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 10 000 units at €10 each. The variable cost is €4 per unit and fixed costs are €24 000. Find the degree of operating leverage DOL at this sales level.
Q = 10 000p = €10v = €4F = €24 000
DOL =
2.Break-even analysisHard
A product sells for €35 per unit, with a variable cost of €20 per unit and fixed costs of €75 000 per year. Budgeted sales are 6 250 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €75 000p = €35v = €20budget = 6 250
MS = %
3.Financial accountingMedium
Under IAS 16, which cost should be included in the cost of a new machine?
- AInstallation costs needed to get it working
- BGeneral office overheads for the year
- CStaff training costs after it starts operating
- DRepairs carried out two years later
4.Financial accountingHard
Operating profit is €200,000 and capital employed (equity plus non-current liabilities) is €1,000,000. What is ROCE?
- A2%
- B5%
- C20%
- D50%
3Solutions
1.Break-even analysis
Answer: DOL = 1.667
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 = 10 000·(10 − 4) = €60 000
Operating profit
Π = 60 000 − 24 000 = €36 000
DOL
DOL = 60 000/36 000 = 1.667
Answer
DOL = 1.667
2.Break-even analysis
Answer: MS = 20 %
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) = 75 000/15 = 5 000
Margin of safety
MS = (6 250 − 5 000)/6 250·100 = 20%
Answer
MS = 20%
3.Financial accounting
Answer: A · Installation costs needed to get it working
Why this is the answer
Purchase price plus directly attributable costs, such as delivery and installation, are capitalised. Training, later repairs and general overheads are expensed.
Answer
A · Installation costs needed to get it working
4.Financial accounting
Answer: C · 20%
Why this is the answer
ROCE = €200,000 ÷ €1,000,000 = 20%. It measures returns on all long-term finance, so it can be compared with the cost of borrowing.
Answer
C · 20%
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