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 can be made in two ways. Method A has fixed costs of €20 000 per year and a variable cost of €10 per unit. Method B, more automated, has fixed costs of €35 000 per year and a variable cost of €4 per unit. At what yearly volume Q do both methods cost the same?
FA = €20 000vA = €10FB = €35 000vB = €4
Q = units
2.Break-even analysisHard
A product sells for €40 per unit, with a variable cost of €30 per unit and fixed costs of €20 000 per year. Budgeted sales are 2 400 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €20 000p = €40v = €30budget = 2 400
MS = %
3.Financial accountingMedium
Under IAS 16, which cost should be included in the cost of a new machine?
- AInstallation costs needed to get it working
- BRepairs carried out two years later
- CStaff training costs after it starts operating
- DGeneral office overheads for the year
4.Financial accountingHard
Under IFRS 16, which lease may a lessee choose to expense on a straight-line basis instead of recognising a right-of-use asset?
- AA lease with a term of 12 months or less
- BAny lease of land and buildings
- CAny lease with monthly payments
- DA ten-year lease of a large production machine
3Solutions
1.Break-even analysis
Answer: Q = 2500 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).
Equal total costs
20 000 + 10Q = 35 000 + 4Q
Solve for Q
Q = (35 000 − 20 000)/(10 − 4) = 2 500
Answer
Q = 2 500 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
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) = 20 000/10 = 2 000
Margin of safety
MS = (2 400 − 2 000)/2 400·100 = 16.67%
Answer
MS = 16.67%
3.Financial accounting
Answer: A · 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
A · Installation costs needed to get it working
4.Financial accounting
Answer: A · A lease with a term of 12 months or less
Why this is the answer
Lessees may elect not to recognise short-term leases (12 months or less) and leases of low-value assets, expensing the payments instead.
Answer
A · A lease with a term of 12 months or less
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