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
Which of these is a closed question in a survey?
- AWhy did you choose this brand?
- BWhat do you think of our new advert?
- CHow would you describe your ideal holiday?
- DHave you bought this product in the last month? (yes/no)
2.Marketing principlesHard
In conjoint analysis, researchers:
- ACount website visitors
- BAnalyse competitors' financial statements
- CObserve shoppers in a store without asking questions
- DAsk respondents to choose between product profiles to estimate the value of each attribute
3.Economics conceptsMedium
A country imposes a tariff on imported steel. Which effect is most likely?
- ADomestic consumers gain surplus
- BDomestic steel prices fall and imports rise
- CDomestic steel prices rise and domestic production increases
- DThe world price of steel rises sharply for all countries that trade it
4.Economics conceptsHard
Okun's law describes:
- AThe link between money supply and prices
- BThe relationship between tax rates and revenue
- CA negative relationship between output growth and changes in unemployment
- DA positive relationship between inflation and nominal interest rates over time
5.Financial accountingMedium
Net working capital is:
- ATotal assets minus total liabilities
- BRevenue minus operating expenses
- CCurrent assets minus current liabilities
- DNon-current assets minus long-term loans
6.Financial accountingHard
Under the IAS 16 revaluation model, a building is revalued upwards for the first time. Where does the gain go?
- ATo other comprehensive income and a revaluation surplus in equity
- BTo a provision on the balance sheet
- CTo retained earnings as a realised profit
- DTo revenue in the income statement
7.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €15 000 per year and a variable cost of €8 per unit. Method B, more automated, has fixed costs of €16 600 per year and a variable cost of €6 per unit. At what yearly volume Q do both methods cost the same?
FA = €15 000vA = €8FB = €16 600vB = €6
Q = units
8.Break-even analysisHard
A product sells for €33 per unit, with a variable cost of €18 per unit and fixed costs of €30 000 per year. Budgeted sales are 3 200 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €30 000p = €33v = €18budget = 3 200
MS = %
3Solutions
1.Marketing principles
Answer: D · Have you bought this product in the last month? (yes/no)
Why this is the answer
Closed questions offer set answers and are easy to analyse statistically. Open questions let people answer in their own words, giving richer but harder-to-code data.
Answer
D · Have you bought this product in the last month? (yes/no)
2.Marketing principles
Answer: D · Ask respondents to choose between product profiles to estimate the value of each attribute
Why this is the answer
Conjoint analysis infers the part-worth utility of attributes (such as price, brand, features) from respondents' choices or rankings of combinations.
Answer
D · Ask respondents to choose between product profiles to estimate the value of each attribute
3.Economics concepts
Answer: C · Domestic steel prices rise and domestic production increases
Why this is the answer
The tariff raises the domestic price, increasing domestic output and government revenue but reducing consumer surplus and creating deadweight losses.
Answer
C · Domestic steel prices rise and domestic production increases
4.Economics concepts
Answer: C · A negative relationship between output growth and changes in unemployment
Why this is the answer
Okun observed that unemployment falls when real GDP grows faster than its trend rate and rises when growth is below trend.
Answer
C · A negative relationship between output growth and changes in unemployment
5.Financial accounting
Answer: C · Current assets minus current liabilities
Why this is the answer
Working capital measures the short-term resources available for daily operations: inventory, receivables and cash minus short-term obligations.
Answer
C · Current assets minus current liabilities
6.Financial accounting
Answer: A · To other comprehensive income and a revaluation surplus in equity
Why this is the answer
Upward revaluations are credited to a revaluation surplus via OCI, unless they reverse an earlier decrease recognised in profit or loss.
Answer
A · To other comprehensive income and a revaluation surplus in equity
7.Break-even analysis
Answer: Q = 800 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
15 000 + 8Q = 16 600 + 6Q
Solve for Q
Q = (16 600 − 15 000)/(8 − 6) = 800
Answer
Q = 800 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: MS = 37.5 %
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) = 30 000/15 = 2 000
Margin of safety
MS = (3 200 − 2 000)/3 200·100 = 37.5%
Answer
MS = 37.5%
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