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 company sells 1 000 units at €22 each. The variable cost is €12 per unit and fixed costs are €8 000. Find the degree of operating leverage DOL at this sales level.
Q = 1 000p = €22v = €12F = €8 000
DOL =
2.Break-even analysisHard
A company sells two products. Product A sells for €17 with a variable cost of €12; product B sells for €30 with a variable cost of €20. They sell in a fixed mix of 2 units of A for every 1 of B. Fixed costs are €20 000 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €17, vA = €12pB = €30, vB = €20A : B = 2 : 1F = €20 000
Q = units
3.Financial accountingMedium
A project has a positive net present value (NPV) at the company's cost of capital. This means:
- AIt recovers its cost within one year
- BIt earns more than the required return and should add value
- CIt has no risk at all
- DIts reported accounting profit will be positive in every year
4.Financial accountingHard
Under IFRS 16, a lessee typically recognises a lease on the balance sheet as:
- AEquity and a provision
- BA right-of-use asset and a lease liability
- CAn operating expense only, spread evenly over the lease term
- DRevenue and inventory
3Solutions
1.Break-even analysis
Answer: DOL = 5
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Total contribution margin
CM = 1 000·(22 − 12) = €10 000
Operating profit
Π = 10 000 − 8 000 = €2 000
DOL
DOL = 10 000/2 000 = 5
Answer
DOL = 5
2.Break-even analysis
Answer: Q = 3000 units
Break-even with a sales mix: when products sell in a fixed ratio, use the weighted average contribution margin: weight each product's p − v by its share of units. Break-even units = F/(weighted contribution margin), split again in the mix ratio.
Contribution margins
cmA = €5, cmB = €10
Weighted contribution margin
(2·5 + 1·10)/3 = €6.67
Break-even units
Q = 20 000/6.667 = 3 000
A: 2 000, B: 1 000
Answer
Q = 3 000 units
3.Financial accounting
Answer: B · It earns more than the required return and should add value
Why this is the answer
A positive NPV means the present value of inflows exceeds the investment at the required rate, so the project increases shareholder wealth.
Answer
B · It earns more than the required return and should add value
4.Financial accounting
Answer: B · A right-of-use asset and a lease liability
Why this is the answer
IFRS 16 removed the operating lease distinction for lessees: they recognise a right-of-use asset and a liability for lease payments, except for short-term and low-value leases.
Answer
B · A right-of-use asset and a lease liability
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