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 brand runs heavy consumer advertising so that shoppers ask retailers to stock its product. Which strategy is this?
- AA push strategy
- BA pull strategy
- CA penetration strategy
- DA diversification strategy
2.Marketing principlesHard
During a major sports tournament, a non-sponsor brand runs ads suggesting a link with the event without paying for official rights. What is this called?
- ACause-related marketing
- BGuerrilla distribution
- CAmbush marketing
- DCo-branding
3.Economics conceptsMedium
A public good is:
- ARival and excludable
- BAny good bought by the government
- CNon-rival and non-excludable
- DProvided only by private firms
4.Economics conceptsHard
The Fisher effect predicts that, in the long run, a permanent 2 percentage point rise in expected inflation will:
- ALower nominal interest rates by about 2 points
- BRaise real interest rates by about 2 points
- CRaise nominal interest rates by about 2 points, leaving real rates unchanged
- DHave no effect on nominal interest rates, so real interest rates fall by about 2 points
5.Financial accountingMedium
An asset costs €50,000, has a residual value of €5,000 and a useful life of 5 years. What is the annual straight-line depreciation?
- A€9,000
- B€11,000
- C€10,000
- D€5,000
6.Financial accountingHard
A parent sold goods to its subsidiary at a profit, and the subsidiary still holds them at year end. What must happen on consolidation?
- AThe profit is shown twice, once for each company
- BThe sale is shown as external revenue of the group
- CNothing, because each company is a separate entity
- DThe unrealised profit in inventory is eliminated
7.Break-even analysisMedium
A product sells for €29 with a variable cost of €25 per unit. Fixed costs are €20 000 per month and profit is taxed at 25%. How many units Q must be sold per month to earn €6 000 after tax?
p = €29v = €25F = €20 000T = 25%after-tax profit = €6 000
Q = units
8.Break-even analysisHard
A product sells for €10 per unit, with a variable cost of €6 per unit and fixed costs of €8 000 per year. Budgeted sales are 2 600 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €8 000p = €10v = €6budget = 2 600
MS = %
3Solutions
1.Marketing principles
Answer: B · A pull strategy
Why this is the answer
A pull strategy builds consumer demand that pulls the product through the channel. A push strategy targets intermediaries with trade promotions and personal selling.
Answer
B · A pull strategy
2.Marketing principles
Answer: C · Ambush marketing
Why this is the answer
Ambush marketing tries to gain association with an event without sponsorship. Organisers often protect sponsors through contracts and trademark rules.
Answer
C · Ambush marketing
3.Economics concepts
Answer: C · Non-rival and non-excludable
Why this is the answer
Public goods can be used by many at once and people cannot easily be excluded, leading to free-riding and under-provision by markets.
Answer
C · Non-rival and non-excludable
4.Economics concepts
Answer: C · Raise nominal interest rates by about 2 points, leaving real rates unchanged
Why this is the answer
Lenders demand compensation for expected inflation, so nominal rates move one-for-one with it in the long run while the real rate is set by real factors.
Answer
C · Raise nominal interest rates by about 2 points, leaving real rates unchanged
5.Financial accounting
Answer: A · €9,000
Why this is the answer
(Cost − residual value) ÷ useful life = (€50,000 − €5,000) ÷ 5 = €9,000 per year.
Answer
A · €9,000
6.Financial accounting
Answer: D · The unrealised profit in inventory is eliminated
Why this is the answer
Intra-group sales and purchases are cancelled, and profit on goods still held in the group is removed from inventory and group profit until sold outside.
Answer
D · The unrealised profit in inventory is eliminated
7.Break-even analysis
Answer: Q = 7000 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).
Pre-tax profit needed
6 000/(1 − 0.25) = €8 000
Units needed
Q = (20 000 + 8 000)/4 = 7 000
Answer
Q = 7 000 units
8.Break-even analysis
Answer: MS = 23.08 %
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) = 8 000/4 = 2 000
Margin of safety
MS = (2 600 − 2 000)/2 600·100 = 23.08%
Answer
MS = 23.08%
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