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
Two established brands from different companies jointly market one product, such as a credit card carrying an airline's brand. This is:
- ABrand extension
- BCo-branding
- CLine extension
- DMultibranding
2.Marketing principlesHard
During a major sports tournament, a non-sponsor brand runs ads suggesting a link with the event without paying for official rights. What is this called?
- ACo-branding
- BCause-related marketing
- CGuerrilla distribution
- DAmbush marketing
3.Economics conceptsMedium
If the ECB raises its main interest rate, the most likely short-term effect is:
- AA fall in the value of the euro
- BLower borrowing and spending, reducing inflationary pressure
- CHigher borrowing and spending, which adds to inflationary pressure
- DAn immediate rise in GDP
4.Economics conceptsHard
The Lerner index (P − MC)/P for a profit-maximising monopolist equals 1/|PED|. If |PED| = 4, the price is:
- A75% above marginal cost, as a share of price
- BEqual to marginal cost
- C4 times marginal cost
- D25% above marginal cost, as a share of price
5.Financial accountingMedium
At 31 December, electricity used in December (€800) has not yet been billed. Which year-end entry is correct?
- ANo entry until the bill arrives
- BDebit electricity expense, credit accruals
- CDebit prepayments, credit cash
- DDebit accruals, credit electricity expense
6.Financial accountingHard
A firm with spare capacity gets a one-off order at €35 per unit. Variable cost is €30 and full cost including fixed overhead is €42. Assuming no other effects, should it accept?
- ANo, the order makes a €7 loss per unit
- BYes, each unit adds €5 contribution
- CNo, the price is below full cost
- DYes, but only if the price exceeds €42
7.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €25 000 per year and a variable cost of €20 per unit. Method B, more automated, has fixed costs of €37 000 per year and a variable cost of €14 per unit. At what yearly volume Q do both methods cost the same?
FA = €25 000vA = €20FB = €37 000vB = €14
Q = units
8.Break-even analysisHard
A product sells for €31 per unit, with a variable cost of €25 per unit and fixed costs of €30 000 per year. Budgeted sales are 7 500 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €30 000p = €31v = €25budget = 7 500
MS = %
3Solutions
1.Marketing principles
Answer: B · Co-branding
Why this is the answer
Co-branding combines the strengths and customer bases of two brands. It can add credibility but links each brand's reputation to the other.
Answer
B · Co-branding
2.Marketing principles
Answer: D · Ambush marketing
Why this is the answer
Ambush marketing tries to gain association with an event without sponsorship. Organisers often protect sponsors through contracts and trademark rules.
Answer
D · Ambush marketing
3.Economics concepts
Answer: B · Lower borrowing and spending, reducing inflationary pressure
Why this is the answer
Higher rates make credit more expensive and saving more attractive, reducing demand and inflation; they also tend to strengthen the currency.
Answer
B · Lower borrowing and spending, reducing inflationary pressure
4.Economics concepts
Answer: D · 25% above marginal cost, as a share of price
Why this is the answer
The markup (P − MC)/P = 1/4 = 0.25, so a quarter of the price is a margin above MC; more elastic demand means less market power.
Answer
D · 25% above marginal cost, as a share of price
5.Financial accounting
Answer: B · Debit electricity expense, credit accruals
Why this is the answer
The accrual records December's cost as an expense this year with a current liability, so expenses match the period of use.
Answer
B · Debit electricity expense, credit accruals
6.Financial accounting
Answer: B · Yes, each unit adds €5 contribution
Why this is the answer
Fixed costs do not change, so the order adds €35 − €30 = €5 per unit to profit. Risks such as upsetting regular customers should still be considered.
Answer
B · Yes, each unit adds €5 contribution
7.Break-even analysis
Answer: Q = 2000 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).
Equal total costs
25 000 + 20Q = 37 000 + 14Q
Solve for Q
Q = (37 000 − 25 000)/(20 − 14) = 2 000
Answer
Q = 2 000 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: MS = 33.33 %
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) = 30 000/6 = 5 000
Margin of safety
MS = (7 500 − 5 000)/7 500·100 = 33.33%
Answer
MS = 33.33%
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