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
Value-based pricing sets prices mainly according to:
- AThe prices charged by the cheapest rival
- BThe firm's target profit for the year
- CCustomers' perception of the product's value
- DThe cost of making the product plus a mark-up
2.Marketing principlesHard
In a B2B buying centre, a purchasing assistant controls which supplier brochures reach the engineers. Which role does the assistant play?
- AGatekeeper
- BDecider
- CUser
- DInfluencer
3.Economics conceptsMedium
A country has 950 employed people and 50 unemployed people seeking work. Its unemployment rate is:
- A50%
- B5.3%
- C95%
- D5%
4.Economics conceptsHard
The time-inconsistency problem in monetary policy (Kydland and Prescott) is a key argument for:
- AGovernments setting interest rates directly, especially before elections
- BFixing the money supply at zero growth
- CAbolishing central banks entirely
- DIndependent central banks with a credible commitment to low inflation
5.Financial accountingMedium
Current assets are €300,000 and current liabilities are €150,000. What is the current ratio?
- A2.0
- B1.5
- C0.5
- D4.5
6.Financial accountingHard
A company issues shares at €5 each with a nominal value of €1. The extra €4 per share is recorded as:
- ARevenue
- BRetained earnings
- CA liability
- DShare premium
7.Break-even analysisMedium
A product sells for €29 per unit with a variable cost of €25 per unit. Fixed costs are €2 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €2 000p = €29v = €25profit = €2 000
Q = units
8.Break-even analysisHard
A company sells 6 250 units at €15 each, with a variable cost of €12 per unit and fixed costs of €7 500. By what percentage %ΔΠ does operating profit change if sales volume falls by 10%?
Q = 6 250p = €15v = €12F = €7 500%ΔQ = −10%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: C · Customers' perception of the product's value
Why this is the answer
Value-based pricing estimates what the offer is worth to buyers. Costs then set a floor, and competitor prices are a reference.
Answer
C · Customers' perception of the product's value
2.Marketing principles
Answer: A · Gatekeeper
Why this is the answer
Buying centre roles include users, influencers, buyers, deciders and gatekeepers. Sellers must reach the right people, and gatekeepers can block access to them.
Answer
A · Gatekeeper
3.Economics concepts
Answer: D · 5%
Why this is the answer
The labour force is 950 + 50 = 1,000, so the rate is 50 / 1,000 = 5%.
Answer
D · 5%
4.Economics concepts
Answer: D · Independent central banks with a credible commitment to low inflation
Why this is the answer
If the public expects policymakers to inflate later, expectations and inflation rise; delegating policy to an independent, credible central bank reduces this bias.
Answer
D · Independent central banks with a credible commitment to low inflation
5.Financial accounting
Answer: A · 2.0
Why this is the answer
€300,000 ÷ €150,000 = 2.0, so current assets cover short-term obligations twice.
Answer
A · 2.0
6.Financial accounting
Answer: D · Share premium
Why this is the answer
The amount above nominal value goes to the share premium account in equity; issuing shares is a financing transaction, not income.
Answer
D · Share premium
7.Break-even analysis
Answer: Q = 1000 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 = 29 − 25 = €4
Units for the target profit
Q = (F + profit)/(p − v) = (2 000 + 2 000)/4 = 1 000
Answer
Q = 1 000 units
8.Break-even analysis
Answer: %ΔΠ = −16.67 %
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 = 6 250·3 = €18 750
Π = 18 750 − 7 500 = €11 250
DOL
DOL = 18 750/11 250 = 1.667
Change in profit
%ΔΠ = 1.667·(−10%) = −16.67%
Answer
%ΔΠ = −16.67%
Check: new profit = 5 625·3 − 7 500 = €9 375.00.
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