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 per unit with a variable cost of €15 per unit. Fixed costs are €10 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €10 000p = €20v = €15profit = €2 000
Q = units
2.Break-even analysisHard
A company sells two products. Product A sells for €11 with a variable cost of €5; product B sells for €37 with a variable cost of €25. They sell in a fixed mix of 5 units of A for every 2 of B. Fixed costs are €54 000 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €11, vA = €5pB = €37, vB = €25A : B = 5 : 2F = €54 000
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€5,000
- B€9,000
- C€11,000
- D€10,000
4.Financial accountingHard
An asset has a carrying amount of €500,000, fair value less costs of disposal of €380,000 and value in use of €420,000. What impairment loss is recognised?
- A€0
- B€80,000
- C€120,000
- D€200,000
3Solutions
1.Break-even analysis
Answer: Q = 2400 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 = 20 − 15 = €5
Units for the target profit
Q = (F + profit)/(p − v) = (10 000 + 2 000)/5 = 2 400
Answer
Q = 2 400 units
2.Break-even analysis
Answer: Q = 7000 units
Break-even with a sales mix: when products sell in a fixed ratio, use the weighted average contribution margin: weight each product's p − v by its share of units. Break-even units = F/(weighted contribution margin), split again in the mix ratio.
Contribution margins
cmA = €6, cmB = €12
Weighted contribution margin
(5·6 + 2·12)/7 = €7.71
Break-even units
Q = 54 000/7.714 = 7 000
A: 5 000, B: 2 000
Answer
Q = 7 000 units
3.Financial accounting
Answer: B · €9,000
Why this is the answer
(Cost − residual value) ÷ useful life = (€50,000 − €5,000) ÷ 5 = €9,000 per year.
Answer
B · €9,000
4.Financial accounting
Answer: B · €80,000
Why this is the answer
Recoverable amount = max(€380,000, €420,000) = €420,000. Impairment = €500,000 − €420,000 = €80,000.
Answer
B · €80,000
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