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?
- ADynamic pricing
- BCompetitive pricing
- CCost-plus pricing
- DValue-based pricing
2.Marketing principlesHard
Theodore Levitt's "Marketing Myopia" (1960) used US railroads as an example. What was their mistake?
- AThey set their prices too low
- BThey defined their business as railways rather than transportation
- CThey expanded into too many countries
- DThey spent too much on advertising
3.Economics conceptsMedium
A currency depreciation tends to:
- AMake imports cheaper
- BReduce the price of all domestic goods and make imports cheaper
- CMake exports cheaper abroad and imports more expensive
- DHave no effect on trade
4.Economics conceptsHard
In the Bertrand model, two firms sell identical products with the same constant marginal cost and compete on price. The equilibrium price is:
- AHalfway between monopoly price and marginal cost
- BThe monopoly price
- CEqual to marginal cost
- DZero
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 recovers its cost within one year
- CIts reported accounting profit will be positive in every year
- DIt earns more than the required return and should add value
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?
- A8.5%
- B15%
- C10%
- D7.5%
7.Break-even analysisMedium
A product sells for €22 per unit with a variable cost of €18 per unit. Fixed costs are €6 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €6 000p = €22v = €18profit = €6 000
Q = units
8.Break-even analysisHard
A company sells 6 250 units at €28 each, with a variable cost of €8 per unit and fixed costs of €50 000. By what percentage %ΔΠ does operating profit change if sales volume falls by 20%?
Q = 6 250p = €28v = €8F = €50 000%ΔQ = −20%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: C · 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
C · Cost-plus pricing
2.Marketing principles
Answer: B · They defined their business as railways rather than transportation
Why this is the answer
Levitt argued firms fail when they focus on their product instead of the customer need it serves. Railroads lost customers to cars, trucks and planes they did not see as rivals.
Answer
B · They defined their business as railways rather than transportation
3.Economics concepts
Answer: C · Make exports cheaper abroad and imports more expensive
Why this is the answer
A weaker currency improves export competitiveness and raises import prices, which can increase inflation.
Answer
C · Make exports cheaper abroad and imports more expensive
4.Economics concepts
Answer: C · Equal to marginal cost
Why this is the answer
Undercutting continues until price equals marginal cost, so even two firms reach the competitive outcome; in Cournot quantity competition, price stays above MC.
Answer
C · Equal to marginal cost
5.Financial accounting
Answer: D · 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
D · It earns more than the required return and should add value
6.Financial accounting
Answer: B · 15%
Why this is the answer
ROE = 5% × 2 × 1.5 = 15%. DuPont shows whether returns come from profitability, asset efficiency or leverage.
Answer
B · 15%
7.Break-even analysis
Answer: Q = 3000 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 = 22 − 18 = €4
Units for the target profit
Q = (F + profit)/(p − v) = (6 000 + 6 000)/4 = 3 000
Answer
Q = 3 000 units
8.Break-even analysis
Answer: %ΔΠ = −33.33 %
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 = 6 250·20 = €125 000
Π = 125 000 − 50 000 = €75 000
DOL
DOL = 125 000/75 000 = 1.667
Change in profit
%ΔΠ = 1.667·(−20%) = −33.33%
Answer
%ΔΠ = −33.33%
Check: new profit = 5 000·20 − 50 000 = €50 000.00.
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