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?
- BWhere did you buy the product?
- CHow much did you pay?
- DHow likely are you to recommend us to a friend or colleague?
2.Marketing principlesHard
Cognitive dissonance after an expensive purchase can be reduced by:
- ARemoving the warranty
- BRaising the price further
- CStopping all communication with the customer so the purchase is forgotten
- DReassuring follow-up communication and good after-sales service
3.Economics conceptsMedium
The marginal cost curve cuts the average total cost curve:
- AAt the maximum point of average total cost
- BNever, as the two curves are parallel
- CAt the minimum point of average total cost
- DWhere average total cost equals zero
4.Economics conceptsHard
Under perfect (first-degree) price discrimination, the monopolist:
- ACreates the largest possible deadweight loss
- BCharges every consumer the same price
- CCaptures all consumer surplus and produces the efficient output
- DProduces less than a single-price monopolist, creating a larger deadweight loss
5.Financial accountingMedium
Under the accrual basis of accounting, revenue is recognised when:
- AThe tax return is filed
- BIt is earned, whether or not cash has been received
- CCash is received
- DThe customer pays the invoice, even if goods were delivered earlier
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?
- ANo, the order makes a €7 loss per unit
- BNo, the price is below full cost
- CYes, but only if the price exceeds €42
- DYes, each unit adds €5 contribution
7.Break-even analysisMedium
A product sells for €14 with a variable cost of €4 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 = €14v = €4F = €40 000T = 20%after-tax profit = €20 000
Q = units
8.Break-even analysisHard
A company sells 5 000 units per month at €31 each, with a variable cost of €25 per unit and fixed costs of €12 000 per month. The variable cost rises by €1 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 5 000p = €31v = €25 → €26F = €12 000
Q = units
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: D · Reassuring follow-up communication and good after-sales service
Why this is the answer
Post-purchase dissonance is reduced when companies confirm the decision, for example through thank-you messages, reviews, support and guarantees.
Answer
D · Reassuring follow-up communication and good after-sales service
3.Economics concepts
Answer: C · At the minimum point of average total cost
Why this is the answer
When MC is below ATC it pulls the average down, and when it is above it pushes the average up, so MC crosses ATC at its minimum.
Answer
C · At the minimum point of average total cost
4.Economics concepts
Answer: C · 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
C · Captures all consumer surplus and produces the efficient output
5.Financial accounting
Answer: B · It is earned, whether or not cash has been received
Why this is the answer
Accrual accounting records revenue when the performance obligation is satisfied and expenses when incurred, not when cash moves.
Answer
B · It is earned, whether or not cash has been received
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 = 6500 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)/10 = 6 500
Answer
Q = 6 500 units
8.Break-even analysis
Answer: Q = 6000 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 = 5 000·(31 − 25) − 12 000 = €18 000
New contribution margin per unit
31 − 26 = €5
Units for the same profit
Q = (12 000 + 18 000)/5 = 6 000
Answer
Q = 6 000 units
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