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
Ansoff's matrix strategy of selling existing products in new markets is called:
- ADiversification
- BMarket penetration
- CMarket development
- DProduct development
2.Marketing principlesHard
A cinema sells small popcorn for €4 and large for €8. Adding a medium size at €7.50 makes many more people buy the large. Which effect is this?
- AThe decoy effect
- BPenetration pricing
- CPrice skimming
- DCaptive product pricing
3.Economics conceptsMedium
A savings account pays a nominal interest rate of 6% and inflation is 4%. The approximate real interest rate is:
- A1.5%
- B24%
- C2%
- D10%
4.Economics conceptsHard
The Lerner index (P − MC)/P for a profit-maximising monopolist equals 1/|PED|. If |PED| = 4, the price is:
- A4 times marginal cost
- BEqual to marginal cost
- C25% above marginal cost, as a share of price
- D75% above marginal cost, as a share of price
5.Financial accountingMedium
A machine with a carrying amount of €3,000 is sold for €4,000. What is recorded in the income statement?
- ARevenue of €4,000
- BA gain on disposal of €1,000
- CA gain on disposal of €4,000
- DA loss on disposal of €1,000
6.Financial accountingHard
Tax rules allow faster depreciation of a machine than the company uses in its accounts. What arises under IAS 12?
- ANo tax effect at all
- BA deferred tax liability
- CA refund of current tax paid
- DA deferred tax asset
7.Break-even analysisMedium
A product sells for €45 per unit with a variable cost of €25 per unit. Fixed costs are €20 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €20 000p = €45v = €25profit = €5 000
Q = units
8.Break-even analysisHard
A product sells for €24 per unit, with a variable cost of €12 per unit and fixed costs of €18 000 per year. Budgeted sales are 1 950 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €18 000p = €24v = €12budget = 1 950
MS = %
3Solutions
1.Marketing principles
Answer: C · Market development
Why this is the answer
Market penetration: existing products, existing markets; market development: existing products, new markets; product development: new products, existing markets; diversification: new products, new markets.
Answer
C · Market development
2.Marketing principles
Answer: A · The decoy effect
Why this is the answer
A decoy is an option that is slightly worse than the target, making the target look like good value by comparison. Choices depend on the set of options shown.
Answer
A · The decoy effect
3.Economics concepts
Answer: C · 2%
Why this is the answer
The real interest rate is approximately the nominal rate minus inflation: 6% − 4% = 2%.
Answer
C · 2%
4.Economics concepts
Answer: C · 25% above marginal cost, as a share of price
Why this is the answer
The markup (P − MC)/P = 1/4 = 0.25, so a quarter of the price is a margin above MC; more elastic demand means less market power.
Answer
C · 25% above marginal cost, as a share of price
5.Financial accounting
Answer: B · 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
B · A gain on disposal of €1,000
6.Financial accounting
Answer: B · A deferred tax liability
Why this is the answer
The tax base falls faster than the carrying amount, creating a taxable temporary difference. The future extra tax is recognised now as a deferred tax liability.
Answer
B · A deferred tax liability
7.Break-even analysis
Answer: Q = 1250 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 = 45 − 25 = €20
Units for the target profit
Q = (F + profit)/(p − v) = (20 000 + 5 000)/20 = 1 250
Answer
Q = 1 250 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) = 18 000/12 = 1 500
Margin of safety
MS = (1 950 − 1 500)/1 950·100 = 23.08%
Answer
MS = 23.08%
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