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?
- AInformation search, need recognition, purchase, evaluation of alternatives, post-purchase behaviour
- BEvaluation of alternatives, need recognition, information search, purchase, post-purchase behaviour
- CNeed recognition, information search, evaluation of alternatives, purchase, post-purchase behaviour
- DPurchase, need recognition, information search, evaluation of alternatives, post-purchase behaviour
2.Marketing principlesHard
In conjoint analysis, researchers:
- AAnalyse competitors' financial statements
- BCount website visitors
- CObserve shoppers in a store without asking questions
- DAsk respondents to choose between product profiles to estimate the value of each attribute
3.Economics conceptsMedium
In perfect competition in the long run, firms earn:
- AMonopoly profits
- BZero economic profit
- CLarge economic profits
- DLosses forever
4.Economics conceptsHard
Moral hazard arises when:
- AA buyer cannot observe product quality before buying, so low-quality sellers dominate the market
- BTwo firms collude on price
- CPrices are too high for poor consumers
- DOne party changes behaviour after a contract because they do not bear the full consequences
5.Financial accountingMedium
Current assets are €300,000 and current liabilities are €150,000. What is the current ratio?
- A4.5
- B2.0
- C1.5
- D0.5
6.Financial accountingHard
Goodwill arises in a business combination when:
- AAssets are revalued upwards
- BThe acquired company makes a loss
- CA company has a good reputation
- DThe consideration paid exceeds the fair value of identifiable net assets acquired
7.Break-even analysisMedium
A product sells for €50 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 €12 000?
F = €20 000p = €50v = €30profit = €12 000
Q = units
8.Break-even analysisHard
A product sells for €40 per unit, with a variable cost of €30 per unit and fixed costs of €40 000 per year. Budgeted sales are 5 200 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €40 000p = €40v = €30budget = 5 200
MS = %
3Solutions
1.Marketing principles
Answer: C · 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
C · Need recognition, information search, evaluation of alternatives, purchase, post-purchase behaviour
2.Marketing principles
Answer: D · Ask respondents to choose between product profiles to estimate the value of each attribute
Why this is the answer
Conjoint analysis infers the part-worth utility of attributes (such as price, brand, features) from respondents' choices or rankings of combinations.
Answer
D · Ask respondents to choose between product profiles to estimate the value of each attribute
3.Economics concepts
Answer: B · Zero economic profit
Why this is the answer
Profits attract entry and losses cause exit until price equals minimum average cost and economic profit is zero.
Answer
B · Zero economic profit
4.Economics concepts
Answer: D · One party changes behaviour after a contract because they do not bear the full consequences
Why this is the answer
Moral hazard is hidden action after the contract, such as an insured driver taking more risks. Adverse selection is hidden information before the contract.
Answer
D · One party changes behaviour after a contract because they do not bear the full consequences
5.Financial accounting
Answer: B · 2.0
Why this is the answer
€300,000 ÷ €150,000 = 2.0, so current assets cover short-term obligations twice.
Answer
B · 2.0
6.Financial accounting
Answer: D · The consideration paid exceeds the fair value of identifiable net assets acquired
Why this is the answer
Goodwill = consideration − fair value of identifiable net assets. Under IFRS it is not amortised but tested for impairment annually.
Answer
D · The consideration paid exceeds the fair value of identifiable net assets acquired
7.Break-even analysis
Answer: Q = 1600 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) = (20 000 + 12 000)/20 = 1 600
Answer
Q = 1 600 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) = 40 000/10 = 4 000
Margin of safety
MS = (5 200 − 4 000)/5 200·100 = 23.08%
Answer
MS = 23.08%
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