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
Integrated marketing communications (IMC) means:
- AUsing only digital channels for advertising
- BMerging the marketing and finance departments
- CCoordinating all communication channels to deliver one consistent message
- DSpending the same budget on each medium
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 number of competitors' free users
- CThe price of the free version
- DThe conversion rate from free users to paying users
3.Economics conceptsMedium
In country A, 1 car costs 2 tonnes of wheat to produce; in country B, 1 car costs 4 tonnes of wheat. Which statement is correct?
- AA has a comparative advantage in cars and B in wheat
- BB has a comparative advantage in cars and A in wheat
- CNeither country gains from trade
- DA has a comparative advantage in both goods
4.Economics conceptsHard
The J-curve effect describes why, after a depreciation, the trade balance may:
- AWorsen at first and then improve
- BImprove immediately and permanently
- CRemain unchanged for many years
- DImprove at first and then worsen
5.Financial accountingMedium
A product sells for €40 and has a variable cost of €30. What is its contribution-to-sales (C/S) ratio?
- A10%
- B75%
- C33%
- D25%
6.Financial accountingHard
A company issues shares at €5 each with a nominal value of €1. The extra €4 per share is recorded as:
- ARetained earnings
- BRevenue
- CA liability
- DShare premium
7.Break-even analysisMedium
A product sells for €26 with a variable cost of €6 per unit. Fixed costs are €40 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €20 000 after tax?
p = €26v = €6F = €40 000T = 20%after-tax profit = €20 000
Q = units
8.Break-even analysisHard
A product sells for €26 per unit, with a variable cost of €20 per unit and fixed costs of €9 000 per year. Budgeted sales are 2 700 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €9 000p = €26v = €20budget = 2 700
MS = %
3Solutions
1.Marketing principles
Answer: C · Coordinating all communication channels to deliver one consistent message
Why this is the answer
IMC aligns advertising, PR, sales promotion, digital and personal selling so they reinforce each other and build a clear brand image.
Answer
C · Coordinating all communication channels to deliver one consistent message
2.Marketing principles
Answer: D · 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
D · The conversion rate from free users to paying users
3.Economics concepts
Answer: A · A has a comparative advantage in cars and B in wheat
Why this is the answer
A gives up less wheat per car, so it should specialise in cars; B's opportunity cost of wheat (1/4 car) is lower than A's (1/2 car), so B specialises in wheat.
Answer
A · A has a comparative advantage in cars and B in wheat
4.Economics concepts
Answer: A · Worsen at first and then improve
Why this is the answer
In the short run, volumes are slow to adjust while import prices rise immediately, so the balance worsens before the Marshall–Lerner condition takes hold.
Answer
A · Worsen at first and then improve
5.Financial accounting
Answer: D · 25%
Why this is the answer
Contribution = €10. C/S ratio = €10 ÷ €40 = 25%. Fixed costs ÷ C/S ratio gives break-even revenue.
Answer
D · 25%
6.Financial accounting
Answer: D · Share premium
Why this is the answer
The amount above nominal value goes to the share premium account in equity; issuing shares is a financing transaction, not income.
Answer
D · Share premium
7.Break-even analysis
Answer: Q = 3250 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).
Pre-tax profit needed
20 000/(1 − 0.2) = €25 000
Units needed
Q = (40 000 + 25 000)/20 = 3 250
Answer
Q = 3 250 units
8.Break-even analysis
Answer: MS = 44.44 %
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) = 9 000/6 = 1 500
Margin of safety
MS = (2 700 − 1 500)/2 700·100 = 44.44%
Answer
MS = 44.44%
ExamProblems · examproblems.com/courses/business-fundamentals