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 €45 per unit with a variable cost of €25 per unit. Fixed costs are €80 000 per month. How many units Q must be sold per month to make a profit of €20 000?
F = €80 000p = €45v = €25profit = €20 000
Q = units
2.Break-even analysisHard
A company sells 750 units at €10 each, with a variable cost of €8 per unit and fixed costs of €1 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 10%?
Q = 750p = €10v = €8F = €1 000%ΔQ = +10%
%ΔΠ = %
3.Financial accountingMedium
A shop buys 100 units at €10, then 100 units at €12, and then sells 150 units. What is cost of sales using FIFO?
- A€1,500
- B€1,600
- C€1,650
- D€1,700
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 = 5000 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 = 45 − 25 = €20
Units for the target profit
Q = (F + profit)/(p − v) = (80 000 + 20 000)/20 = 5 000
Answer
Q = 5 000 units
2.Break-even analysis
Answer: %ΔΠ = 30 %
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.
Contribution margin and profit
CM = 750·2 = €1 500
Π = 1 500 − 1 000 = €500
DOL
DOL = 1 500/500 = 3
Change in profit
%ΔΠ = 3·(+10%) = +30%
Answer
%ΔΠ = +30%
Check: new profit = 825·2 − 1 000 = €650.00.
3.Financial accounting
Answer: B · €1,600
Why this is the answer
FIFO: 100 × €10 + 50 × €12 = €1,600. The 50 units left are valued at the latest cost of €12.
Answer
B · €1,600
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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