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
- BIntangibility
- CHeterogeneity
- DPerishability
2.Marketing principlesHard
A survey asks: "Don't you agree that our excellent staff are very helpful?" What is the main problem?
- AIt is too short to be understood
- BIt is a leading question that pushes respondents towards agreement
- CIt is an open question that is hard to analyse
- DIt asks about two unrelated products
3.Economics conceptsMedium
The law of diminishing marginal returns states that:
- ALong-run average costs always fall as output rises
- BAdding more of a variable input to a fixed input eventually lowers the extra output per unit added
- CConsumers get less satisfaction as prices rise
- DTotal output always falls as more workers are hired
4.Economics conceptsHard
Why is the real-world government spending multiplier usually smaller than the simple 1/(1 − MPC)?
- AGovernments cannot borrow money
- BTaxes, imports and crowding out leak part of each round of spending
- CConsumers never spend extra income
- DThe MPC is always above 1
5.Financial accountingMedium
Fixed costs are €20,000, the selling price is €50 and the variable cost is €30 per unit. What is the break-even point?
- A400 units
- B2,000 units
- C1,000 units
- D667 units
6.Financial accountingHard
Under IFRS 15, revenue is recognised:
- AAt the end of the financial year
- BOnly when cash is received
- CWhen (or as) the entity satisfies a performance obligation by transferring control to the customer
- DWhen the contract is signed
7.Break-even analysisMedium
A product sells for €65 per unit with a variable cost of €45 per unit. Fixed costs are €10 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €10 000p = €65v = €45profit = €2 000
Q = units
8.Break-even analysisHard
A product sells for €33 per unit, with a variable cost of €25 per unit and fixed costs of €8 000 per year. Budgeted sales are 1 600 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €8 000p = €33v = €25budget = 1 600
MS = %
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: B · It is a leading question that pushes respondents towards agreement
Why this is the answer
Leading questions bias answers through wording. A neutral version would be "How helpful were our staff?" with a balanced rating scale.
Answer
B · It is a leading question that pushes respondents towards agreement
3.Economics concepts
Answer: B · Adding more of a variable input to a fixed input eventually lowers the extra output per unit added
Why this is the answer
In the short run, with at least one fixed factor, marginal product eventually falls, which makes marginal cost rise.
Answer
B · Adding more of a variable input to a fixed input eventually lowers the extra output per unit added
4.Economics concepts
Answer: B · 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
B · Taxes, imports and crowding out leak part of each round of spending
5.Financial accounting
Answer: C · 1,000 units
Why this is the answer
Contribution per unit = €50 − €30 = €20. Break-even = €20,000 ÷ €20 = 1,000 units.
Answer
C · 1,000 units
6.Financial accounting
Answer: C · When (or as) the entity satisfies a performance obligation by transferring control to the customer
Why this is the answer
The steps: identify the contract, identify performance obligations, determine the price, allocate it, and recognise revenue as each obligation is satisfied.
Answer
C · When (or as) the entity satisfies a performance obligation by transferring control to the customer
7.Break-even analysis
Answer: Q = 600 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 = 65 − 45 = €20
Units for the target profit
Q = (F + profit)/(p − v) = (10 000 + 2 000)/20 = 600
Answer
Q = 600 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) = 8 000/8 = 1 000
Margin of safety
MS = (1 600 − 1 000)/1 600·100 = 37.5%
Answer
MS = 37.5%
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