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
- BMultibranding
- CCo-branding
- DBrand extension
2.Marketing principlesHard
A manufacturer starts selling online directly to consumers at lower prices than its retailers. Retailers complain. What is this?
- ACannibalisation by a rival brand
- BVertical channel conflict
- CA pull strategy
- DHorizontal channel conflict
3.Economics conceptsMedium
When a central bank buys government bonds from banks in open market operations, it usually:
- AHas no effect on the money supply
- BIncreases bank reserves and the money supply
- CRaises tax revenue for the government
- DReduces bank reserves and so shrinks the money supply
4.Economics conceptsHard
In Spence's job market signalling model, education can be valuable to employers even if it does not raise productivity because:
- AIt reduces the wages employers must pay
- BEmployers are required by law to hire graduates
- CIt guarantees that every graduate is highly productive
- DIt is less costly for high-ability workers to acquire, so it reveals their type
5.Financial accountingMedium
A machine costs €10,000 and is depreciated at 20% a year on the reducing balance. What is the depreciation charge in year 2?
- A€1,600
- B€2,000
- C€1,800
- D€4,000
6.Financial accountingHard
A company issues shares at €5 each with a nominal value of €1. The extra €4 per share is recorded as:
- AShare premium
- BRevenue
- CRetained earnings
- DA liability
7.Break-even analysisMedium
A company sells 3 000 units at €20 each. The variable cost is €8 per unit and fixed costs are €12 000. Find the degree of operating leverage DOL at this sales level.
Q = 3 000p = €20v = €8F = €12 000
DOL =
8.Break-even analysisHard
A company sells 2 000 units per month at €55 each, with a variable cost of €45 per unit and fixed costs of €8 000 per month. The variable cost rises by €2 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 2 000p = €55v = €45 → €47F = €8 000
Q = units
3Solutions
1.Marketing principles
Answer: C · 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
C · Co-branding
2.Marketing principles
Answer: B · Vertical channel conflict
Why this is the answer
Vertical conflict arises between levels, such as manufacturer and retailer. Horizontal conflict is between firms at the same level, such as two retailers.
Answer
B · Vertical channel conflict
3.Economics concepts
Answer: B · Increases bank reserves and the money supply
Why this is the answer
Buying bonds injects reserves into the banking system, which tends to increase the money supply and lower interest rates.
Answer
B · Increases bank reserves and the money supply
4.Economics concepts
Answer: D · It is less costly for high-ability workers to acquire, so it reveals their type
Why this is the answer
If acquiring education costs less for able workers, only they find it worth getting, so it separates types and solves the hidden information problem.
Answer
D · It is less costly for high-ability workers to acquire, so it reveals their type
5.Financial accounting
Answer: A · €1,600
Why this is the answer
Year 1: 20% × €10,000 = €2,000, leaving €8,000. Year 2: 20% × €8,000 = €1,600. Reducing balance charges less each year.
Answer
A · €1,600
6.Financial accounting
Answer: A · Share premium
Why this is the answer
The amount above nominal value goes to the share premium account in equity; issuing shares is a financing transaction, not income.
Answer
A · Share premium
7.Break-even analysis
Answer: DOL = 1.5
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 = 3 000·(20 − 8) = €36 000
Operating profit
Π = 36 000 − 12 000 = €24 000
DOL
DOL = 36 000/24 000 = 1.5
Answer
DOL = 1.5
8.Break-even analysis
Answer: Q = 2500 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).
Current profit
Π = 2 000·(55 − 45) − 8 000 = €12 000
New contribution margin per unit
55 − 47 = €8
Units for the same profit
Q = (8 000 + 12 000)/8 = 2 500
Answer
Q = 2 500 units
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