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 chocolate brand launches an ice cream under the same brand name. This is an example of:
- ABrand extension
- BLine extension
- CPrivate labelling
- DCo-branding
2.Marketing principlesHard
After a hotel solves a guest's complaint quickly and generously, the guest is more loyal than before the problem. What is this called?
- APost-purchase cognitive dissonance
- BMarketing myopia
- CThe decoy effect
- DThe service recovery paradox
3.Economics conceptsMedium
In a simple closed economy without taxes, the MPC is 0.8. The Keynesian spending multiplier is:
- A0.8
- B8
- C5
- D1.25
4.Economics conceptsHard
A monopolist maximises profit where:
- AMarginal revenue equals marginal cost
- BTotal revenue is at its maximum
- CPrice equals marginal cost
- DAverage cost is at its minimum
5.Financial accountingMedium
Under IAS 38, how are research and development costs treated?
- ABoth are always capitalised as intangible assets
- BResearch is expensed; development is capitalised only when strict criteria are met
- CResearch is capitalised; development is expensed
- DBoth are always expensed immediately
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?
- AProspectively, from the date of the change only
- BRetrospectively, restating comparative figures as if FIFO had always been used
- CBy recognising the whole effect as income this year
- DIt is not allowed to change inventory methods
7.Break-even analysisMedium
A product sells for €35 per unit with a variable cost of €25 per unit. Fixed costs are €12 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €12 000p = €35v = €25profit = €6 000
Q = units
8.Break-even analysisHard
A company sells 1 000 units per month at €27 each, with a variable cost of €15 per unit and fixed costs of €9 600 per month. The variable cost rises by €4 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 1 000p = €27v = €15 → €19F = €9 600
Q = units
3Solutions
1.Marketing principles
Answer: A · Brand extension
Why this is the answer
A brand extension uses an existing brand name in a new category. A line extension adds variants in the same category, such as new flavours.
Answer
A · Brand extension
2.Marketing principles
Answer: D · The service recovery paradox
Why this is the answer
The service recovery paradox suggests excellent recovery can raise satisfaction above its earlier level. It does not mean failures are good; recovery must be outstanding.
Answer
D · The service recovery paradox
3.Economics concepts
Answer: C · 5
Why this is the answer
1 / (1 − 0.8) = 1 / 0.2 = 5, so an extra €1 of spending can raise income by up to €5.
Answer
C · 5
4.Economics concepts
Answer: A · Marginal revenue equals marginal cost
Why this is the answer
Profit is maximised where MR = MC. For a monopolist, price is above MR, so P > MC, causing a deadweight loss.
Answer
A · Marginal revenue equals marginal cost
5.Financial accounting
Answer: B · Research is expensed; development is capitalised only when strict criteria are met
Why this is the answer
Research costs are always expensed. Development costs are capitalised when, for example, technical feasibility, intention, ability and probable future benefits can be shown.
Answer
B · Research is expensed; development is capitalised only when strict criteria are met
6.Financial accounting
Answer: B · 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
B · Retrospectively, restating comparative figures as if FIFO had always been used
7.Break-even analysis
Answer: Q = 1800 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 − 25 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (12 000 + 6 000)/10 = 1 800
Answer
Q = 1 800 units
8.Break-even analysis
Answer: Q = 1500 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).
Current profit
Π = 1 000·(27 − 15) − 9 600 = €2 400
New contribution margin per unit
27 − 19 = €8
Units for the same profit
Q = (9 600 + 2 400)/8 = 1 500
Answer
Q = 1 500 units
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