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
In the Boston Consulting Group matrix, a "cash cow" has:
- AHigh market share in a low-growth market
- BLow market share in a high-growth market
- CHigh market share in a high-growth market
- DLow market share in a low-growth market
2.Marketing principlesHard
After a hotel solves a guest's complaint quickly and generously, the guest is more loyal than before the problem. What is this called?
- AMarketing myopia
- BPost-purchase cognitive dissonance
- CThe service recovery paradox
- DThe decoy effect
3.Economics conceptsMedium
A firm has spent €1 million on research for a product that now looks unprofitable. When deciding whether to continue, the €1 million should be:
- AAdded to the expected future costs
- BTreated as the opportunity cost of stopping
- CIgnored, because it is a sunk cost
- DRecovered by raising prices
4.Economics conceptsHard
Purchasing power parity (PPP) suggests that, in the long run, exchange rates adjust so that:
- AEvery currency ends up having the same nominal value as the US dollar
- BThe same basket of goods costs the same in different countries
- CTrade balances are always zero
- DInterest rates are equal in all countries
5.Financial accountingMedium
A provision is recognised when a company has:
- ACash set aside in a separate account
- BA possible future loss with no obligation
- CA present obligation from a past event, a probable outflow and a reliable estimate
- DA profit to distribute
6.Financial accountingHard
Under IFRS 16, a lessee typically recognises a lease on the balance sheet as:
- AA right-of-use asset and a lease liability
- BRevenue and inventory
- CAn operating expense only, spread evenly over the lease term
- DEquity and a provision
7.Break-even analysisMedium
A product sells for €24 per unit with a variable cost of €18 per unit. Fixed costs are €6 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €6 000p = €24v = €18profit = €6 000
Q = units
8.Break-even analysisHard
A product sells for €36 per unit, with a variable cost of €30 per unit and fixed costs of €24 000 per year. Budgeted sales are 4 600 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €24 000p = €36v = €30budget = 4 600
MS = %
3Solutions
1.Marketing principles
Answer: A · High market share in a low-growth market
Why this is the answer
Cash cows fund other products. Stars have high share and growth, question marks low share in high growth, dogs low share and low growth.
Answer
A · High market share in a low-growth market
2.Marketing principles
Answer: C · The service recovery paradox
Why this is the answer
The service recovery paradox suggests excellent recovery can raise satisfaction above its earlier level. It does not mean failures are good; recovery must be outstanding.
Answer
C · The service recovery paradox
3.Economics concepts
Answer: C · Ignored, because it is a sunk cost
Why this is the answer
Sunk costs cannot be recovered and do not change with the decision, so rational choices compare only future costs and benefits.
Answer
C · Ignored, because it is a sunk cost
4.Economics concepts
Answer: B · The same basket of goods costs the same in different countries
Why this is the answer
PPP is based on the law of one price: if a good is cheaper in one country, arbitrage should push exchange rates towards equalising prices, though transport costs and non-traded goods limit this.
Answer
B · The same basket of goods costs the same in different countries
5.Financial accounting
Answer: C · A present obligation from a past event, a probable outflow and a reliable estimate
Why this is the answer
Provisions are liabilities of uncertain timing or amount. Possible obligations that do not meet the criteria are disclosed as contingent liabilities.
Answer
C · A present obligation from a past event, a probable outflow and a reliable estimate
6.Financial accounting
Answer: A · 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
A · 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 = 24 − 18 = €6
Units for the target profit
Q = (F + profit)/(p − v) = (6 000 + 6 000)/6 = 2 000
Answer
Q = 2 000 units
8.Break-even analysis
Answer: MS = 13.04 %
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) = 24 000/6 = 4 000
Margin of safety
MS = (4 600 − 4 000)/4 600·100 = 13.04%
Answer
MS = 13.04%
ExamProblems · examproblems.com/courses/business-fundamentals