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
Which of these is one of Porter's five competitive forces?
- AThe political stability of a country
- BThe threat of substitute products
- CThe firm's brand awareness
- DThe level of inflation
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?
- ACause-related marketing
- BCo-branding
- CGuerrilla distribution
- DAmbush marketing
3.Economics conceptsMedium
In country A, 1 car costs 2 tonnes of wheat to produce; in country B, 1 car costs 4 tonnes of wheat. Which statement is correct?
- AA has a comparative advantage in both goods
- BA has a comparative advantage in cars and B in wheat
- CB has a comparative advantage in cars and A in wheat
- DNeither country gains from trade
4.Economics conceptsHard
Using the "rule of 70", an economy growing at 7% per year will double its real GDP in about:
- A10 years
- B7 years
- C49 years
- D70 years
5.Financial accountingMedium
A project costs €100,000 and brings in €25,000 cash per year. What is its payback period?
- A2.5 years
- B4 years
- C5 years
- D25 years
6.Financial accountingHard
A company borrows at 5% interest to invest in assets that earn 12%. What is the likely effect on return on equity?
- AROE rises and financial risk falls
- BROE falls, because interest is an expense
- CROE rises, but financial risk also increases
- DROE stays the same, because debt is not equity
7.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €20 000 per year and a variable cost of €20 per unit. Method B, more automated, has fixed costs of €30 000 per year and a variable cost of €15 per unit. At what yearly volume Q do both methods cost the same?
FA = €20 000vA = €20FB = €30 000vB = €15
Q = units
8.Break-even analysisHard
A product sells for €47 per unit, with a variable cost of €45 per unit and fixed costs of €1 000 per year. Budgeted sales are 900 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €1 000p = €47v = €45budget = 900
MS = %
3Solutions
1.Marketing principles
Answer: B · The threat of substitute products
Why this is the answer
The five forces are rivalry among competitors, threat of new entrants, threat of substitutes, and the bargaining power of buyers and of suppliers.
Answer
B · The threat of substitute products
2.Marketing principles
Answer: D · 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
D · Ambush marketing
3.Economics concepts
Answer: B · A has a comparative advantage in cars and B in wheat
Why this is the answer
A gives up less wheat per car, so it should specialise in cars; B's opportunity cost of wheat (1/4 car) is lower than A's (1/2 car), so B specialises in wheat.
Answer
B · A has a comparative advantage in cars and B in wheat
4.Economics concepts
Answer: A · 10 years
Why this is the answer
The doubling time is approximately 70 divided by the percentage growth rate, so 70 / 7 = 10 years, showing the power of compound growth.
Answer
A · 10 years
5.Financial accounting
Answer: B · 4 years
Why this is the answer
€100,000 ÷ €25,000 = 4 years. Payback is simple but ignores the time value of money and cash flows after payback.
Answer
B · 4 years
6.Financial accounting
Answer: C · ROE rises, but financial risk also increases
Why this is the answer
Positive financial leverage: assets earn more than the debt costs, so profit per euro of equity rises. If returns drop below 5%, leverage works against shareholders.
Answer
C · ROE rises, but financial risk also increases
7.Break-even analysis
Answer: Q = 2000 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
20 000 + 20Q = 30 000 + 15Q
Solve for Q
Q = (30 000 − 20 000)/(20 − 15) = 2 000
Answer
Q = 2 000 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: MS = 44.44 %
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) = 1 000/2 = 500
Margin of safety
MS = (900 − 500)/900·100 = 44.44%
Answer
MS = 44.44%
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