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
Content marketing mainly aims to:
- AReplace all customer service with chatbots
- BAttract and keep an audience by offering useful or entertaining content
- CInterrupt viewers with as many adverts as possible
- DReduce product prices for loyal customers
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 threat of new entrants into the market
- BLow bargaining power of suppliers
- CHigh bargaining power of buyers
- DHigh bargaining power of suppliers
3.Economics conceptsMedium
When a central bank buys government bonds from banks in open market operations, it usually:
- AHas no effect on the money supply
- BReduces bank reserves and so shrinks the money supply
- CIncreases bank reserves and the money supply
- DRaises tax revenue for the government
4.Economics conceptsHard
Which is a key difference between the CPI and the GDP deflator?
- AThe CPI covers investment goods; the GDP deflator does not
- BThe CPI includes prices of imported consumer goods; the GDP deflator covers only domestically produced goods
- CThe GDP deflator includes imported goods; the CPI does not
- DThey always give exactly the same inflation rate
5.Financial accountingMedium
Operating profit is €120,000 and interest expense is €30,000. What is interest cover?
- A4 times
- B90,000 times
- C0.25 times
- D3 times
6.Financial accountingHard
In the indirect method of the cash flow statement, depreciation is:
- AAdded back to net profit because it is a non-cash expense
- BIgnored completely
- CShown in financing activities
- DSubtracted from net profit
7.Break-even analysisMedium
A product sells for €11 per unit with a variable cost of €6 per unit. Fixed costs are €6 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €6 000p = €11v = €6profit = €5 000
Q = units
8.Break-even analysisHard
A company sells 4 000 units at €48 each, with a variable cost of €45 per unit and fixed costs of €6 000. By what percentage %ΔΠ does operating profit change if sales volume falls by 12%?
Q = 4 000p = €48v = €45F = €6 000%ΔQ = −12%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: B · Attract and keep an audience by offering useful or entertaining content
Why this is the answer
Content marketing provides value first, such as guides, videos or articles. It builds trust and search visibility, leading to sales over time.
Answer
B · Attract and keep an audience by offering useful or entertaining content
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 · Increases bank reserves and the money supply
Why this is the answer
Buying bonds injects reserves into the banking system, which tends to increase the money supply and lower interest rates.
Answer
C · Increases bank reserves and the money supply
4.Economics concepts
Answer: B · The CPI includes prices of imported consumer goods; the GDP deflator covers only domestically produced goods
Why this is the answer
The CPI uses a fixed basket of consumer goods, including imports, while the deflator covers all domestically produced output with changing weights.
Answer
B · The CPI includes prices of imported consumer goods; the GDP deflator covers only domestically produced goods
5.Financial accounting
Answer: A · 4 times
Why this is the answer
€120,000 ÷ €30,000 = 4. The company earns its interest four times over; low cover signals a risk of not meeting interest payments.
Answer
A · 4 times
6.Financial accounting
Answer: A · 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
A · Added back to net profit because it is a non-cash expense
7.Break-even analysis
Answer: Q = 2200 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 = 11 − 6 = €5
Units for the target profit
Q = (F + profit)/(p − v) = (6 000 + 5 000)/5 = 2 200
Answer
Q = 2 200 units
8.Break-even analysis
Answer: %ΔΠ = −24 %
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 = 4 000·3 = €12 000
Π = 12 000 − 6 000 = €6 000
DOL
DOL = 12 000/6 000 = 2
Change in profit
%ΔΠ = 2·(−12%) = −24%
Answer
%ΔΠ = −24%
Check: new profit = 3 520·3 − 6 000 = €4 560.00.
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