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 can be made in two ways. Method A has fixed costs of €30 000 per year and a variable cost of €20 per unit. Method B, more automated, has fixed costs of €37 500 per year and a variable cost of €15 per unit. At what yearly volume Q do both methods cost the same?
FA = €30 000vA = €20FB = €37 500vB = €15
Q = units
2.Break-even analysisHard
A product sells for €10 per unit, with a variable cost of €4 per unit and fixed costs of €12 000 per year. Budgeted sales are 2 300 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €12 000p = €10v = €4budget = 2 300
MS = %
3.Financial accountingMedium
Which costs are relevant when making a business decision?
- AAllocated fixed overheads that do not change with the decision
- BFuture cash flows that differ between the alternatives
- CCosts already paid for the project
- DAll costs in last year's income statement
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 overheads are very small compared with direct costs
- CWhen a firm makes only one standard product
- DWhen all costs are variable with labour hours
3Solutions
1.Break-even analysis
Answer: Q = 1500 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).
Equal total costs
30 000 + 20Q = 37 500 + 15Q
Solve for Q
Q = (37 500 − 30 000)/(20 − 15) = 1 500
Answer
Q = 1 500 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
2.Break-even analysis
Answer: MS = 13.04 %
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) = 12 000/6 = 2 000
Margin of safety
MS = (2 300 − 2 000)/2 300·100 = 13.04%
Answer
MS = 13.04%
3.Financial accounting
Answer: B · Future cash flows that differ between the alternatives
Why this is the answer
Relevant costs are future, incremental cash flows. Sunk costs, committed costs and unchanged allocated overheads are ignored.
Answer
B · Future cash flows that differ between the alternatives
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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