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
Business Fundamentals: cram pack
Formula sheets, the key method steps for every topic and 8 practice problems, with full solutions at the back.
1Formulas and methods
2Practice problems
1.Marketing principlesMedium
Two established brands from different companies jointly market one product, such as a credit card carrying an airline's brand. This is:
- ALine extension
- BCo-branding
- CBrand extension
- DMultibranding
2.Marketing principlesHard
In the BCG matrix, a firm has 20% market share and its largest competitor has 40%. What is the firm's relative market share?
- A0.2
- B0.5
- C20%
- D2.0
3.Economics conceptsMedium
The marginal cost curve cuts the average total cost curve:
- AAt the minimum point of average total cost
- BAt the maximum point of average total cost
- CNever, as the two curves are parallel
- DWhere average total cost equals zero
4.Economics conceptsHard
The Phillips curve originally suggested:
- AA trade-off between inflation and unemployment in the short run
- BThat inflation and unemployment always rise and fall together in the short run
- CThat higher taxes always reduce inflation
- DThat unemployment has no link to inflation
5.Financial accountingMedium
A company finds that a machine will last 8 years instead of the 5 originally estimated. Under IAS 8, how is this change applied?
- ABy changing the original cost of the machine
- BRetrospectively, by restating all prior years
- CProspectively, by spreading the remaining carrying amount over the new remaining life
- DBy recognising a large gain in the current year
6.Financial accountingHard
Operating profit is €200,000 and capital employed (equity plus non-current liabilities) is €1,000,000. What is ROCE?
- A20%
- B50%
- C5%
- D2%
7.Break-even analysisMedium
A company sells 4 000 units at €45 each. The variable cost is €30 per unit and fixed costs are €37 500. Find the degree of operating leverage DOL at this sales level.
Q = 4 000p = €45v = €30F = €37 500
DOL =
8.Break-even analysisHard
A company sells 1 880 units at €40 each, with a variable cost of €25 per unit and fixed costs of €22 500. By what percentage %ΔΠ does operating profit change if sales volume falls by 5%?
Q = 1 880p = €40v = €25F = €22 500%ΔQ = −5%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: B · Co-branding
Why this is the answer
Co-branding combines the strengths and customer bases of two brands. It can add credibility but links each brand's reputation to the other.
Answer
B · Co-branding
2.Marketing principles
Answer: B · 0.5
Why this is the answer
Relative market share = 20% ÷ 40% = 0.5. A value below 1 means the firm is not the market leader, placing it on the low-share side of the matrix.
Answer
B · 0.5
3.Economics concepts
Answer: A · At the minimum point of average total cost
Why this is the answer
When MC is below ATC it pulls the average down, and when it is above it pushes the average up, so MC crosses ATC at its minimum.
Answer
A · At the minimum point of average total cost
4.Economics concepts
Answer: A · A trade-off between inflation and unemployment in the short run
Why this is the answer
Phillips found an inverse relationship between wage inflation and unemployment; expectations-augmented versions show no long-run trade-off at the natural rate.
Answer
A · A trade-off between inflation and unemployment in the short run
5.Financial accounting
Answer: C · Prospectively, by spreading the remaining carrying amount over the new remaining life
Why this is the answer
Changes in estimates affect the current and future periods only. Prior-period restatement is for changes in policy and corrections of errors.
Answer
C · Prospectively, by spreading the remaining carrying amount over the new remaining life
6.Financial accounting
Answer: A · 20%
Why this is the answer
ROCE = €200,000 ÷ €1,000,000 = 20%. It measures returns on all long-term finance, so it can be compared with the cost of borrowing.
Answer
A · 20%
7.Break-even analysis
Answer: DOL = 2.667
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 = 4 000·(45 − 30) = €60 000
Operating profit
Π = 60 000 − 37 500 = €22 500
DOL
DOL = 60 000/22 500 = 2.667
Answer
DOL = 2.667
8.Break-even analysis
Answer: %ΔΠ = −24.74 %
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 = 1 880·15 = €28 200
Π = 28 200 − 22 500 = €5 700
DOL
DOL = 28 200/5 700 = 4.947
Change in profit
%ΔΠ = 4.947·(−5%) = −24.74%
Answer
%ΔΠ = −24.74%
Check: new profit = 1 786·15 − 22 500 = €4 290.00.
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