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
In the Boston Consulting Group matrix, a "cash cow" has:
- AHigh market share in a high-growth market
- BLow market share in a low-growth market
- CLow market share in a high-growth market
- DHigh market share in a low-growth market
2.Marketing principlesHard
Which metric best shows the efficiency of acquiring customers through online advertising?
- ATotal impressions only
- BCustomer acquisition cost compared with customer lifetime value
- CThe number of likes on posts
- DThe number of employees in marketing
3.Economics conceptsMedium
A price ceiling set below the equilibrium price typically causes:
- ANo change in the market
- BA shortage
- CAn increase in supply
- DA surplus
4.Economics conceptsHard
Using the "rule of 70", an economy growing at 7% per year will double its real GDP in about:
- A7 years
- B10 years
- C70 years
- D49 years
5.Financial accountingMedium
A company increases its allowance for doubtful receivables. What is the effect?
- AOnly the notes change; no figures move
- BCash decreases immediately
- CRevenue increases and gross receivables rise by the same amount
- DAn expense is recognised and net receivables fall
6.Financial accountingHard
Under the IAS 16 revaluation model, a building is revalued upwards for the first time. Where does the gain go?
- ATo retained earnings as a realised profit
- BTo other comprehensive income and a revaluation surplus in equity
- CTo a provision on the balance sheet
- DTo revenue in the income statement
7.Break-even analysisMedium
A product sells for €12 with a variable cost of €8 per unit. Fixed costs are €20 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €4 000 after tax?
p = €12v = €8F = €20 000T = 20%after-tax profit = €4 000
Q = units
8.Break-even analysisHard
A product sells for €26 per unit, with a variable cost of €18 per unit and fixed costs of €12 000 per year. Budgeted sales are 2 100 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €12 000p = €26v = €18budget = 2 100
MS = %
3Solutions
1.Marketing principles
Answer: D · High market share in a low-growth market
Why this is the answer
Cash cows fund other products. Stars have high share and growth, question marks low share in high growth, dogs low share and low growth.
Answer
D · High market share in a low-growth market
2.Marketing principles
Answer: B · Customer acquisition cost compared with customer lifetime value
Why this is the answer
CAC relative to CLV shows whether acquisition is profitable; vanity metrics like likes do not measure business value.
Answer
B · Customer acquisition cost compared with customer lifetime value
3.Economics concepts
Answer: B · A shortage
Why this is the answer
A binding maximum price raises quantity demanded and lowers quantity supplied, creating excess demand, as with rent control.
Answer
B · A shortage
4.Economics concepts
Answer: B · 10 years
Why this is the answer
The doubling time is approximately 70 divided by the percentage growth rate, so 70 / 7 = 10 years, showing the power of compound growth.
Answer
B · 10 years
5.Financial accounting
Answer: D · An expense is recognised and net receivables fall
Why this is the answer
The increase is charged to profit, and the allowance is deducted from gross receivables, so the balance sheet shows the amount expected to be collected.
Answer
D · An expense is recognised and net receivables fall
6.Financial accounting
Answer: B · To other comprehensive income and a revaluation surplus in equity
Why this is the answer
Upward revaluations are credited to a revaluation surplus via OCI, unless they reverse an earlier decrease recognised in profit or loss.
Answer
B · To other comprehensive income and a revaluation surplus in equity
7.Break-even analysis
Answer: Q = 6250 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).
Pre-tax profit needed
4 000/(1 − 0.2) = €5 000
Units needed
Q = (20 000 + 5 000)/4 = 6 250
Answer
Q = 6 250 units
8.Break-even analysis
Answer: MS = 28.57 %
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) = 12 000/8 = 1 500
Margin of safety
MS = (2 100 − 1 500)/2 100·100 = 28.57%
Answer
MS = 28.57%
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