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 of these is a closed question in a survey?
- AWhat do you think of our new advert?
- BHow would you describe your ideal holiday?
- CHave you bought this product in the last month? (yes/no)
- DWhy did you choose this brand?
2.Marketing principlesHard
In a B2B buying centre, a purchasing assistant controls which supplier brochures reach the engineers. Which role does the assistant play?
- AInfluencer
- BDecider
- CUser
- DGatekeeper
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
- CProvide exactly the efficient amount of education, as prices reflect all benefits
- DStop providing education altogether
4.Economics conceptsHard
A Giffen good is one where:
- AQuantity demanded rises when its price rises, because a strong income effect outweighs the substitution effect
- BDemand rises with income, like most goods
- CDemand rises because the good is a status symbol
- DThe price never changes
5.Financial accountingMedium
The prudence (conservatism) concept suggests that accountants should:
- AAlways record the highest possible profit to attract investors
- BIgnore possible losses
- CAvoid overstating assets and income under uncertainty
- DValue assets at their selling price
6.Financial accountingHard
A firm has a net profit margin of 5%, asset turnover of 2 and an equity multiplier (assets ÷ equity) of 1.5. Using the DuPont analysis, what is ROE?
- A15%
- B8.5%
- C10%
- D7.5%
7.Break-even analysisMedium
A product sells for €13 per unit with a variable cost of €8 per unit. Fixed costs are €25 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €25 000p = €13v = €8profit = €6 000
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €17 with a variable cost of €12; product B sells for €37 with a variable cost of €25. They sell in a fixed mix of 2 units of A for every 3 of B. Fixed costs are €36 800 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €17, vA = €12pB = €37, vB = €25A : B = 2 : 3F = €36 800
Q = units
3Solutions
1.Marketing principles
Answer: C · Have you bought this product in the last month? (yes/no)
Why this is the answer
Closed questions offer set answers and are easy to analyse statistically. Open questions let people answer in their own words, giving richer but harder-to-code data.
Answer
C · Have you bought this product in the last month? (yes/no)
2.Marketing principles
Answer: D · 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
D · Gatekeeper
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 · Quantity demanded rises when its price rises, because a strong income effect outweighs the substitution effect
Why this is the answer
For a Giffen good the income effect of a price rise (feeling poorer, buying more of the cheap staple) dominates the substitution effect, so demand slopes upward.
Answer
A · Quantity demanded rises when its price rises, because a strong income effect outweighs the substitution effect
5.Financial accounting
Answer: C · Avoid overstating assets and income under uncertainty
Why this is the answer
Prudence means exercising caution so that assets and income are not overstated and liabilities and expenses not understated.
Answer
C · Avoid overstating assets and income under uncertainty
6.Financial accounting
Answer: A · 15%
Why this is the answer
ROE = 5% × 2 × 1.5 = 15%. DuPont shows whether returns come from profitability, asset efficiency or leverage.
Answer
A · 15%
7.Break-even analysis
Answer: Q = 6200 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 = 13 − 8 = €5
Units for the target profit
Q = (F + profit)/(p − v) = (25 000 + 6 000)/5 = 6 200
Answer
Q = 6 200 units
8.Break-even analysis
Answer: Q = 4000 units
Break-even with a sales mix: when products sell in a fixed ratio, use the weighted average contribution margin: weight each product's p − v by its share of units. Break-even units = F/(weighted contribution margin), split again in the mix ratio.
Contribution margins
cmA = €5, cmB = €12
Weighted contribution margin
(2·5 + 3·12)/5 = €9.20
Break-even units
Q = 36 800/9.2 = 4 000
A: 1 600, B: 2 400
Answer
Q = 4 000 units
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