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 small firm makes premium climbing gear and targets only serious climbers. Which targeting strategy is this?
- AMicromarketing for each individual
- BUndifferentiated (mass) marketing
- CConcentrated (niche) marketing
- DDifferentiated marketing
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?
- ARepositioning the brand through new communication and image
- BCutting the price to the lowest in the market
- CWithdrawing the product immediately
- DChanging the distribution to exclusive dealers only
3.Economics conceptsMedium
Comparative advantage means a country should specialise in goods it can produce:
- AOnly for its own consumption
- BAt a lower opportunity cost than other countries
- CWith the most workers
- DMore cheaply in absolute terms than every other country
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?
- A16 times a year
- B6 times a year
- C0.17 times a year
- D60 times a year
6.Financial accountingHard
A company changes its inventory method from weighted average to FIFO because it gives more relevant information. Under IAS 8, how is this applied?
- ARetrospectively, restating comparative figures as if FIFO had always been used
- BIt is not allowed to change inventory methods
- CProspectively, from the date of the change only
- DBy recognising the whole effect as income this year
7.Break-even analysisMedium
A product sells for €13 per unit with a variable cost of €8 per unit. Fixed costs are €7 500 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €7 500p = €13v = €8profit = €5 000
Q = units
8.Break-even analysisHard
A product sells for €26 per unit, with a variable cost of €6 per unit and fixed costs of €10 000 per year. Budgeted sales are 630 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €10 000p = €26v = €6budget = 630
MS = %
3Solutions
1.Marketing principles
Answer: C · Concentrated (niche) marketing
Why this is the answer
Concentrated marketing focuses resources on one segment. It builds deep expertise but makes the firm dependent on that segment.
Answer
C · Concentrated (niche) marketing
2.Marketing principles
Answer: A · 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
A · Repositioning the brand through new communication and image
3.Economics concepts
Answer: B · At a lower opportunity cost than other countries
Why this is the answer
Even a country that is less efficient at everything gains from trade by specialising where its opportunity cost is lowest.
Answer
B · At a lower opportunity cost than other countries
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: A · Retrospectively, restating comparative figures as if FIFO had always been used
Why this is the answer
Voluntary policy changes are applied retrospectively where practicable, so comparatives remain consistent. Changes in estimates, by contrast, are applied prospectively.
Answer
A · Retrospectively, restating comparative figures as if FIFO had always been used
7.Break-even analysis
Answer: Q = 2500 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 = 13 − 8 = €5
Units for the target profit
Q = (F + profit)/(p − v) = (7 500 + 5 000)/5 = 2 500
Answer
Q = 2 500 units
8.Break-even analysis
Answer: MS = 20.63 %
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 = (630 − 500)/630·100 = 20.63%
Answer
MS = 20.63%
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