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 €24 per unit with a variable cost of €4 per unit. Fixed costs are €20 000 per month. How many units Q must be sold per month to make a profit of €10 000?
F = €20 000p = €24v = €4profit = €10 000
Q = units
2.Break-even analysisHard
A product sells for €23 per unit, with a variable cost of €15 per unit and fixed costs of €40 000 per year. Budgeted sales are 8 000 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €40 000p = €23v = €15budget = 8 000
MS = %
3.Financial accountingMedium
Retained earnings represent:
- ACash kept in the bank
- BMoney owed to shareholders
- CAccumulated profits that have not been paid out as dividends
- DThe share price
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€80,000
- B€120,000
- C€0
- D€200,000
3Solutions
1.Break-even analysis
Answer: Q = 1500 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 = 24 − 4 = €20
Units for the target profit
Q = (F + profit)/(p − v) = (20 000 + 10 000)/20 = 1 500
Answer
Q = 1 500 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) = 40 000/8 = 5 000
Margin of safety
MS = (8 000 − 5 000)/8 000·100 = 37.5%
Answer
MS = 37.5%
3.Financial accounting
Answer: C · Accumulated profits that have not been paid out as dividends
Why this is the answer
Retained earnings are cumulative net profits minus dividends; they are part of equity, not a pile of cash.
Answer
C · Accumulated profits that have not been paid out as dividends
4.Financial accounting
Answer: A · €80,000
Why this is the answer
Recoverable amount = max(€380,000, €420,000) = €420,000. Impairment = €500,000 − €420,000 = €80,000.
Answer
A · €80,000
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