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
Soft drinks are sold in supermarkets, petrol stations, vending machines and kiosks. Which distribution strategy is this?
- AExclusive distribution
- BIntensive distribution
- CDirect distribution only
- DSelective distribution
2.Marketing principlesHard
Theodore Levitt's "Marketing Myopia" (1960) used US railroads as an example. What was their mistake?
- AThey spent too much on advertising
- BThey defined their business as railways rather than transportation
- CThey expanded into too many countries
- DThey set their prices too low
3.Economics conceptsMedium
A savings account pays a nominal interest rate of 6% and inflation is 4%. The approximate real interest rate is:
- A24%
- B2%
- C10%
- D1.5%
4.Economics conceptsHard
The Phillips curve originally suggested:
- AThat higher taxes always reduce inflation
- BA trade-off between inflation and unemployment in the short run
- CThat unemployment has no link to inflation
- DThat inflation and unemployment always rise and fall together in the short run
5.Financial accountingMedium
Which depreciation method charges the same amount every year?
- AStraight-line
- BSum-of-the-years'-digits
- CUnits of production
- DReducing balance
6.Financial accountingHard
Over three years a company reports rising profits while operating cash flow keeps falling. What should an analyst suspect?
- AThe company has very high earnings quality
- BProfits may be driven by aggressive accruals, such as rising receivables or capitalised costs
- CThe company must have repaid all its loans
- DDepreciation must have been too high
7.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €15 000 per year and a variable cost of €18 per unit. Method B, more automated, has fixed costs of €31 000 per year and a variable cost of €14 per unit. At what yearly volume Q do both methods cost the same?
FA = €15 000vA = €18FB = €31 000vB = €14
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €19 with a variable cost of €15; product B sells for €35 with a variable cost of €20. They sell in a fixed mix of 3 units of A for every 2 of B. Fixed costs are €21 000 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €19, vA = €15pB = €35, vB = €20A : B = 3 : 2F = €21 000
Q = units
3Solutions
1.Marketing principles
Answer: B · Intensive distribution
Why this is the answer
Intensive distribution suits convenience products that customers buy on impulse and will not search for.
Answer
B · Intensive distribution
2.Marketing principles
Answer: B · They defined their business as railways rather than transportation
Why this is the answer
Levitt argued firms fail when they focus on their product instead of the customer need it serves. Railroads lost customers to cars, trucks and planes they did not see as rivals.
Answer
B · They defined their business as railways rather than transportation
3.Economics concepts
Answer: B · 2%
Why this is the answer
The real interest rate is approximately the nominal rate minus inflation: 6% − 4% = 2%.
Answer
B · 2%
4.Economics concepts
Answer: B · 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
B · A trade-off between inflation and unemployment in the short run
5.Financial accounting
Answer: A · Straight-line
Why this is the answer
Straight-line spreads the depreciable amount evenly. Reducing balance charges more in early years; units of production follows actual use.
Answer
A · Straight-line
6.Financial accounting
Answer: B · Profits may be driven by aggressive accruals, such as rising receivables or capitalised costs
Why this is the answer
A widening gap between profit and operating cash flow often signals working capital build-up or aggressive recognition, suggesting low earnings quality.
Answer
B · Profits may be driven by aggressive accruals, such as rising receivables or capitalised costs
7.Break-even analysis
Answer: Q = 4000 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
15 000 + 18Q = 31 000 + 14Q
Solve for Q
Q = (31 000 − 15 000)/(18 − 14) = 4 000
Answer
Q = 4 000 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: Q = 2500 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 = €4, cmB = €15
Weighted contribution margin
(3·4 + 2·15)/5 = €8.40
Break-even units
Q = 21 000/8.4 = 2 500
A: 1 500, B: 1 000
Answer
Q = 2 500 units
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