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 small firm makes premium climbing gear and targets only serious climbers. Which targeting strategy is this?
- ADifferentiated marketing
- BUndifferentiated (mass) marketing
- CMicromarketing for each individual
- DConcentrated (niche) marketing
2.Marketing principlesHard
In a B2B buying centre, a purchasing assistant controls which supplier brochures reach the engineers. Which role does the assistant play?
- ADecider
- BGatekeeper
- CUser
- DInfluencer
3.Economics conceptsMedium
A savings account pays a nominal interest rate of 6% and inflation is 4%. The approximate real interest rate is:
- A2%
- B24%
- C1.5%
- D10%
4.Economics conceptsHard
Moral hazard arises when:
- ATwo firms collude on price
- BPrices are too high for poor consumers
- 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
Which costs are relevant when making a business decision?
- ACosts already paid for the project
- BFuture cash flows that differ between the alternatives
- CAll costs in last year's income statement
- DAllocated fixed overheads that do not change with the decision
6.Financial accountingHard
Production exceeds sales this period, so inventory rises. How does absorption costing profit compare with marginal costing profit?
- AAbsorption costing shows a loss
- BThey are always equal
- CMarginal costing profit is higher this period
- DAbsorption costing profit is higher
7.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €25 000 per year and a variable cost of €25 per unit. Method B, more automated, has fixed costs of €40 000 per year and a variable cost of €22 per unit. At what yearly volume Q do both methods cost the same?
FA = €25 000vA = €25FB = €40 000vB = €22
Q = units
8.Break-even analysisHard
A product sells for €9 per unit, with a variable cost of €6 per unit and fixed costs of €1 500 per year. Budgeted sales are 700 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €1 500p = €9v = €6budget = 700
MS = %
3Solutions
1.Marketing principles
Answer: D · Concentrated (niche) marketing
Why this is the answer
Concentrated marketing focuses resources on one segment. It builds deep expertise but makes the firm dependent on that segment.
Answer
D · Concentrated (niche) marketing
2.Marketing principles
Answer: B · Gatekeeper
Why this is the answer
Buying centre roles include users, influencers, buyers, deciders and gatekeepers. Sellers must reach the right people, and gatekeepers can block access to them.
Answer
B · Gatekeeper
3.Economics concepts
Answer: A · 2%
Why this is the answer
The real interest rate is approximately the nominal rate minus inflation: 6% − 4% = 2%.
Answer
A · 2%
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 · Future cash flows that differ between the alternatives
Why this is the answer
Relevant costs are future, incremental cash flows. Sunk costs, committed costs and unchanged allocated overheads are ignored.
Answer
B · Future cash flows that differ between the alternatives
6.Financial accounting
Answer: D · Absorption costing profit is higher
Why this is the answer
Under absorption costing part of this period's fixed overhead sits in closing inventory instead of being expensed, so reported profit is higher when inventory rises.
Answer
D · Absorption costing profit is higher
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).
Equal total costs
25 000 + 25Q = 40 000 + 22Q
Solve for Q
Q = (40 000 − 25 000)/(25 − 22) = 5 000
Answer
Q = 5 000 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: MS = 28.57 %
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) = 1 500/3 = 500
Margin of safety
MS = (700 − 500)/700·100 = 28.57%
Answer
MS = 28.57%
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