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 €9 per unit with a variable cost of €4 per unit. Fixed costs are €12 500 per month. How many units Q must be sold per month to make a profit of €12 000?
F = €12 500p = €9v = €4profit = €12 000
Q = units
2.Break-even analysisHard
A company sells 2 000 units at €18 each, with a variable cost of €6 per unit and fixed costs of €12 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 12%?
Q = 2 000p = €18v = €6F = €12 000%ΔQ = +12%
%ΔΠ = %
3.Financial accountingMedium
What is the key difference between absorption costing and marginal costing?
- AMarginal costing is required by IFRS for external reporting
- BMarginal costing includes all overheads in inventory; absorption costing excludes them
- CAbsorption costing ignores variable costs
- DAbsorption costing includes fixed production overheads in inventory; marginal costing treats them as period costs
4.Financial accountingHard
A company "sells" inventory to a bank and must buy it back later at a higher price, keeping the risks and rewards. How should it be accounted for?
- AAs a gain on disposal of inventory
- BAs revenue on the date of transfer
- CAs a secured loan, not a sale
- DAs a contingent asset in the notes
3Solutions
1.Break-even analysis
Answer: Q = 4900 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 = 9 − 4 = €5
Units for the target profit
Q = (F + profit)/(p − v) = (12 500 + 12 000)/5 = 4 900
Answer
Q = 4 900 units
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 = 2 000·12 = €24 000
Π = 24 000 − 12 000 = €12 000
DOL
DOL = 24 000/12 000 = 2
Change in profit
%ΔΠ = 2·(+12%) = +24%
Answer
%ΔΠ = +24%
Check: new profit = 2 240·12 − 12 000 = €14 880.00.
3.Financial accounting
Answer: D · 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
D · Absorption costing includes fixed production overheads in inventory; marginal costing treats them as period costs
4.Financial accounting
Answer: C · As a secured loan, not a sale
Why this is the answer
Control and risks stay with the company, so the transaction is in substance borrowing secured on inventory. The price difference is an interest cost.
Answer
C · As a secured loan, not a sale
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