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 web shop has 2,000 visitors and 50 of them make a purchase. What is the conversion rate?
- A4%
- B25%
- C0.25%
- D2.5%
2.Marketing principlesHard
In a B2B buying centre, a purchasing assistant controls which supplier brochures reach the engineers. Which role does the assistant play?
- AGatekeeper
- BDecider
- CUser
- DInfluencer
3.Economics conceptsMedium
A per-unit tax is placed on a good with very inelastic demand and elastic supply. Who bears most of the tax burden?
- AProducers
- BIt is always split equally
- CConsumers
- DThe government
4.Economics conceptsHard
For a normal good, when its price falls, the substitution effect and income effect:
- ABoth decrease the quantity demanded
- BBoth increase the quantity demanded
- CWork in opposite directions
- DCancel out exactly
5.Financial accountingMedium
Budgeted sales are 1,500 units and the break-even point is 1,000 units. What is the margin of safety?
- A500 units
- B2,500 units
- C1,500 units
- D1,000 units
6.Financial accountingHard
The standard price of material is €5 per kg. The company buys 1,000 kg for €5,400. What is the material price variance?
- A€400 favourable
- B€0.40 adverse
- C€400 adverse
- D€5,400 adverse
7.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €10 000 per year and a variable cost of €25 per unit. Method B, more automated, has fixed costs of €12 000 per year and a variable cost of €23 per unit. At what yearly volume Q do both methods cost the same?
FA = €10 000vA = €25FB = €12 000vB = €23
Q = units
8.Break-even analysisHard
A product sells for €57 per unit, with a variable cost of €45 per unit and fixed costs of €6 000 per year. Budgeted sales are 630 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €6 000p = €57v = €45budget = 630
MS = %
3Solutions
1.Marketing principles
Answer: D · 2.5%
Why this is the answer
50 ÷ 2,000 = 0.025 = 2.5%. Conversion rate measures how well a site turns visits into the desired action.
Answer
D · 2.5%
2.Marketing principles
Answer: A · Gatekeeper
Why this is the answer
Buying centre roles include users, influencers, buyers, deciders and gatekeepers. Sellers must reach the right people, and gatekeepers can block access to them.
Answer
A · Gatekeeper
3.Economics concepts
Answer: C · Consumers
Why this is the answer
The tax burden falls mainly on the side of the market that is less elastic; here buyers cannot cut back, so the price they pay rises by most of the tax.
Answer
C · Consumers
4.Economics concepts
Answer: B · Both increase the quantity demanded
Why this is the answer
The substitution effect always favours the cheaper good, and for a normal good the higher real income also raises demand, so both effects reinforce each other.
Answer
B · Both increase the quantity demanded
5.Financial accounting
Answer: A · 500 units
Why this is the answer
Margin of safety = budgeted sales − break-even sales = 500 units, or one third of budgeted sales.
Answer
A · 500 units
6.Financial accounting
Answer: C · €400 adverse
Why this is the answer
Standard cost of 1,000 kg = €5,000; actual cost = €5,400. Paying more than standard gives a €400 adverse price variance.
Answer
C · €400 adverse
7.Break-even analysis
Answer: Q = 1000 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).
Equal total costs
10 000 + 25Q = 12 000 + 23Q
Solve for Q
Q = (12 000 − 10 000)/(25 − 23) = 1 000
Answer
Q = 1 000 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: MS = 20.63 %
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) = 6 000/12 = 500
Margin of safety
MS = (630 − 500)/630·100 = 20.63%
Answer
MS = 20.63%
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