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
The Net Promoter Score (NPS) is based on the question:
- AHow old are you?
- BHow much did you pay?
- CWhere did you buy the product?
- DHow likely are you to recommend us to a friend or colleague?
2.Marketing principlesHard
A software firm offers a free basic version and charges for premium features. Which metric is most critical for this freemium model's revenue?
- AThe number of printed brochures distributed
- BThe price of the free version
- CThe conversion rate from free users to paying users
- DThe number of competitors' free users
3.Economics conceptsMedium
Unemployment benefits and progressive income taxes are called automatic stabilisers because they:
- AKeep the government budget balanced in every year of the business cycle
- BPrevent all recessions from happening
- CReduce fluctuations in demand without new government decisions
- DFix the exchange rate automatically
4.Economics conceptsHard
A monopolist faces demand P = 100 − Q and has constant marginal cost of 20. What are its profit-maximising output and price?
- AQ = 40, P = 20
- BQ = 80, P = 20
- CQ = 50, P = 50
- DQ = 40, P = 60
5.Financial accountingMedium
An item cost €80. It can be sold for €90, but €20 must be spent to sell it. At what amount is it shown in inventory?
- A€70
- B€90
- C€80
- D€60
6.Financial accountingHard
In the indirect method of the cash flow statement, depreciation is:
- AIgnored completely
- BAdded back to net profit because it is a non-cash expense
- CShown in financing activities
- DSubtracted from net profit
7.Break-even analysisMedium
A product sells for €18 per unit with a variable cost of €8 per unit. Fixed costs are €20 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €20 000p = €18v = €8profit = €2 000
Q = units
8.Break-even analysisHard
A product sells for €33 per unit, with a variable cost of €25 per unit and fixed costs of €40 000 per year. Budgeted sales are 6 250 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €40 000p = €33v = €25budget = 6 250
MS = %
3Solutions
1.Marketing principles
Answer: D · How likely are you to recommend us to a friend or colleague?
Why this is the answer
NPS = % promoters (9–10) minus % detractors (0–6) on a 0–10 recommendation scale.
Answer
D · How likely are you to recommend us to a friend or colleague?
2.Marketing principles
Answer: C · The conversion rate from free users to paying users
Why this is the answer
Freemium revenue depends on attracting many free users and converting a share of them to paid plans, while keeping the cost of serving free users low.
Answer
C · The conversion rate from free users to paying users
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 · Q = 40, P = 60
Why this is the answer
Setting MR = MC gives 100 − 2Q = 20, so Q = 40; the price from the demand curve is 100 − 40 = 60.
Answer
D · Q = 40, P = 60
5.Financial accounting
Answer: A · €70
Why this is the answer
NRV = €90 − €20 = €70, which is below cost of €80. Inventory is measured at the lower amount, €70, with a €10 write-down.
Answer
A · €70
6.Financial accounting
Answer: B · Added back to net profit because it is a non-cash expense
Why this is the answer
Starting from profit, non-cash charges like depreciation are added back, and changes in working capital are adjusted.
Answer
B · Added back to net profit because it is a non-cash expense
7.Break-even analysis
Answer: Q = 2200 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 = 18 − 8 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (20 000 + 2 000)/10 = 2 200
Answer
Q = 2 200 units
8.Break-even analysis
Answer: MS = 20 %
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) = 40 000/8 = 5 000
Margin of safety
MS = (6 250 − 5 000)/6 250·100 = 20%
Answer
MS = 20%
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