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
Psychographic segmentation divides customers by:
- APurchase frequency only
- BAge and income only
- CCountry and climate
- DLifestyle, values and personality
2.Marketing principlesHard
A survey asks: "Don't you agree that our excellent staff are very helpful?" What is the main problem?
- AIt is a leading question that pushes respondents towards agreement
- BIt asks about two unrelated products
- CIt is an open question that is hard to analyse
- DIt is too short to be understood
3.Economics conceptsMedium
A country has 950 employed people and 50 unemployed people seeking work. Its unemployment rate is:
- A50%
- B95%
- C5%
- D5.3%
4.Economics conceptsHard
A deadweight loss represents:
- AThe tax revenue collected by the government
- BThe loss of total surplus when output differs from the efficient level
- CThe profit of a monopolist
- DLosses made by firms that are forced to leave the market in the long run
5.Financial accountingMedium
Which depreciation method charges the same amount every year?
- AReducing balance
- BSum-of-the-years'-digits
- CStraight-line
- DUnits of production
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?
- AKeep the investment at cost and report only the dividends received from S
- BShow one equity-method investment line for its 70% share of S
- CConsolidate 100% of S line by line and show a non-controlling interest
- DAdd only 70% of each of S's assets, liabilities, income and expenses
7.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €25 000 per year and a variable cost of €25 per unit. Method B, more automated, has fixed costs of €50 000 per year and a variable cost of €20 per unit. At what yearly volume Q do both methods cost the same?
FA = €25 000vA = €25FB = €50 000vB = €20
Q = units
8.Break-even analysisHard
A product sells for €21 per unit, with a variable cost of €18 per unit and fixed costs of €4 500 per year. Budgeted sales are 1 950 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €4 500p = €21v = €18budget = 1 950
MS = %
3Solutions
1.Marketing principles
Answer: D · Lifestyle, values and personality
Why this is the answer
Psychographic segmentation looks at attitudes, interests, values and lifestyles; behavioural segmentation uses usage and loyalty.
Answer
D · Lifestyle, values and personality
2.Marketing principles
Answer: A · It is a leading question that pushes respondents towards agreement
Why this is the answer
Leading questions bias answers through wording. A neutral version would be "How helpful were our staff?" with a balanced rating scale.
Answer
A · It is a leading question that pushes respondents towards agreement
3.Economics concepts
Answer: C · 5%
Why this is the answer
The labour force is 950 + 50 = 1,000, so the rate is 50 / 1,000 = 5%.
Answer
C · 5%
4.Economics concepts
Answer: B · The loss of total surplus when output differs from the efficient level
Why this is the answer
Deadweight loss is the reduction in combined consumer and producer surplus caused by distortions such as taxes, monopoly or price controls.
Answer
B · The loss of total surplus when output differs from the efficient level
5.Financial accounting
Answer: C · Straight-line
Why this is the answer
Straight-line spreads the depreciable amount evenly. Reducing balance charges more in early years; units of production follows actual use.
Answer
C · Straight-line
6.Financial accounting
Answer: C · 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
C · Consolidate 100% of S line by line and show a non-controlling interest
7.Break-even analysis
Answer: Q = 5000 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).
Equal total costs
25 000 + 25Q = 50 000 + 20Q
Solve for Q
Q = (50 000 − 25 000)/(25 − 20) = 5 000
Answer
Q = 5 000 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: MS = 23.08 %
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) = 4 500/3 = 1 500
Margin of safety
MS = (1 950 − 1 500)/1 950·100 = 23.08%
Answer
MS = 23.08%
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