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 haircut is produced and consumed at the same time, with the customer present. Which service characteristic is this?
- AInseparability
- BHeterogeneity
- CPerishability
- DIntangibility
2.Marketing principlesHard
Theodore Levitt's "Marketing Myopia" (1960) used US railroads as an example. What was their mistake?
- AThey set their prices too low
- BThey expanded into too many countries
- CThey spent too much on advertising
- DThey defined their business as railways rather than transportation
3.Economics conceptsMedium
Nominal GDP grew by 5% and the GDP deflator rose by 2%. Real GDP grew by approximately:
- A7%
- B10%
- C3%
- D2.5%
4.Economics conceptsHard
The "paradox of thrift" suggests that if all households try to save more during a recession:
- AInterest rates will rise sharply
- BTotal income may fall, so total saving does not rise
- CInflation will increase
- DInvestment and growth will rise immediately
5.Financial accountingMedium
Under IAS 16, which cost should be included in the cost of a new machine?
- ARepairs carried out two years later
- BInstallation costs needed to get it working
- CStaff training costs after it starts operating
- DGeneral office overheads for the year
6.Financial accountingHard
Inventory days are 60, receivable days 45 and payable days 30. What is the cash conversion (operating) cycle?
- A105 days
- B15 days
- C135 days
- D75 days
7.Break-even analysisMedium
A product sells for €40 per unit with a variable cost of €20 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 = €40v = €20profit = €5 000
Q = units
8.Break-even analysisHard
A company sells 3 000 units per month at €22 each, with a variable cost of €18 per unit and fixed costs of €6 000 per month. The variable cost rises by €1 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 3 000p = €22v = €18 → €19F = €6 000
Q = units
3Solutions
1.Marketing principles
Answer: A · Inseparability
Why this is the answer
Inseparability means production and consumption happen together, so staff behaviour and customer participation shape the service quality.
Answer
A · Inseparability
2.Marketing principles
Answer: D · They defined their business as railways rather than transportation
Why this is the answer
Levitt argued firms fail when they focus on their product instead of the customer need it serves. Railroads lost customers to cars, trucks and planes they did not see as rivals.
Answer
D · They defined their business as railways rather than transportation
3.Economics concepts
Answer: C · 3%
Why this is the answer
Subtracting the rise in prices from nominal growth gives real growth of roughly 5% − 2% = 3%.
Answer
C · 3%
4.Economics concepts
Answer: B · 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
B · Total income may fall, so total saving does not rise
5.Financial accounting
Answer: B · Installation costs needed to get it working
Why this is the answer
Purchase price plus directly attributable costs, such as delivery and installation, are capitalised. Training, later repairs and general overheads are expensed.
Answer
B · Installation costs needed to get it working
6.Financial accounting
Answer: D · 75 days
Why this is the answer
60 + 45 − 30 = 75 days between paying suppliers and collecting cash from customers. A shorter cycle needs less working capital finance.
Answer
D · 75 days
7.Break-even analysis
Answer: Q = 1250 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) = (20 000 + 5 000)/20 = 1 250
Answer
Q = 1 250 units
8.Break-even analysis
Answer: Q = 4000 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).
Current profit
Π = 3 000·(22 − 18) − 6 000 = €6 000
New contribution margin per unit
22 − 19 = €3
Units for the same profit
Q = (6 000 + 6 000)/3 = 4 000
Answer
Q = 4 000 units
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