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?
- AMarket development
- BDifferentiation focus
- CCost leadership
- DDifferentiation
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
According to the quantity theory of money (MV = PY), if velocity and real output are constant, a 5% rise in the money supply leads to:
- AAbout a 5% rise in real output
- BA 5% fall in velocity
- CNo change in prices
- DAbout a 5% rise in the price level
5.Financial accountingMedium
An asset costs €50,000, has a residual value of €5,000 and a useful life of 5 years. What is the annual straight-line depreciation?
- A€10,000
- B€9,000
- C€5,000
- D€11,000
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 price is below full cost
- BYes, each unit adds €5 contribution
- CNo, the order makes a €7 loss per unit
- DYes, but only if the price exceeds €42
7.Break-even analysisMedium
A product sells for €28 with a variable cost of €18 per unit. Fixed costs are €15 000 per month and profit is taxed at 25%. How many units Q must be sold per month to earn €3 000 after tax?
p = €28v = €18F = €15 000T = 25%after-tax profit = €3 000
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €18 with a variable cost of €10; product B sells for €42 with a variable cost of €30. They sell in a fixed mix of 5 units of A for every 2 of B. Fixed costs are €51 200 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €18, vA = €10pB = €42, vB = €30A : B = 5 : 2F = €51 200
Q = units
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 · 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 · About a 5% rise in the price level
Why this is the answer
With V and Y constant, M and P move proportionally, so prices rise about 5%. This is the classical view of money neutrality in the long run.
Answer
D · About a 5% rise in the price level
5.Financial accounting
Answer: B · €9,000
Why this is the answer
(Cost − residual value) ÷ useful life = (€50,000 − €5,000) ÷ 5 = €9,000 per year.
Answer
B · €9,000
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 = 1900 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
3 000/(1 − 0.25) = €4 000
Units needed
Q = (15 000 + 4 000)/10 = 1 900
Answer
Q = 1 900 units
8.Break-even analysis
Answer: Q = 5600 units
Break-even with a sales mix: when products sell in a fixed ratio, use the weighted average contribution margin: weight each product's p − v by its share of units. Break-even units = F/(weighted contribution margin), split again in the mix ratio.
Contribution margins
cmA = €8, cmB = €12
Weighted contribution margin
(5·8 + 2·12)/7 = €9.14
Break-even units
Q = 51 200/9.143 = 5 600
A: 4 000, B: 1 600
Answer
Q = 5 600 units
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