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 €28 each. The variable cost is €8 per unit and fixed costs are €80 000. Find the degree of operating leverage DOL at this sales level.
Q = 5 000p = €28v = €8F = €80 000
DOL =
2.Break-even analysisHard
A company sells 12 500 units per month at €28 each, with a variable cost of €18 per unit and fixed costs of €50 000 per month. The variable cost rises by €5 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 12 500p = €28v = €18 → €23F = €50 000
Q = units
3.Financial accountingMedium
A company pays its insurance for next year in advance. How is the payment recorded at the year end?
- AAs revenue
- BAs an expense of the current year in full
- CAs a liability
- DAs a prepaid expense (asset)
4.Financial accountingHard
The going concern assumption means financial statements are prepared assuming the entity:
- AWill make a profit every year
- BHas no debts
- CWill be sold within one year
- DWill continue to operate for the foreseeable future
3Solutions
1.Break-even analysis
Answer: DOL = 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 = 5 000·(28 − 8) = €100 000
Operating profit
Π = 100 000 − 80 000 = €20 000
DOL
DOL = 100 000/20 000 = 5
Answer
DOL = 5
2.Break-even analysis
Answer: Q = 25000 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 = 12 500·(28 − 18) − 50 000 = €75 000
New contribution margin per unit
28 − 23 = €5
Units for the same profit
Q = (50 000 + 75 000)/5 = 25 000
Answer
Q = 25 000 units
3.Financial accounting
Answer: D · As a prepaid expense (asset)
Why this is the answer
The unused part of the payment is an asset (prepayment) and becomes an expense in the period it covers.
Answer
D · As a prepaid expense (asset)
4.Financial accounting
Answer: D · Will continue to operate for the foreseeable future
Why this is the answer
Unless management intends or must liquidate, assets and liabilities are measured assuming continued operations; material doubts must be disclosed.
Answer
D · Will continue to operate for the foreseeable future
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