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 €53 per unit with a variable cost of €45 per unit. Fixed costs are €6 400 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €6 400p = €53v = €45profit = €2 000
Q = units
2.Break-even analysisHard
A product sells for €12 per unit, with a variable cost of €4 per unit and fixed costs of €40 000 per year. Budgeted sales are 6 500 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €40 000p = €12v = €4budget = 6 500
MS = %
3.Financial accountingMedium
An asset costs €50,000, has a residual value of €5,000 and a useful life of 5 years. What is the annual straight-line depreciation?
- A€5,000
- B€11,000
- C€10,000
- D€9,000
4.Financial accountingHard
A parent sold goods to its subsidiary at a profit, and the subsidiary still holds them at year end. What must happen on consolidation?
- ANothing, because each company is a separate entity
- BThe sale is shown as external revenue of the group
- CThe profit is shown twice, once for each company
- DThe unrealised profit in inventory is eliminated
3Solutions
1.Break-even analysis
Answer: Q = 1050 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 = 53 − 45 = €8
Units for the target profit
Q = (F + profit)/(p − v) = (6 400 + 2 000)/8 = 1 050
Answer
Q = 1 050 units
2.Break-even analysis
Answer: MS = 23.08 %
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) = 40 000/8 = 5 000
Margin of safety
MS = (6 500 − 5 000)/6 500·100 = 23.08%
Answer
MS = 23.08%
3.Financial accounting
Answer: D · €9,000
Why this is the answer
(Cost − residual value) ÷ useful life = (€50,000 − €5,000) ÷ 5 = €9,000 per year.
Answer
D · €9,000
4.Financial accounting
Answer: D · The unrealised profit in inventory is eliminated
Why this is the answer
Intra-group sales and purchases are cancelled, and profit on goods still held in the group is removed from inventory and group profit until sold outside.
Answer
D · The unrealised profit in inventory is eliminated
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