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 €14 per unit with a variable cost of €6 per unit. Fixed costs are €40 000 per month. How many units Q must be sold per month to make a profit of €10 000?
F = €40 000p = €14v = €6profit = €10 000
Q = units
2.Break-even analysisHard
A company sells 1 200 units per month at €24 each, with a variable cost of €4 per unit and fixed costs of €16 000 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 200p = €24v = €4 → €8F = €16 000
Q = units
3.Financial accountingMedium
The prudence (conservatism) concept suggests that accountants should:
- AIgnore possible losses
- BValue assets at their selling price
- CAvoid overstating assets and income under uncertainty
- DAlways record the highest possible profit to attract investors
4.Financial accountingHard
A company sells a software licence together with two years of support for one price. Under IFRS 15, how is revenue recognised?
- ADefer the whole price and recognise it when the two years of support end
- BRecognise the whole price at once when the customer signs the contract
- CAllocate the price using standalone selling prices; recognise the licence at delivery and support over two years
- DRecognise half the price in each year without splitting it by obligation
3Solutions
1.Break-even analysis
Answer: Q = 6250 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 = 14 − 6 = €8
Units for the target profit
Q = (F + profit)/(p − v) = (40 000 + 10 000)/8 = 6 250
Answer
Q = 6 250 units
2.Break-even analysis
Answer: Q = 1500 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 = 1 200·(24 − 4) − 16 000 = €8 000
New contribution margin per unit
24 − 8 = €16
Units for the same profit
Q = (16 000 + 8 000)/16 = 1 500
Answer
Q = 1 500 units
3.Financial accounting
Answer: C · Avoid overstating assets and income under uncertainty
Why this is the answer
Prudence means exercising caution so that assets and income are not overstated and liabilities and expenses not understated.
Answer
C · Avoid overstating assets and income under uncertainty
4.Financial accounting
Answer: C · Allocate the price using standalone selling prices; recognise the licence at delivery and support over two years
Why this is the answer
The licence and support are distinct obligations. The price is split by relative standalone selling prices, and each part is recognised when or as that obligation is satisfied.
Answer
C · Allocate the price using standalone selling prices; recognise the licence at delivery and support over two years
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