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 €53 per unit with a variable cost of €45 per unit. Fixed costs are €8 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €8 000p = €53v = €45profit = €6 000
Q = units
2.Break-even analysisHard
A product sells for €16 per unit, with a variable cost of €12 per unit and fixed costs of €2 000 per year. Budgeted sales are 630 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €2 000p = €16v = €12budget = 630
MS = %
3.Financial accountingMedium
A company is being sued. Its lawyers say losing is possible but not probable. How is this treated under IAS 37?
- ARecognised as a provision on the balance sheet
- BDisclosed as a contingent liability in the notes
- CRecognised as an expense and paid into a reserve
- DIgnored completely
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?
- ABy full consolidation as a subsidiary
- BUsing the equity method as an associate
- CAt cost with no changes ever
- DAs a joint operation with line-by-line sharing
3Solutions
1.Break-even analysis
Answer: Q = 1750 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 = 53 − 45 = €8
Units for the target profit
Q = (F + profit)/(p − v) = (8 000 + 6 000)/8 = 1 750
Answer
Q = 1 750 units
2.Break-even analysis
Answer: MS = 20.63 %
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) = 2 000/4 = 500
Margin of safety
MS = (630 − 500)/630·100 = 20.63%
Answer
MS = 20.63%
3.Financial accounting
Answer: B · Disclosed as a contingent liability in the notes
Why this is the answer
A possible obligation is not recognised but disclosed, unless the chance of outflow is remote. A probable, measurable outflow would require a provision.
Answer
B · Disclosed as a contingent liability in the notes
4.Financial accounting
Answer: B · 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
B · Using the equity method as an associate
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