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 researcher divides the population into age groups and draws a random sample from each group. This is:
- AConvenience sampling
- BStratified random sampling
- CQuota sampling with free choice
- DSnowball sampling
2.Marketing principlesHard
In the services marketing "gap model" (SERVQUAL), the customer gap is the difference between:
- AOnline and offline sales
- BCustomer expectations and perceptions of the service
- CPlanned advertising spend and the actual spend in each period
- DPrice and cost
3.Economics conceptsMedium
Unemployment benefits and progressive income taxes are called automatic stabilisers because they:
- APrevent all recessions from happening
- BFix the exchange rate automatically
- CReduce fluctuations in demand without new government decisions
- DKeep the government budget balanced in every year of the business cycle
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 guarantees that every graduate is highly productive
- BEmployers are required by law to hire graduates
- CIt reduces the wages employers must pay
- DIt is less costly for high-ability workers to acquire, so it reveals their type
5.Financial accountingMedium
A project costs €100,000 and brings in €25,000 cash per year. What is its payback period?
- A4 years
- B25 years
- C5 years
- D2.5 years
6.Financial accountingHard
A company's debt-to-equity ratio rises sharply. What does this usually indicate?
- AHigher profitability
- BHigher financial risk because the company relies more on borrowed money
- CThat shareholders invested more money
- DBetter liquidity in the short term
7.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €30 000 per year and a variable cost of €8 per unit. Method B, more automated, has fixed costs of €36 000 per year and a variable cost of €5 per unit. At what yearly volume Q do both methods cost the same?
FA = €30 000vA = €8FB = €36 000vB = €5
Q = units
8.Break-even analysisHard
A product sells for €18 per unit, with a variable cost of €6 per unit and fixed costs of €6 000 per year. Budgeted sales are 580 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €6 000p = €18v = €6budget = 580
MS = %
3Solutions
1.Marketing principles
Answer: B · Stratified random sampling
Why this is the answer
Stratified sampling ensures each subgroup is represented while keeping random selection. Quota sampling sets numbers per group but lets interviewers choose people, so it is non-probability.
Answer
B · Stratified random sampling
2.Marketing principles
Answer: B · Customer expectations and perceptions of the service
Why this is the answer
The customer gap is expected service minus perceived service; the provider gaps (knowledge, standards, delivery, communication) explain it.
Answer
B · Customer expectations and perceptions of the service
3.Economics concepts
Answer: C · Reduce fluctuations in demand without new government decisions
Why this is the answer
In a downturn tax revenue falls and benefit payments rise automatically, supporting incomes and spending; the reverse happens in a boom.
Answer
C · Reduce fluctuations in demand without new government decisions
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 · 4 years
Why this is the answer
€100,000 ÷ €25,000 = 4 years. Payback is simple but ignores the time value of money and cash flows after payback.
Answer
A · 4 years
6.Financial accounting
Answer: B · Higher financial risk because the company relies more on borrowed money
Why this is the answer
A higher ratio means more leverage: interest and repayments must be met whatever the results, so financial risk rises, although returns to shareholders may also rise.
Answer
B · Higher financial risk because the company relies more on borrowed money
7.Break-even analysis
Answer: Q = 2000 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
30 000 + 8Q = 36 000 + 5Q
Solve for Q
Q = (36 000 − 30 000)/(8 − 5) = 2 000
Answer
Q = 2 000 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: MS = 13.79 %
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) = 6 000/12 = 500
Margin of safety
MS = (580 − 500)/580·100 = 13.79%
Answer
MS = 13.79%
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