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 car maker offers separate models and campaigns for students, families and luxury buyers. Which targeting strategy is this?
- AUndifferentiated marketing
- BMass customisation of one model
- CConcentrated marketing
- DDifferentiated marketing
2.Marketing principlesHard
Which metric best shows the efficiency of acquiring customers through online advertising?
- AThe number of employees in marketing
- BThe number of likes on posts
- CCustomer acquisition cost compared with customer lifetime value
- DTotal impressions only
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
- CTreated as the opportunity cost of stopping
- DAdded to the expected future costs
4.Economics conceptsHard
In the Prisoner's Dilemma, the Nash equilibrium is:
- AThere is no equilibrium
- BBoth players cooperate
- COne player cooperates and the other defects, so only one of them gains
- DBoth players defect, even though both cooperating would be better
5.Financial accountingMedium
A shop buys 100 units at €10, then 100 units at €12, and then sells 150 units. What is cost of sales using FIFO?
- A€1,700
- B€1,600
- C€1,650
- D€1,500
6.Financial accountingHard
A company "sells" inventory to a bank and must buy it back later at a higher price, keeping the risks and rewards. How should it be accounted for?
- AAs revenue on the date of transfer
- BAs a secured loan, not a sale
- CAs a gain on disposal of inventory
- DAs a contingent asset in the notes
7.Break-even analysisMedium
A company sells 7 500 units at €17 each. The variable cost is €12 per unit and fixed costs are €12 500. Find the degree of operating leverage DOL at this sales level.
Q = 7 500p = €17v = €12F = €12 500
DOL =
8.Break-even analysisHard
A product sells for €13 per unit, with a variable cost of €8 per unit and fixed costs of €20 000 per year. Budgeted sales are 4 800 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €20 000p = €13v = €8budget = 4 800
MS = %
3Solutions
1.Marketing principles
Answer: D · Differentiated marketing
Why this is the answer
Differentiated marketing targets several segments with different products or messages. It can raise sales but also costs.
Answer
D · Differentiated marketing
2.Marketing principles
Answer: C · Customer acquisition cost compared with customer lifetime value
Why this is the answer
CAC relative to CLV shows whether acquisition is profitable; vanity metrics like likes do not measure business value.
Answer
C · Customer acquisition cost compared with customer lifetime value
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 · Both players defect, even though both cooperating would be better
Why this is the answer
Each player's best response is to defect whatever the other does, so mutual defection is the equilibrium, although mutual cooperation would give both a higher payoff.
Answer
D · Both players defect, even though both cooperating would be better
5.Financial accounting
Answer: B · €1,600
Why this is the answer
FIFO: 100 × €10 + 50 × €12 = €1,600. The 50 units left are valued at the latest cost of €12.
Answer
B · €1,600
6.Financial accounting
Answer: B · As a secured loan, not a sale
Why this is the answer
Control and risks stay with the company, so the transaction is in substance borrowing secured on inventory. The price difference is an interest cost.
Answer
B · As a secured loan, not a sale
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 = 7 500·(17 − 12) = €37 500
Operating profit
Π = 37 500 − 12 500 = €25 000
DOL
DOL = 37 500/25 000 = 1.5
Answer
DOL = 1.5
8.Break-even analysis
Answer: MS = 16.67 %
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) = 20 000/5 = 4 000
Margin of safety
MS = (4 800 − 4 000)/4 800·100 = 16.67%
Answer
MS = 16.67%
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