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 produce statistically representative percentages for the market
- BTo avoid any interviewer influence
- CTo survey thousands of people cheaply
- DTo explore customers' motives and feelings in detail
2.Marketing principlesHard
In the SERVQUAL gap model, the "knowledge gap" (gap 1) is the difference between:
- AThe service standards set by managers and the service actually delivered
- BThe price paid and the cost of providing the service
- CWhat customers expect and what managers think customers expect
- DThe service delivered and what advertising promised
3.Economics conceptsMedium
A sharp rise in world oil prices leading to higher inflation is an example of:
- ADemand-pull inflation
- BDeflation
- CDisinflation
- DCost-push inflation
4.Economics conceptsHard
Under perfect (first-degree) price discrimination, the monopolist:
- ACreates the largest possible deadweight loss
- BCharges every consumer the same price
- CCaptures all consumer surplus and produces the efficient output
- DProduces less than a single-price monopolist, creating a larger deadweight loss
5.Financial accountingMedium
A machine costs €10,000 and is depreciated at 20% a year on the reducing balance. What is the depreciation charge in year 2?
- A€4,000
- B€1,800
- C€1,600
- D€2,000
6.Financial accountingHard
Under IFRS 16, a lessee typically recognises a lease on the balance sheet as:
- ARevenue and inventory
- BA right-of-use asset and a lease liability
- CEquity and a provision
- DAn operating expense only, spread evenly over the lease term
7.Break-even analysisMedium
A product sells for €25 with a variable cost of €15 per unit. Fixed costs are €5 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €2 000 after tax?
p = €25v = €15F = €5 000T = 20%after-tax profit = €2 000
Q = units
8.Break-even analysisHard
A company sells 3 750 units at €25 each, with a variable cost of €20 per unit and fixed costs of €7 500. By what percentage %ΔΠ does operating profit change if sales volume rises by 5%?
Q = 3 750p = €25v = €20F = €7 500%ΔQ = +5%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: D · 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
D · To explore customers' motives and feelings in detail
2.Marketing principles
Answer: C · What customers expect and what managers think customers expect
Why this is the answer
Gap 1 arises when managers misread expectations, often due to poor research. Other provider gaps cover standards, delivery and communication, which together create the customer gap.
Answer
C · What customers expect and what managers think customers expect
3.Economics concepts
Answer: D · Cost-push inflation
Why this is the answer
Higher input costs shift aggregate supply to the left, raising prices and possibly lowering output; demand-pull inflation comes from excess aggregate demand.
Answer
D · Cost-push inflation
4.Economics concepts
Answer: C · Captures all consumer surplus and produces the efficient output
Why this is the answer
Charging each buyer their reservation price means it sells until price equals MC, so there is no deadweight loss, but all surplus goes to the producer.
Answer
C · Captures all consumer surplus and produces the efficient output
5.Financial accounting
Answer: C · €1,600
Why this is the answer
Year 1: 20% × €10,000 = €2,000, leaving €8,000. Year 2: 20% × €8,000 = €1,600. Reducing balance charges less each year.
Answer
C · €1,600
6.Financial accounting
Answer: B · 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
B · A right-of-use asset and a lease liability
7.Break-even analysis
Answer: Q = 750 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).
Pre-tax profit needed
2 000/(1 − 0.2) = €2 500
Units needed
Q = (5 000 + 2 500)/10 = 750
Answer
Q = 750 units
8.Break-even analysis
Answer: %ΔΠ = 8.333 %
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Contribution margin and profit
CM = 3 750·5 = €18 750
Π = 18 750 − 7 500 = €11 250
DOL
DOL = 18 750/11 250 = 1.667
Change in profit
%ΔΠ = 1.667·(+5%) = +8.333%
Answer
%ΔΠ = +8.333%
Check: new profit = 3 938·5 − 7 500 = €12 187.50.
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