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 the BCG matrix, what are the usual options for a "question mark"?
- AKeep it unchanged because it is the market leader
- BInvest heavily to build market share, or divest
- CAlways close it immediately
- DHarvest cash with minimal investment
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 standards set by managers and the service actually delivered
- DThe service delivered and what advertising promised
3.Economics conceptsMedium
Overfishing in international waters is an example of:
- AA natural monopoly
- BThe tragedy of the commons
- CA Giffen good
- DPrice discrimination
4.Economics conceptsHard
The J-curve effect describes why, after a depreciation, the trade balance may:
- AImprove at first and then worsen
- BWorsen at first and then improve
- CRemain unchanged for many years
- DImprove immediately and permanently
5.Financial accountingMedium
A shop buys 100 units at €10, then 100 units at €12, and then sells 150 units. What is cost of sales using FIFO?
- A€1,500
- B€1,700
- C€1,600
- D€1,650
6.Financial accountingHard
A firm has a net profit margin of 5%, asset turnover of 2 and an equity multiplier (assets ÷ equity) of 1.5. Using the DuPont analysis, what is ROE?
- A8.5%
- B15%
- C7.5%
- D10%
7.Break-even analysisMedium
A company sells 960 units at €23 each. The variable cost is €8 per unit and fixed costs are €12 000. Find the degree of operating leverage DOL at this sales level.
Q = 960p = €23v = €8F = €12 000
DOL =
8.Break-even analysisHard
A product sells for €35 per unit, with a variable cost of €20 per unit and fixed costs of €15 000 per year. Budgeted sales are 1 250 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €15 000p = €35v = €20budget = 1 250
MS = %
3Solutions
1.Marketing principles
Answer: B · Invest heavily to build market share, or divest
Why this is the answer
Question marks need cash to grow. Managers must decide whether they can become stars; if not, it may be better to sell or drop them.
Answer
B · Invest heavily to build market share, or divest
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 · The tragedy of the commons
Why this is the answer
When a common resource is rival but people cannot be excluded, each user ignores the cost they impose on others, leading to overuse.
Answer
B · The tragedy of the commons
4.Economics concepts
Answer: B · Worsen at first and then improve
Why this is the answer
In the short run, volumes are slow to adjust while import prices rise immediately, so the balance worsens before the Marshall–Lerner condition takes hold.
Answer
B · Worsen at first and then improve
5.Financial accounting
Answer: C · €1,600
Why this is the answer
FIFO: 100 × €10 + 50 × €12 = €1,600. The 50 units left are valued at the latest cost of €12.
Answer
C · €1,600
6.Financial accounting
Answer: B · 15%
Why this is the answer
ROE = 5% × 2 × 1.5 = 15%. DuPont shows whether returns come from profitability, asset efficiency or leverage.
Answer
B · 15%
7.Break-even analysis
Answer: DOL = 6
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.
Total contribution margin
CM = 960·(23 − 8) = €14 400
Operating profit
Π = 14 400 − 12 000 = €2 400
DOL
DOL = 14 400/2 400 = 6
Answer
DOL = 6
8.Break-even analysis
Answer: MS = 20 %
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) = 15 000/15 = 1 000
Margin of safety
MS = (1 250 − 1 000)/1 250·100 = 20%
Answer
MS = 20%
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