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
In Rogers' diffusion of innovations, which group adopts a new product first?
- AInnovators
- BLaggards
- CEarly adopters
- DEarly majority
2.Marketing principlesHard
Which metric best shows the efficiency of acquiring customers through online advertising?
- ACustomer acquisition cost compared with customer lifetime value
- BThe number of employees in marketing
- CThe number of likes on posts
- DTotal impressions only
3.Economics conceptsMedium
The marginal propensity to consume is:
- AThe total consumption in an economy
- BThe share of an extra euro of income that is spent on consumption
- CThe average share of total income that households save over a year
- DThe interest rate on consumer loans
4.Economics conceptsHard
Moral hazard arises when:
- ATwo firms collude on price
- BPrices are too high for poor consumers
- CA buyer cannot observe product quality before buying, so low-quality sellers dominate the market
- DOne party changes behaviour after a contract because they do not bear the full consequences
5.Financial accountingMedium
Which inventory valuation method assumes the oldest goods are sold first?
- AFIFO (first in, first out)
- BWeighted average cost
- CLIFO (last in, first out)
- DSpecific identification of each item
6.Financial accountingHard
Inventory days are 60, receivable days 45 and payable days 30. What is the cash conversion (operating) cycle?
- A135 days
- B15 days
- C75 days
- D105 days
7.Break-even analysisMedium
A product sells for €38 per unit with a variable cost of €18 per unit. Fixed costs are €16 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €16 000p = €38v = €18profit = €6 000
Q = units
8.Break-even analysisHard
A product sells for €24 per unit, with a variable cost of €18 per unit and fixed costs of €12 000 per year. Budgeted sales are 2 600 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €12 000p = €24v = €18budget = 2 600
MS = %
3Solutions
1.Marketing principles
Answer: A · Innovators
Why this is the answer
The order is innovators, early adopters, early majority, late majority and laggards. Early adopters are often opinion leaders who influence others.
Answer
A · Innovators
2.Marketing principles
Answer: A · Customer acquisition cost compared with customer lifetime value
Why this is the answer
CAC relative to CLV shows whether acquisition is profitable; vanity metrics like likes do not measure business value.
Answer
A · Customer acquisition cost compared with customer lifetime value
3.Economics concepts
Answer: B · 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
B · The share of an extra euro of income that is spent on consumption
4.Economics concepts
Answer: D · One party changes behaviour after a contract because they do not bear the full consequences
Why this is the answer
Moral hazard is hidden action after the contract, such as an insured driver taking more risks. Adverse selection is hidden information before the contract.
Answer
D · One party changes behaviour after a contract because they do not bear the full consequences
5.Financial accounting
Answer: A · FIFO (first in, first out)
Why this is the answer
Under FIFO, cost of sales uses the oldest costs and closing inventory reflects recent costs. IFRS does not allow LIFO.
Answer
A · FIFO (first in, first out)
6.Financial accounting
Answer: C · 75 days
Why this is the answer
60 + 45 − 30 = 75 days between paying suppliers and collecting cash from customers. A shorter cycle needs less working capital finance.
Answer
C · 75 days
7.Break-even analysis
Answer: Q = 1100 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 = 38 − 18 = €20
Units for the target profit
Q = (F + profit)/(p − v) = (16 000 + 6 000)/20 = 1 100
Answer
Q = 1 100 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) = 12 000/6 = 2 000
Margin of safety
MS = (2 600 − 2 000)/2 600·100 = 23.08%
Answer
MS = 23.08%
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