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 €49 per unit with a variable cost of €45 per unit. Fixed costs are €20 000 per month. How many units Q must be sold per month to make a profit of €20 000?
F = €20 000p = €49v = €45profit = €20 000
Q = units
2.Break-even analysisHard
A company sells 6 250 units per month at €40 each, with a variable cost of €30 per unit and fixed costs of €25 000 per month. The variable cost rises by €5 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 6 250p = €40v = €30 → €35F = €25 000
Q = units
3.Financial accountingMedium
Which inventory valuation method assumes the oldest goods are sold first?
- ALIFO (last in, first out)
- BSpecific identification of each item
- CWeighted average cost
- DFIFO (first in, first out)
4.Financial accountingHard
Over three years a company reports rising profits while operating cash flow keeps falling. What should an analyst suspect?
- AProfits may be driven by aggressive accruals, such as rising receivables or capitalised costs
- BThe company must have repaid all its loans
- CDepreciation must have been too high
- DThe company has very high earnings quality
3Solutions
1.Break-even analysis
Answer: Q = 10000 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 = 49 − 45 = €4
Units for the target profit
Q = (F + profit)/(p − v) = (20 000 + 20 000)/4 = 10 000
Answer
Q = 10 000 units
2.Break-even analysis
Answer: Q = 12500 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).
Current profit
Π = 6 250·(40 − 30) − 25 000 = €37 500
New contribution margin per unit
40 − 35 = €5
Units for the same profit
Q = (25 000 + 37 500)/5 = 12 500
Answer
Q = 12 500 units
3.Financial accounting
Answer: D · FIFO (first in, first out)
Why this is the answer
Under FIFO, cost of sales uses the oldest costs and closing inventory reflects recent costs. IFRS does not allow LIFO.
Answer
D · FIFO (first in, first out)
4.Financial accounting
Answer: A · Profits may be driven by aggressive accruals, such as rising receivables or capitalised costs
Why this is the answer
A widening gap between profit and operating cash flow often signals working capital build-up or aggressive recognition, suggesting low earnings quality.
Answer
A · Profits may be driven by aggressive accruals, such as rising receivables or capitalised costs
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