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 luxury watch brand sells only through a few carefully chosen dealers in each country. Which distribution strategy is this?
- ASelective distribution in all outlets
- BMass distribution
- CExclusive distribution
- DIntensive distribution
2.Marketing principlesHard
A supermarket sells bread below cost to attract shoppers who then buy other, higher-margin items. This is:
- APrice skimming
- BValue-based pricing
- CLoss leader pricing
- DCost-plus pricing
3.Economics conceptsMedium
A sharp rise in world oil prices leading to higher inflation is an example of:
- ADisinflation
- BCost-push inflation
- CDeflation
- DDemand-pull inflation
4.Economics conceptsHard
Why does the deadweight loss of a tax grow when the good's demand and supply are more elastic?
- AElastic markets have no consumer surplus
- BThe government collects more tax revenue
- CQuantity traded falls more, so more mutually beneficial trades are lost
- DPrices do not change, so consumers bear the whole burden of the tax instead
5.Financial accountingMedium
A machine with a carrying amount of €3,000 is sold for €4,000. What is recorded in the income statement?
- AA gain on disposal of €4,000
- BA loss on disposal of €1,000
- CRevenue of €4,000
- DA gain on disposal of €1,000
6.Financial accountingHard
Goodwill arises in a business combination when:
- AA company has a good reputation
- BThe consideration paid exceeds the fair value of identifiable net assets acquired
- CAssets are revalued upwards
- DThe acquired company makes a loss
7.Break-even analysisMedium
A product sells for €40 with a variable cost of €25 per unit. Fixed costs are €22 500 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €4 500 after tax?
p = €40v = €25F = €22 500T = 20%after-tax profit = €4 500
Q = units
8.Break-even analysisHard
A company sells 5 000 units per month at €12 each, with a variable cost of €6 per unit and fixed costs of €12 000 per month. The variable cost rises by €1 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 5 000p = €12v = €6 → €7F = €12 000
Q = units
3Solutions
1.Marketing principles
Answer: C · Exclusive distribution
Why this is the answer
Exclusive distribution uses very few outlets to keep control and a premium image. Intensive distribution places products in as many outlets as possible.
Answer
C · Exclusive distribution
2.Marketing principles
Answer: C · Loss leader pricing
Why this is the answer
A loss leader brings traffic into the store. It works when customers buy enough profitable items during the same visit.
Answer
C · Loss leader pricing
3.Economics concepts
Answer: B · Cost-push inflation
Why this is the answer
Higher input costs shift aggregate supply to the left, raising prices and possibly lowering output; demand-pull inflation comes from excess aggregate demand.
Answer
B · Cost-push inflation
4.Economics concepts
Answer: C · Quantity traded falls more, so more mutually beneficial trades are lost
Why this is the answer
The more responsive buyers and sellers are, the more the tax reduces quantity, and the bigger the triangle of lost surplus; DWL also rises roughly with the square of the tax.
Answer
C · Quantity traded falls more, so more mutually beneficial trades are lost
5.Financial accounting
Answer: D · A gain on disposal of €1,000
Why this is the answer
Gain or loss on disposal = proceeds − carrying amount = €4,000 − €3,000 = €1,000 gain. It is not part of normal revenue.
Answer
D · A gain on disposal of €1,000
6.Financial accounting
Answer: B · The consideration paid exceeds the fair value of identifiable net assets acquired
Why this is the answer
Goodwill = consideration − fair value of identifiable net assets. Under IFRS it is not amortised but tested for impairment annually.
Answer
B · The consideration paid exceeds the fair value of identifiable net assets acquired
7.Break-even analysis
Answer: Q = 1875 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
4 500/(1 − 0.2) = €5 625
Units needed
Q = (22 500 + 5 625)/15 = 1 875
Answer
Q = 1 875 units
8.Break-even analysis
Answer: Q = 6000 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 = 5 000·(12 − 6) − 12 000 = €18 000
New contribution margin per unit
12 − 7 = €5
Units for the same profit
Q = (12 000 + 18 000)/5 = 6 000
Answer
Q = 6 000 units
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