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
Two established brands from different companies jointly market one product, such as a credit card carrying an airline's brand. This is:
- AMultibranding
- BBrand extension
- CCo-branding
- DLine extension
2.Marketing principlesHard
Research shows young consumers see a long-established brand as old-fashioned, although product quality is good. What is the most suitable strategy?
- AWithdrawing the product immediately
- BRepositioning the brand through new communication and image
- CCutting the price to the lowest in the market
- DChanging the distribution to exclusive dealers only
3.Economics conceptsMedium
In the long run in monopolistic competition, firms typically:
- AProduce at the minimum of average total cost
- BEarn large economic profits protected by entry barriers
- CCharge a price equal to marginal cost
- DEarn zero economic profit and have excess capacity
4.Economics conceptsHard
According to the quantity theory of money (MV = PY), if velocity and real output are constant, a 5% rise in the money supply leads to:
- AAbout a 5% rise in real output
- BAbout a 5% rise in the price level
- CA 5% fall in velocity
- DNo change in prices
5.Financial accountingMedium
Which ratio measures a company's ability to pay its short-term obligations?
- AReturn on equity
- BEarnings per share
- CThe gross margin
- DThe current ratio
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 stays the same, because debt is not equity
- BROE rises, but financial risk also increases
- CROE falls, because interest is an expense
- DROE rises and financial risk falls
7.Break-even analysisMedium
A product sells for €33 per unit with a variable cost of €25 per unit. Fixed costs are €9 600 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €9 600p = €33v = €25profit = €2 000
Q = units
8.Break-even analysisHard
A product sells for €16 per unit, with a variable cost of €6 per unit and fixed costs of €50 000 per year. Budgeted sales are 6 250 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €50 000p = €16v = €6budget = 6 250
MS = %
3Solutions
1.Marketing principles
Answer: C · Co-branding
Why this is the answer
Co-branding combines the strengths and customer bases of two brands. It can add credibility but links each brand's reputation to the other.
Answer
C · Co-branding
2.Marketing principles
Answer: B · Repositioning the brand through new communication and image
Why this is the answer
Repositioning changes how the target segment sees the brand, for example with updated design, new messages and channels the younger audience uses.
Answer
B · Repositioning the brand through new communication and image
3.Economics concepts
Answer: D · Earn zero economic profit and have excess capacity
Why this is the answer
Entry removes profits, but because each firm faces a downward-sloping demand curve, the tangency is to the left of minimum ATC, leaving excess capacity.
Answer
D · Earn zero economic profit and have excess capacity
4.Economics concepts
Answer: B · About a 5% rise in the price level
Why this is the answer
With V and Y constant, M and P move proportionally, so prices rise about 5%. This is the classical view of money neutrality in the long run.
Answer
B · About a 5% rise in the price level
5.Financial accounting
Answer: D · The current ratio
Why this is the answer
The current ratio (current assets/current liabilities) indicates liquidity; a value below 1 can signal problems paying short-term debts.
Answer
D · The current ratio
6.Financial accounting
Answer: B · 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
B · ROE rises, but financial risk also increases
7.Break-even analysis
Answer: Q = 1450 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 = 33 − 25 = €8
Units for the target profit
Q = (F + profit)/(p − v) = (9 600 + 2 000)/8 = 1 450
Answer
Q = 1 450 units
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) = 50 000/10 = 5 000
Margin of safety
MS = (6 250 − 5 000)/6 250·100 = 20%
Answer
MS = 20%
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