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 7 500 units at €15 each. The variable cost is €12 per unit and fixed costs are €7 500. Find the degree of operating leverage DOL at this sales level.
Q = 7 500p = €15v = €12F = €7 500
DOL =
2.Break-even analysisHard
A company sells 10 000 units per month at €21 each, with a variable cost of €6 per unit and fixed costs of €60 000 per month. The variable cost rises by €3 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 10 000p = €21v = €6 → €9F = €60 000
Q = units
3.Financial accountingMedium
Trade receivables are €50,000 and annual credit sales are €365,000. What are the receivable days?
- A7.3 days
- B50 days
- C36.5 days
- D73 days
4.Financial accountingHard
Tax rules allow faster depreciation of a machine than the company uses in its accounts. What arises under IAS 12?
- ANo tax effect at all
- BA deferred tax asset
- CA deferred tax liability
- DA refund of current tax paid
3Solutions
1.Break-even analysis
Answer: DOL = 1.5
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 = 7 500·(15 − 12) = €22 500
Operating profit
Π = 22 500 − 7 500 = €15 000
DOL
DOL = 22 500/15 000 = 1.5
Answer
DOL = 1.5
2.Break-even analysis
Answer: Q = 12500 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 = 10 000·(21 − 6) − 60 000 = €90 000
New contribution margin per unit
21 − 9 = €12
Units for the same profit
Q = (60 000 + 90 000)/12 = 12 500
Answer
Q = 12 500 units
3.Financial accounting
Answer: B · 50 days
Why this is the answer
€50,000 ÷ €365,000 × 365 = 50 days. This is the average time customers take to pay.
Answer
B · 50 days
4.Financial accounting
Answer: C · A deferred tax liability
Why this is the answer
The tax base falls faster than the carrying amount, creating a taxable temporary difference. The future extra tax is recognised now as a deferred tax liability.
Answer
C · A deferred tax liability
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