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 can be made in two ways. Method A has fixed costs of €25 000 per year and a variable cost of €8 per unit. Method B, more automated, has fixed costs of €26 000 per year and a variable cost of €6 per unit. At what yearly volume Q do both methods cost the same?
FA = €25 000vA = €8FB = €26 000vB = €6
Q = units
2.Break-even analysisHard
A company sells 12 500 units per month at €21 each, with a variable cost of €6 per unit and fixed costs of €75 000 per month. The variable cost rises by €5 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 12 500p = €21v = €6 → €11F = €75 000
Q = units
3.Financial accountingMedium
Budgeted sales are 1,500 units and the break-even point is 1,000 units. What is the margin of safety?
- A1,000 units
- B500 units
- C1,500 units
- D2,500 units
4.Financial accountingHard
Goodwill arises in a business combination when:
- AAssets are revalued upwards
- BThe consideration paid exceeds the fair value of identifiable net assets acquired
- CThe acquired company makes a loss
- DA company has a good reputation
3Solutions
1.Break-even analysis
Answer: Q = 500 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).
Equal total costs
25 000 + 8Q = 26 000 + 6Q
Solve for Q
Q = (26 000 − 25 000)/(8 − 6) = 500
Answer
Q = 500 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
2.Break-even analysis
Answer: Q = 18750 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).
Current profit
Π = 12 500·(21 − 6) − 75 000 = €112 500
New contribution margin per unit
21 − 11 = €10
Units for the same profit
Q = (75 000 + 112 500)/10 = 18 750
Answer
Q = 18 750 units
3.Financial accounting
Answer: B · 500 units
Why this is the answer
Margin of safety = budgeted sales − break-even sales = 500 units, or one third of budgeted sales.
Answer
B · 500 units
4.Financial accounting
Answer: B · The consideration paid exceeds the fair value of identifiable net assets acquired
Why this is the answer
Goodwill = consideration − fair value of identifiable net assets. Under IFRS it is not amortised but tested for impairment annually.
Answer
B · The consideration paid exceeds the fair value of identifiable net assets acquired
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