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
Price elasticity matters for pricing because:
- AElasticity only affects costs
- BIt has no effect on pricing decisions
- CIf demand is inelastic, a price rise will lower total revenue
- DIf demand is elastic, a price cut can raise total revenue
2.Marketing principlesHard
A company launches a premium version of its product under the same brand name. This is an example of:
- ABrand extension into a new category
- BLine extension
- CCo-branding
- DMultibranding
3.Economics conceptsMedium
Overfishing in international waters is an example of:
- APrice discrimination
- BA Giffen good
- CThe tragedy of the commons
- DA natural monopoly
4.Economics conceptsHard
Moral hazard arises when:
- APrices are too high for poor consumers
- BTwo firms collude on price
- CA buyer cannot observe product quality before buying, so low-quality sellers dominate the market
- DOne party changes behaviour after a contract because they do not bear the full consequences
5.Financial accountingMedium
A project has a positive net present value (NPV) at the company's cost of capital. This means:
- AIt has no risk at all
- BIt earns more than the required return and should add value
- CIt recovers its cost within one year
- DIts reported accounting profit will be positive in every year
6.Financial accountingHard
Machine hours are scarce. Product X earns €20 contribution and needs 4 hours; product Y earns €15 and needs 2 hours. Which should be made first?
- AX, because it earns more contribution per unit
- BX, because it uses more machine time
- CY, because it earns €7.50 per hour versus €5 for X
- DEither, because the total contribution is the same
7.Break-even analysisMedium
A company sells 1 500 units at €55 each. The variable cost is €45 per unit and fixed costs are €12 000. Find the degree of operating leverage DOL at this sales level.
Q = 1 500p = €55v = €45F = €12 000
DOL =
8.Break-even analysisHard
A product sells for €48 per unit, with a variable cost of €45 per unit and fixed costs of €12 000 per year. Budgeted sales are 5 200 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €12 000p = €48v = €45budget = 5 200
MS = %
3Solutions
1.Marketing principles
Answer: D · If demand is elastic, a price cut can raise total revenue
Why this is the answer
With elastic demand, quantity responds strongly, so a lower price can increase revenue; with inelastic demand, a price rise increases revenue.
Answer
D · If demand is elastic, a price cut can raise total revenue
2.Marketing principles
Answer: B · Line extension
Why this is the answer
A line extension adds new variants in the same category under the existing brand; brand extension uses the brand in a new category.
Answer
B · Line extension
3.Economics concepts
Answer: C · The tragedy of the commons
Why this is the answer
When a common resource is rival but people cannot be excluded, each user ignores the cost they impose on others, leading to overuse.
Answer
C · The tragedy of the commons
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 · It earns more than the required return and should add value
Why this is the answer
A positive NPV means the present value of inflows exceeds the investment at the required rate, so the project increases shareholder wealth.
Answer
B · It earns more than the required return and should add value
6.Financial accounting
Answer: C · Y, because it earns €7.50 per hour versus €5 for X
Why this is the answer
X earns €20 ÷ 4 = €5 per hour, Y earns €15 ÷ 2 = €7.50 per hour. With a scarce resource, maximise contribution per scarce hour.
Answer
C · Y, because it earns €7.50 per hour versus €5 for X
7.Break-even analysis
Answer: DOL = 5
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 = 1 500·(55 − 45) = €15 000
Operating profit
Π = 15 000 − 12 000 = €3 000
DOL
DOL = 15 000/3 000 = 5
Answer
DOL = 5
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) = 12 000/3 = 4 000
Margin of safety
MS = (5 200 − 4 000)/5 200·100 = 23.08%
Answer
MS = 23.08%
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