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 customer is buying a first new car. How does this high-involvement purchase usually differ from buying a pack of chewing gum?
- AThe buyer is not influenced by the brand at all
- BThe buyer searches for more information and compares alternatives carefully
- CThe buyer decides on impulse at the checkout
- DThe buyer skips the evaluation stage
2.Marketing principlesHard
Under the EU General Data Protection Regulation (GDPR), sending marketing emails based on consent requires consent that is:
- AGiven once for all future purposes by any company
- BFreely given, specific, informed and unambiguous
- CAssumed when a customer visits the website
- DImplied by pre-ticked boxes
3.Economics conceptsMedium
In the short run, a firm in perfect competition should shut down if the market price is below:
- AAverage variable cost
- BAverage fixed cost
- CAverage total cost
- DMarginal revenue
4.Economics conceptsHard
Under perfect (first-degree) price discrimination, the monopolist:
- ACharges every consumer the same price
- BCreates the largest possible deadweight loss
- CProduces less than a single-price monopolist, creating a larger deadweight loss
- DCaptures all consumer surplus and produces the efficient output
5.Financial accountingMedium
Under the accrual basis of accounting, revenue is recognised when:
- AThe tax return is filed
- BCash is received
- CIt is earned, whether or not cash has been received
- DThe customer pays the invoice, even if goods were delivered earlier
6.Financial accountingHard
Operating profit is €200,000 and capital employed (equity plus non-current liabilities) is €1,000,000. What is ROCE?
- A20%
- B2%
- C5%
- D50%
7.Break-even analysisMedium
A product sells for €34 per unit with a variable cost of €30 per unit. Fixed costs are €20 000 per month. How many units Q must be sold per month to make a profit of €10 000?
F = €20 000p = €34v = €30profit = €10 000
Q = units
8.Break-even analysisHard
A company sells 750 units per month at €45 each, with a variable cost of €30 per unit and fixed costs of €7 500 per month. The variable cost rises by €5 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 750p = €45v = €30 → €35F = €7 500
Q = units
3Solutions
1.Marketing principles
Answer: B · The buyer searches for more information and compares alternatives carefully
Why this is the answer
High involvement leads to extended problem solving with much information search and evaluation. Low-involvement items are bought by habit or impulse.
Answer
B · The buyer searches for more information and compares alternatives carefully
2.Marketing principles
Answer: B · Freely given, specific, informed and unambiguous
Why this is the answer
Consent must be a clear affirmative act; pre-ticked boxes or silence are not valid, and it must be as easy to withdraw as to give.
Answer
B · Freely given, specific, informed and unambiguous
3.Economics concepts
Answer: A · Average variable cost
Why this is the answer
If price covers average variable cost, producing reduces losses by contributing to fixed costs; below AVC, shutting down loses less.
Answer
A · Average variable cost
4.Economics concepts
Answer: D · 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
D · Captures all consumer surplus and produces the efficient output
5.Financial accounting
Answer: C · 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
C · It is earned, whether or not cash has been received
6.Financial accounting
Answer: A · 20%
Why this is the answer
ROCE = €200,000 ÷ €1,000,000 = 20%. It measures returns on all long-term finance, so it can be compared with the cost of borrowing.
Answer
A · 20%
7.Break-even analysis
Answer: Q = 7500 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 = 34 − 30 = €4
Units for the target profit
Q = (F + profit)/(p − v) = (20 000 + 10 000)/4 = 7 500
Answer
Q = 7 500 units
8.Break-even analysis
Answer: Q = 1125 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 = 750·(45 − 30) − 7 500 = €3 750
New contribution margin per unit
45 − 35 = €10
Units for the same profit
Q = (7 500 + 3 750)/10 = 1 125
Answer
Q = 1 125 units
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