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 €35 with a variable cost of €20 per unit. Fixed costs are €15 000 per month and profit is taxed at 25%. How many units Q must be sold per month to earn €4 500 after tax?
p = €35v = €20F = €15 000T = 25%after-tax profit = €4 500
Q = units
2.Break-even analysisHard
A product sells for €9 per unit, with a variable cost of €6 per unit and fixed costs of €12 000 per year. Budgeted sales are 5 000 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €12 000p = €9v = €6budget = 5 000
MS = %
3.Financial accountingMedium
Budgeted sales are 1,500 units and the break-even point is 1,000 units. What is the margin of safety?
- A2,500 units
- B1,000 units
- C500 units
- D1,500 units
4.Financial accountingHard
An investor holds 30% of a company's shares and has significant influence but not control. How is the investment usually accounted for in group accounts?
- AUsing the equity method as an associate
- BAs a joint operation with line-by-line sharing
- CBy full consolidation as a subsidiary
- DAt cost with no changes ever
3Solutions
1.Break-even analysis
Answer: Q = 1400 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).
Pre-tax profit needed
4 500/(1 − 0.25) = €6 000
Units needed
Q = (15 000 + 6 000)/15 = 1 400
Answer
Q = 1 400 units
2.Break-even analysis
Answer: MS = 20 %
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) = 12 000/3 = 4 000
Margin of safety
MS = (5 000 − 4 000)/5 000·100 = 20%
Answer
MS = 20%
3.Financial accounting
Answer: C · 500 units
Why this is the answer
Margin of safety = budgeted sales − break-even sales = 500 units, or one third of budgeted sales.
Answer
C · 500 units
4.Financial accounting
Answer: A · Using the equity method as an associate
Why this is the answer
Under IAS 28 the investment starts at cost and is adjusted for the investor's share of the associate's profits or losses, less dividends received.
Answer
A · Using the equity method as an associate
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