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 €35 per unit with a variable cost of €25 per unit. Fixed costs are €50 000 per month. How many units Q must be sold per month to make a profit of €10 000?
F = €50 000p = €35v = €25profit = €10 000
Q = units
2.Break-even analysisHard
A product sells for €23 per unit, with a variable cost of €20 per unit and fixed costs of €4 500 per year. Budgeted sales are 2 250 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €4 500p = €23v = €20budget = 2 250
MS = %
3.Financial accountingMedium
Which costs are relevant when making a business decision?
- AFuture cash flows that differ between the alternatives
- BAll costs in last year's income statement
- CCosts already paid for the project
- DAllocated fixed overheads that do not change with the decision
4.Financial accountingHard
A firm has a net profit margin of 5%, asset turnover of 2 and an equity multiplier (assets ÷ equity) of 1.5. Using the DuPont analysis, what is ROE?
- A7.5%
- B10%
- C15%
- D8.5%
3Solutions
1.Break-even analysis
Answer: Q = 6000 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 = 35 − 25 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (50 000 + 10 000)/10 = 6 000
Answer
Q = 6 000 units
2.Break-even analysis
Answer: MS = 33.33 %
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) = 4 500/3 = 1 500
Margin of safety
MS = (2 250 − 1 500)/2 250·100 = 33.33%
Answer
MS = 33.33%
3.Financial accounting
Answer: A · 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
A · Future cash flows that differ between the alternatives
4.Financial accounting
Answer: C · 15%
Why this is the answer
ROE = 5% × 2 × 1.5 = 15%. DuPont shows whether returns come from profitability, asset efficiency or leverage.
Answer
C · 15%
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