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 €10 per unit with a variable cost of €6 per unit. Fixed costs are €6 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €6 000p = €10v = €6profit = €6 000
Q = units
2.Break-even analysisHard
A product sells for €23 per unit, with a variable cost of €18 per unit and fixed costs of €2 500 per year. Budgeted sales are 600 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €2 500p = €23v = €18budget = 600
MS = %
3.Financial accountingMedium
Current assets are €300,000, including inventory of €100,000. Current liabilities are €200,000. What is the quick (acid-test) ratio?
- A2.0
- B1.0
- C0.5
- D1.5
4.Financial accountingHard
Under IFRS, how is purchased goodwill treated after acquisition?
- AIt is written off against equity immediately
- BIt is amortised over 20 years
- CIt is not amortised but tested for impairment at least annually
- DIt is revalued upwards every year
3Solutions
1.Break-even analysis
Answer: Q = 3000 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 = 10 − 6 = €4
Units for the target profit
Q = (F + profit)/(p − v) = (6 000 + 6 000)/4 = 3 000
Answer
Q = 3 000 units
2.Break-even analysis
Answer: MS = 16.67 %
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) = 2 500/5 = 500
Margin of safety
MS = (600 − 500)/600·100 = 16.67%
Answer
MS = 16.67%
3.Financial accounting
Answer: B · 1.0
Why this is the answer
Quick ratio = (current assets − inventory) ÷ current liabilities = €200,000 ÷ €200,000 = 1.0. Inventory is excluded because it may be slow to turn into cash.
Answer
B · 1.0
4.Financial accounting
Answer: C · 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
C · It is not amortised but tested for impairment at least annually
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