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
A fast-food chain changes its menu in each country to suit local tastes. This international strategy is called:
- AStandardisation
- BLicensing
- CAdaptation
- DExporting
2.Marketing principlesHard
A firm launches a cheaper version of its best-selling product. Total sales rise slightly, but sales of the original fall sharply. What has happened?
- ACannibalisation of the original product's sales
- BA pull strategy failure
- CSuccessful market development into a new segment
- DBrand dilution by a competitor
3.Economics conceptsMedium
A negative externality occurs when:
- AA third party bears a cost not paid by the producer or consumer
- BConsumers pay more for a product than it costs the firm to produce
- CA firm makes a loss
- DThe government taxes a product
4.Economics conceptsHard
The "convergence hypothesis" from the Solow model predicts that:
- AExchange rates converge to a fixed value
- BRich countries always grow faster than poor ones, because they have more capital
- CAll countries will eventually have the same population
- DPoorer countries with similar fundamentals tend to grow faster than richer ones
5.Financial accountingMedium
An item cost €80. It can be sold for €90, but €20 must be spent to sell it. At what amount is it shown in inventory?
- A€90
- B€70
- C€60
- D€80
6.Financial accountingHard
A company borrows at 5% interest to invest in assets that earn 12%. What is the likely effect on return on equity?
- AROE stays the same, because debt is not equity
- BROE falls, because interest is an expense
- CROE rises and financial risk falls
- DROE rises, but financial risk also increases
7.Break-even analysisMedium
A product sells for €21 with a variable cost of €6 per unit. Fixed costs are €75 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €37 500 after tax?
p = €21v = €6F = €75 000T = 20%after-tax profit = €37 500
Q = units
8.Break-even analysisHard
A company sells 6 000 units at €24 each, with a variable cost of €20 per unit and fixed costs of €16 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 12%?
Q = 6 000p = €24v = €20F = €16 000%ΔQ = +12%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: C · Adaptation
Why this is the answer
Adaptation tailors products or communications to local preferences. Standardisation uses the same offer everywhere to gain scale economies and a uniform image.
Answer
C · Adaptation
2.Marketing principles
Answer: A · Cannibalisation of the original product's sales
Why this is the answer
Cannibalisation occurs when a new offer mainly takes sales from the firm's existing products. It is a problem if the new product has a lower margin.
Answer
A · Cannibalisation of the original product's sales
3.Economics concepts
Answer: A · A third party bears a cost not paid by the producer or consumer
Why this is the answer
Negative externalities lead to overproduction relative to the social optimum; Pigouvian taxes or tradeable permits can correct them.
Answer
A · A third party bears a cost not paid by the producer or consumer
4.Economics concepts
Answer: D · Poorer countries with similar fundamentals tend to grow faster than richer ones
Why this is the answer
Capital-poor economies have higher returns to investment, so, given similar saving rates and technology, they should catch up (conditional convergence).
Answer
D · Poorer countries with similar fundamentals tend to grow faster than richer ones
5.Financial accounting
Answer: B · €70
Why this is the answer
NRV = €90 − €20 = €70, which is below cost of €80. Inventory is measured at the lower amount, €70, with a €10 write-down.
Answer
B · €70
6.Financial accounting
Answer: D · ROE rises, but financial risk also increases
Why this is the answer
Positive financial leverage: assets earn more than the debt costs, so profit per euro of equity rises. If returns drop below 5%, leverage works against shareholders.
Answer
D · ROE rises, but financial risk also increases
7.Break-even analysis
Answer: Q = 8125 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).
Pre-tax profit needed
37 500/(1 − 0.2) = €46 875
Units needed
Q = (75 000 + 46 875)/15 = 8 125
Answer
Q = 8 125 units
8.Break-even analysis
Answer: %ΔΠ = 36 %
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 = 6 000·4 = €24 000
Π = 24 000 − 16 000 = €8 000
DOL
DOL = 24 000/8 000 = 3
Change in profit
%ΔΠ = 3·(+12%) = +36%
Answer
%ΔΠ = +36%
Check: new profit = 6 720·4 − 16 000 = €10 880.00.
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