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 firm competes across a broad market by having the lowest costs in its industry and passing savings on as low prices. Which Porter generic strategy is this?
- ACost leadership
- BDifferentiation focus
- CMarket development
- DDifferentiation
2.Marketing principlesHard
An airline can buy a certain aircraft model only from one manufacturer, and switching to another model is very costly. In Porter's five forces, what does this mean?
- AHigh bargaining power of buyers
- BHigh bargaining power of suppliers
- CHigh threat of new entrants into the market
- DLow bargaining power of suppliers
3.Economics conceptsMedium
A minimum wage set above the equilibrium wage in a competitive labour market is predicted to cause:
- ANo change in employment
- BA shortage of labour
- CA fall in the wage rate
- DA surplus of labour (unemployment)
4.Economics conceptsHard
The principal–agent problem arises when:
- AA buyer and seller have identical information
- BThe government owns a firm
- CTwo firms agree to fix prices
- DAn agent acting for a principal has different goals and the principal cannot fully monitor them
5.Financial accountingMedium
Retained earnings represent:
- AThe share price
- BAccumulated profits that have not been paid out as dividends
- CMoney owed to shareholders
- DCash kept in the bank
6.Financial accountingHard
Making a part costs €10 materials, €6 labour and €4 variable overhead, plus €5 of fixed overhead that continues anyway. A supplier offers it at €22. What should the firm do on cost grounds?
- AMake it, because the relevant cost of €20 is below €22
- BMake it, because the full cost of €25 is below €22
- CBuy it, because the full cost of €25 per unit is above €22
- DBuy it, because fixed costs are always relevant
7.Break-even analysisMedium
A product sells for €12 with a variable cost of €8 per unit. Fixed costs are €16 000 per month and profit is taxed at 25%. How many units Q must be sold per month to earn €3 000 after tax?
p = €12v = €8F = €16 000T = 25%after-tax profit = €3 000
Q = units
8.Break-even analysisHard
A company sells 1 600 units at €36 each, with a variable cost of €30 per unit and fixed costs of €4 800. By what percentage %ΔΠ does operating profit change if sales volume rises by 10%?
Q = 1 600p = €36v = €30F = €4 800%ΔQ = +10%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: A · Cost leadership
Why this is the answer
Cost leadership seeks the lowest cost position in a broad market. Differentiation offers unique value at a premium; focus strategies target a narrow segment.
Answer
A · Cost leadership
2.Marketing principles
Answer: B · High bargaining power of suppliers
Why this is the answer
When suppliers are concentrated and switching is expensive, they can demand higher prices or better terms, reducing industry profitability.
Answer
B · High bargaining power of suppliers
3.Economics concepts
Answer: D · A surplus of labour (unemployment)
Why this is the answer
At the higher wage more people want to work and firms hire fewer, so labour supplied exceeds labour demanded in the simple competitive model.
Answer
D · A surplus of labour (unemployment)
4.Economics concepts
Answer: D · An agent acting for a principal has different goals and the principal cannot fully monitor them
Why this is the answer
Hidden action and conflicting interests let the agent pursue their own aims; incentive contracts such as performance pay try to align interests.
Answer
D · An agent acting for a principal has different goals and the principal cannot fully monitor them
5.Financial accounting
Answer: B · 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
B · Accumulated profits that have not been paid out as dividends
6.Financial accounting
Answer: A · Make it, because the relevant cost of €20 is below €22
Why this is the answer
Only the €20 of variable cost is avoided by buying; the €5 fixed overhead stays. Making costs €20 versus €22 to buy, so making saves €2 per unit.
Answer
A · Make it, because the relevant cost of €20 is below €22
7.Break-even analysis
Answer: Q = 5000 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
3 000/(1 − 0.25) = €4 000
Units needed
Q = (16 000 + 4 000)/4 = 5 000
Answer
Q = 5 000 units
8.Break-even analysis
Answer: %ΔΠ = 20 %
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Contribution margin and profit
CM = 1 600·6 = €9 600
Π = 9 600 − 4 800 = €4 800
DOL
DOL = 9 600/4 800 = 2
Change in profit
%ΔΠ = 2·(+10%) = +20%
Answer
%ΔΠ = +20%
Check: new profit = 1 760·6 − 4 800 = €5 760.00.
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