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
Integrated marketing communications (IMC) means:
- AMerging the marketing and finance departments
- BCoordinating all communication channels to deliver one consistent message
- CSpending the same budget on each medium
- DUsing only digital channels for advertising
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
A minimum wage set above the equilibrium wage in a competitive labour market is predicted to cause:
- AA surplus of labour (unemployment)
- BA fall in the wage rate
- CNo change in employment
- DA shortage of labour
4.Economics conceptsHard
The Fisher effect predicts that, in the long run, a permanent 2 percentage point rise in expected inflation will:
- ARaise nominal interest rates by about 2 points, leaving real rates unchanged
- BHave no effect on nominal interest rates, so real interest rates fall by about 2 points
- CLower nominal interest rates by about 2 points
- DRaise real interest rates by about 2 points
5.Financial accountingMedium
Retained earnings represent:
- AThe share price
- BAccumulated profits that have not been paid out as dividends
- CMoney owed to shareholders
- DCash kept in the bank
6.Financial accountingHard
An increase in accounts receivable during the year, in the indirect cash flow method, is:
- ANot relevant to cash flow
- BShown as an investing outflow
- CAdded to profit
- DSubtracted from profit to get operating cash flow
7.Break-even analysisMedium
A product sells for €27 with a variable cost of €25 per unit. Fixed costs are €10 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €3 000 after tax?
p = €27v = €25F = €10 000T = 20%after-tax profit = €3 000
Q = units
8.Break-even analysisHard
A product sells for €40 per unit, with a variable cost of €20 per unit and fixed costs of €24 000 per year. Budgeted sales are 1 380 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €24 000p = €40v = €20budget = 1 380
MS = %
3Solutions
1.Marketing principles
Answer: B · Coordinating all communication channels to deliver one consistent message
Why this is the answer
IMC aligns advertising, PR, sales promotion, digital and personal selling so they reinforce each other and build a clear brand image.
Answer
B · Coordinating all communication channels to deliver one consistent message
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: A · A surplus of labour (unemployment)
Why this is the answer
At the higher wage more people want to work and firms hire fewer, so labour supplied exceeds labour demanded in the simple competitive model.
Answer
A · A surplus of labour (unemployment)
4.Economics concepts
Answer: A · Raise nominal interest rates by about 2 points, leaving real rates unchanged
Why this is the answer
Lenders demand compensation for expected inflation, so nominal rates move one-for-one with it in the long run while the real rate is set by real factors.
Answer
A · Raise nominal interest rates by about 2 points, leaving real rates unchanged
5.Financial accounting
Answer: B · Accumulated profits that have not been paid out as dividends
Why this is the answer
Retained earnings are cumulative net profits minus dividends; they are part of equity, not a pile of cash.
Answer
B · Accumulated profits that have not been paid out as dividends
6.Financial accounting
Answer: D · Subtracted from profit to get operating cash flow
Why this is the answer
Higher receivables mean some revenue was not received in cash, so the increase is deducted.
Answer
D · Subtracted from profit to get operating cash flow
7.Break-even analysis
Answer: Q = 6875 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 − 0.2) = €3 750
Units needed
Q = (10 000 + 3 750)/2 = 6 875
Answer
Q = 6 875 units
8.Break-even analysis
Answer: MS = 13.04 %
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) = 24 000/20 = 1 200
Margin of safety
MS = (1 380 − 1 200)/1 380·100 = 13.04%
Answer
MS = 13.04%
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