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
Positioning refers to:
- AWhere products are physically placed on shop shelves and in store displays
- BThe geographical location of the company
- CHow a brand is perceived relative to competitors in customers' minds
- DThe order of products in a catalogue
2.Marketing principlesHard
In the SERVQUAL gap model, the "knowledge gap" (gap 1) is the difference between:
- AThe price paid and the cost of providing the service
- BWhat customers expect and what managers think customers expect
- CThe service standards set by managers and the service actually delivered
- DThe service delivered and what advertising promised
3.Economics conceptsMedium
Education generates benefits for society beyond the individual student. Without intervention, the market will likely:
- AStop providing education altogether
- BOver-provide education compared with the social optimum
- CProvide exactly the efficient amount of education, as prices reflect all benefits
- DUnder-provide education compared with the social optimum
4.Economics conceptsHard
Under perfect (first-degree) price discrimination, the monopolist:
- ACharges every consumer the same price
- BCaptures all consumer surplus and produces the efficient output
- CCreates the largest possible deadweight loss
- DProduces less than a single-price monopolist, creating a larger deadweight loss
5.Financial accountingMedium
A company increases its allowance for doubtful receivables. What is the effect?
- AAn expense is recognised and net receivables fall
- BRevenue increases and gross receivables rise by the same amount
- CCash decreases immediately
- DOnly the notes change; no figures move
6.Financial accountingHard
Under the matching principle, the cost of a product warranty sold with goods this year should be:
- AEstimated and recognised as an expense in the year of sale
- BRecorded as revenue
- CIgnored until the warranty expires
- DRecognised only when a customer actually makes a warranty claim
7.Break-even analysisMedium
A product sells for €14 per unit with a variable cost of €12 per unit. Fixed costs are €10 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €10 000p = €14v = €12profit = €2 000
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €17 with a variable cost of €12; product B sells for €37 with a variable cost of €25. They sell in a fixed mix of 4 units of A for every 1 of B. Fixed costs are €6 400 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €17, vA = €12pB = €37, vB = €25A : B = 4 : 1F = €6 400
Q = units
3Solutions
1.Marketing principles
Answer: C · How a brand is perceived relative to competitors in customers' minds
Why this is the answer
Positioning defines the distinctive place a brand wants to occupy in the target customers' minds, based on benefits and differences from rivals.
Answer
C · How a brand is perceived relative to competitors in customers' minds
2.Marketing principles
Answer: B · 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
B · What customers expect and what managers think customers expect
3.Economics concepts
Answer: D · Under-provide education compared with the social optimum
Why this is the answer
Private decisions ignore external benefits, so output is below the socially optimal level; subsidies or public provision can raise it.
Answer
D · Under-provide education compared with the social optimum
4.Economics concepts
Answer: B · 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
B · Captures all consumer surplus and produces the efficient output
5.Financial accounting
Answer: A · An expense is recognised and net receivables fall
Why this is the answer
The increase is charged to profit, and the allowance is deducted from gross receivables, so the balance sheet shows the amount expected to be collected.
Answer
A · An expense is recognised and net receivables fall
6.Financial accounting
Answer: A · Estimated and recognised as an expense in the year of sale
Why this is the answer
A provision for expected warranty costs is recognised when the goods are sold, matching the expense with the related revenue (IAS 37).
Answer
A · Estimated and recognised as an expense in the year of sale
7.Break-even analysis
Answer: Q = 6000 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 = 14 − 12 = €2
Units for the target profit
Q = (F + profit)/(p − v) = (10 000 + 2 000)/2 = 6 000
Answer
Q = 6 000 units
8.Break-even analysis
Answer: Q = 1000 units
Break-even with a sales mix: when products sell in a fixed ratio, use the weighted average contribution margin: weight each product's p − v by its share of units. Break-even units = F/(weighted contribution margin), split again in the mix ratio.
Contribution margins
cmA = €5, cmB = €12
Weighted contribution margin
(4·5 + 1·12)/5 = €6.40
Break-even units
Q = 6 400/6.4 = 1 000
A: 800, B: 200
Answer
Q = 1 000 units
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