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 firm raises its price by 10% and the quantity sold falls by 20%. What is the price elasticity of demand, and what happens to revenue?
- A−0.5, elastic, so revenue falls
- B−0.5, inelastic, so revenue rises
- C−2, inelastic, so revenue rises
- D−2, elastic, so revenue falls
2.Marketing principlesHard
A company launches a product that is easy to copy, with highly price-sensitive buyers and strong economies of scale. Which launch pricing strategy fits best?
- ACaptive product pricing
- BPrestige pricing
- CPrice skimming
- DPenetration pricing
3.Economics conceptsMedium
Nominal GDP grew by 5% and the GDP deflator rose by 2%. Real GDP grew by approximately:
- A10%
- B2.5%
- C3%
- D7%
4.Economics conceptsHard
In the Solow growth model, sustained long-run growth in output per worker comes from:
- AGovernment budget deficits
- BA higher saving rate alone
- CTechnological progress
- DPopulation growth
5.Financial accountingMedium
A firm buys 200 units at €5 and 300 units at €6, then sells 400 units. Using weighted average cost, what is closing inventory?
- A€550
- B€560
- C€600
- D€500
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€400 adverse
- C€5,400 adverse
- D€0.40 adverse
7.Break-even analysisMedium
A product sells for €17 with a variable cost of €12 per unit. Fixed costs are €6 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €2 000 after tax?
p = €17v = €12F = €6 000T = 20%after-tax profit = €2 000
Q = units
8.Break-even analysisHard
A product sells for €27 per unit, with a variable cost of €12 per unit and fixed costs of €30 000 per year. Budgeted sales are 2 600 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €30 000p = €27v = €12budget = 2 600
MS = %
3Solutions
1.Marketing principles
Answer: D · −2, elastic, so revenue falls
Why this is the answer
PED = −20% ÷ 10% = −2. Because its size is above 1, demand is elastic and the price rise reduces total revenue.
Answer
D · −2, elastic, so revenue falls
2.Marketing principles
Answer: D · Penetration pricing
Why this is the answer
Low prices build share quickly, lower unit costs through scale and discourage imitators. Skimming suits unique products with buyers who are less sensitive to price.
Answer
D · Penetration pricing
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: C · Technological progress
Why this is the answer
A higher saving rate raises the steady-state level of output per worker but not its long-run growth rate; only technological progress produces continuous growth.
Answer
C · Technological progress
5.Financial accounting
Answer: B · €560
Why this is the answer
Average cost = (€1,000 + €1,800) ÷ 500 = €5.60. Closing inventory = 100 × €5.60 = €560.
Answer
B · €560
6.Financial accounting
Answer: B · €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
B · €400 adverse
7.Break-even analysis
Answer: Q = 1700 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).
Pre-tax profit needed
2 000/(1 − 0.2) = €2 500
Units needed
Q = (6 000 + 2 500)/5 = 1 700
Answer
Q = 1 700 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) = 30 000/15 = 2 000
Margin of safety
MS = (2 600 − 2 000)/2 600·100 = 23.08%
Answer
MS = 23.08%
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