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 researcher divides the population into age groups and draws a random sample from each group. This is:
- AStratified random sampling
- BQuota sampling with free choice
- CConvenience sampling
- DSnowball sampling
2.Marketing principlesHard
In the BCG matrix, a firm has 20% market share and its largest competitor has 40%. What is the firm's relative market share?
- A2.0
- B0.5
- C20%
- D0.2
3.Economics conceptsMedium
A firm has spent €1 million on research for a product that now looks unprofitable. When deciding whether to continue, the €1 million should be:
- AAdded to the expected future costs
- BIgnored, because it is a sunk cost
- CRecovered by raising prices
- DTreated as the opportunity cost of stopping
4.Economics conceptsHard
The "Taylor principle" says that, to stabilise inflation, a central bank should respond to a 1 percentage point rise in inflation by:
- ACutting the nominal rate
- BKeeping the nominal rate unchanged
- CRaising the nominal interest rate, but by less than 1 percentage point
- DRaising the nominal interest rate by more than 1 percentage point
5.Financial accountingMedium
Budgeted sales are 1,500 units and the break-even point is 1,000 units. What is the margin of safety?
- A1,500 units
- B2,500 units
- C500 units
- D1,000 units
6.Financial accountingHard
In the indirect method of the cash flow statement, depreciation is:
- AShown in financing activities
- BAdded back to net profit because it is a non-cash expense
- CIgnored completely
- DSubtracted from net profit
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 €12 per unit. Method B, more automated, has fixed costs of €18 000 per year and a variable cost of €10 per unit. At what yearly volume Q do both methods cost the same?
FA = €10 000vA = €12FB = €18 000vB = €10
Q = units
8.Break-even analysisHard
A company sells 7 500 units per month at €28 each, with a variable cost of €20 per unit and fixed costs of €40 000 per month. The variable cost rises by €3 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 7 500p = €28v = €20 → €23F = €40 000
Q = units
3Solutions
1.Marketing principles
Answer: A · Stratified random sampling
Why this is the answer
Stratified sampling ensures each subgroup is represented while keeping random selection. Quota sampling sets numbers per group but lets interviewers choose people, so it is non-probability.
Answer
A · Stratified random sampling
2.Marketing principles
Answer: B · 0.5
Why this is the answer
Relative market share = 20% ÷ 40% = 0.5. A value below 1 means the firm is not the market leader, placing it on the low-share side of the matrix.
Answer
B · 0.5
3.Economics concepts
Answer: B · Ignored, because it is a sunk cost
Why this is the answer
Sunk costs cannot be recovered and do not change with the decision, so rational choices compare only future costs and benefits.
Answer
B · Ignored, because it is a sunk cost
4.Economics concepts
Answer: D · Raising the nominal interest rate by more than 1 percentage point
Why this is the answer
Only by raising nominal rates more than one-for-one does the real interest rate rise, cooling demand and bringing inflation back down.
Answer
D · Raising the nominal interest rate by more than 1 percentage point
5.Financial accounting
Answer: C · 500 units
Why this is the answer
Margin of safety = budgeted sales − break-even sales = 500 units, or one third of budgeted sales.
Answer
C · 500 units
6.Financial accounting
Answer: B · Added back to net profit because it is a non-cash expense
Why this is the answer
Starting from profit, non-cash charges like depreciation are added back, and changes in working capital are adjusted.
Answer
B · Added back to net profit because it is a non-cash expense
7.Break-even analysis
Answer: Q = 4000 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 + 12Q = 18 000 + 10Q
Solve for Q
Q = (18 000 − 10 000)/(12 − 10) = 4 000
Answer
Q = 4 000 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: Q = 12000 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 = 7 500·(28 − 20) − 40 000 = €20 000
New contribution margin per unit
28 − 23 = €5
Units for the same profit
Q = (40 000 + 20 000)/5 = 12 000
Answer
Q = 12 000 units
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