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?
- AMicromarketing for each individual
- BUndifferentiated (mass) marketing
- CDifferentiated marketing
- DConcentrated (niche) marketing
2.Marketing principlesHard
Theodore Levitt's "Marketing Myopia" (1960) used US railroads as an example. What was their mistake?
- AThey defined their business as railways rather than transportation
- BThey spent too much on advertising
- CThey set their prices too low
- DThey expanded into too many countries
3.Economics conceptsMedium
Both supply and demand for a good increase. What can we say for certain about the new equilibrium?
- ABoth price and quantity rise
- BBoth price and quantity fall
- CQuantity rises, but the change in price is uncertain
- DPrice rises, but the change in quantity is uncertain
4.Economics conceptsHard
Under perfect (first-degree) price discrimination, the monopolist:
- ACaptures all consumer surplus and produces the efficient output
- BProduces less than a single-price monopolist, creating a larger deadweight loss
- CCreates the largest possible deadweight loss
- DCharges every consumer the same price
5.Financial accountingMedium
A product sells for €40 and has a variable cost of €30. What is its contribution-to-sales (C/S) ratio?
- A75%
- B25%
- C33%
- D10%
6.Financial accountingHard
A parent sold goods to its subsidiary at a profit, and the subsidiary still holds them at year end. What must happen on consolidation?
- AThe profit is shown twice, once for each company
- BThe unrealised profit in inventory is eliminated
- CThe sale is shown as external revenue of the group
- DNothing, because each company is a separate entity
7.Break-even analysisMedium
A product sells for €29 per unit with a variable cost of €25 per unit. Fixed costs are €2 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €2 000p = €29v = €25profit = €2 000
Q = units
8.Break-even analysisHard
A company sells 1 000 units at €23 each, with a variable cost of €18 per unit and fixed costs of €4 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 12%?
Q = 1 000p = €23v = €18F = €4 000%ΔQ = +12%
%ΔΠ = %
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: A · 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
A · They defined their business as railways rather than transportation
3.Economics concepts
Answer: C · Quantity rises, but the change in price is uncertain
Why this is the answer
Both shifts raise quantity, but the demand shift raises price while the supply shift lowers it, so the price effect depends on their relative size.
Answer
C · Quantity rises, but the change in price is uncertain
4.Economics concepts
Answer: A · Captures all consumer surplus and produces the efficient output
Why this is the answer
Charging each buyer their reservation price means it sells until price equals MC, so there is no deadweight loss, but all surplus goes to the producer.
Answer
A · Captures all consumer surplus and produces the efficient output
5.Financial accounting
Answer: B · 25%
Why this is the answer
Contribution = €10. C/S ratio = €10 ÷ €40 = 25%. Fixed costs ÷ C/S ratio gives break-even revenue.
Answer
B · 25%
6.Financial accounting
Answer: B · The unrealised profit in inventory is eliminated
Why this is the answer
Intra-group sales and purchases are cancelled, and profit on goods still held in the group is removed from inventory and group profit until sold outside.
Answer
B · The unrealised profit in inventory is eliminated
7.Break-even analysis
Answer: Q = 1000 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 = 29 − 25 = €4
Units for the target profit
Q = (F + profit)/(p − v) = (2 000 + 2 000)/4 = 1 000
Answer
Q = 1 000 units
8.Break-even analysis
Answer: %ΔΠ = 60 %
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 = 1 000·5 = €5 000
Π = 5 000 − 4 000 = €1 000
DOL
DOL = 5 000/1 000 = 5
Change in profit
%ΔΠ = 5·(+12%) = +60%
Answer
%ΔΠ = +60%
Check: new profit = 1 120·5 − 4 000 = €1 600.00.
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