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 €14 per unit with a variable cost of €12 per unit. Fixed costs are €10 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €10 000p = €14v = €12profit = €2 000
Q = units
2.Break-even analysisHard
A product sells for €12 per unit, with a variable cost of €4 per unit and fixed costs of €16 000 per year. Budgeted sales are 3 200 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €16 000p = €12v = €4budget = 3 200
MS = %
3.Financial accountingMedium
On 1 October a company pays €12,000 rent for the next 12 months. Its year ends on 31 December. What is the rent expense for this year?
- A€1,000
- B€3,000
- C€12,000
- D€9,000
4.Financial accountingHard
Making a part costs €10 materials, €6 labour and €4 variable overhead, plus €5 of fixed overhead that continues anyway. A supplier offers it at €22. What should the firm do on cost grounds?
- ABuy it, because fixed costs are always relevant
- BMake it, because the relevant cost of €20 is below €22
- CMake it, because the full cost of €25 is below €22
- DBuy it, because the full cost of €25 per unit is above €22
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 = 14 − 12 = €2
Units for the target profit
Q = (F + profit)/(p − v) = (10 000 + 2 000)/2 = 6 000
Answer
Q = 6 000 units
2.Break-even analysis
Answer: MS = 37.5 %
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) = 16 000/8 = 2 000
Margin of safety
MS = (3 200 − 2 000)/3 200·100 = 37.5%
Answer
MS = 37.5%
3.Financial accounting
Answer: B · €3,000
Why this is the answer
October to December is 3 months: 3/12 × €12,000 = €3,000. The remaining €9,000 is a prepayment (asset) at year end.
Answer
B · €3,000
4.Financial accounting
Answer: B · Make it, because the relevant cost of €20 is below €22
Why this is the answer
Only the €20 of variable cost is avoided by buying; the €5 fixed overhead stays. Making costs €20 versus €22 to buy, so making saves €2 per unit.
Answer
B · Make it, because the relevant cost of €20 is below €22
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