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 €53 per unit with a variable cost of €45 per unit. Fixed costs are €12 000 per month. How many units Q must be sold per month to make a profit of €12 000?
F = €12 000p = €53v = €45profit = €12 000
Q = units
2.Break-even analysisHard
A product sells for €9 per unit, with a variable cost of €6 per unit and fixed costs of €2 400 per year. Budgeted sales are 1 000 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €2 400p = €9v = €6budget = 1 000
MS = %
3.Financial accountingMedium
Current assets are €300,000 and current liabilities are €150,000. What is the current ratio?
- A4.5
- B0.5
- C2.0
- D1.5
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%
- C50%
- D20%
3Solutions
1.Break-even analysis
Answer: Q = 3000 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 = 53 − 45 = €8
Units for the target profit
Q = (F + profit)/(p − v) = (12 000 + 12 000)/8 = 3 000
Answer
Q = 3 000 units
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) = 2 400/3 = 800
Margin of safety
MS = (1 000 − 800)/1 000·100 = 20%
Answer
MS = 20%
3.Financial accounting
Answer: C · 2.0
Why this is the answer
€300,000 ÷ €150,000 = 2.0, so current assets cover short-term obligations twice.
Answer
C · 2.0
4.Financial accounting
Answer: D · 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
D · 20%
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