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 €49 per unit with a variable cost of €45 per unit. Fixed costs are €20 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €20 000p = €49v = €45profit = €2 000
Q = units
2.Break-even analysisHard
A product sells for €35 per unit, with a variable cost of €20 per unit and fixed costs of €18 000 per year. Budgeted sales are 1 440 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €18 000p = €35v = €20budget = 1 440
MS = %
3.Financial accountingMedium
Cost of sales is €600,000 and average inventory is €100,000. What is the inventory turnover?
- A6 times a year
- B0.17 times a year
- C60 times a year
- D16 times a year
4.Financial accountingHard
An asset has a carrying amount of €500,000, fair value less costs of disposal of €380,000 and value in use of €420,000. What impairment loss is recognised?
- A€200,000
- B€0
- C€80,000
- D€120,000
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 = 49 − 45 = €4
Units for the target profit
Q = (F + profit)/(p − v) = (20 000 + 2 000)/4 = 5 500
Answer
Q = 5 500 units
2.Break-even analysis
Answer: MS = 16.67 %
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) = 18 000/15 = 1 200
Margin of safety
MS = (1 440 − 1 200)/1 440·100 = 16.67%
Answer
MS = 16.67%
3.Financial accounting
Answer: A · 6 times a year
Why this is the answer
€600,000 ÷ €100,000 = 6, so inventory is replaced about every 61 days (365 ÷ 6).
Answer
A · 6 times a year
4.Financial accounting
Answer: C · €80,000
Why this is the answer
Recoverable amount = max(€380,000, €420,000) = €420,000. Impairment = €500,000 − €420,000 = €80,000.
Answer
C · €80,000
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