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 €5 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €5 000p = €9v = €4profit = €5 000
Q = units
2.Break-even analysisHard
A product sells for €11 per unit, with a variable cost of €6 per unit and fixed costs of €7 500 per year. Budgeted sales are 2 400 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €7 500p = €11v = €6budget = 2 400
MS = %
3.Financial accountingMedium
A machine costs €10,000 and is depreciated at 20% a year on the reducing balance. What is the depreciation charge in year 2?
- A€1,600
- B€2,000
- C€1,800
- D€4,000
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€1,000 adverse
- B€22,000 adverse
- C€2,000 favourable
- D€2,000 adverse
3Solutions
1.Break-even analysis
Answer: Q = 2000 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) = (5 000 + 5 000)/5 = 2 000
Answer
Q = 2 000 units
2.Break-even analysis
Answer: MS = 37.5 %
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) = 7 500/5 = 1 500
Margin of safety
MS = (2 400 − 1 500)/2 400·100 = 37.5%
Answer
MS = 37.5%
3.Financial accounting
Answer: A · €1,600
Why this is the answer
Year 1: 20% × €10,000 = €2,000, leaving €8,000. Year 2: 20% × €8,000 = €1,600. Reducing balance charges less each year.
Answer
A · €1,600
4.Financial accounting
Answer: D · €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
D · €2,000 adverse
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