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 12 000 units at €7 each. The variable cost is €4 per unit and fixed costs are €12 000. Find the degree of operating leverage DOL at this sales level.
Q = 12 000p = €7v = €4F = €12 000
DOL =
2.Break-even analysisHard
A company sells 2 250 units at €24 each, with a variable cost of €4 per unit and fixed costs of €30 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 8%?
Q = 2 250p = €24v = €4F = €30 000%ΔQ = +8%
%ΔΠ = %
3.Financial accountingMedium
What is the key difference between absorption costing and marginal costing?
- AAbsorption costing ignores variable costs
- BMarginal costing includes all overheads in inventory; absorption costing excludes them
- CAbsorption costing includes fixed production overheads in inventory; marginal costing treats them as period costs
- DMarginal costing is required by IFRS for external reporting
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
- BRecognise the whole price at once when the customer signs the contract
- CDefer the whole price and recognise it when the two years of support end
- DAllocate the price using standalone selling prices; recognise the licence at delivery and support over two years
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 = 12 000·(7 − 4) = €36 000
Operating profit
Π = 36 000 − 12 000 = €24 000
DOL
DOL = 36 000/24 000 = 1.5
Answer
DOL = 1.5
2.Break-even analysis
Answer: %ΔΠ = 24 %
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 = 2 250·20 = €45 000
Π = 45 000 − 30 000 = €15 000
DOL
DOL = 45 000/15 000 = 3
Change in profit
%ΔΠ = 3·(+8%) = +24%
Answer
%ΔΠ = +24%
Check: new profit = 2 430·20 − 30 000 = €18 600.00.
3.Financial accounting
Answer: C · Absorption costing includes fixed production overheads in inventory; marginal costing treats them as period costs
Why this is the answer
Under absorption costing each unit carries a share of fixed production overhead. Marginal costing values inventory at variable cost only and expenses fixed costs in the period.
Answer
C · Absorption costing includes fixed production overheads in inventory; marginal costing treats them as period costs
4.Financial accounting
Answer: D · 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
D · Allocate the price using standalone selling prices; recognise the licence at delivery and support over two years
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