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
Which pricing method adds a fixed percentage to the cost of a product?
- AValue-based pricing
- BCompetitive pricing
- CDynamic pricing
- DCost-plus pricing
2.Marketing principlesHard
An ice cream brand finds that its sales and its advertising spend both peak in summer. Why can it not conclude that advertising caused the sales?
- ASummer sales are too small to measure
- BAdvertising never affects sales of food
- CSales data is always unreliable
- DHot weather may drive both, so correlation does not prove causation
3.Economics conceptsMedium
Education generates benefits for society beyond the individual student. Without intervention, the market will likely:
- AUnder-provide education compared with the social optimum
- BOver-provide education compared with the social optimum
- CStop providing education altogether
- DProvide exactly the efficient amount of education, as prices reflect all benefits
4.Economics conceptsHard
The principal–agent problem arises when:
- AAn agent acting for a principal has different goals and the principal cannot fully monitor them
- BA buyer and seller have identical information
- CThe government owns a firm
- DTwo firms agree to fix prices
5.Financial accountingMedium
A shop buys 100 units at €10, then 100 units at €12, and then sells 150 units. What is cost of sales using FIFO?
- A€1,650
- B€1,500
- C€1,700
- D€1,600
6.Financial accountingHard
Under the IAS 16 revaluation model, a building is revalued upwards for the first time. Where does the gain go?
- ATo other comprehensive income and a revaluation surplus in equity
- BTo retained earnings as a realised profit
- CTo revenue in the income statement
- DTo a provision on the balance sheet
7.Break-even analysisMedium
A company sells 1 440 units at €16 each. The variable cost is €12 per unit and fixed costs are €4 800. Find the degree of operating leverage DOL at this sales level.
Q = 1 440p = €16v = €12F = €4 800
DOL =
8.Break-even analysisHard
A product sells for €27 per unit, with a variable cost of €15 per unit and fixed costs of €30 000 per year. Budgeted sales are 4 500 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €30 000p = €27v = €15budget = 4 500
MS = %
3Solutions
1.Marketing principles
Answer: D · Cost-plus pricing
Why this is the answer
Cost-plus pricing is simple but ignores customer willingness to pay; value-based pricing starts from the value perceived by customers.
Answer
D · Cost-plus pricing
2.Marketing principles
Answer: D · Hot weather may drive both, so correlation does not prove causation
Why this is the answer
A confounding factor, such as temperature, can create a correlation between two variables. Controlled tests or models that account for seasonality are needed to estimate the ad effect.
Answer
D · Hot weather may drive both, so correlation does not prove causation
3.Economics concepts
Answer: A · Under-provide education compared with the social optimum
Why this is the answer
Private decisions ignore external benefits, so output is below the socially optimal level; subsidies or public provision can raise it.
Answer
A · Under-provide education compared with the social optimum
4.Economics concepts
Answer: A · 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
A · An agent acting for a principal has different goals and the principal cannot fully monitor them
5.Financial accounting
Answer: D · €1,600
Why this is the answer
FIFO: 100 × €10 + 50 × €12 = €1,600. The 50 units left are valued at the latest cost of €12.
Answer
D · €1,600
6.Financial accounting
Answer: A · To other comprehensive income and a revaluation surplus in equity
Why this is the answer
Upward revaluations are credited to a revaluation surplus via OCI, unless they reverse an earlier decrease recognised in profit or loss.
Answer
A · To other comprehensive income and a revaluation surplus in equity
7.Break-even analysis
Answer: DOL = 6
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.
Total contribution margin
CM = 1 440·(16 − 12) = €5 760
Operating profit
Π = 5 760 − 4 800 = €960
DOL
DOL = 5 760/960 = 6
Answer
DOL = 6
8.Break-even analysis
Answer: MS = 44.44 %
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) = 30 000/12 = 2 500
Margin of safety
MS = (4 500 − 2 500)/4 500·100 = 44.44%
Answer
MS = 44.44%
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