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 €16 per unit with a variable cost of €12 per unit. Fixed costs are €16 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €16 000p = €16v = €12profit = €6 000
Q = units
2.Break-even analysisHard
A product sells for €49 per unit, with a variable cost of €45 per unit and fixed costs of €10 000 per year. Budgeted sales are 3 130 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €10 000p = €49v = €45budget = 3 130
MS = %
3.Financial accountingMedium
Trade receivables are €50,000 and annual credit sales are €365,000. What are the receivable days?
- A36.5 days
- B7.3 days
- C50 days
- D73 days
4.Financial accountingHard
Under IFRS, how is purchased goodwill treated after acquisition?
- AIt is revalued upwards every year
- BIt is written off against equity immediately
- CIt is amortised over 20 years
- DIt is not amortised but tested for impairment at least annually
3Solutions
1.Break-even analysis
Answer: Q = 5500 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 = 16 − 12 = €4
Units for the target profit
Q = (F + profit)/(p − v) = (16 000 + 6 000)/4 = 5 500
Answer
Q = 5 500 units
2.Break-even analysis
Answer: MS = 20.13 %
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) = 10 000/4 = 2 500
Margin of safety
MS = (3 130 − 2 500)/3 130·100 = 20.13%
Answer
MS = 20.13%
3.Financial accounting
Answer: C · 50 days
Why this is the answer
€50,000 ÷ €365,000 × 365 = 50 days. This is the average time customers take to pay.
Answer
C · 50 days
4.Financial accounting
Answer: D · 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
D · It is not amortised but tested for impairment at least annually
ExamProblems · examproblems.com/courses/management-accounting