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 Rogers' diffusion of innovations, which group adopts a new product first?
- AInnovators
- BEarly majority
- CLaggards
- DEarly adopters
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?
- ACause-related marketing
- BGuerrilla distribution
- CAmbush marketing
- DCo-branding
3.Economics conceptsMedium
Using the expenditure approach, GDP equals:
- AC + I + G + X + M
- BWages + profits − taxes
- CC − I + G − (X + M)
- DC + I + G + (X − M)
4.Economics conceptsHard
The Marshall–Lerner condition states that a currency depreciation improves the trade balance if:
- AInterest rates rise at the same time
- BThe country has a budget surplus
- CThe sum of the price elasticities of demand for exports and imports exceeds 1
- DExports and imports have zero price elasticity
5.Financial accountingMedium
A project costs €100,000 and brings in €25,000 cash per year. What is its payback period?
- A25 years
- B2.5 years
- C5 years
- D4 years
6.Financial accountingHard
Company P buys 70% of the voting shares of S and gains control. How does P report S in its group accounts?
- AConsolidate 100% of S line by line and show a non-controlling interest
- BAdd only 70% of each of S's assets, liabilities, income and expenses
- CShow one equity-method investment line for its 70% share of S
- DKeep the investment at cost and report only the dividends received from S
7.Break-even analysisMedium
A product sells for €35 per unit with a variable cost of €30 per unit. Fixed costs are €25 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €25 000p = €35v = €30profit = €5 000
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €14 with a variable cost of €10; product B sells for €18 with a variable cost of €10. They sell in a fixed mix of 3 units of A for every 2 of B. Fixed costs are €16 800 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €14, vA = €10pB = €18, vB = €10A : B = 3 : 2F = €16 800
Q = units
3Solutions
1.Marketing principles
Answer: A · Innovators
Why this is the answer
The order is innovators, early adopters, early majority, late majority and laggards. Early adopters are often opinion leaders who influence others.
Answer
A · Innovators
2.Marketing principles
Answer: C · 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
C · Ambush marketing
3.Economics concepts
Answer: D · C + I + G + (X − M)
Why this is the answer
GDP is consumption plus investment plus government purchases plus net exports (exports minus imports).
Answer
D · C + I + G + (X − M)
4.Economics concepts
Answer: C · The sum of the price elasticities of demand for exports and imports exceeds 1
Why this is the answer
If export and import demand are elastic enough (absolute values summing to more than 1), volume effects outweigh the higher import prices and the balance improves.
Answer
C · The sum of the price elasticities of demand for exports and imports exceeds 1
5.Financial accounting
Answer: D · 4 years
Why this is the answer
€100,000 ÷ €25,000 = 4 years. Payback is simple but ignores the time value of money and cash flows after payback.
Answer
D · 4 years
6.Financial accounting
Answer: A · Consolidate 100% of S line by line and show a non-controlling interest
Why this is the answer
A subsidiary is consolidated line by line at 100%. The 30% owned by others is shown as a non-controlling interest within equity.
Answer
A · Consolidate 100% of S line by line and show a non-controlling interest
7.Break-even analysis
Answer: Q = 6000 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 = 35 − 30 = €5
Units for the target profit
Q = (F + profit)/(p − v) = (25 000 + 5 000)/5 = 6 000
Answer
Q = 6 000 units
8.Break-even analysis
Answer: Q = 3000 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 = €4, cmB = €8
Weighted contribution margin
(3·4 + 2·8)/5 = €5.60
Break-even units
Q = 16 800/5.6 = 3 000
A: 1 800, B: 1 200
Answer
Q = 3 000 units
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