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
In the extended services marketing mix (7Ps), which three Ps are added to the original four?
- APartners, publicity and performance
- BPositioning, proof and productivity
- CPeople, process and physical evidence
- DPrice, promotion and physical distribution
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?
- A20%
- B0.2
- C0.5
- D2.0
3.Economics conceptsMedium
The income elasticity of demand for a good is -0.4. The good is:
- AAn inferior good
- BA luxury good
- CA normal necessity
- DA complement
4.Economics conceptsHard
Which is a key difference between the CPI and the GDP deflator?
- AThe CPI covers investment goods; the GDP deflator does not
- BThe GDP deflator includes imported goods; the CPI does not
- CThey always give exactly the same inflation rate
- DThe CPI includes prices of imported consumer goods; the GDP deflator covers only domestically produced goods
5.Financial accountingMedium
A product sells for €40 and has a variable cost of €30. What is its contribution-to-sales (C/S) ratio?
- A33%
- B10%
- C75%
- D25%
6.Financial accountingHard
Goodwill arises in a business combination when:
- AThe consideration paid exceeds the fair value of identifiable net assets acquired
- BA company has a good reputation
- CAssets are revalued upwards
- DThe acquired company makes a loss
7.Break-even analysisMedium
A company sells 2 500 units at €9 each. The variable cost is €4 per unit and fixed costs are €10 000. Find the degree of operating leverage DOL at this sales level.
Q = 2 500p = €9v = €4F = €10 000
DOL =
8.Break-even analysisHard
A company sells two products. Product A sells for €11 with a variable cost of €5; product B sells for €45 with a variable cost of €25. They sell in a fixed mix of 3 units of A for every 1 of B. Fixed costs are €19 000 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €11, vA = €5pB = €45, vB = €25A : B = 3 : 1F = €19 000
Q = units
3Solutions
1.Marketing principles
Answer: C · People, process and physical evidence
Why this is the answer
Booms and Bitner added people, process and physical evidence, because services are intangible and produced with the customer present.
Answer
C · People, process and physical evidence
2.Marketing principles
Answer: C · 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
C · 0.5
3.Economics concepts
Answer: A · An inferior good
Why this is the answer
A negative income elasticity means demand falls as income rises, which defines an inferior good; luxuries have income elasticity above 1.
Answer
A · An inferior good
4.Economics concepts
Answer: D · The CPI includes prices of imported consumer goods; the GDP deflator covers only domestically produced goods
Why this is the answer
The CPI uses a fixed basket of consumer goods, including imports, while the deflator covers all domestically produced output with changing weights.
Answer
D · The CPI includes prices of imported consumer goods; the GDP deflator covers only domestically produced goods
5.Financial accounting
Answer: D · 25%
Why this is the answer
Contribution = €10. C/S ratio = €10 ÷ €40 = 25%. Fixed costs ÷ C/S ratio gives break-even revenue.
Answer
D · 25%
6.Financial accounting
Answer: A · The consideration paid exceeds the fair value of identifiable net assets acquired
Why this is the answer
Goodwill = consideration − fair value of identifiable net assets. Under IFRS it is not amortised but tested for impairment annually.
Answer
A · The consideration paid exceeds the fair value of identifiable net assets acquired
7.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 = 2 500·(9 − 4) = €12 500
Operating profit
Π = 12 500 − 10 000 = €2 500
DOL
DOL = 12 500/2 500 = 5
Answer
DOL = 5
8.Break-even analysis
Answer: Q = 2000 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 = €6, cmB = €20
Weighted contribution margin
(3·6 + 1·20)/4 = €9.50
Break-even units
Q = 19 000/9.5 = 2 000
A: 1 500, B: 500
Answer
Q = 2 000 units
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