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
Why might a researcher choose in-depth interviews rather than a large questionnaire?
- ATo survey thousands of people cheaply
- BTo avoid any interviewer influence
- CTo explore customers' motives and feelings in detail
- DTo produce statistically representative percentages for the market
2.Marketing principlesHard
In the BCG matrix, a firm has 20% market share and its largest competitor has 40%. What is the firm's relative market share?
- A0.2
- B0.5
- C2.0
- D20%
3.Economics conceptsMedium
The income elasticity of demand for a good is -0.4. The good is:
- AA complement
- BA normal necessity
- CA luxury good
- DAn inferior good
4.Economics conceptsHard
A deadweight loss represents:
- AThe tax revenue collected by the government
- BThe profit of a monopolist
- CLosses made by firms that are forced to leave the market in the long run
- DThe loss of total surplus when output differs from the efficient level
5.Financial accountingMedium
A company is being sued. Its lawyers say losing is possible but not probable. How is this treated under IAS 37?
- ARecognised as an expense and paid into a reserve
- BDisclosed as a contingent liability in the notes
- CIgnored completely
- DRecognised as a provision on the balance sheet
6.Financial accountingHard
Under IFRS 16, a lessee typically recognises a lease on the balance sheet as:
- AEquity and a provision
- BAn operating expense only, spread evenly over the lease term
- CRevenue and inventory
- DA right-of-use asset and a lease liability
7.Break-even analysisMedium
A product sells for €45 per unit with a variable cost of €25 per unit. Fixed costs are €50 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €50 000p = €45v = €25profit = €2 000
Q = units
8.Break-even analysisHard
A product sells for €35 per unit, with a variable cost of €15 per unit and fixed costs of €40 000 per year. Budgeted sales are 3 000 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €40 000p = €35v = €15budget = 3 000
MS = %
3Solutions
1.Marketing principles
Answer: C · To explore customers' motives and feelings in detail
Why this is the answer
In-depth interviews give rich, qualitative insight into why people behave as they do. Questionnaires suit measuring how many people think or do something.
Answer
C · To explore customers' motives and feelings in detail
2.Marketing principles
Answer: B · 0.5
Why this is the answer
Relative market share = 20% ÷ 40% = 0.5. A value below 1 means the firm is not the market leader, placing it on the low-share side of the matrix.
Answer
B · 0.5
3.Economics concepts
Answer: D · An inferior good
Why this is the answer
A negative income elasticity means demand falls as income rises, which defines an inferior good; luxuries have income elasticity above 1.
Answer
D · An inferior good
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 · Disclosed as a contingent liability in the notes
Why this is the answer
A possible obligation is not recognised but disclosed, unless the chance of outflow is remote. A probable, measurable outflow would require a provision.
Answer
B · Disclosed as a contingent liability in the notes
6.Financial accounting
Answer: D · A right-of-use asset and a lease liability
Why this is the answer
IFRS 16 removed the operating lease distinction for lessees: they recognise a right-of-use asset and a liability for lease payments, except for short-term and low-value leases.
Answer
D · A right-of-use asset and a lease liability
7.Break-even analysis
Answer: Q = 2600 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 = 45 − 25 = €20
Units for the target profit
Q = (F + profit)/(p − v) = (50 000 + 2 000)/20 = 2 600
Answer
Q = 2 600 units
8.Break-even analysis
Answer: MS = 33.33 %
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) = 40 000/20 = 2 000
Margin of safety
MS = (3 000 − 2 000)/3 000·100 = 33.33%
Answer
MS = 33.33%
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