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
Why might a researcher choose in-depth interviews rather than a large questionnaire?
- ATo avoid any interviewer influence
- BTo explore customers' motives and feelings in detail
- CTo survey thousands of people cheaply
- DTo produce statistically representative percentages for the market
2.Marketing principlesHard
A manufacturer starts selling online directly to consumers at lower prices than its retailers. Retailers complain. What is this?
- AHorizontal channel conflict
- BA pull strategy
- CVertical channel conflict
- DCannibalisation by a rival brand
3.Economics conceptsMedium
A firm has spent €1 million on research for a product that now looks unprofitable. When deciding whether to continue, the €1 million should be:
- AIgnored, because it is a sunk cost
- BRecovered by raising prices
- CAdded to the expected future costs
- DTreated as the opportunity cost of stopping
4.Economics conceptsHard
A lump-sum tax (a fixed amount, independent of output) is imposed on a profit-maximising monopolist. In the short run, its output will:
- AFall to zero
- BFall, because the tax raises the firm's average cost
- CRise to make up for the tax
- DStay the same, because MR and MC do not change
5.Financial accountingMedium
A machine costs €10,000 and is depreciated at 20% a year on the reducing balance. What is the depreciation charge in year 2?
- A€1,800
- B€2,000
- C€1,600
- D€4,000
6.Financial accountingHard
Machine hours are scarce. Product X earns €20 contribution and needs 4 hours; product Y earns €15 and needs 2 hours. Which should be made first?
- AEither, because the total contribution is the same
- BY, because it earns €7.50 per hour versus €5 for X
- CX, because it earns more contribution per unit
- DX, because it uses more machine time
7.Break-even analysisMedium
A company sells 4 500 units at €34 each. The variable cost is €30 per unit and fixed costs are €6 000. Find the degree of operating leverage DOL at this sales level.
Q = 4 500p = €34v = €30F = €6 000
DOL =
8.Break-even analysisHard
A company sells two products. Product A sells for €13 with a variable cost of €5; product B sells for €40 with a variable cost of €30. They sell in a fixed mix of 2 units of A for every 1 of B. Fixed costs are €26 000 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €13, vA = €5pB = €40, vB = €30A : B = 2 : 1F = €26 000
Q = units
3Solutions
1.Marketing principles
Answer: B · To explore customers' motives and feelings in detail
Why this is the answer
In-depth interviews give rich, qualitative insight into why people behave as they do. Questionnaires suit measuring how many people think or do something.
Answer
B · To explore customers' motives and feelings in detail
2.Marketing principles
Answer: C · Vertical channel conflict
Why this is the answer
Vertical conflict arises between levels, such as manufacturer and retailer. Horizontal conflict is between firms at the same level, such as two retailers.
Answer
C · Vertical channel conflict
3.Economics concepts
Answer: A · Ignored, because it is a sunk cost
Why this is the answer
Sunk costs cannot be recovered and do not change with the decision, so rational choices compare only future costs and benefits.
Answer
A · Ignored, because it is a sunk cost
4.Economics concepts
Answer: D · Stay the same, because MR and MC do not change
Why this is the answer
A lump-sum tax is like a fixed cost: it lowers profit but does not change MR or MC, so the optimal quantity and price stay the same (unless the firm exits).
Answer
D · Stay the same, because MR and MC do not change
5.Financial accounting
Answer: C · €1,600
Why this is the answer
Year 1: 20% × €10,000 = €2,000, leaving €8,000. Year 2: 20% × €8,000 = €1,600. Reducing balance charges less each year.
Answer
C · €1,600
6.Financial accounting
Answer: B · Y, because it earns €7.50 per hour versus €5 for X
Why this is the answer
X earns €20 ÷ 4 = €5 per hour, Y earns €15 ÷ 2 = €7.50 per hour. With a scarce resource, maximise contribution per scarce hour.
Answer
B · Y, because it earns €7.50 per hour versus €5 for X
7.Break-even analysis
Answer: DOL = 1.5
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Total contribution margin
CM = 4 500·(34 − 30) = €18 000
Operating profit
Π = 18 000 − 6 000 = €12 000
DOL
DOL = 18 000/12 000 = 1.5
Answer
DOL = 1.5
8.Break-even analysis
Answer: Q = 3000 units
Break-even with a sales mix: when products sell in a fixed ratio, use the weighted average contribution margin: weight each product's p − v by its share of units. Break-even units = F/(weighted contribution margin), split again in the mix ratio.
Contribution margins
cmA = €8, cmB = €10
Weighted contribution margin
(2·8 + 1·10)/3 = €8.67
Break-even units
Q = 26 000/8.667 = 3 000
A: 2 000, B: 1 000
Answer
Q = 3 000 units
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