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 firm competes across a broad market by having the lowest costs in its industry and passing savings on as low prices. Which Porter generic strategy is this?
- ADifferentiation focus
- BMarket development
- CCost leadership
- DDifferentiation
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 spent too much on advertising
- CThey expanded into too many countries
- DThey defined their business as railways rather than transportation
3.Economics conceptsMedium
In the short run, a firm in perfect competition should shut down if the market price is below:
- AAverage fixed cost
- BAverage total cost
- CAverage variable cost
- DMarginal revenue
4.Economics conceptsHard
In the Prisoner's Dilemma, the Nash equilibrium is:
- AOne player cooperates and the other defects, so only one of them gains
- BThere is no equilibrium
- CBoth players cooperate
- DBoth players defect, even though both cooperating would be better
5.Financial accountingMedium
Current assets are €300,000 and current liabilities are €150,000. What is the current ratio?
- A4.5
- B2.0
- C0.5
- D1.5
6.Financial accountingHard
Inventory days are 60, receivable days 45 and payable days 30. What is the cash conversion (operating) cycle?
- A105 days
- B75 days
- C15 days
- D135 days
7.Break-even analysisMedium
A product sells for €30 per unit with a variable cost of €15 per unit. Fixed costs are €60 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €60 000p = €30v = €15profit = €6 000
Q = units
8.Break-even analysisHard
A product sells for €40 per unit, with a variable cost of €25 per unit and fixed costs of €30 000 per year. Budgeted sales are 2 400 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €30 000p = €40v = €25budget = 2 400
MS = %
3Solutions
1.Marketing principles
Answer: C · Cost leadership
Why this is the answer
Cost leadership seeks the lowest cost position in a broad market. Differentiation offers unique value at a premium; focus strategies target a narrow segment.
Answer
C · Cost leadership
2.Marketing principles
Answer: D · 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
D · They defined their business as railways rather than transportation
3.Economics concepts
Answer: C · Average variable cost
Why this is the answer
If price covers average variable cost, producing reduces losses by contributing to fixed costs; below AVC, shutting down loses less.
Answer
C · Average variable cost
4.Economics concepts
Answer: D · Both players defect, even though both cooperating would be better
Why this is the answer
Each player's best response is to defect whatever the other does, so mutual defection is the equilibrium, although mutual cooperation would give both a higher payoff.
Answer
D · Both players defect, even though both cooperating would be better
5.Financial accounting
Answer: B · 2.0
Why this is the answer
€300,000 ÷ €150,000 = 2.0, so current assets cover short-term obligations twice.
Answer
B · 2.0
6.Financial accounting
Answer: B · 75 days
Why this is the answer
60 + 45 − 30 = 75 days between paying suppliers and collecting cash from customers. A shorter cycle needs less working capital finance.
Answer
B · 75 days
7.Break-even analysis
Answer: Q = 4400 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 = 30 − 15 = €15
Units for the target profit
Q = (F + profit)/(p − v) = (60 000 + 6 000)/15 = 4 400
Answer
Q = 4 400 units
8.Break-even analysis
Answer: MS = 16.67 %
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) = 30 000/15 = 2 000
Margin of safety
MS = (2 400 − 2 000)/2 400·100 = 16.67%
Answer
MS = 16.67%
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