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
Soft drinks are sold in supermarkets, petrol stations, vending machines and kiosks. Which distribution strategy is this?
- AIntensive distribution
- BExclusive distribution
- CSelective distribution
- DDirect distribution only
2.Marketing principlesHard
A manufacturer starts selling online directly to consumers at lower prices than its retailers. Retailers complain. What is this?
- AVertical channel conflict
- BCannibalisation by a rival brand
- CA pull strategy
- DHorizontal channel conflict
3.Economics conceptsMedium
Crowding out refers to:
- AHigher government borrowing raising interest rates and reducing private investment
- BImports replacing domestic production
- COvercrowded public services
- DToo many firms entering a market
4.Economics conceptsHard
In the "Battle of the Sexes" coordination game, how many pure-strategy Nash equilibria are there?
- ATwo
- BFour
- CNone
- DOne
5.Financial accountingMedium
Current assets are €300,000 and current liabilities are €150,000. What is the current ratio?
- A4.5
- B1.5
- C0.5
- D2.0
6.Financial accountingHard
An increase in accounts receivable during the year, in the indirect cash flow method, is:
- ANot relevant to cash flow
- BAdded to profit
- CSubtracted from profit to get operating cash flow
- DShown as an investing outflow
7.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €30 000 per year and a variable cost of €8 per unit. Method B, more automated, has fixed costs of €37 500 per year and a variable cost of €3 per unit. At what yearly volume Q do both methods cost the same?
FA = €30 000vA = €8FB = €37 500vB = €3
Q = units
8.Break-even analysisHard
A company sells 3 000 units at €18 each, with a variable cost of €15 per unit and fixed costs of €6 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 5%?
Q = 3 000p = €18v = €15F = €6 000%ΔQ = +5%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: A · Intensive distribution
Why this is the answer
Intensive distribution suits convenience products that customers buy on impulse and will not search for.
Answer
A · Intensive distribution
2.Marketing principles
Answer: A · Vertical channel conflict
Why this is the answer
Vertical conflict arises between levels, such as manufacturer and retailer. Horizontal conflict is between firms at the same level, such as two retailers.
Answer
A · Vertical channel conflict
3.Economics concepts
Answer: A · Higher government borrowing raising interest rates and reducing private investment
Why this is the answer
When government borrowing raises interest rates, some private investment is no longer profitable, reducing the net effect of fiscal expansion.
Answer
A · Higher government borrowing raising interest rates and reducing private investment
4.Economics concepts
Answer: A · Two
Why this is the answer
Both outcomes where the players choose the same activity are Nash equilibria, so the problem is coordinating on one of them rather than avoiding defection.
Answer
A · Two
5.Financial accounting
Answer: D · 2.0
Why this is the answer
€300,000 ÷ €150,000 = 2.0, so current assets cover short-term obligations twice.
Answer
D · 2.0
6.Financial accounting
Answer: C · Subtracted from profit to get operating cash flow
Why this is the answer
Higher receivables mean some revenue was not received in cash, so the increase is deducted.
Answer
C · Subtracted from profit to get operating cash flow
7.Break-even analysis
Answer: Q = 1500 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).
Equal total costs
30 000 + 8Q = 37 500 + 3Q
Solve for Q
Q = (37 500 − 30 000)/(8 − 3) = 1 500
Answer
Q = 1 500 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: %ΔΠ = 15 %
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 = 3 000·3 = €9 000
Π = 9 000 − 6 000 = €3 000
DOL
DOL = 9 000/3 000 = 3
Change in profit
%ΔΠ = 3·(+5%) = +15%
Answer
%ΔΠ = +15%
Check: new profit = 3 150·3 − 6 000 = €3 450.00.
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