety
MS = (3 130 − 2 500)/3 130·100 = 20.13%
Answer
MS = 20.13%
3.Financial accounting
Answer: A · Absorption costing includes fixed production overheads in inventory; marginal costing treats them as period costs
Why this is the answer
Under absorption costing each unit carries a share of fixed production overhead. Marginal costing values inventory at variable cost only and expenses fixed costs in the period.
Answer
A · Absorption costing includes fixed production overheads in inventory; marginal costing treats them as period costs
4.Financial accounting
Answer: B · 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
B · When overheads are large and driven by activities like set-ups rather than volume
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