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 €14 per unit with a variable cost of €12 per unit. Fixed costs are €2 400 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €2 400p = €14v = €12profit = €2 000
Q = units
2.Break-even analysisHard
A product sells for €6 per unit, with a variable cost of €4 per unit and fixed costs of €8 000 per year. Budgeted sales are 5 000 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €8 000p = €6v = €4budget = 5 000
MS = %
3.Financial accountingMedium
Under IAS 16, which cost should be included in the cost of a new machine?
- ARepairs carried out two years later
- BStaff training costs after it starts operating
- CGeneral office overheads for the year
- DInstallation costs needed to get it working
4.Financial accountingHard
A company issues shares at €5 each with a nominal value of €1. The extra €4 per share is recorded as:
- ARevenue
- BRetained earnings
- CShare premium
- DA liability
3Solutions
1.Break-even analysis
Answer: Q = 2200 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 = 14 − 12 = €2
Units for the target profit
Q = (F + profit)/(p − v) = (2 400 + 2 000)/2 = 2 200
Answer
Q = 2 200 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) = 8 000/2 = 4 000
Margin of safety
MS = (5 000 − 4 000)/5 000·100 = 20%
Answer
MS = 20%
3.Financial accounting
Answer: D · Installation costs needed to get it working
Why this is the answer
Purchase price plus directly attributable costs, such as delivery and installation, are capitalised. Training, later repairs and general overheads are expensed.
Answer
D · Installation costs needed to get it working
4.Financial accounting
Answer: C · Share premium
Why this is the answer
The amount above nominal value goes to the share premium account in equity; issuing shares is a financing transaction, not income.
Answer
C · Share premium
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