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 order of products in a catalogue
- CHow a brand is perceived relative to competitors in customers' minds
- DThe geographical location of the company
2.Marketing principlesHard
A customer sees a social ad, later reads a review, then clicks a search ad and buys. What is the main weakness of last-click attribution here?
- AIt gives all credit to the search ad and ignores earlier touchpoints
- BIt cannot record online purchases
- CIt gives too much credit to the social ad
- DIt counts the same sale three times
3.Economics conceptsMedium
The price of petrol rises sharply. What happens to the demand curve for large cars?
- AIt becomes vertical
- BThere is a movement along it
- CIt shifts to the left
- DIt shifts to the right
4.Economics conceptsHard
Akerlof's "market for lemons" explains how:
- APublic goods are under-provided
- BMonopolies set high prices
- CLemons become cheaper in summer
- DAsymmetric information can drive good-quality products out of a market
5.Financial accountingMedium
Trade receivables are €50,000 and annual credit sales are €365,000. What are the receivable days?
- A36.5 days
- B50 days
- C73 days
- D7.3 days
6.Financial accountingHard
Goodwill arises in a business combination when:
- AAssets are revalued upwards
- BThe consideration paid exceeds the fair value of identifiable net assets acquired
- CA company has a good reputation
- DThe acquired company makes a loss
7.Break-even analysisMedium
A product sells for €18 per unit with a variable cost of €8 per unit. Fixed costs are €20 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €20 000p = €18v = €8profit = €5 000
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €11 with a variable cost of €5; product B sells for €37 with a variable cost of €25. They sell in a fixed mix of 3 units of A for every 1 of B. Fixed costs are €12 000 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €11, vA = €5pB = €37, vB = €25A : B = 3 : 1F = €12 000
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: A · It gives all credit to the search ad and ignores earlier touchpoints
Why this is the answer
Last-click models undervalue channels that create awareness early in the journey. Multi-touch attribution or experiments give a fairer picture of each channel's contribution.
Answer
A · It gives all credit to the search ad and ignores earlier touchpoints
3.Economics concepts
Answer: C · It shifts to the left
Why this is the answer
Petrol and cars are complements, so a higher petrol price lowers demand for cars at every car price, shifting the demand curve left.
Answer
C · It shifts to the left
4.Economics concepts
Answer: D · 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
D · Asymmetric information can drive good-quality products out of a market
5.Financial accounting
Answer: B · 50 days
Why this is the answer
€50,000 ÷ €365,000 × 365 = 50 days. This is the average time customers take to pay.
Answer
B · 50 days
6.Financial accounting
Answer: B · The consideration paid exceeds the fair value of identifiable net assets acquired
Why this is the answer
Goodwill = consideration − fair value of identifiable net assets. Under IFRS it is not amortised but tested for impairment annually.
Answer
B · The consideration paid exceeds the fair value of identifiable net assets acquired
7.Break-even analysis
Answer: Q = 2500 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 = 18 − 8 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (20 000 + 5 000)/10 = 2 500
Answer
Q = 2 500 units
8.Break-even analysis
Answer: Q = 1600 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 = €6, cmB = €12
Weighted contribution margin
(3·6 + 1·12)/4 = €7.50
Break-even units
Q = 12 000/7.5 = 1 600
A: 1 200, B: 400
Answer
Q = 1 600 units
ExamProblems · examproblems.com/courses/business-fundamentals