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
- BReduce product prices for loyal customers
- CInterrupt viewers with as many adverts as possible
- DAttract and keep an audience by offering useful or entertaining content
2.Marketing principlesHard
During a major sports tournament, a non-sponsor brand runs ads suggesting a link with the event without paying for official rights. What is this called?
- AAmbush marketing
- BCause-related marketing
- CCo-branding
- DGuerrilla distribution
3.Economics conceptsMedium
If demand for a product is price inelastic, a price increase will:
- ADecrease total revenue
- BIncrease total revenue
- CReduce quantity demanded to zero
- DLeave total revenue unchanged
4.Economics conceptsHard
Under perfect (first-degree) price discrimination, the monopolist:
- ACreates the largest possible deadweight loss
- BCaptures all consumer surplus and produces the efficient output
- CCharges every consumer the same price
- DProduces less than a single-price monopolist, creating a larger deadweight loss
5.Financial accountingMedium
Revenue is €200,000 and cost of sales is €140,000. What is the gross profit margin?
- A70%
- B43%
- C60%
- D30%
6.Financial accountingHard
Company P buys 70% of the voting shares of S and gains control. How does P report S in its group accounts?
- AAdd only 70% of each of S's assets, liabilities, income and expenses
- BKeep the investment at cost and report only the dividends received from S
- CConsolidate 100% of S line by line and show a non-controlling interest
- DShow one equity-method investment line for its 70% share of S
7.Break-even analysisMedium
A product sells for €55 per unit with a variable cost of €45 per unit. Fixed costs are €20 000 per month. How many units Q must be sold per month to make a profit of €12 000?
F = €20 000p = €55v = €45profit = €12 000
Q = units
8.Break-even analysisHard
A product sells for €18 per unit, with a variable cost of €8 per unit and fixed costs of €12 000 per year. Budgeted sales are 2 160 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €12 000p = €18v = €8budget = 2 160
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: A · Ambush marketing
Why this is the answer
Ambush marketing tries to gain association with an event without sponsorship. Organisers often protect sponsors through contracts and trademark rules.
Answer
A · Ambush marketing
3.Economics concepts
Answer: B · Increase total revenue
Why this is the answer
With inelastic demand the percentage fall in quantity is smaller than the percentage price rise, so price × quantity rises.
Answer
B · Increase total revenue
4.Economics concepts
Answer: B · Captures all consumer surplus and produces the efficient output
Why this is the answer
Charging each buyer their reservation price means it sells until price equals MC, so there is no deadweight loss, but all surplus goes to the producer.
Answer
B · Captures all consumer surplus and produces the efficient output
5.Financial accounting
Answer: D · 30%
Why this is the answer
Gross profit = €60,000. Margin = €60,000 ÷ €200,000 = 30%.
Answer
D · 30%
6.Financial accounting
Answer: C · Consolidate 100% of S line by line and show a non-controlling interest
Why this is the answer
A subsidiary is consolidated line by line at 100%. The 30% owned by others is shown as a non-controlling interest within equity.
Answer
C · Consolidate 100% of S line by line and show a non-controlling interest
7.Break-even analysis
Answer: Q = 3200 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 = 55 − 45 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (20 000 + 12 000)/10 = 3 200
Answer
Q = 3 200 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) = 12 000/10 = 1 200
Margin of safety
MS = (2 160 − 1 200)/2 160·100 = 44.44%
Answer
MS = 44.44%
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