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 €25 per unit with a variable cost of €20 per unit. Fixed costs are €10 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €10 000p = €25v = €20profit = €5 000
Q = units
2.Break-even analysisHard
A company sells two products. Product A sells for €18 with a variable cost of €10; product B sells for €45 with a variable cost of €25. They sell in a fixed mix of 2 units of A for every 1 of B. Fixed costs are €36 000 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €18, vA = €10pB = €45, vB = €25A : B = 2 : 1F = €36 000
Q = units
3.Financial accountingMedium
Return on equity (ROE) is calculated as:
- ACurrent assets / current liabilities
- BNet profit / shareholders' equity
- CTotal assets / equity
- DNet profit / total revenue
4.Financial accountingHard
Under the IAS 16 revaluation model, a building is revalued upwards for the first time. Where does the gain go?
- ATo a provision on the balance sheet
- BTo retained earnings as a realised profit
- CTo revenue in the income statement
- DTo other comprehensive income and a revaluation surplus in equity
3Solutions
1.Break-even analysis
Answer: Q = 3000 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 = 25 − 20 = €5
Units for the target profit
Q = (F + profit)/(p − v) = (10 000 + 5 000)/5 = 3 000
Answer
Q = 3 000 units
2.Break-even analysis
Answer: Q = 3000 units
Break-even with a sales mix: when products sell in a fixed ratio, use the weighted average contribution margin: weight each product's p − v by its share of units. Break-even units = F/(weighted contribution margin), split again in the mix ratio.
Contribution margins
cmA = €8, cmB = €20
Weighted contribution margin
(2·8 + 1·20)/3 = €12.00
Break-even units
Q = 36 000/12 = 3 000
A: 2 000, B: 1 000
Answer
Q = 3 000 units
3.Financial accounting
Answer: B · Net profit / shareholders' equity
Why this is the answer
ROE shows how much profit the company generates for each euro of equity invested by shareholders.
Answer
B · Net profit / shareholders' equity
4.Financial accounting
Answer: D · To other comprehensive income and a revaluation surplus in equity
Why this is the answer
Upward revaluations are credited to a revaluation surplus via OCI, unless they reverse an earlier decrease recognised in profit or loss.
Answer
D · To other comprehensive income and a revaluation surplus in equity
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