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:
- AAttract and keep an audience by offering useful or entertaining content
- BReduce product prices for loyal customers
- CInterrupt viewers with as many adverts as possible
- DReplace all customer service with chatbots
2.Marketing principlesHard
During a major sports tournament, a non-sponsor brand runs ads suggesting a link with the event without paying for official rights. What is this called?
- AGuerrilla distribution
- BCo-branding
- CAmbush marketing
- DCause-related marketing
3.Economics conceptsMedium
In an oligopoly, firms are typically:
- AMany and too small to affect the price
- BFew and interdependent in their decisions
- CA single seller in the market
- DCompletely unregulated by competition law
4.Economics conceptsHard
A liquidity trap is a situation where:
- AInterest rates are near zero and further monetary expansion has little effect on demand
- BBanks have no money left to lend
- CInflation is very high and rising
- DThe central bank raises interest rates sharply to fight high and rapidly rising inflation
5.Financial accountingMedium
Profit for ordinary shareholders is €500,000 and there are 1,000,000 ordinary shares. What are basic earnings per share?
- A€5.00
- B€0.05
- C€2.00
- D€0.50
6.Financial accountingHard
Under IFRS 15, revenue is recognised:
- AOnly when cash is received
- BAt the end of the financial year
- CWhen (or as) the entity satisfies a performance obligation by transferring control to the customer
- DWhen the contract is signed
7.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €20 000 per year and a variable cost of €25 per unit. Method B, more automated, has fixed costs of €40 000 per year and a variable cost of €20 per unit. At what yearly volume Q do both methods cost the same?
FA = €20 000vA = €25FB = €40 000vB = €20
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 €24 000 per year. Budgeted sales are 2 800 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €24 000p = €18v = €6budget = 2 800
MS = %
3Solutions
1.Marketing principles
Answer: A · 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
A · Attract and keep an audience by offering useful or entertaining content
2.Marketing principles
Answer: C · Ambush marketing
Why this is the answer
Ambush marketing tries to gain association with an event without sponsorship. Organisers often protect sponsors through contracts and trademark rules.
Answer
C · Ambush marketing
3.Economics concepts
Answer: B · Few and interdependent in their decisions
Why this is the answer
Oligopolies have a few large firms whose pricing and output decisions affect each other, often analysed with game theory.
Answer
B · Few and interdependent in their decisions
4.Economics concepts
Answer: A · Interest rates are near zero and further monetary expansion has little effect on demand
Why this is the answer
When nominal rates are near their lower bound, people hold extra money rather than spend it, so conventional monetary policy loses power and fiscal policy or unconventional tools matter more.
Answer
A · Interest rates are near zero and further monetary expansion has little effect on demand
5.Financial accounting
Answer: D · €0.50
Why this is the answer
Basic EPS = €500,000 ÷ 1,000,000 = €0.50 per share. Dividing the share price by EPS gives the P/E ratio.
Answer
D · €0.50
6.Financial accounting
Answer: C · When (or as) the entity satisfies a performance obligation by transferring control to the customer
Why this is the answer
The steps: identify the contract, identify performance obligations, determine the price, allocate it, and recognise revenue as each obligation is satisfied.
Answer
C · When (or as) the entity satisfies a performance obligation by transferring control to the customer
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
20 000 + 25Q = 40 000 + 20Q
Solve for Q
Q = (40 000 − 20 000)/(25 − 20) = 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: MS = 28.57 %
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) = 24 000/12 = 2 000
Margin of safety
MS = (2 800 − 2 000)/2 800·100 = 28.57%
Answer
MS = 28.57%
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