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 €19 per unit with a variable cost of €15 per unit. Fixed costs are €20 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €20 000p = €19v = €15profit = €2 000
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 €30 000 per year. Budgeted sales are 3 250 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €30 000p = €32v = €20budget = 3 250
MS = %
3.Financial accountingMedium
Current assets are €300,000 and current liabilities are €150,000. What is the current ratio?
- A0.5
- B4.5
- C1.5
- D2.0
4.Financial accountingHard
Under IFRS, how is purchased goodwill treated after acquisition?
- AIt is amortised over 20 years
- BIt is written off against equity immediately
- CIt is revalued upwards every year
- DIt is not amortised but tested for impairment at least annually
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).
Contribution margin per unit
p − v = 19 − 15 = €4
Units for the target profit
Q = (F + profit)/(p − v) = (20 000 + 2 000)/4 = 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) = 30 000/12 = 2 500
Margin of safety
MS = (3 250 − 2 500)/3 250·100 = 23.08%
Answer
MS = 23.08%
3.Financial accounting
Answer: D · 2.0
Why this is the answer
€300,000 ÷ €150,000 = 2.0, so current assets cover short-term obligations twice.
Answer
D · 2.0
4.Financial accounting
Answer: D · It is not amortised but tested for impairment at least annually
Why this is the answer
Goodwill has an indefinite life under IFRS. It is allocated to cash-generating units and tested for impairment yearly, or more often if there are signs of impairment.
Answer
D · It is not amortised but tested for impairment at least annually
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