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 €51 with a variable cost of €45 per unit. Fixed costs are €30 000 per month and profit is taxed at 25%. How many units Q must be sold per month to earn €9 000 after tax?
p = €51v = €45F = €30 000T = 25%after-tax profit = €9 000
Q = units
2.Break-even analysisHard
A product sells for €10 per unit, with a variable cost of €4 per unit and fixed costs of €7 200 per year. Budgeted sales are 1 680 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €7 200p = €10v = €4budget = 1 680
MS = %
3.Financial accountingMedium
When preparing a bank reconciliation, which item explains why the bank statement balance is higher than the cash book balance?
- ACash deposited but not yet credited on the bank statement
- BCheques issued but not yet presented to the bank
- CA direct debit not yet entered in the cash book
- DBank charges not yet entered in the cash book
4.Financial accountingHard
Under IFRS 16, which lease may a lessee choose to expense on a straight-line basis instead of recognising a right-of-use asset?
- AAny lease of land and buildings
- BAny lease with monthly payments
- CA ten-year lease of a large production machine
- DA lease with a term of 12 months or less
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).
Pre-tax profit needed
9 000/(1 − 0.25) = €12 000
Units needed
Q = (30 000 + 12 000)/6 = 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) = 7 200/6 = 1 200
Margin of safety
MS = (1 680 − 1 200)/1 680·100 = 28.57%
Answer
MS = 28.57%
3.Financial accounting
Answer: B · Cheques issued but not yet presented to the bank
Why this is the answer
Unpresented cheques have reduced the cash book but not the bank balance. Outstanding deposits, bank charges and unrecorded direct debits work the other way.
Answer
B · Cheques issued but not yet presented to the bank
4.Financial accounting
Answer: D · A lease with a term of 12 months or less
Why this is the answer
Lessees may elect not to recognise short-term leases (12 months or less) and leases of low-value assets, expensing the payments instead.
Answer
D · A lease with a term of 12 months or less
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