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 €18 per unit with a variable cost of €8 per unit. Fixed costs are €12 000 per month. How many units Q must be sold per month to make a profit of €10 000?
F = €12 000p = €18v = €8profit = €10 000
Q = units
2.Break-even analysisHard
A company sells 8 000 units per month at €19 each, with a variable cost of €4 per unit and fixed costs of €60 000 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 = 8 000p = €19v = €4 → €9F = €60 000
Q = units
3.Financial accountingMedium
Under IAS 38, how are research and development costs treated?
- AResearch is capitalised; development is expensed
- BBoth are always expensed immediately
- CResearch is expensed; development is capitalised only when strict criteria are met
- DBoth are always capitalised as intangible assets
4.Financial accountingHard
Under the matching principle, the cost of a product warranty sold with goods this year should be:
- AEstimated and recognised as an expense in the year of sale
- BIgnored until the warranty expires
- CRecorded as revenue
- DRecognised only when a customer actually makes a warranty claim
3Solutions
1.Break-even analysis
Answer: Q = 2200 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 = 18 − 8 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (12 000 + 10 000)/10 = 2 200
Answer
Q = 2 200 units
2.Break-even analysis
Answer: Q = 12000 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 = 8 000·(19 − 4) − 60 000 = €60 000
New contribution margin per unit
19 − 9 = €10
Units for the same profit
Q = (60 000 + 60 000)/10 = 12 000
Answer
Q = 12 000 units
3.Financial accounting
Answer: C · Research is expensed; development is capitalised only when strict criteria are met
Why this is the answer
Research costs are always expensed. Development costs are capitalised when, for example, technical feasibility, intention, ability and probable future benefits can be shown.
Answer
C · Research is expensed; development is capitalised only when strict criteria are met
4.Financial accounting
Answer: A · Estimated and recognised as an expense in the year of sale
Why this is the answer
A provision for expected warranty costs is recognised when the goods are sold, matching the expense with the related revenue (IAS 37).
Answer
A · Estimated and recognised as an expense in the year of sale
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