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 €25 000 per month. How many units Q must be sold per month to make a profit of €10 000?
F = €25 000p = €9v = €4profit = €10 000
Q = units
2.Break-even analysisHard
A product sells for €14 per unit, with a variable cost of €6 per unit and fixed costs of €40 000 per year. Budgeted sales are 7 000 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €40 000p = €14v = €6budget = 7 000
MS = %
3.Financial accountingMedium
At 31 December, electricity used in December (€800) has not yet been billed. Which year-end entry is correct?
- ANo entry until the bill arrives
- BDebit prepayments, credit cash
- CDebit accruals, credit electricity expense
- DDebit electricity expense, credit accruals
4.Financial accountingHard
Under the matching principle, the cost of a product warranty sold with goods this year should be:
- ARecorded as revenue
- BIgnored until the warranty expires
- CRecognised only when a customer actually makes a warranty claim
- DEstimated and recognised as an expense in the year of sale
3Solutions
1.Break-even analysis
Answer: Q = 7000 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) = (25 000 + 10 000)/5 = 7 000
Answer
Q = 7 000 units
2.Break-even analysis
Answer: MS = 28.57 %
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).
Break-even quantity
Q = F/(p − v) = 40 000/8 = 5 000
Margin of safety
MS = (7 000 − 5 000)/7 000·100 = 28.57%
Answer
MS = 28.57%
3.Financial accounting
Answer: D · Debit electricity expense, credit accruals
Why this is the answer
The accrual records December's cost as an expense this year with a current liability, so expenses match the period of use.
Answer
D · Debit electricity expense, credit accruals
4.Financial accounting
Answer: D · 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
D · Estimated and recognised as an expense in the year of sale
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