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 €15 per unit. Method B, more automated, has fixed costs of €33 000 per year and a variable cost of €12 per unit. At what yearly volume Q do both methods cost the same?
FA = €30 000vA = €15FB = €33 000vB = €12
Q = units
2.Break-even analysisHard
A product sells for €57 per unit, with a variable cost of €45 per unit and fixed costs of €60 000 per year. Budgeted sales are 6 500 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €60 000p = €57v = €45budget = 6 500
MS = %
3.Financial accountingMedium
Which costs are relevant when making a business decision?
- AAll costs in last year's income statement
- BAllocated fixed overheads that do not change with the decision
- CCosts already paid for the project
- DFuture cash flows that differ between the alternatives
4.Financial accountingHard
Under the IAS 16 revaluation model, a building is revalued upwards for the first time. Where does the gain go?
- ATo other comprehensive income and a revaluation surplus in equity
- BTo retained earnings as a realised profit
- CTo a provision on the balance sheet
- DTo revenue in the income statement
3Solutions
1.Break-even analysis
Answer: Q = 1000 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 + 15Q = 33 000 + 12Q
Solve for Q
Q = (33 000 − 30 000)/(15 − 12) = 1 000
Answer
Q = 1 000 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
2.Break-even analysis
Answer: MS = 23.08 %
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) = 60 000/12 = 5 000
Margin of safety
MS = (6 500 − 5 000)/6 500·100 = 23.08%
Answer
MS = 23.08%
3.Financial accounting
Answer: D · 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
D · Future cash flows that differ between the alternatives
4.Financial accounting
Answer: A · To other comprehensive income and a revaluation surplus in equity
Why this is the answer
Upward revaluations are credited to a revaluation surplus via OCI, unless they reverse an earlier decrease recognised in profit or loss.
Answer
A · To other comprehensive income and a revaluation surplus in equity
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