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
Which of these is one of Porter's five competitive forces?
- AThe threat of substitute products
- BThe firm's brand awareness
- CThe political stability of a country
- DThe level of inflation
2.Marketing principlesHard
Which metric best shows the efficiency of acquiring customers through online advertising?
- ATotal impressions only
- BThe number of employees in marketing
- CThe number of likes on posts
- DCustomer acquisition cost compared with customer lifetime value
3.Economics conceptsMedium
Education generates benefits for society beyond the individual student. Without intervention, the market will likely:
- AStop providing education altogether
- BProvide exactly the efficient amount of education, as prices reflect all benefits
- CUnder-provide education compared with the social optimum
- DOver-provide education compared with the social optimum
4.Economics conceptsHard
The Marshall–Lerner condition states that a currency depreciation improves the trade balance if:
- AExports and imports have zero price elasticity
- BThe sum of the price elasticities of demand for exports and imports exceeds 1
- CThe country has a budget surplus
- DInterest rates rise at the same time
5.Financial accountingMedium
Which costs are relevant when making a business decision?
- AAllocated fixed overheads that do not change with the decision
- BFuture cash flows that differ between the alternatives
- CCosts already paid for the project
- DAll costs in last year's income statement
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?
- AIt is not allowed to change inventory methods
- BProspectively, from the date of the change only
- CBy recognising the whole effect as income this year
- DRetrospectively, restating comparative figures as if FIFO had always been used
7.Break-even analysisMedium
A product sells for €38 per unit with a variable cost of €18 per unit. Fixed costs are €24 000 per month. How many units Q must be sold per month to make a profit of €10 000?
F = €24 000p = €38v = €18profit = €10 000
Q = units
8.Break-even analysisHard
A product sells for €18 per unit, with a variable cost of €15 per unit and fixed costs of €3 600 per year. Budgeted sales are 1 800 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €3 600p = €18v = €15budget = 1 800
MS = %
3Solutions
1.Marketing principles
Answer: A · The threat of substitute products
Why this is the answer
The five forces are rivalry among competitors, threat of new entrants, threat of substitutes, and the bargaining power of buyers and of suppliers.
Answer
A · The threat of substitute products
2.Marketing principles
Answer: D · Customer acquisition cost compared with customer lifetime value
Why this is the answer
CAC relative to CLV shows whether acquisition is profitable; vanity metrics like likes do not measure business value.
Answer
D · Customer acquisition cost compared with customer lifetime value
3.Economics concepts
Answer: C · 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
C · Under-provide education compared with the social optimum
4.Economics concepts
Answer: B · The sum of the price elasticities of demand for exports and imports exceeds 1
Why this is the answer
If export and import demand are elastic enough (absolute values summing to more than 1), volume effects outweigh the higher import prices and the balance improves.
Answer
B · The sum of the price elasticities of demand for exports and imports exceeds 1
5.Financial accounting
Answer: B · Future cash flows that differ between the alternatives
Why this is the answer
Relevant costs are future, incremental cash flows. Sunk costs, committed costs and unchanged allocated overheads are ignored.
Answer
B · Future cash flows that differ between the alternatives
6.Financial accounting
Answer: D · 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
D · Retrospectively, restating comparative figures as if FIFO had always been used
7.Break-even analysis
Answer: Q = 1700 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 = 38 − 18 = €20
Units for the target profit
Q = (F + profit)/(p − v) = (24 000 + 10 000)/20 = 1 700
Answer
Q = 1 700 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) = 3 600/3 = 1 200
Margin of safety
MS = (1 800 − 1 200)/1 800·100 = 33.33%
Answer
MS = 33.33%
ExamProblems · examproblems.com/courses/business-fundamentals