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 1 500 units at €30 each. The variable cost is €15 per unit and fixed costs are €7 500. Find the degree of operating leverage DOL at this sales level.
Q = 1 500p = €30v = €15F = €7 500
DOL =
2.Break-even analysisHard
A company sells 8 000 units at €50 each, with a variable cost of €45 per unit and fixed costs of €20 000. By what percentage %ΔΠ does operating profit change if sales volume falls by 10%?
Q = 8 000p = €50v = €45F = €20 000%ΔQ = −10%
%ΔΠ = %
3.Financial accountingMedium
Trade receivables are €50,000 and annual credit sales are €365,000. What are the receivable days?
- A7.3 days
- B73 days
- C50 days
- D36.5 days
4.Financial accountingHard
A company sells a software licence together with two years of support for one price. Under IFRS 15, how is revenue recognised?
- ARecognise half the price in each year without splitting it by obligation
- BAllocate the price using standalone selling prices; recognise the licence at delivery and support over two years
- CRecognise the whole price at once when the customer signs the contract
- DDefer the whole price and recognise it when the two years of support end
3Solutions
1.Break-even analysis
Answer: DOL = 1.5
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 = 1 500·(30 − 15) = €22 500
Operating profit
Π = 22 500 − 7 500 = €15 000
DOL
DOL = 22 500/15 000 = 1.5
Answer
DOL = 1.5
2.Break-even analysis
Answer: %ΔΠ = −20 %
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 = 8 000·5 = €40 000
Π = 40 000 − 20 000 = €20 000
DOL
DOL = 40 000/20 000 = 2
Change in profit
%ΔΠ = 2·(−10%) = −20%
Answer
%ΔΠ = −20%
Check: new profit = 7 200·5 − 20 000 = €16 000.00.
3.Financial accounting
Answer: C · 50 days
Why this is the answer
€50,000 ÷ €365,000 × 365 = 50 days. This is the average time customers take to pay.
Answer
C · 50 days
4.Financial accounting
Answer: B · Allocate the price using standalone selling prices; recognise the licence at delivery and support over two years
Why this is the answer
The licence and support are distinct obligations. The price is split by relative standalone selling prices, and each part is recognised when or as that obligation is satisfied.
Answer
B · Allocate the price using standalone selling prices; recognise the licence at delivery and support over two years
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