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 €24 per unit with a variable cost of €18 per unit. Fixed costs are €6 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €6 000p = €24v = €18profit = €6 000
Q = units
2.Break-even analysisHard
A product sells for €30 per unit, with a variable cost of €25 per unit and fixed costs of €4 000 per year. Budgeted sales are 1 000 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €4 000p = €30v = €25budget = 1 000
MS = %
3.Financial accountingMedium
At 31 December, electricity used in December (€800) has not yet been billed. Which year-end entry is correct?
- ADebit electricity expense, credit accruals
- BNo entry until the bill arrives
- CDebit accruals, credit electricity expense
- DDebit prepayments, credit cash
4.Financial accountingHard
Under IFRS, how is purchased goodwill treated after acquisition?
- AIt is not amortised but tested for impairment at least annually
- BIt is revalued upwards every year
- CIt is amortised over 20 years
- DIt is written off against equity immediately
3Solutions
1.Break-even analysis
Answer: Q = 2000 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 = 24 − 18 = €6
Units for the target profit
Q = (F + profit)/(p − v) = (6 000 + 6 000)/6 = 2 000
Answer
Q = 2 000 units
2.Break-even analysis
Answer: MS = 20 %
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) = 4 000/5 = 800
Margin of safety
MS = (1 000 − 800)/1 000·100 = 20%
Answer
MS = 20%
3.Financial accounting
Answer: A · Debit electricity expense, credit accruals
Why this is the answer
The accrual records December's cost as an expense this year with a current liability, so expenses match the period of use.
Answer
A · Debit electricity expense, credit accruals
4.Financial accounting
Answer: A · It is not amortised but tested for impairment at least annually
Why this is the answer
Goodwill has an indefinite life under IFRS. It is allocated to cash-generating units and tested for impairment yearly, or more often if there are signs of impairment.
Answer
A · It is not amortised but tested for impairment at least annually
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