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 customer is buying a first new car. How does this high-involvement purchase usually differ from buying a pack of chewing gum?
- AThe buyer decides on impulse at the checkout
- BThe buyer searches for more information and compares alternatives carefully
- CThe buyer skips the evaluation stage
- DThe buyer is not influenced by the brand at all
2.Marketing principlesHard
When is price skimming most suitable?
- AWhen the firm wants the largest market share at launch
- BWhen customers are very sensitive to price
- CFor a commodity product in a crowded market
- DFor an innovative product with few rivals and early buyers willing to pay a premium
3.Economics conceptsMedium
Both supply and demand for a good increase. What can we say for certain about the new equilibrium?
- ABoth price and quantity rise
- BQuantity rises, but the change in price is uncertain
- CBoth price and quantity fall
- DPrice rises, but the change in quantity is uncertain
4.Economics conceptsHard
The "paradox of thrift" suggests that if all households try to save more during a recession:
- AInflation will increase
- BInvestment and growth will rise immediately
- CTotal income may fall, so total saving does not rise
- DInterest rates will rise sharply
5.Financial accountingMedium
A product sells for €40 and has a variable cost of €30. What is its contribution-to-sales (C/S) ratio?
- A10%
- B25%
- C33%
- D75%
6.Financial accountingHard
An asset is impaired when its carrying amount is higher than its:
- ADepreciation charge
- BResidual value only
- COriginal purchase price
- DRecoverable amount (the higher of fair value less costs of disposal and value in use)
7.Break-even analysisMedium
A product sells for €40 per unit with a variable cost of €20 per unit. Fixed costs are €50 000 per month. How many units Q must be sold per month to make a profit of €12 000?
F = €50 000p = €40v = €20profit = €12 000
Q = units
8.Break-even analysisHard
A product sells for €21 per unit, with a variable cost of €6 per unit and fixed costs of €22 500 per year. Budgeted sales are 1 950 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €22 500p = €21v = €6budget = 1 950
MS = %
3Solutions
1.Marketing principles
Answer: B · The buyer searches for more information and compares alternatives carefully
Why this is the answer
High involvement leads to extended problem solving with much information search and evaluation. Low-involvement items are bought by habit or impulse.
Answer
B · The buyer searches for more information and compares alternatives carefully
2.Marketing principles
Answer: D · For an innovative product with few rivals and early buyers willing to pay a premium
Why this is the answer
Skimming works when the product is distinctive, entry barriers protect it for a while, and some customers value being first enough to pay more.
Answer
D · For an innovative product with few rivals and early buyers willing to pay a premium
3.Economics concepts
Answer: B · 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
B · Quantity rises, but the change in price is uncertain
4.Economics concepts
Answer: C · Total income may fall, so total saving does not rise
Why this is the answer
Higher saving reduces consumption and aggregate demand, lowering income; with lower income, aggregate saving may end up no higher, as Keynes argued.
Answer
C · Total income may fall, so total saving does not rise
5.Financial accounting
Answer: B · 25%
Why this is the answer
Contribution = €10. C/S ratio = €10 ÷ €40 = 25%. Fixed costs ÷ C/S ratio gives break-even revenue.
Answer
B · 25%
6.Financial accounting
Answer: D · Recoverable amount (the higher of fair value less costs of disposal and value in use)
Why this is the answer
If the carrying amount exceeds the recoverable amount, the difference is written off as an impairment loss.
Answer
D · Recoverable amount (the higher of fair value less costs of disposal and value in use)
7.Break-even analysis
Answer: Q = 3100 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 = 40 − 20 = €20
Units for the target profit
Q = (F + profit)/(p − v) = (50 000 + 12 000)/20 = 3 100
Answer
Q = 3 100 units
8.Break-even analysis
Answer: MS = 23.08 %
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) = 22 500/15 = 1 500
Margin of safety
MS = (1 950 − 1 500)/1 950·100 = 23.08%
Answer
MS = 23.08%
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