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 €26 per unit with a variable cost of €6 per unit. Fixed costs are €50 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €50 000p = €26v = €6profit = €2 000
Q = units
2.Break-even analysisHard
A company sells 3 000 units at €60 each, with a variable cost of €45 per unit and fixed costs of €30 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 8%?
Q = 3 000p = €60v = €45F = €30 000%ΔQ = +8%
%ΔΠ = %
3.Financial accountingMedium
On 1 October a company pays €12,000 rent for the next 12 months. Its year ends on 31 December. What is the rent expense for this year?
- A€9,000
- B€3,000
- C€12,000
- D€1,000
4.Financial accountingHard
A firm with spare capacity gets a one-off order at €35 per unit. Variable cost is €30 and full cost including fixed overhead is €42. Assuming no other effects, should it accept?
- AYes, each unit adds €5 contribution
- BNo, the price is below full cost
- CNo, the order makes a €7 loss per unit
- DYes, but only if the price exceeds €42
3Solutions
1.Break-even analysis
Answer: Q = 2600 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 = 26 − 6 = €20
Units for the target profit
Q = (F + profit)/(p − v) = (50 000 + 2 000)/20 = 2 600
Answer
Q = 2 600 units
2.Break-even analysis
Answer: %ΔΠ = 24 %
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 = 3 000·15 = €45 000
Π = 45 000 − 30 000 = €15 000
DOL
DOL = 45 000/15 000 = 3
Change in profit
%ΔΠ = 3·(+8%) = +24%
Answer
%ΔΠ = +24%
Check: new profit = 3 240·15 − 30 000 = €18 600.00.
3.Financial accounting
Answer: B · €3,000
Why this is the answer
October to December is 3 months: 3/12 × €12,000 = €3,000. The remaining €9,000 is a prepayment (asset) at year end.
Answer
B · €3,000
4.Financial accounting
Answer: A · Yes, each unit adds €5 contribution
Why this is the answer
Fixed costs do not change, so the order adds €35 − €30 = €5 per unit to profit. Risks such as upsetting regular customers should still be considered.
Answer
A · Yes, each unit adds €5 contribution
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