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 company sells 5 000 units at €16 each. The variable cost is €12 per unit and fixed costs are €10 000. Find the degree of operating leverage DOL at this sales level.
Q = 5 000p = €16v = €12F = €10 000
DOL =
2.Break-even analysisHard
A company sells 1 000 units per month at €38 each, with a variable cost of €18 per unit and fixed costs of €10 000 per month. The variable cost rises by €4 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 1 000p = €38v = €18 → €22F = €10 000
Q = units
3.Financial accountingMedium
Under IAS 38, how are research and development costs treated?
- ABoth are always expensed immediately
- BResearch is expensed; development is capitalised only when strict criteria are met
- CBoth are always capitalised as intangible assets
- DResearch is capitalised; development is expensed
4.Financial accountingHard
An asset is impaired when its carrying amount is higher than its:
- ADepreciation charge
- BResidual value only
- CRecoverable amount (the higher of fair value less costs of disposal and value in use)
- DOriginal purchase price
3Solutions
1.Break-even analysis
Answer: DOL = 2
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Total contribution margin
CM = 5 000·(16 − 12) = €20 000
Operating profit
Π = 20 000 − 10 000 = €10 000
DOL
DOL = 20 000/10 000 = 2
Answer
DOL = 2
2.Break-even analysis
Answer: Q = 1250 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).
Current profit
Π = 1 000·(38 − 18) − 10 000 = €10 000
New contribution margin per unit
38 − 22 = €16
Units for the same profit
Q = (10 000 + 10 000)/16 = 1 250
Answer
Q = 1 250 units
3.Financial accounting
Answer: B · Research is expensed; development is capitalised only when strict criteria are met
Why this is the answer
Research costs are always expensed. Development costs are capitalised when, for example, technical feasibility, intention, ability and probable future benefits can be shown.
Answer
B · Research is expensed; development is capitalised only when strict criteria are met
4.Financial accounting
Answer: C · Recoverable amount (the higher of fair value less costs of disposal and value in use)
Why this is the answer
If the carrying amount exceeds the recoverable amount, the difference is written off as an impairment loss.
Answer
C · Recoverable amount (the higher of fair value less costs of disposal and value in use)
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