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?
- AWhat do you think of our new advert?
- BWhy did you choose this brand?
- CHave you bought this product in the last month? (yes/no)
- DHow would you describe your ideal holiday?
2.Marketing principlesHard
In the BCG matrix, a firm has 20% market share and its largest competitor has 40%. What is the firm's relative market share?
- A0.5
- B0.2
- C2.0
- D20%
3.Economics conceptsMedium
A price ceiling set below the equilibrium price typically causes:
- AA shortage
- BA surplus
- CAn increase in supply
- DNo change in the market
4.Economics conceptsHard
The "convergence hypothesis" from the Solow model predicts that:
- ARich countries always grow faster than poor ones, because they have more capital
- BExchange rates converge to a fixed value
- CAll countries will eventually have the same population
- DPoorer countries with similar fundamentals tend to grow faster than richer ones
5.Financial accountingMedium
A machine costs €10,000 and is depreciated at 20% a year on the reducing balance. What is the depreciation charge in year 2?
- A€1,800
- B€2,000
- C€4,000
- D€1,600
6.Financial accountingHard
The standard is 2 labour hours per unit at €20 an hour. 500 units are made in 1,100 hours. What is the labour efficiency variance?
- A€1,000 adverse
- B€2,000 adverse
- C€22,000 adverse
- D€2,000 favourable
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 €15 per unit. Method B, more automated, has fixed costs of €19 500 per year and a variable cost of €12 per unit. At what yearly volume Q do both methods cost the same?
FA = €15 000vA = €15FB = €19 500vB = €12
Q = units
8.Break-even analysisHard
A company sells 2 500 units at €35 each, with a variable cost of €25 per unit and fixed costs of €10 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 10%?
Q = 2 500p = €35v = €25F = €10 000%ΔQ = +10%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: C · 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
C · Have you bought this product in the last month? (yes/no)
2.Marketing principles
Answer: A · 0.5
Why this is the answer
Relative market share = 20% ÷ 40% = 0.5. A value below 1 means the firm is not the market leader, placing it on the low-share side of the matrix.
Answer
A · 0.5
3.Economics concepts
Answer: A · A shortage
Why this is the answer
A binding maximum price raises quantity demanded and lowers quantity supplied, creating excess demand, as with rent control.
Answer
A · A shortage
4.Economics concepts
Answer: D · Poorer countries with similar fundamentals tend to grow faster than richer ones
Why this is the answer
Capital-poor economies have higher returns to investment, so, given similar saving rates and technology, they should catch up (conditional convergence).
Answer
D · Poorer countries with similar fundamentals tend to grow faster than richer ones
5.Financial accounting
Answer: D · €1,600
Why this is the answer
Year 1: 20% × €10,000 = €2,000, leaving €8,000. Year 2: 20% × €8,000 = €1,600. Reducing balance charges less each year.
Answer
D · €1,600
6.Financial accounting
Answer: B · €2,000 adverse
Why this is the answer
Standard hours = 500 × 2 = 1,000. Extra 100 hours × €20 = €2,000 adverse, because more hours were used than the standard allows.
Answer
B · €2,000 adverse
7.Break-even analysis
Answer: Q = 1500 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 + 15Q = 19 500 + 12Q
Solve for Q
Q = (19 500 − 15 000)/(15 − 12) = 1 500
Answer
Q = 1 500 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
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 = 2 500·10 = €25 000
Π = 25 000 − 10 000 = €15 000
DOL
DOL = 25 000/15 000 = 1.667
Change in profit
%ΔΠ = 1.667·(+10%) = +16.67%
Answer
%ΔΠ = +16.67%
Check: new profit = 2 750·10 − 10 000 = €17 500.00.
ExamProblems · examproblems.com/courses/business-fundamentals