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 small firm makes premium climbing gear and targets only serious climbers. Which targeting strategy is this?
- AConcentrated (niche) marketing
- BMicromarketing for each individual
- CUndifferentiated (mass) marketing
- DDifferentiated marketing
2.Marketing principlesHard
In the SERVQUAL gap model, the "knowledge gap" (gap 1) is the difference between:
- AThe price paid and the cost of providing the service
- BWhat customers expect and what managers think customers expect
- CThe service delivered and what advertising promised
- DThe service standards set by managers and the service actually delivered
3.Economics conceptsMedium
Using the expenditure approach, GDP equals:
- AC − I + G − (X + M)
- BC + I + G + (X − M)
- CWages + profits − taxes
- DC + I + G + X + M
4.Economics conceptsHard
The Marshall–Lerner condition states that a currency depreciation improves the trade balance if:
- AExports and imports have zero price elasticity
- BThe sum of the price elasticities of demand for exports and imports exceeds 1
- CThe country has a budget surplus
- DInterest rates rise at the same time
5.Financial accountingMedium
Return on equity (ROE) is calculated as:
- ANet profit / shareholders' equity
- BNet profit / total revenue
- CTotal assets / equity
- DCurrent assets / current liabilities
6.Financial accountingHard
A firm has spent €50,000 on market research for a new product and must decide whether to launch it. How should the €50,000 be treated in the decision?
- ADeducted from expected sales
- BSpread over the product's expected life
- CAdded to the launch cost
- DIgnored, because it is a sunk cost
7.Break-even analysisMedium
A product sells for €18 with a variable cost of €8 per unit. Fixed costs are €20 000 per month and profit is taxed at 25%. How many units Q must be sold per month to earn €6 000 after tax?
p = €18v = €8F = €20 000T = 25%after-tax profit = €6 000
Q = units
8.Break-even analysisHard
A company sells 630 units at €23 each, with a variable cost of €18 per unit and fixed costs of €2 500. By what percentage %ΔΠ does operating profit change if sales volume rises by 20%?
Q = 630p = €23v = €18F = €2 500%ΔQ = +20%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: A · Concentrated (niche) marketing
Why this is the answer
Concentrated marketing focuses resources on one segment. It builds deep expertise but makes the firm dependent on that segment.
Answer
A · Concentrated (niche) marketing
2.Marketing principles
Answer: B · What customers expect and what managers think customers expect
Why this is the answer
Gap 1 arises when managers misread expectations, often due to poor research. Other provider gaps cover standards, delivery and communication, which together create the customer gap.
Answer
B · What customers expect and what managers think customers expect
3.Economics concepts
Answer: B · 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
B · C + I + G + (X − M)
4.Economics concepts
Answer: B · 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
B · The sum of the price elasticities of demand for exports and imports exceeds 1
5.Financial accounting
Answer: A · Net profit / shareholders' equity
Why this is the answer
ROE shows how much profit the company generates for each euro of equity invested by shareholders.
Answer
A · Net profit / shareholders' equity
6.Financial accounting
Answer: D · Ignored, because it is a sunk cost
Why this is the answer
The research money is spent whichever choice is made, so it is irrelevant. Only future incremental cash flows from launching should be compared.
Answer
D · Ignored, because it is a sunk cost
7.Break-even analysis
Answer: Q = 2800 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
6 000/(1 − 0.25) = €8 000
Units needed
Q = (20 000 + 8 000)/10 = 2 800
Answer
Q = 2 800 units
8.Break-even analysis
Answer: %ΔΠ = 96.92 %
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 = 630·5 = €3 150
Π = 3 150 − 2 500 = €650
DOL
DOL = 3 150/650 = 4.846
Change in profit
%ΔΠ = 4.846·(+20%) = +96.92%
Answer
%ΔΠ = +96.92%
Check: new profit = 756·5 − 2 500 = €1 280.00.
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