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 researcher divides the population into age groups and draws a random sample from each group. This is:
- AQuota sampling with free choice
- BStratified random sampling
- CConvenience sampling
- DSnowball sampling
2.Marketing principlesHard
An ice cream brand finds that its sales and its advertising spend both peak in summer. Why can it not conclude that advertising caused the sales?
- ASales data is always unreliable
- BSummer sales are too small to measure
- CHot weather may drive both, so correlation does not prove causation
- DAdvertising never affects sales of food
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 fall
- BPrice rises, but the change in quantity is uncertain
- CBoth price and quantity rise
- DQuantity rises, but the change in price is uncertain
4.Economics conceptsHard
Why is the real-world government spending multiplier usually smaller than the simple 1/(1 − MPC)?
- AGovernments cannot borrow money
- BConsumers never spend extra income
- CTaxes, imports and crowding out leak part of each round of spending
- DThe MPC is always above 1
5.Financial accountingMedium
An asset costs €50,000, has a residual value of €5,000 and a useful life of 5 years. What is the annual straight-line depreciation?
- A€10,000
- B€5,000
- C€9,000
- D€11,000
6.Financial accountingHard
After the year end, but before the accounts are approved, a customer who owed money at year end goes bankrupt. Under IAS 10 this is:
- AIgnored, because it happened after the year end
- BAn adjusting event, so receivables are reduced
- CA non-adjusting event, disclosed only
- DA change in accounting policy
7.Break-even analysisMedium
A product sells for €34 per unit with a variable cost of €30 per unit. Fixed costs are €6 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €6 000p = €34v = €30profit = €6 000
Q = units
8.Break-even analysisHard
A product sells for €28 per unit, with a variable cost of €20 per unit and fixed costs of €16 000 per year. Budgeted sales are 3 200 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €16 000p = €28v = €20budget = 3 200
MS = %
3Solutions
1.Marketing principles
Answer: B · Stratified random sampling
Why this is the answer
Stratified sampling ensures each subgroup is represented while keeping random selection. Quota sampling sets numbers per group but lets interviewers choose people, so it is non-probability.
Answer
B · Stratified random sampling
2.Marketing principles
Answer: C · Hot weather may drive both, so correlation does not prove causation
Why this is the answer
A confounding factor, such as temperature, can create a correlation between two variables. Controlled tests or models that account for seasonality are needed to estimate the ad effect.
Answer
C · Hot weather may drive both, so correlation does not prove causation
3.Economics concepts
Answer: D · 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
D · Quantity rises, but the change in price is uncertain
4.Economics concepts
Answer: C · Taxes, imports and crowding out leak part of each round of spending
Why this is the answer
Income taxes, spending on imports, higher interest rates (crowding out) and saving reduce the extra spending in each round, so the multiplier shrinks.
Answer
C · Taxes, imports and crowding out leak part of each round of spending
5.Financial accounting
Answer: C · €9,000
Why this is the answer
(Cost − residual value) ÷ useful life = (€50,000 − €5,000) ÷ 5 = €9,000 per year.
Answer
C · €9,000
6.Financial accounting
Answer: B · An adjusting event, so receivables are reduced
Why this is the answer
The customer's inability to pay existed at year end, so the accounts are adjusted. A fire after year end would be non-adjusting, because it is a new condition.
Answer
B · An adjusting event, so receivables are reduced
7.Break-even analysis
Answer: Q = 3000 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 = 34 − 30 = €4
Units for the target profit
Q = (F + profit)/(p − v) = (6 000 + 6 000)/4 = 3 000
Answer
Q = 3 000 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) = 16 000/8 = 2 000
Margin of safety
MS = (3 200 − 2 000)/3 200·100 = 37.5%
Answer
MS = 37.5%
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