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 company sells 1 500 units at €57 each. The variable cost is €45 per unit and fixed costs are €14 400. Find the degree of operating leverage DOL at this sales level.
Q = 1 500p = €57v = €45F = €14 400
DOL =
2.Break-even analysisHard
A product sells for €32 per unit, with a variable cost of €20 per unit and fixed costs of €18 000 per year. Budgeted sales are 1 720 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €18 000p = €32v = €20budget = 1 720
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€3,000
- B€9,000
- C€1,000
- D€12,000
4.Financial accountingHard
The going concern assumption means financial statements are prepared assuming the entity:
- AWill make a profit every year
- BHas no debts
- CWill continue to operate for the foreseeable future
- DWill be sold within one year
3Solutions
1.Break-even analysis
Answer: DOL = 5
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Total contribution margin
CM = 1 500·(57 − 45) = €18 000
Operating profit
Π = 18 000 − 14 400 = €3 600
DOL
DOL = 18 000/3 600 = 5
Answer
DOL = 5
2.Break-even analysis
Answer: MS = 12.79 %
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) = 18 000/12 = 1 500
Margin of safety
MS = (1 720 − 1 500)/1 720·100 = 12.79%
Answer
MS = 12.79%
3.Financial accounting
Answer: A · €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
A · €3,000
4.Financial accounting
Answer: C · Will continue to operate for the foreseeable future
Why this is the answer
Unless management intends or must liquidate, assets and liabilities are measured assuming continued operations; material doubts must be disclosed.
Answer
C · Will continue to operate for the foreseeable future
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