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:
- AReduce product prices for loyal customers
- BInterrupt viewers with as many adverts as possible
- CReplace all customer service with chatbots
- DAttract and keep an audience by offering useful or entertaining content
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
- BHigh threat of new entrants into the market
- CLow bargaining power of suppliers
- 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
- BAn immediate rise in GDP
- CHigher borrowing and spending, which adds to inflationary pressure
- DLower borrowing and spending, reducing inflationary pressure
4.Economics conceptsHard
In the "Battle of the Sexes" coordination game, how many pure-strategy Nash equilibria are there?
- ATwo
- BOne
- CFour
- DNone
5.Financial accountingMedium
Under IAS 16, which cost should be included in the cost of a new machine?
- AInstallation costs needed to get it working
- BGeneral office overheads for the year
- CStaff training costs after it starts operating
- DRepairs carried out two years later
6.Financial accountingHard
A company's debt-to-equity ratio rises sharply. What does this usually indicate?
- AHigher profitability
- BHigher financial risk because the company relies more on borrowed money
- CThat shareholders invested more money
- DBetter liquidity in the short term
7.Break-even analysisMedium
A product sells for €35 per unit with a variable cost of €25 per unit. Fixed costs are €15 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €15 000p = €35v = €25profit = €5 000
Q = units
8.Break-even analysisHard
A product sells for €47 per unit, with a variable cost of €45 per unit and fixed costs of €1 000 per year. Budgeted sales are 900 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €1 000p = €47v = €45budget = 900
MS = %
3Solutions
1.Marketing principles
Answer: D · 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
D · 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: D · 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
D · Lower borrowing and spending, reducing inflationary pressure
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: A · Installation costs needed to get it working
Why this is the answer
Purchase price plus directly attributable costs, such as delivery and installation, are capitalised. Training, later repairs and general overheads are expensed.
Answer
A · Installation costs needed to get it working
6.Financial accounting
Answer: B · Higher financial risk because the company relies more on borrowed money
Why this is the answer
A higher ratio means more leverage: interest and repayments must be met whatever the results, so financial risk rises, although returns to shareholders may also rise.
Answer
B · Higher financial risk because the company relies more on borrowed money
7.Break-even analysis
Answer: Q = 2000 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 = 35 − 25 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (15 000 + 5 000)/10 = 2 000
Answer
Q = 2 000 units
8.Break-even analysis
Answer: MS = 44.44 %
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) = 1 000/2 = 500
Margin of safety
MS = (900 − 500)/900·100 = 44.44%
Answer
MS = 44.44%
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