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 €20 per unit with a variable cost of €15 per unit. Fixed costs are €7 500 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €7 500p = €20v = €15profit = €6 000
Q = units
2.Break-even analysisHard
A product sells for €24 per unit, with a variable cost of €20 per unit and fixed costs of €8 000 per year. Budgeted sales are 3 600 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €8 000p = €24v = €20budget = 3 600
MS = %
3.Financial accountingMedium
What is the key difference between absorption costing and marginal costing?
- AAbsorption costing ignores variable costs
- BMarginal costing is required by IFRS for external reporting
- CAbsorption costing includes fixed production overheads in inventory; marginal costing treats them as period costs
- DMarginal costing includes all overheads in inventory; absorption costing excludes them
4.Financial accountingHard
The standard is 2 labour hours per unit at €20 an hour. 500 units are made in 1,100 hours. What is the labour efficiency variance?
- A€22,000 adverse
- B€2,000 adverse
- C€1,000 adverse
- D€2,000 favourable
3Solutions
1.Break-even analysis
Answer: Q = 2700 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 = 20 − 15 = €5
Units for the target profit
Q = (F + profit)/(p − v) = (7 500 + 6 000)/5 = 2 700
Answer
Q = 2 700 units
2.Break-even analysis
Answer: MS = 44.44 %
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) = 8 000/4 = 2 000
Margin of safety
MS = (3 600 − 2 000)/3 600·100 = 44.44%
Answer
MS = 44.44%
3.Financial accounting
Answer: C · 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
C · Absorption costing includes fixed production overheads in inventory; marginal costing treats them as period costs
4.Financial accounting
Answer: B · €2,000 adverse
Why this is the answer
Standard hours = 500 × 2 = 1,000. Extra 100 hours × €20 = €2,000 adverse, because more hours were used than the standard allows.
Answer
B · €2,000 adverse
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