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 €4 per unit. Fixed costs are €14 400 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €14 400p = €16v = €4profit = €6 000
Q = units
2.Break-even analysisHard
A product sells for €47 per unit, with a variable cost of €45 per unit and fixed costs of €1 000 per year. Budgeted sales are 580 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €1 000p = €47v = €45budget = 580
MS = %
3.Financial accountingMedium
A company is being sued. Its lawyers say losing is possible but not probable. How is this treated under IAS 37?
- ADisclosed as a contingent liability in the notes
- BRecognised as an expense and paid into a reserve
- CRecognised as a provision on the balance sheet
- DIgnored completely
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?
- AThe sale is shown as external revenue of the group
- BThe unrealised profit in inventory is eliminated
- CThe profit is shown twice, once for each company
- DNothing, because each company is a separate entity
3Solutions
1.Break-even analysis
Answer: Q = 1700 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 − 4 = €12
Units for the target profit
Q = (F + profit)/(p − v) = (14 400 + 6 000)/12 = 1 700
Answer
Q = 1 700 units
2.Break-even analysis
Answer: MS = 13.79 %
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) = 1 000/2 = 500
Margin of safety
MS = (580 − 500)/580·100 = 13.79%
Answer
MS = 13.79%
3.Financial accounting
Answer: A · Disclosed as a contingent liability in the notes
Why this is the answer
A possible obligation is not recognised but disclosed, unless the chance of outflow is remote. A probable, measurable outflow would require a provision.
Answer
A · Disclosed as a contingent liability in the notes
4.Financial accounting
Answer: B · 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
B · The unrealised profit in inventory is eliminated
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