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
Price elasticity matters for pricing because:
- AIt has no effect on pricing decisions
- BIf demand is inelastic, a price rise will lower total revenue
- CElasticity only affects costs
- DIf demand is elastic, a price cut can raise total revenue
2.Marketing principlesHard
In the BCG matrix, a firm has 20% market share and its largest competitor has 40%. What is the firm's relative market share?
- A2.0
- B0.5
- C0.2
- D20%
3.Economics conceptsMedium
Nominal GDP grew by 5% and the GDP deflator rose by 2%. Real GDP grew by approximately:
- A2.5%
- B3%
- C7%
- D10%
4.Economics conceptsHard
A monopolist faces demand P = 100 − Q and has constant marginal cost of 20. What are its profit-maximising output and price?
- AQ = 40, P = 60
- BQ = 80, P = 20
- CQ = 50, P = 50
- DQ = 40, P = 20
5.Financial accountingMedium
Budgeted sales are 1,500 units and the break-even point is 1,000 units. What is the margin of safety?
- A2,500 units
- B1,500 units
- C1,000 units
- D500 units
6.Financial accountingHard
A firm with spare capacity gets a one-off order at €35 per unit. Variable cost is €30 and full cost including fixed overhead is €42. Assuming no other effects, should it accept?
- AYes, but only if the price exceeds €42
- BNo, the price is below full cost
- CYes, each unit adds €5 contribution
- DNo, the order makes a €7 loss per unit
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 €8 per unit. Method B, more automated, has fixed costs of €16 000 per year and a variable cost of €4 per unit. At what yearly volume Q do both methods cost the same?
FA = €10 000vA = €8FB = €16 000vB = €4
Q = units
8.Break-even analysisHard
A product sells for €23 per unit, with a variable cost of €20 per unit and fixed costs of €3 000 per year. Budgeted sales are 1 600 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €3 000p = €23v = €20budget = 1 600
MS = %
3Solutions
1.Marketing principles
Answer: D · If demand is elastic, a price cut can raise total revenue
Why this is the answer
With elastic demand, quantity responds strongly, so a lower price can increase revenue; with inelastic demand, a price rise increases revenue.
Answer
D · If demand is elastic, a price cut can raise total revenue
2.Marketing principles
Answer: B · 0.5
Why this is the answer
Relative market share = 20% ÷ 40% = 0.5. A value below 1 means the firm is not the market leader, placing it on the low-share side of the matrix.
Answer
B · 0.5
3.Economics concepts
Answer: B · 3%
Why this is the answer
Subtracting the rise in prices from nominal growth gives real growth of roughly 5% − 2% = 3%.
Answer
B · 3%
4.Economics concepts
Answer: A · Q = 40, P = 60
Why this is the answer
Setting MR = MC gives 100 − 2Q = 20, so Q = 40; the price from the demand curve is 100 − 40 = 60.
Answer
A · Q = 40, P = 60
5.Financial accounting
Answer: D · 500 units
Why this is the answer
Margin of safety = budgeted sales − break-even sales = 500 units, or one third of budgeted sales.
Answer
D · 500 units
6.Financial accounting
Answer: C · Yes, each unit adds €5 contribution
Why this is the answer
Fixed costs do not change, so the order adds €35 − €30 = €5 per unit to profit. Risks such as upsetting regular customers should still be considered.
Answer
C · Yes, each unit adds €5 contribution
7.Break-even analysis
Answer: Q = 1500 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 + 8Q = 16 000 + 4Q
Solve for Q
Q = (16 000 − 10 000)/(8 − 4) = 1 500
Answer
Q = 1 500 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
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) = 3 000/3 = 1 000
Margin of safety
MS = (1 600 − 1 000)/1 600·100 = 37.5%
Answer
MS = 37.5%
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