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
In online advertising, what does CPM mean?
- ACost per minute of video viewing
- BClicks per month
- CCost per thousand impressions
- DCustomers per market
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
If the ECB raises its main interest rate, the most likely short-term effect is:
- AA fall in the value of the euro
- BLower borrowing and spending, reducing inflationary pressure
- CHigher borrowing and spending, which adds to inflationary pressure
- DAn immediate rise in GDP
4.Economics conceptsHard
The J-curve effect describes why, after a depreciation, the trade balance may:
- AWorsen at first and then improve
- BRemain unchanged for many years
- CImprove at first and then worsen
- DImprove immediately and permanently
5.Financial accountingMedium
Why can a profitable company run out of cash?
- AProfitable companies never pay taxes
- BCash is not recorded in accounting
- CProfit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
- DProfit always equals cash
6.Financial accountingHard
In the indirect method of the cash flow statement, depreciation is:
- ASubtracted from net profit
- BAdded back to net profit because it is a non-cash expense
- CShown in financing activities
- DIgnored completely
7.Break-even analysisMedium
A product sells for €30 per unit with a variable cost of €20 per unit. Fixed costs are €25 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €25 000p = €30v = €20profit = €6 000
Q = units
8.Break-even analysisHard
A company sells 1 250 units per month at €35 each, with a variable cost of €25 per unit and fixed costs of €10 000 per month. The variable cost rises by €5 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 1 250p = €35v = €25 → €30F = €10 000
Q = units
3Solutions
1.Marketing principles
Answer: C · Cost per thousand impressions
Why this is the answer
CPM is the price for 1,000 ad impressions. It suits awareness goals; cost per click (CPC) and cost per acquisition (CPA) tie spending to actions.
Answer
C · Cost per thousand impressions
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: B · Lower borrowing and spending, reducing inflationary pressure
Why this is the answer
Higher rates make credit more expensive and saving more attractive, reducing demand and inflation; they also tend to strengthen the currency.
Answer
B · Lower borrowing and spending, reducing inflationary pressure
4.Economics concepts
Answer: A · Worsen at first and then improve
Why this is the answer
In the short run, volumes are slow to adjust while import prices rise immediately, so the balance worsens before the Marshall–Lerner condition takes hold.
Answer
A · Worsen at first and then improve
5.Financial accounting
Answer: C · Profit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
Why this is the answer
Profit is measured on an accrual basis; growth can tie up cash in inventory and receivables, so cash flow can be negative despite profits.
Answer
C · Profit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
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 = 3100 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 = 30 − 20 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (25 000 + 6 000)/10 = 3 100
Answer
Q = 3 100 units
8.Break-even analysis
Answer: Q = 2500 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 = 1 250·(35 − 25) − 10 000 = €2 500
New contribution margin per unit
35 − 30 = €5
Units for the same profit
Q = (10 000 + 2 500)/5 = 2 500
Answer
Q = 2 500 units
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