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 product costs €60 and sells for €80. What is the profit margin as a percentage of the selling price?
- A75%
- B20%
- C33%
- D25%
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?
- ACo-branding
- BCause-related marketing
- CAmbush marketing
- DGuerrilla distribution
3.Economics conceptsMedium
Crowding out refers to:
- AToo many firms entering a market
- BOvercrowded public services
- CImports replacing domestic production
- DHigher government borrowing raising interest rates and reducing private investment
4.Economics conceptsHard
A deadweight loss represents:
- AThe tax revenue collected by the government
- BLosses made by firms that are forced to leave the market in the long run
- CThe profit of a monopolist
- DThe loss of total surplus when output differs from the efficient level
5.Financial accountingMedium
Cost of sales is €600,000 and average inventory is €100,000. What is the inventory turnover?
- A60 times a year
- B6 times a year
- C0.17 times a year
- D16 times a year
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?
- AShow one equity-method investment line for its 70% share of S
- BAdd only 70% of each of S's assets, liabilities, income and expenses
- CConsolidate 100% of S line by line and show a non-controlling interest
- 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 €2 000?
F = €25 000p = €35v = €30profit = €2 000
Q = units
8.Break-even analysisHard
A product sells for €24 per unit, with a variable cost of €4 per unit and fixed costs of €10 000 per year. Budgeted sales are 650 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €10 000p = €24v = €4budget = 650
MS = %
3Solutions
1.Marketing principles
Answer: D · 25%
Why this is the answer
Profit = €20. Margin = €20 ÷ €80 = 25%. The mark-up on cost is €20 ÷ €60 ≈ 33%.
Answer
D · 25%
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 · Higher government borrowing raising interest rates and reducing private investment
Why this is the answer
When government borrowing raises interest rates, some private investment is no longer profitable, reducing the net effect of fiscal expansion.
Answer
D · Higher government borrowing raising interest rates and reducing private investment
4.Economics concepts
Answer: D · 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
D · The loss of total surplus when output differs from the efficient level
5.Financial accounting
Answer: B · 6 times a year
Why this is the answer
€600,000 ÷ €100,000 = 6, so inventory is replaced about every 61 days (365 ÷ 6).
Answer
B · 6 times a year
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 = 5400 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 + 2 000)/5 = 5 400
Answer
Q = 5 400 units
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) = 10 000/20 = 500
Margin of safety
MS = (650 − 500)/650·100 = 23.08%
Answer
MS = 23.08%
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