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 luxury watch brand sells only through a few carefully chosen dealers in each country. Which distribution strategy is this?
- AMass distribution
- BSelective distribution in all outlets
- CIntensive distribution
- DExclusive distribution
2.Marketing principlesHard
In Rogers' diffusion curve, roughly what share of adopters are laggards?
- A34%
- B16%
- C13.5%
- D2.5%
3.Economics conceptsMedium
A firm has spent €1 million on research for a product that now looks unprofitable. When deciding whether to continue, the €1 million should be:
- AIgnored, because it is a sunk cost
- BTreated as the opportunity cost of stopping
- CAdded to the expected future costs
- DRecovered by raising prices
4.Economics conceptsHard
The "convergence hypothesis" from the Solow model predicts that:
- ARich countries always grow faster than poor ones, because they have more capital
- BPoorer countries with similar fundamentals tend to grow faster than richer ones
- CAll countries will eventually have the same population
- DExchange rates converge to a fixed value
5.Financial accountingMedium
Current assets are €300,000 and current liabilities are €150,000. What is the current ratio?
- A1.5
- B0.5
- C2.0
- D4.5
6.Financial accountingHard
An asset is impaired when its carrying amount is higher than its:
- AResidual value only
- BOriginal purchase price
- CRecoverable amount (the higher of fair value less costs of disposal and value in use)
- DDepreciation charge
7.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €25 000 per year and a variable cost of €18 per unit. Method B, more automated, has fixed costs of €30 000 per year and a variable cost of €13 per unit. At what yearly volume Q do both methods cost the same?
FA = €25 000vA = €18FB = €30 000vB = €13
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €21 with a variable cost of €15; product B sells for €25 with a variable cost of €10. They sell in a fixed mix of 2 units of A for every 3 of B. Fixed costs are €57 000 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €21, vA = €15pB = €25, vB = €10A : B = 2 : 3F = €57 000
Q = units
3Solutions
1.Marketing principles
Answer: D · Exclusive distribution
Why this is the answer
Exclusive distribution uses very few outlets to keep control and a premium image. Intensive distribution places products in as many outlets as possible.
Answer
D · Exclusive distribution
2.Marketing principles
Answer: B · 16%
Why this is the answer
Innovators 2.5%, early adopters 13.5%, early majority 34%, late majority 34% and laggards 16%, based on a normal distribution of adoption time.
Answer
B · 16%
3.Economics concepts
Answer: A · Ignored, because it is a sunk cost
Why this is the answer
Sunk costs cannot be recovered and do not change with the decision, so rational choices compare only future costs and benefits.
Answer
A · Ignored, because it is a sunk cost
4.Economics concepts
Answer: B · 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
B · Poorer countries with similar fundamentals tend to grow faster than richer ones
5.Financial accounting
Answer: C · 2.0
Why this is the answer
€300,000 ÷ €150,000 = 2.0, so current assets cover short-term obligations twice.
Answer
C · 2.0
6.Financial accounting
Answer: C · Recoverable amount (the higher of fair value less costs of disposal and value in use)
Why this is the answer
If the carrying amount exceeds the recoverable amount, the difference is written off as an impairment loss.
Answer
C · Recoverable amount (the higher of fair value less costs of disposal and value in use)
7.Break-even analysis
Answer: Q = 1000 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).
Equal total costs
25 000 + 18Q = 30 000 + 13Q
Solve for Q
Q = (30 000 − 25 000)/(18 − 13) = 1 000
Answer
Q = 1 000 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: Q = 5000 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 = €15
Weighted contribution margin
(2·6 + 3·15)/5 = €11.40
Break-even units
Q = 57 000/11.4 = 5 000
A: 2 000, B: 3 000
Answer
Q = 5 000 units
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