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
A web shop has 2,000 visitors and 50 of them make a purchase. What is the conversion rate?
- A0.25%
- B25%
- C4%
- D2.5%
2.Marketing principlesHard
A customer sees a social ad, later reads a review, then clicks a search ad and buys. What is the main weakness of last-click attribution here?
- AIt gives too much credit to the social ad
- BIt counts the same sale three times
- CIt cannot record online purchases
- DIt gives all credit to the search ad and ignores earlier touchpoints
3.Economics conceptsMedium
A country imposes a tariff on imported steel. Which effect is most likely?
- ADomestic steel prices rise and domestic production increases
- BThe world price of steel rises sharply for all countries that trade it
- CDomestic steel prices fall and imports rise
- DDomestic consumers gain surplus
4.Economics conceptsHard
In the Solow growth model, sustained long-run growth in output per worker comes from:
- AA higher saving rate alone
- BGovernment budget deficits
- CPopulation growth
- DTechnological progress
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€0.05
- B€0.50
- C€2.00
- D€5.00
6.Financial accountingHard
A firm with spare capacity gets a one-off order at €35 per unit. Variable cost is €30 and full cost including fixed overhead is €42. Assuming no other effects, should it accept?
- AYes, but only if the price exceeds €42
- BNo, the price is below full cost
- CNo, the order makes a €7 loss per unit
- DYes, each unit adds €5 contribution
7.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €10 000 per year and a variable cost of €8 per unit. Method B, more automated, has fixed costs of €11 000 per year and a variable cost of €6 per unit. At what yearly volume Q do both methods cost the same?
FA = €10 000vA = €8FB = €11 000vB = €6
Q = units
8.Break-even analysisHard
A company sells 1 200 units per month at €22 each, with a variable cost of €12 per unit and fixed costs of €8 000 per month. The variable cost rises by €2 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 1 200p = €22v = €12 → €14F = €8 000
Q = units
3Solutions
1.Marketing principles
Answer: D · 2.5%
Why this is the answer
50 ÷ 2,000 = 0.025 = 2.5%. Conversion rate measures how well a site turns visits into the desired action.
Answer
D · 2.5%
2.Marketing principles
Answer: D · It gives all credit to the search ad and ignores earlier touchpoints
Why this is the answer
Last-click models undervalue channels that create awareness early in the journey. Multi-touch attribution or experiments give a fairer picture of each channel's contribution.
Answer
D · It gives all credit to the search ad and ignores earlier touchpoints
3.Economics concepts
Answer: A · Domestic steel prices rise and domestic production increases
Why this is the answer
The tariff raises the domestic price, increasing domestic output and government revenue but reducing consumer surplus and creating deadweight losses.
Answer
A · Domestic steel prices rise and domestic production increases
4.Economics concepts
Answer: D · Technological progress
Why this is the answer
A higher saving rate raises the steady-state level of output per worker but not its long-run growth rate; only technological progress produces continuous growth.
Answer
D · Technological progress
5.Financial accounting
Answer: B · €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
B · €0.50
6.Financial accounting
Answer: D · Yes, each unit adds €5 contribution
Why this is the answer
Fixed costs do not change, so the order adds €35 − €30 = €5 per unit to profit. Risks such as upsetting regular customers should still be considered.
Answer
D · Yes, each unit adds €5 contribution
7.Break-even analysis
Answer: Q = 500 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
10 000 + 8Q = 11 000 + 6Q
Solve for Q
Q = (11 000 − 10 000)/(8 − 6) = 500
Answer
Q = 500 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: Q = 1500 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).
Current profit
Π = 1 200·(22 − 12) − 8 000 = €4 000
New contribution margin per unit
22 − 14 = €8
Units for the same profit
Q = (8 000 + 4 000)/8 = 1 500
Answer
Q = 1 500 units
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