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 €33 per unit with a variable cost of €25 per unit. Fixed costs are €8 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €8 000p = €33v = €25profit = €5 000
Q = units
2.Break-even analysisHard
A company sells 630 units at €32 each, with a variable cost of €30 per unit and fixed costs of €1 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 12%?
Q = 630p = €32v = €30F = €1 000%ΔQ = +12%
%ΔΠ = %
3.Financial accountingMedium
A shop buys 100 units at €10, then 100 units at €12, and then sells 150 units. What is cost of sales using FIFO?
- A€1,650
- B€1,600
- C€1,500
- D€1,700
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?
- AAny lease with monthly payments
- BAny lease of land and buildings
- CA lease with a term of 12 months or less
- DA ten-year lease of a large production machine
3Solutions
1.Break-even analysis
Answer: Q = 1625 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 = 33 − 25 = €8
Units for the target profit
Q = (F + profit)/(p − v) = (8 000 + 5 000)/8 = 1 625
Answer
Q = 1 625 units
2.Break-even analysis
Answer: %ΔΠ = 58.15 %
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.
Contribution margin and profit
CM = 630·2 = €1 260
Π = 1 260 − 1 000 = €260
DOL
DOL = 1 260/260 = 4.846
Change in profit
%ΔΠ = 4.846·(+12%) = +58.15%
Answer
%ΔΠ = +58.15%
Check: new profit = 706·2 − 1 000 = €411.20.
3.Financial accounting
Answer: B · €1,600
Why this is the answer
FIFO: 100 × €10 + 50 × €12 = €1,600. The 50 units left are valued at the latest cost of €12.
Answer
B · €1,600
4.Financial accounting
Answer: C · 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
C · A lease with a term of 12 months or less
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