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
Customer lifetime value (CLV) estimates:
- AThe value of one purchase
- BThe age of the customer
- CThe total net profit expected from a customer over the whole relationship
- DThe cost of acquiring a new customer through marketing and sales activities
2.Marketing principlesHard
A company launches a product that is easy to copy, with highly price-sensitive buyers and strong economies of scale. Which launch pricing strategy fits best?
- APrice skimming
- BPrestige pricing
- CPenetration pricing
- DCaptive product pricing
3.Economics conceptsMedium
Overfishing in international waters is an example of:
- APrice discrimination
- BThe tragedy of the commons
- CA Giffen good
- DA natural monopoly
4.Economics conceptsHard
Akerlof's "market for lemons" explains how:
- AAsymmetric information can drive good-quality products out of a market
- BMonopolies set high prices
- CPublic goods are under-provided
- DLemons become cheaper in summer
5.Financial accountingMedium
Operating profit is €120,000 and interest expense is €30,000. What is interest cover?
- A90,000 times
- B0.25 times
- C4 times
- D3 times
6.Financial accountingHard
Under IFRS 16, a lessee typically recognises a lease on the balance sheet as:
- AAn operating expense only, spread evenly over the lease term
- BEquity and a provision
- CA right-of-use asset and a lease liability
- DRevenue and inventory
7.Break-even analysisMedium
A product sells for €16 per unit with a variable cost of €6 per unit. Fixed costs are €10 000 per month. How many units Q must be sold per month to make a profit of €10 000?
F = €10 000p = €16v = €6profit = €10 000
Q = units
8.Break-even analysisHard
A product sells for €30 per unit, with a variable cost of €25 per unit and fixed costs of €25 000 per year. Budgeted sales are 6 500 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €25 000p = €30v = €25budget = 6 500
MS = %
3Solutions
1.Marketing principles
Answer: C · The total net profit expected from a customer over the whole relationship
Why this is the answer
CLV combines purchase frequency, margin, retention and duration (often discounted), guiding acquisition and retention spending.
Answer
C · The total net profit expected from a customer over the whole relationship
2.Marketing principles
Answer: C · Penetration pricing
Why this is the answer
Low prices build share quickly, lower unit costs through scale and discourage imitators. Skimming suits unique products with buyers who are less sensitive to price.
Answer
C · Penetration pricing
3.Economics concepts
Answer: B · The tragedy of the commons
Why this is the answer
When a common resource is rival but people cannot be excluded, each user ignores the cost they impose on others, leading to overuse.
Answer
B · The tragedy of the commons
4.Economics concepts
Answer: A · Asymmetric information can drive good-quality products out of a market
Why this is the answer
When buyers cannot judge quality they pay an average price; owners of good cars withdraw, average quality falls, and the market may collapse.
Answer
A · Asymmetric information can drive good-quality products out of a market
5.Financial accounting
Answer: C · 4 times
Why this is the answer
€120,000 ÷ €30,000 = 4. The company earns its interest four times over; low cover signals a risk of not meeting interest payments.
Answer
C · 4 times
6.Financial accounting
Answer: C · A right-of-use asset and a lease liability
Why this is the answer
IFRS 16 removed the operating lease distinction for lessees: they recognise a right-of-use asset and a liability for lease payments, except for short-term and low-value leases.
Answer
C · A right-of-use asset and a lease liability
7.Break-even analysis
Answer: Q = 2000 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 = 16 − 6 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (10 000 + 10 000)/10 = 2 000
Answer
Q = 2 000 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) = 25 000/5 = 5 000
Margin of safety
MS = (6 500 − 5 000)/6 500·100 = 23.08%
Answer
MS = 23.08%
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