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 6 400 units at €32 each. The variable cost is €30 per unit and fixed costs are €8 000. Find the degree of operating leverage DOL at this sales level.
Q = 6 400p = €32v = €30F = €8 000
DOL =
2.Break-even analysisHard
A product sells for €17 per unit, with a variable cost of €15 per unit and fixed costs of €1 000 per year. Budgeted sales are 800 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €1 000p = €17v = €15budget = 800
MS = %
3.Financial accountingMedium
A project costs €100,000 and brings in €25,000 cash per year. What is its payback period?
- A2.5 years
- B5 years
- C4 years
- D25 years
4.Financial accountingHard
An asset is impaired when its carrying amount is higher than its:
- ARecoverable amount (the higher of fair value less costs of disposal and value in use)
- BOriginal purchase price
- CDepreciation charge
- DResidual value only
3Solutions
1.Break-even analysis
Answer: DOL = 2.667
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 = 6 400·(32 − 30) = €12 800
Operating profit
Π = 12 800 − 8 000 = €4 800
DOL
DOL = 12 800/4 800 = 2.667
Answer
DOL = 2.667
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) = 1 000/2 = 500
Margin of safety
MS = (800 − 500)/800·100 = 37.5%
Answer
MS = 37.5%
3.Financial accounting
Answer: C · 4 years
Why this is the answer
€100,000 ÷ €25,000 = 4 years. Payback is simple but ignores the time value of money and cash flows after payback.
Answer
C · 4 years
4.Financial accounting
Answer: A · Recoverable amount (the higher of fair value less costs of disposal and value in use)
Why this is the answer
If the carrying amount exceeds the recoverable amount, the difference is written off as an impairment loss.
Answer
A · Recoverable amount (the higher of fair value less costs of disposal and value in use)
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