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:
- AMarket development
- BProduct development
- CMarket penetration
- DDiversification
2.Marketing principlesHard
An airline can buy a certain aircraft model only from one manufacturer, and switching to another model is very costly. In Porter's five forces, what does this mean?
- AHigh bargaining power of buyers
- BLow bargaining power of suppliers
- CHigh threat of new entrants into the market
- DHigh bargaining power of suppliers
3.Economics conceptsMedium
In a simple closed economy without taxes, the MPC is 0.8. The Keynesian spending multiplier is:
- A0.8
- B1.25
- C5
- D8
4.Economics conceptsHard
A deadweight loss represents:
- AThe loss of total surplus when output differs from the efficient level
- BThe tax revenue collected by the government
- CLosses made by firms that are forced to leave the market in the long run
- DThe profit of a monopolist
5.Financial accountingMedium
When preparing a bank reconciliation, which item explains why the bank statement balance is higher than the cash book balance?
- ACheques issued but not yet presented to the bank
- BBank charges not yet entered in the cash book
- CCash deposited but not yet credited on the bank statement
- DA direct debit not yet entered in the cash book
6.Financial accountingHard
An increase in accounts receivable during the year, in the indirect cash flow method, is:
- AShown as an investing outflow
- BSubtracted from profit to get operating cash flow
- CAdded to profit
- DNot relevant to cash flow
7.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €10 000 per year and a variable cost of €15 per unit. Method B, more automated, has fixed costs of €11 000 per year and a variable cost of €13 per unit. At what yearly volume Q do both methods cost the same?
FA = €10 000vA = €15FB = €11 000vB = €13
Q = units
8.Break-even analysisHard
A product sells for €21 per unit, with a variable cost of €15 per unit and fixed costs of €24 000 per year. Budgeted sales are 5 000 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €24 000p = €21v = €15budget = 5 000
MS = %
3Solutions
1.Marketing principles
Answer: A · 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
A · Market development
2.Marketing principles
Answer: D · High bargaining power of suppliers
Why this is the answer
When suppliers are concentrated and switching is expensive, they can demand higher prices or better terms, reducing industry profitability.
Answer
D · High bargaining power of suppliers
3.Economics concepts
Answer: C · 5
Why this is the answer
1 / (1 − 0.8) = 1 / 0.2 = 5, so an extra €1 of spending can raise income by up to €5.
Answer
C · 5
4.Economics concepts
Answer: A · The loss of total surplus when output differs from the efficient level
Why this is the answer
Deadweight loss is the reduction in combined consumer and producer surplus caused by distortions such as taxes, monopoly or price controls.
Answer
A · The loss of total surplus when output differs from the efficient level
5.Financial accounting
Answer: A · Cheques issued but not yet presented to the bank
Why this is the answer
Unpresented cheques have reduced the cash book but not the bank balance. Outstanding deposits, bank charges and unrecorded direct debits work the other way.
Answer
A · Cheques issued but not yet presented to the bank
6.Financial accounting
Answer: B · 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
B · Subtracted from profit to get operating cash flow
7.Break-even analysis
Answer: Q = 500 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
10 000 + 15Q = 11 000 + 13Q
Solve for Q
Q = (11 000 − 10 000)/(15 − 13) = 500
Answer
Q = 500 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: MS = 20 %
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) = 24 000/6 = 4 000
Margin of safety
MS = (5 000 − 4 000)/5 000·100 = 20%
Answer
MS = 20%
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