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
Content marketing mainly aims to:
- AInterrupt viewers with as many adverts as possible
- BAttract and keep an audience by offering useful or entertaining content
- CReplace all customer service with chatbots
- DReduce product prices for loyal customers
2.Marketing principlesHard
In 1985 Coca-Cola replaced its formula with "New Coke", then brought back the original within months. What is the main marketing lesson?
- ABrands should change their formula every year
- BBlind taste tests can miss consumers' emotional attachment to a brand
- CConsumers always prefer the cheapest product
- DAdvertising cannot influence soft drink sales
3.Economics conceptsMedium
A savings account pays a nominal interest rate of 6% and inflation is 4%. The approximate real interest rate is:
- A24%
- B10%
- C2%
- D1.5%
4.Economics conceptsHard
Under perfect (first-degree) price discrimination, the monopolist:
- ACaptures all consumer surplus and produces the efficient output
- BCharges every consumer the same price
- CCreates the largest possible deadweight loss
- DProduces less than a single-price monopolist, creating a larger deadweight loss
5.Financial accountingMedium
A product sells for €40 and has a variable cost of €30. What is its contribution-to-sales (C/S) ratio?
- A25%
- B75%
- C10%
- D33%
6.Financial accountingHard
Budgeted overhead is €200,000 for 40,000 machine hours. Actual hours are 42,000 and actual overhead is €205,000. What is the result?
- AOverhead under-absorbed by €5,000
- BOverhead over-absorbed by €5,000
- COverhead exactly absorbed
- DOverhead under-absorbed by €10,000
7.Break-even analysisMedium
A product sells for €34 with a variable cost of €30 per unit. Fixed costs are €8 000 per month and profit is taxed at 25%. How many units Q must be sold per month to earn €1 500 after tax?
p = €34v = €30F = €8 000T = 25%after-tax profit = €1 500
Q = units
8.Break-even analysisHard
A product sells for €16 per unit, with a variable cost of €6 per unit and fixed costs of €20 000 per year. Budgeted sales are 3 600 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €20 000p = €16v = €6budget = 3 600
MS = %
3Solutions
1.Marketing principles
Answer: B · Attract and keep an audience by offering useful or entertaining content
Why this is the answer
Content marketing provides value first, such as guides, videos or articles. It builds trust and search visibility, leading to sales over time.
Answer
B · Attract and keep an audience by offering useful or entertaining content
2.Marketing principles
Answer: B · Blind taste tests can miss consumers' emotional attachment to a brand
Why this is the answer
Taste tests favoured the new formula, but loyal customers felt something meaningful had been taken away. Brand equity includes emotional and symbolic meaning, not just product attributes.
Answer
B · Blind taste tests can miss consumers' emotional attachment to a brand
3.Economics concepts
Answer: C · 2%
Why this is the answer
The real interest rate is approximately the nominal rate minus inflation: 6% − 4% = 2%.
Answer
C · 2%
4.Economics concepts
Answer: A · Captures all consumer surplus and produces the efficient output
Why this is the answer
Charging each buyer their reservation price means it sells until price equals MC, so there is no deadweight loss, but all surplus goes to the producer.
Answer
A · Captures all consumer surplus and produces the efficient output
5.Financial accounting
Answer: A · 25%
Why this is the answer
Contribution = €10. C/S ratio = €10 ÷ €40 = 25%. Fixed costs ÷ C/S ratio gives break-even revenue.
Answer
A · 25%
6.Financial accounting
Answer: B · Overhead over-absorbed by €5,000
Why this is the answer
Rate = €5 per hour. Absorbed = 42,000 × €5 = €210,000, which exceeds actual €205,000, so €5,000 is over-absorbed and added back to profit.
Answer
B · Overhead over-absorbed by €5,000
7.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).
Pre-tax profit needed
1 500/(1 − 0.25) = €2 000
Units needed
Q = (8 000 + 2 000)/4 = 2 500
Answer
Q = 2 500 units
8.Break-even analysis
Answer: MS = 44.44 %
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).
Break-even quantity
Q = F/(p − v) = 20 000/10 = 2 000
Margin of safety
MS = (3 600 − 2 000)/3 600·100 = 44.44%
Answer
MS = 44.44%
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