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 €4 per unit. Fixed costs are €20 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €20 000p = €14v = €4profit = €2 000
Q = units
2.Break-even analysisHard
A product sells for €53 per unit, with a variable cost of €45 per unit and fixed costs of €9 600 per year. Budgeted sales are 1 800 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €9 600p = €53v = €45budget = 1 800
MS = %
3.Financial accountingMedium
A project costs €100,000 and brings in €25,000 cash per year. What is its payback period?
- A25 years
- B4 years
- C2.5 years
- D5 years
4.Financial accountingHard
Operating profit is €200,000 and capital employed (equity plus non-current liabilities) is €1,000,000. What is ROCE?
- A20%
- B50%
- C2%
- D5%
3Solutions
1.Break-even analysis
Answer: Q = 2200 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 − 4 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (20 000 + 2 000)/10 = 2 200
Answer
Q = 2 200 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) = 9 600/8 = 1 200
Margin of safety
MS = (1 800 − 1 200)/1 800·100 = 33.33%
Answer
MS = 33.33%
3.Financial accounting
Answer: B · 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
B · 4 years
4.Financial accounting
Answer: A · 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
A · 20%
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