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 €13 with a variable cost of €8 per unit. Fixed costs are €12 500 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €6 500 after tax?
p = €13v = €8F = €12 500T = 20%after-tax profit = €6 500
Q = units
2.Break-even analysisHard
A company sells 4 000 units per month at €18 each, with a variable cost of €15 per unit and fixed costs of €6 000 per month. The variable cost rises by €1 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 4 000p = €18v = €15 → €16F = €6 000
Q = units
3.Financial accountingMedium
An asset costs €50,000, has a residual value of €5,000 and a useful life of 5 years. What is the annual straight-line depreciation?
- A€11,000
- B€10,000
- C€9,000
- D€5,000
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€2,000 adverse
- B€1,000 adverse
- C€2,000 favourable
- D€22,000 adverse
3Solutions
1.Break-even analysis
Answer: Q = 4125 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
6 500/(1 − 0.2) = €8 125
Units needed
Q = (12 500 + 8 125)/5 = 4 125
Answer
Q = 4 125 units
2.Break-even analysis
Answer: Q = 6000 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 = 4 000·(18 − 15) − 6 000 = €6 000
New contribution margin per unit
18 − 16 = €2
Units for the same profit
Q = (6 000 + 6 000)/2 = 6 000
Answer
Q = 6 000 units
3.Financial accounting
Answer: C · €9,000
Why this is the answer
(Cost − residual value) ÷ useful life = (€50,000 − €5,000) ÷ 5 = €9,000 per year.
Answer
C · €9,000
4.Financial accounting
Answer: A · €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
A · €2,000 adverse
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