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 €57 per unit with a variable cost of €45 per unit. Fixed costs are €60 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €60 000p = €57v = €45profit = €6 000
Q = units
2.Break-even analysisHard
A company sells 1 250 units at €16 each, with a variable cost of €12 per unit and fixed costs of €4 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 5%?
Q = 1 250p = €16v = €12F = €4 000%ΔQ = +5%
%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
Under IFRS, how is purchased goodwill treated after acquisition?
- AIt is not amortised but tested for impairment at least annually
- BIt is amortised over 20 years
- CIt is revalued upwards every year
- DIt is written off against equity immediately
3Solutions
1.Break-even analysis
Answer: Q = 5500 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 = 57 − 45 = €12
Units for the target profit
Q = (F + profit)/(p − v) = (60 000 + 6 000)/12 = 5 500
Answer
Q = 5 500 units
2.Break-even analysis
Answer: %ΔΠ = 25 %
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 = 1 250·4 = €5 000
Π = 5 000 − 4 000 = €1 000
DOL
DOL = 5 000/1 000 = 5
Change in profit
%ΔΠ = 5·(+5%) = +25%
Answer
%ΔΠ = +25%
Check: new profit = 1 313·4 − 4 000 = €1 250.00.
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: A · It is not amortised but tested for impairment at least annually
Why this is the answer
Goodwill has an indefinite life under IFRS. It is allocated to cash-generating units and tested for impairment yearly, or more often if there are signs of impairment.
Answer
A · It is not amortised but tested for impairment at least annually
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