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 researcher divides the population into age groups and draws a random sample from each group. This is:
- AQuota sampling with free choice
- BSnowball sampling
- CStratified random sampling
- DConvenience sampling
2.Marketing principlesHard
In the services marketing "gap model" (SERVQUAL), the customer gap is the difference between:
- AOnline and offline sales
- BPlanned advertising spend and the actual spend in each period
- CCustomer expectations and perceptions of the service
- DPrice and cost
3.Economics conceptsMedium
A minimum wage set above the equilibrium wage in a competitive labour market is predicted to cause:
- AA shortage of labour
- BA fall in the wage rate
- CA surplus of labour (unemployment)
- DNo change in employment
4.Economics conceptsHard
Akerlof's "market for lemons" explains how:
- ALemons become cheaper in summer
- BPublic goods are under-provided
- CAsymmetric information can drive good-quality products out of a market
- DMonopolies set high prices
5.Financial accountingMedium
Current assets are €300,000, including inventory of €100,000. Current liabilities are €200,000. What is the quick (acid-test) ratio?
- A1.5
- B2.0
- C1.0
- D0.5
6.Financial accountingHard
A company "sells" inventory to a bank and must buy it back later at a higher price, keeping the risks and rewards. How should it be accounted for?
- AAs a contingent asset in the notes
- BAs revenue on the date of transfer
- CAs a secured loan, not a sale
- DAs a gain on disposal of inventory
7.Break-even analysisMedium
A product sells for €28 with a variable cost of €20 per unit. Fixed costs are €40 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €12 000 after tax?
p = €28v = €20F = €40 000T = 20%after-tax profit = €12 000
Q = units
8.Break-even analysisHard
A company sells 6 400 units at €22 each, with a variable cost of €18 per unit and fixed costs of €16 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 8%?
Q = 6 400p = €22v = €18F = €16 000%ΔQ = +8%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: C · Stratified random sampling
Why this is the answer
Stratified sampling ensures each subgroup is represented while keeping random selection. Quota sampling sets numbers per group but lets interviewers choose people, so it is non-probability.
Answer
C · Stratified random sampling
2.Marketing principles
Answer: C · Customer expectations and perceptions of the service
Why this is the answer
The customer gap is expected service minus perceived service; the provider gaps (knowledge, standards, delivery, communication) explain it.
Answer
C · Customer expectations and perceptions of the service
3.Economics concepts
Answer: C · A surplus of labour (unemployment)
Why this is the answer
At the higher wage more people want to work and firms hire fewer, so labour supplied exceeds labour demanded in the simple competitive model.
Answer
C · A surplus of labour (unemployment)
4.Economics concepts
Answer: C · Asymmetric information can drive good-quality products out of a market
Why this is the answer
When buyers cannot judge quality they pay an average price; owners of good cars withdraw, average quality falls, and the market may collapse.
Answer
C · Asymmetric information can drive good-quality products out of a market
5.Financial accounting
Answer: C · 1.0
Why this is the answer
Quick ratio = (current assets − inventory) ÷ current liabilities = €200,000 ÷ €200,000 = 1.0. Inventory is excluded because it may be slow to turn into cash.
Answer
C · 1.0
6.Financial accounting
Answer: C · As a secured loan, not a sale
Why this is the answer
Control and risks stay with the company, so the transaction is in substance borrowing secured on inventory. The price difference is an interest cost.
Answer
C · As a secured loan, not a sale
7.Break-even analysis
Answer: Q = 6875 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
12 000/(1 − 0.2) = €15 000
Units needed
Q = (40 000 + 15 000)/8 = 6 875
Answer
Q = 6 875 units
8.Break-even analysis
Answer: %ΔΠ = 21.33 %
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 = 6 400·4 = €25 600
Π = 25 600 − 16 000 = €9 600
DOL
DOL = 25 600/9 600 = 2.667
Change in profit
%ΔΠ = 2.667·(+8%) = +21.33%
Answer
%ΔΠ = +21.33%
Check: new profit = 6 912·4 − 16 000 = €11 648.00.
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