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 €20 with a variable cost of €15 per unit. Fixed costs are €20 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €6 000 after tax?
p = €20v = €15F = €20 000T = 20%after-tax profit = €6 000
Q = units
2.Break-even analysisHard
A product sells for €32 per unit, with a variable cost of €20 per unit and fixed costs of €12 000 per year. Budgeted sales are 1 300 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €12 000p = €32v = €20budget = 1 300
MS = %
3.Financial accountingMedium
Under the accrual basis of accounting, revenue is recognised when:
- ACash is received
- BIt is earned, whether or not cash has been received
- CThe tax return is filed
- DThe customer pays the invoice, even if goods were delivered earlier
4.Financial accountingHard
The standard is 2 labour hours per unit at €20 an hour. 500 units are made in 1,100 hours. What is the labour efficiency variance?
- A€1,000 adverse
- B€22,000 adverse
- C€2,000 adverse
- D€2,000 favourable
3Solutions
1.Break-even analysis
Answer: Q = 5500 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
6 000/(1 − 0.2) = €7 500
Units needed
Q = (20 000 + 7 500)/5 = 5 500
Answer
Q = 5 500 units
2.Break-even analysis
Answer: MS = 23.08 %
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) = 12 000/12 = 1 000
Margin of safety
MS = (1 300 − 1 000)/1 300·100 = 23.08%
Answer
MS = 23.08%
3.Financial accounting
Answer: B · It is earned, whether or not cash has been received
Why this is the answer
Accrual accounting records revenue when the performance obligation is satisfied and expenses when incurred, not when cash moves.
Answer
B · It is earned, whether or not cash has been received
4.Financial accounting
Answer: C · €2,000 adverse
Why this is the answer
Standard hours = 500 × 2 = 1,000. Extra 100 hours × €20 = €2,000 adverse, because more hours were used than the standard allows.
Answer
C · €2,000 adverse
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