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 €35 per unit with a variable cost of €15 per unit. Fixed costs are €50 000 per month. How many units Q must be sold per month to make a profit of €12 000?
F = €50 000p = €35v = €15profit = €12 000
Q = units
2.Break-even analysisHard
A product sells for €40 per unit, with a variable cost of €30 per unit and fixed costs of €12 000 per year. Budgeted sales are 1 440 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €12 000p = €40v = €30budget = 1 440
MS = %
3.Financial accountingMedium
At 31 December, electricity used in December (€800) has not yet been billed. Which year-end entry is correct?
- ADebit prepayments, credit cash
- BNo entry until the bill arrives
- CDebit accruals, credit electricity expense
- DDebit electricity expense, credit accruals
4.Financial accountingHard
A company sells a software licence together with two years of support for one price. Under IFRS 15, how is revenue recognised?
- ARecognise half the price in each year without splitting it by obligation
- BAllocate the price using standalone selling prices; recognise the licence at delivery and support over two years
- CRecognise the whole price at once when the customer signs the contract
- DDefer the whole price and recognise it when the two years of support end
3Solutions
1.Break-even analysis
Answer: Q = 3100 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 = 35 − 15 = €20
Units for the target profit
Q = (F + profit)/(p − v) = (50 000 + 12 000)/20 = 3 100
Answer
Q = 3 100 units
2.Break-even analysis
Answer: MS = 16.67 %
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) = 12 000/10 = 1 200
Margin of safety
MS = (1 440 − 1 200)/1 440·100 = 16.67%
Answer
MS = 16.67%
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: B · Allocate the price using standalone selling prices; recognise the licence at delivery and support over two years
Why this is the answer
The licence and support are distinct obligations. The price is split by relative standalone selling prices, and each part is recognised when or as that obligation is satisfied.
Answer
B · Allocate the price using standalone selling prices; recognise the licence at delivery and support over two years
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