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
In Rogers' diffusion of innovations, which group adopts a new product first?
- AEarly adopters
- BLaggards
- CEarly majority
- DInnovators
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
- B20%
- C0.5
- D0.2
3.Economics conceptsMedium
A Nash equilibrium is a situation where:
- AOne player has won and the others have lost
- BNo player can improve their payoff by changing strategy alone, given the others' strategies
- CThe players agree to cooperate through a binding contract that maximises their combined total payoff
- DAll players achieve the highest possible total payoff
4.Economics conceptsHard
A monopolist maximises profit where:
- AMarginal revenue equals marginal cost
- BPrice equals marginal cost
- CAverage cost is at its minimum
- DTotal revenue is at its maximum
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€1,500
- B€1,600
- C€1,700
- D€1,650
6.Financial accountingHard
After the year end, but before the accounts are approved, a customer who owed money at year end goes bankrupt. Under IAS 10 this is:
- AA non-adjusting event, disclosed only
- BAn adjusting event, so receivables are reduced
- CIgnored, because it happened after the year end
- DA change in accounting policy
7.Break-even analysisMedium
A product sells for €30 per unit with a variable cost of €20 per unit. Fixed costs are €40 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €40 000p = €30v = €20profit = €2 000
Q = units
8.Break-even analysisHard
A company sells 2 000 units at €18 each, with a variable cost of €15 per unit and fixed costs of €3 000. By what percentage %ΔΠ does operating profit change if sales volume falls by 12%?
Q = 2 000p = €18v = €15F = €3 000%ΔQ = −12%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: D · Innovators
Why this is the answer
The order is innovators, early adopters, early majority, late majority and laggards. Early adopters are often opinion leaders who influence others.
Answer
D · Innovators
2.Marketing principles
Answer: C · 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
C · 0.5
3.Economics concepts
Answer: B · No player can improve their payoff by changing strategy alone, given the others' strategies
Why this is the answer
In a Nash equilibrium each strategy is a best response to the others; the outcome need not be efficient, as the Prisoner's Dilemma shows.
Answer
B · No player can improve their payoff by changing strategy alone, given the others' strategies
4.Economics concepts
Answer: A · Marginal revenue equals marginal cost
Why this is the answer
Profit is maximised where MR = MC. For a monopolist, price is above MR, so P > MC, causing a deadweight loss.
Answer
A · Marginal revenue equals marginal cost
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 · An adjusting event, so receivables are reduced
Why this is the answer
The customer's inability to pay existed at year end, so the accounts are adjusted. A fire after year end would be non-adjusting, because it is a new condition.
Answer
B · An adjusting event, so receivables are reduced
7.Break-even analysis
Answer: Q = 4200 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 = 30 − 20 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (40 000 + 2 000)/10 = 4 200
Answer
Q = 4 200 units
8.Break-even analysis
Answer: %ΔΠ = −24 %
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.
Contribution margin and profit
CM = 2 000·3 = €6 000
Π = 6 000 − 3 000 = €3 000
DOL
DOL = 6 000/3 000 = 2
Change in profit
%ΔΠ = 2·(−12%) = −24%
Answer
%ΔΠ = −24%
Check: new profit = 1 760·3 − 3 000 = €2 280.00.
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