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 competes across a broad market by having the lowest costs in its industry and passing savings on as low prices. Which Porter generic strategy is this?
- ACost leadership
- BDifferentiation focus
- CMarket development
- DDifferentiation
2.Marketing principlesHard
A company launches a premium version of its product under the same brand name. This is an example of:
- ALine extension
- BBrand extension into a new category
- CCo-branding
- DMultibranding
3.Economics conceptsMedium
If demand for a product is price inelastic, a price increase will:
- ALeave total revenue unchanged
- BReduce quantity demanded to zero
- CIncrease total revenue
- DDecrease total revenue
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 = 80, P = 20
- BQ = 50, P = 50
- CQ = 40, P = 60
- DQ = 40, P = 20
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€500
- D€600
6.Financial accountingHard
Production exceeds sales this period, so inventory rises. How does absorption costing profit compare with marginal costing profit?
- AAbsorption costing shows a loss
- BThey are always equal
- CMarginal costing profit is higher this period
- DAbsorption costing profit is higher
7.Break-even analysisMedium
A product sells for €20 per unit with a variable cost of €15 per unit. Fixed costs are €6 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €6 000p = €20v = €15profit = €2 000
Q = units
8.Break-even analysisHard
A company sells 2 250 units per month at €32 each, with a variable cost of €20 per unit and fixed costs of €18 000 per month. The variable cost rises by €3 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 2 250p = €32v = €20 → €23F = €18 000
Q = units
3Solutions
1.Marketing principles
Answer: A · Cost leadership
Why this is the answer
Cost leadership seeks the lowest cost position in a broad market. Differentiation offers unique value at a premium; focus strategies target a narrow segment.
Answer
A · Cost leadership
2.Marketing principles
Answer: A · Line extension
Why this is the answer
A line extension adds new variants in the same category under the existing brand; brand extension uses the brand in a new category.
Answer
A · Line extension
3.Economics concepts
Answer: C · Increase total revenue
Why this is the answer
With inelastic demand the percentage fall in quantity is smaller than the percentage price rise, so price × quantity rises.
Answer
C · Increase total revenue
4.Economics concepts
Answer: C · 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
C · Q = 40, P = 60
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: D · Absorption costing profit is higher
Why this is the answer
Under absorption costing part of this period's fixed overhead sits in closing inventory instead of being expensed, so reported profit is higher when inventory rises.
Answer
D · Absorption costing profit is higher
7.Break-even analysis
Answer: Q = 1600 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 = 20 − 15 = €5
Units for the target profit
Q = (F + profit)/(p − v) = (6 000 + 2 000)/5 = 1 600
Answer
Q = 1 600 units
8.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).
Current profit
Π = 2 250·(32 − 20) − 18 000 = €9 000
New contribution margin per unit
32 − 23 = €9
Units for the same profit
Q = (18 000 + 9 000)/9 = 3 000
Answer
Q = 3 000 units
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