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
What is the usual order of stages in the consumer buying decision process?
- ANeed recognition, information search, evaluation of alternatives, purchase, post-purchase behaviour
- BPurchase, need recognition, information search, evaluation of alternatives, post-purchase behaviour
- CEvaluation of alternatives, need recognition, information search, purchase, post-purchase behaviour
- DInformation search, need recognition, purchase, evaluation of alternatives, post-purchase behaviour
2.Marketing principlesHard
In the services marketing "gap model" (SERVQUAL), the customer gap is the difference between:
- APlanned advertising spend and the actual spend in each period
- BPrice and cost
- COnline and offline sales
- DCustomer expectations and perceptions of the service
3.Economics conceptsMedium
A country imposes a tariff on imported steel. Which effect is most likely?
- ADomestic consumers gain surplus
- BDomestic steel prices rise and domestic production increases
- CThe world price of steel rises sharply for all countries that trade it
- DDomestic steel prices fall and imports rise
4.Economics conceptsHard
A liquidity trap is a situation where:
- ABanks have no money left to lend
- BThe central bank raises interest rates sharply to fight high and rapidly rising inflation
- CInterest rates are near zero and further monetary expansion has little effect on demand
- DInflation is very high and rising
5.Financial accountingMedium
Retained earnings represent:
- AAccumulated profits that have not been paid out as dividends
- BThe share price
- CMoney owed to shareholders
- DCash kept in the bank
6.Financial accountingHard
A company "sells" inventory to a bank and must buy it back later at a higher price, keeping the risks and rewards. How should it be accounted for?
- AAs a contingent asset in the notes
- BAs a secured loan, not a sale
- CAs revenue on the date of transfer
- DAs a gain on disposal of inventory
7.Break-even analysisMedium
A product sells for €50 per unit with a variable cost of €30 per unit. Fixed costs are €30 000 per month. How many units Q must be sold per month to make a profit of €10 000?
F = €30 000p = €50v = €30profit = €10 000
Q = units
8.Break-even analysisHard
A product sells for €42 per unit, with a variable cost of €30 per unit and fixed costs of €18 000 per year. Budgeted sales are 2 100 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €18 000p = €42v = €30budget = 2 100
MS = %
3Solutions
1.Marketing principles
Answer: A · Need recognition, information search, evaluation of alternatives, purchase, post-purchase behaviour
Why this is the answer
Buyers recognise a need, look for information, compare options, buy and then judge their satisfaction. Routine purchases may skip stages.
Answer
A · Need recognition, information search, evaluation of alternatives, purchase, post-purchase behaviour
2.Marketing principles
Answer: D · Customer expectations and perceptions of the service
Why this is the answer
The customer gap is expected service minus perceived service; the provider gaps (knowledge, standards, delivery, communication) explain it.
Answer
D · Customer expectations and perceptions of the service
3.Economics concepts
Answer: B · Domestic steel prices rise and domestic production increases
Why this is the answer
The tariff raises the domestic price, increasing domestic output and government revenue but reducing consumer surplus and creating deadweight losses.
Answer
B · Domestic steel prices rise and domestic production increases
4.Economics concepts
Answer: C · Interest rates are near zero and further monetary expansion has little effect on demand
Why this is the answer
When nominal rates are near their lower bound, people hold extra money rather than spend it, so conventional monetary policy loses power and fiscal policy or unconventional tools matter more.
Answer
C · Interest rates are near zero and further monetary expansion has little effect on demand
5.Financial accounting
Answer: A · Accumulated profits that have not been paid out as dividends
Why this is the answer
Retained earnings are cumulative net profits minus dividends; they are part of equity, not a pile of cash.
Answer
A · Accumulated profits that have not been paid out as dividends
6.Financial accounting
Answer: B · As a secured loan, not a sale
Why this is the answer
Control and risks stay with the company, so the transaction is in substance borrowing secured on inventory. The price difference is an interest cost.
Answer
B · As a secured loan, not a sale
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 = 50 − 30 = €20
Units for the target profit
Q = (F + profit)/(p − v) = (30 000 + 10 000)/20 = 2 000
Answer
Q = 2 000 units
8.Break-even analysis
Answer: MS = 28.57 %
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) = 18 000/12 = 1 500
Margin of safety
MS = (2 100 − 1 500)/2 100·100 = 28.57%
Answer
MS = 28.57%
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