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:
- AReplace all customer service with chatbots
- BInterrupt viewers with as many adverts as possible
- CReduce product prices for loyal customers
- DAttract and keep an audience by offering useful or entertaining content
2.Marketing principlesHard
A campaign costs €20,000 and generates €50,000 of extra contribution. What is the marketing ROI?
- A40%
- B150%
- C250%
- D60%
3.Economics conceptsMedium
The marginal propensity to consume is:
- AThe share of an extra euro of income that is spent on consumption
- BThe total consumption in an economy
- CThe interest rate on consumer loans
- DThe average share of total income that households save over a year
4.Economics conceptsHard
In the Bertrand model, two firms sell identical products with the same constant marginal cost and compete on price. The equilibrium price is:
- AZero
- BEqual to marginal cost
- CHalfway between monopoly price and marginal cost
- DThe monopoly price
5.Financial accountingMedium
On 1 October a company pays €12,000 rent for the next 12 months. Its year ends on 31 December. What is the rent expense for this year?
- A€9,000
- B€1,000
- C€12,000
- D€3,000
6.Financial accountingHard
Under IFRS 16, which lease may a lessee choose to expense on a straight-line basis instead of recognising a right-of-use asset?
- AAny lease with monthly payments
- BA ten-year lease of a large production machine
- CAny lease of land and buildings
- DA lease with a term of 12 months or less
7.Break-even analysisMedium
A product sells for €30 per unit with a variable cost of €25 per unit. Fixed costs are €5 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €5 000p = €30v = €25profit = €2 000
Q = units
8.Break-even analysisHard
A product sells for €17 per unit, with a variable cost of €12 per unit and fixed costs of €7 500 per year. Budgeted sales are 1 950 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €7 500p = €17v = €12budget = 1 950
MS = %
3Solutions
1.Marketing principles
Answer: D · 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
D · Attract and keep an audience by offering useful or entertaining content
2.Marketing principles
Answer: B · 150%
Why this is the answer
ROI = (€50,000 − €20,000) ÷ €20,000 = 1.5 = 150%. Using contribution rather than revenue avoids overstating the return.
Answer
B · 150%
3.Economics concepts
Answer: A · The share of an extra euro of income that is spent on consumption
Why this is the answer
The MPC measures how consumption changes with income; it determines the size of the Keynesian multiplier, 1/(1 − MPC).
Answer
A · The share of an extra euro of income that is spent on consumption
4.Economics concepts
Answer: B · Equal to marginal cost
Why this is the answer
Undercutting continues until price equals marginal cost, so even two firms reach the competitive outcome; in Cournot quantity competition, price stays above MC.
Answer
B · Equal to marginal cost
5.Financial accounting
Answer: D · €3,000
Why this is the answer
October to December is 3 months: 3/12 × €12,000 = €3,000. The remaining €9,000 is a prepayment (asset) at year end.
Answer
D · €3,000
6.Financial accounting
Answer: D · A lease with a term of 12 months or less
Why this is the answer
Lessees may elect not to recognise short-term leases (12 months or less) and leases of low-value assets, expensing the payments instead.
Answer
D · A lease with a term of 12 months or less
7.Break-even analysis
Answer: Q = 1400 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 = 30 − 25 = €5
Units for the target profit
Q = (F + profit)/(p − v) = (5 000 + 2 000)/5 = 1 400
Answer
Q = 1 400 units
8.Break-even analysis
Answer: MS = 23.08 %
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) = 7 500/5 = 1 500
Margin of safety
MS = (1 950 − 1 500)/1 950·100 = 23.08%
Answer
MS = 23.08%
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