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 firm's target profit for the year
- BCustomers' perception of the product's value
- CThe cost of making the product plus a mark-up
- DThe prices charged by the cheapest rival
2.Marketing principlesHard
Under the EU General Data Protection Regulation (GDPR), sending marketing emails based on consent requires consent that is:
- AFreely given, specific, informed and unambiguous
- BImplied by pre-ticked boxes
- CAssumed when a customer visits the website
- DGiven once for all future purposes by any company
3.Economics conceptsMedium
Unemployment benefits and progressive income taxes are called automatic stabilisers because they:
- AFix the exchange rate automatically
- BReduce fluctuations in demand without new government decisions
- CPrevent all recessions from happening
- DKeep the government budget balanced in every year of the business cycle
4.Economics conceptsHard
A liquidity trap is a situation where:
- AThe central bank raises interest rates sharply to fight high and rapidly rising inflation
- BInflation is very high and rising
- CBanks have no money left to lend
- DInterest rates are near zero and further monetary expansion has little effect on demand
5.Financial accountingMedium
Profit for ordinary shareholders is €500,000 and there are 1,000,000 ordinary shares. What are basic earnings per share?
- A€5.00
- B€0.50
- C€2.00
- D€0.05
6.Financial accountingHard
In the indirect method of the cash flow statement, depreciation is:
- ASubtracted from net profit
- BShown in financing activities
- CAdded back to net profit because it is a non-cash expense
- DIgnored completely
7.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €25 000 per year and a variable cost of €15 per unit. Method B, more automated, has fixed costs of €29 000 per year and a variable cost of €11 per unit. At what yearly volume Q do both methods cost the same?
FA = €25 000vA = €15FB = €29 000vB = €11
Q = units
8.Break-even analysisHard
A product sells for €18 per unit, with a variable cost of €6 per unit and fixed costs of €24 000 per year. Budgeted sales are 2 300 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €24 000p = €18v = €6budget = 2 300
MS = %
3Solutions
1.Marketing principles
Answer: B · 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
B · Customers' perception of the product's value
2.Marketing principles
Answer: A · Freely given, specific, informed and unambiguous
Why this is the answer
Consent must be a clear affirmative act; pre-ticked boxes or silence are not valid, and it must be as easy to withdraw as to give.
Answer
A · Freely given, specific, informed and unambiguous
3.Economics concepts
Answer: B · Reduce fluctuations in demand without new government decisions
Why this is the answer
In a downturn tax revenue falls and benefit payments rise automatically, supporting incomes and spending; the reverse happens in a boom.
Answer
B · Reduce fluctuations in demand without new government decisions
4.Economics concepts
Answer: D · Interest rates are near zero and further monetary expansion has little effect on demand
Why this is the answer
When nominal rates are near their lower bound, people hold extra money rather than spend it, so conventional monetary policy loses power and fiscal policy or unconventional tools matter more.
Answer
D · Interest rates are near zero and further monetary expansion has little effect on demand
5.Financial accounting
Answer: B · €0.50
Why this is the answer
Basic EPS = €500,000 ÷ 1,000,000 = €0.50 per share. Dividing the share price by EPS gives the P/E ratio.
Answer
B · €0.50
6.Financial accounting
Answer: C · 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
C · Added back to net profit because it is a non-cash expense
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).
Equal total costs
25 000 + 15Q = 29 000 + 11Q
Solve for Q
Q = (29 000 − 25 000)/(15 − 11) = 1 000
Answer
Q = 1 000 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: MS = 13.04 %
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) = 24 000/12 = 2 000
Margin of safety
MS = (2 300 − 2 000)/2 300·100 = 13.04%
Answer
MS = 13.04%
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