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
Integrated marketing communications (IMC) means:
- AUsing only digital channels for advertising
- BSpending the same budget on each medium
- CMerging the marketing and finance departments
- DCoordinating all communication channels to deliver one consistent message
2.Marketing principlesHard
An online shop randomly shows half of its visitors a new checkout page and half the old one. Why is random assignment important?
- AIt makes the groups comparable, so differences in conversion can be attributed to the page
- BIt guarantees that the new page will win
- CIt makes the test cheaper than a survey
- DIt removes the need to measure conversion rates
3.Economics conceptsMedium
Stagflation is a combination of:
- ALow inflation and low unemployment
- BDeflation and rapid growth
- CHigh inflation and high unemployment with low growth
- DHigh growth and falling prices
4.Economics conceptsHard
The Coase theorem states that, if property rights are clearly defined and transaction costs are low:
- APrivate bargaining can reach an efficient outcome regardless of who holds the rights
- BThe polluter must always compensate the victim
- CExternalities cannot be corrected without direct government regulation or a Pigouvian tax
- DGovernments must always tax externalities
5.Financial accountingMedium
Revenue is €200,000 and cost of sales is €140,000. What is the gross profit margin?
- A70%
- B43%
- C60%
- D30%
6.Financial accountingHard
An investor holds 30% of a company's shares and has significant influence but not control. How is the investment usually accounted for in group accounts?
- AAs a joint operation with line-by-line sharing
- BUsing the equity method as an associate
- CAt cost with no changes ever
- DBy full consolidation as a subsidiary
7.Break-even analysisMedium
A product sells for €20 per unit with a variable cost of €15 per unit. Fixed costs are €10 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €10 000p = €20v = €15profit = €5 000
Q = units
8.Break-even analysisHard
A product sells for €22 per unit, with a variable cost of €12 per unit and fixed costs of €50 000 per year. Budgeted sales are 7 500 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €50 000p = €22v = €12budget = 7 500
MS = %
3Solutions
1.Marketing principles
Answer: D · Coordinating all communication channels to deliver one consistent message
Why this is the answer
IMC aligns advertising, PR, sales promotion, digital and personal selling so they reinforce each other and build a clear brand image.
Answer
D · Coordinating all communication channels to deliver one consistent message
2.Marketing principles
Answer: A · It makes the groups comparable, so differences in conversion can be attributed to the page
Why this is the answer
Randomisation balances other influences across both groups. Then a significant difference in results can be causally linked to the change being tested.
Answer
A · It makes the groups comparable, so differences in conversion can be attributed to the page
3.Economics concepts
Answer: C · High inflation and high unemployment with low growth
Why this is the answer
Stagflation combines stagnant output, rising unemployment and high inflation, usually after supply shocks.
Answer
C · High inflation and high unemployment with low growth
4.Economics concepts
Answer: A · Private bargaining can reach an efficient outcome regardless of who holds the rights
Why this is the answer
With costless bargaining, parties will negotiate to the efficient level of the externality; who holds the rights only decides who pays whom.
Answer
A · Private bargaining can reach an efficient outcome regardless of who holds the rights
5.Financial accounting
Answer: D · 30%
Why this is the answer
Gross profit = €60,000. Margin = €60,000 ÷ €200,000 = 30%.
Answer
D · 30%
6.Financial accounting
Answer: B · Using the equity method as an associate
Why this is the answer
Under IAS 28 the investment starts at cost and is adjusted for the investor's share of the associate's profits or losses, less dividends received.
Answer
B · Using the equity method as an associate
7.Break-even analysis
Answer: Q = 3000 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).
Contribution margin per unit
p − v = 20 − 15 = €5
Units for the target profit
Q = (F + profit)/(p − v) = (10 000 + 5 000)/5 = 3 000
Answer
Q = 3 000 units
8.Break-even analysis
Answer: MS = 33.33 %
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) = 50 000/10 = 5 000
Margin of safety
MS = (7 500 − 5 000)/7 500·100 = 33.33%
Answer
MS = 33.33%
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