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
Price elasticity matters for pricing because:
- AIt has no effect on pricing decisions
- BElasticity only affects costs
- CIf demand is inelastic, a price rise will lower total revenue
- DIf demand is elastic, a price cut can raise total revenue
2.Marketing principlesHard
Research shows young consumers see a long-established brand as old-fashioned, although product quality is good. What is the most suitable strategy?
- AWithdrawing the product immediately
- BChanging the distribution to exclusive dealers only
- CCutting the price to the lowest in the market
- DRepositioning the brand through new communication and image
3.Economics conceptsMedium
Comparative advantage means a country should specialise in goods it can produce:
- AAt a lower opportunity cost than other countries
- BWith the most workers
- COnly for its own consumption
- DMore cheaply in absolute terms than every other country
4.Economics conceptsHard
A monopolist maximises profit where:
- APrice equals marginal cost
- BTotal revenue is at its maximum
- CMarginal revenue equals marginal cost
- DAverage cost is at its minimum
5.Financial accountingMedium
Revenue is €200,000 and cost of sales is €140,000. What is the gross profit margin?
- A30%
- B70%
- C43%
- D60%
6.Financial accountingHard
An asset has a carrying amount of €500,000, fair value less costs of disposal of €380,000 and value in use of €420,000. What impairment loss is recognised?
- A€80,000
- B€200,000
- C€0
- D€120,000
7.Break-even analysisMedium
A product sells for €28 per unit with a variable cost of €18 per unit. Fixed costs are €40 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €40 000p = €28v = €18profit = €6 000
Q = units
8.Break-even analysisHard
A product sells for €23 per unit, with a variable cost of €18 per unit and fixed costs of €5 000 per year. Budgeted sales are 1 600 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €5 000p = €23v = €18budget = 1 600
MS = %
3Solutions
1.Marketing principles
Answer: D · If demand is elastic, a price cut can raise total revenue
Why this is the answer
With elastic demand, quantity responds strongly, so a lower price can increase revenue; with inelastic demand, a price rise increases revenue.
Answer
D · If demand is elastic, a price cut can raise total revenue
2.Marketing principles
Answer: D · Repositioning the brand through new communication and image
Why this is the answer
Repositioning changes how the target segment sees the brand, for example with updated design, new messages and channels the younger audience uses.
Answer
D · Repositioning the brand through new communication and image
3.Economics concepts
Answer: A · At a lower opportunity cost than other countries
Why this is the answer
Even a country that is less efficient at everything gains from trade by specialising where its opportunity cost is lowest.
Answer
A · At a lower opportunity cost than other countries
4.Economics concepts
Answer: C · Marginal revenue equals marginal cost
Why this is the answer
Profit is maximised where MR = MC. For a monopolist, price is above MR, so P > MC, causing a deadweight loss.
Answer
C · Marginal revenue equals marginal cost
5.Financial accounting
Answer: A · 30%
Why this is the answer
Gross profit = €60,000. Margin = €60,000 ÷ €200,000 = 30%.
Answer
A · 30%
6.Financial accounting
Answer: A · €80,000
Why this is the answer
Recoverable amount = max(€380,000, €420,000) = €420,000. Impairment = €500,000 − €420,000 = €80,000.
Answer
A · €80,000
7.Break-even analysis
Answer: Q = 4600 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 = 28 − 18 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (40 000 + 6 000)/10 = 4 600
Answer
Q = 4 600 units
8.Break-even analysis
Answer: MS = 37.5 %
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) = 5 000/5 = 1 000
Margin of safety
MS = (1 600 − 1 000)/1 600·100 = 37.5%
Answer
MS = 37.5%
ExamProblems · examproblems.com/courses/business-fundamentals