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
Value-based pricing sets prices mainly according to:
- ACustomers' perception of the product's value
- BThe firm's target profit for the year
- CThe prices charged by the cheapest rival
- DThe cost of making the product plus a mark-up
2.Marketing principlesHard
Procter and Gamble sells Pampers, Ariel and Gillette under separate brand names, not under the company name. Which brand architecture is this?
- AA branded house
- BA private label strategy
- CA house of brands
- DCo-branding
3.Economics conceptsMedium
Both supply and demand for a good increase. What can we say for certain about the new equilibrium?
- AQuantity rises, but the change in price is uncertain
- BBoth price and quantity rise
- CPrice rises, but the change in quantity is uncertain
- DBoth price and quantity fall
4.Economics conceptsHard
In Spence's job market signalling model, education can be valuable to employers even if it does not raise productivity because:
- AEmployers are required by law to hire graduates
- BIt is less costly for high-ability workers to acquire, so it reveals their type
- CIt guarantees that every graduate is highly productive
- DIt reduces the wages employers must pay
5.Financial accountingMedium
Return on equity (ROE) is calculated as:
- ANet profit / shareholders' equity
- BTotal assets / equity
- CNet profit / total revenue
- DCurrent assets / current liabilities
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€200,000
- B€0
- C€80,000
- D€120,000
7.Break-even analysisMedium
A product sells for €23 per unit with a variable cost of €18 per unit. Fixed costs are €20 000 per month. How many units Q must be sold per month to make a profit of €12 000?
F = €20 000p = €23v = €18profit = €12 000
Q = units
8.Break-even analysisHard
A product sells for €50 per unit, with a variable cost of €45 per unit and fixed costs of €20 000 per year. Budgeted sales are 6 400 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €20 000p = €50v = €45budget = 6 400
MS = %
3Solutions
1.Marketing principles
Answer: A · Customers' perception of the product's value
Why this is the answer
Value-based pricing estimates what the offer is worth to buyers. Costs then set a floor, and competitor prices are a reference.
Answer
A · Customers' perception of the product's value
2.Marketing principles
Answer: C · A house of brands
Why this is the answer
A house of brands gives each product its own identity, so brands can target different segments and problems with one do not spread easily. A branded house, like Virgin, uses one master brand.
Answer
C · A house of brands
3.Economics concepts
Answer: A · Quantity rises, but the change in price is uncertain
Why this is the answer
Both shifts raise quantity, but the demand shift raises price while the supply shift lowers it, so the price effect depends on their relative size.
Answer
A · Quantity rises, but the change in price is uncertain
4.Economics concepts
Answer: B · It is less costly for high-ability workers to acquire, so it reveals their type
Why this is the answer
If acquiring education costs less for able workers, only they find it worth getting, so it separates types and solves the hidden information problem.
Answer
B · It is less costly for high-ability workers to acquire, so it reveals their type
5.Financial accounting
Answer: A · Net profit / shareholders' equity
Why this is the answer
ROE shows how much profit the company generates for each euro of equity invested by shareholders.
Answer
A · Net profit / shareholders' equity
6.Financial accounting
Answer: C · €80,000
Why this is the answer
Recoverable amount = max(€380,000, €420,000) = €420,000. Impairment = €500,000 − €420,000 = €80,000.
Answer
C · €80,000
7.Break-even analysis
Answer: Q = 6400 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 = 23 − 18 = €5
Units for the target profit
Q = (F + profit)/(p − v) = (20 000 + 12 000)/5 = 6 400
Answer
Q = 6 400 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) = 20 000/5 = 4 000
Margin of safety
MS = (6 400 − 4 000)/6 400·100 = 37.5%
Answer
MS = 37.5%
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