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
Content marketing mainly aims to:
- AInterrupt viewers with as many adverts as possible
- BAttract and keep an audience by offering useful or entertaining content
- CReplace all customer service with chatbots
- DReduce product prices for loyal customers
2.Marketing principlesHard
In Rogers' diffusion curve, roughly what share of adopters are laggards?
- A34%
- B2.5%
- C16%
- D13.5%
3.Economics conceptsMedium
A per-unit tax is placed on a good with very inelastic demand and elastic supply. Who bears most of the tax burden?
- AConsumers
- BProducers
- CThe government
- DIt is always split equally
4.Economics conceptsHard
Which is a key difference between the CPI and the GDP deflator?
- AThe CPI includes prices of imported consumer goods; the GDP deflator covers only domestically produced goods
- BThe GDP deflator includes imported goods; the CPI does not
- CThe CPI covers investment goods; the GDP deflator does not
- DThey always give exactly the same inflation rate
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
- CIt earns more than the required return and should add value
- DIts reported accounting profit will be positive in every year
6.Financial accountingHard
Inventory days are 60, receivable days 45 and payable days 30. What is the cash conversion (operating) cycle?
- A135 days
- B75 days
- C105 days
- D15 days
7.Break-even analysisMedium
A product sells for €12 per unit with a variable cost of €6 per unit. Fixed costs are €15 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €15 000p = €12v = €6profit = €6 000
Q = units
8.Break-even analysisHard
A company sells 6 250 units at €30 each, with a variable cost of €15 per unit and fixed costs of €37 500. By what percentage %ΔΠ does operating profit change if sales volume rises by 5%?
Q = 6 250p = €30v = €15F = €37 500%ΔQ = +5%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: B · Attract and keep an audience by offering useful or entertaining content
Why this is the answer
Content marketing provides value first, such as guides, videos or articles. It builds trust and search visibility, leading to sales over time.
Answer
B · Attract and keep an audience by offering useful or entertaining content
2.Marketing principles
Answer: C · 16%
Why this is the answer
Innovators 2.5%, early adopters 13.5%, early majority 34%, late majority 34% and laggards 16%, based on a normal distribution of adoption time.
Answer
C · 16%
3.Economics concepts
Answer: A · Consumers
Why this is the answer
The tax burden falls mainly on the side of the market that is less elastic; here buyers cannot cut back, so the price they pay rises by most of the tax.
Answer
A · Consumers
4.Economics concepts
Answer: A · The CPI includes prices of imported consumer goods; the GDP deflator covers only domestically produced goods
Why this is the answer
The CPI uses a fixed basket of consumer goods, including imports, while the deflator covers all domestically produced output with changing weights.
Answer
A · The CPI includes prices of imported consumer goods; the GDP deflator covers only domestically produced goods
5.Financial accounting
Answer: C · 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
C · It earns more than the required return and should add value
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 = 3500 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 = 12 − 6 = €6
Units for the target profit
Q = (F + profit)/(p − v) = (15 000 + 6 000)/6 = 3 500
Answer
Q = 3 500 units
8.Break-even analysis
Answer: %ΔΠ = 8.333 %
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 = 6 250·15 = €93 750
Π = 93 750 − 37 500 = €56 250
DOL
DOL = 93 750/56 250 = 1.667
Change in profit
%ΔΠ = 1.667·(+5%) = +8.333%
Answer
%ΔΠ = +8.333%
Check: new profit = 6 563·15 − 37 500 = €60 937.50.
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