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
Why might a researcher choose in-depth interviews rather than a large questionnaire?
- ATo explore customers' motives and feelings in detail
- BTo survey thousands of people cheaply
- CTo avoid any interviewer influence
- DTo produce statistically representative percentages for the market
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?
- A0.2
- B2.0
- C0.5
- D20%
3.Economics conceptsMedium
A country has 950 employed people and 50 unemployed people seeking work. Its unemployment rate is:
- A95%
- B5.3%
- C5%
- D50%
4.Economics conceptsHard
The Laffer curve illustrates that:
- ATax revenue is unrelated to tax rates
- BBeyond some point, raising tax rates can reduce total tax revenue
- CLower tax rates always reduce tax revenue, whatever the starting rate
- DHigher tax rates always increase tax revenue
5.Financial accountingMedium
Why can a profitable company run out of cash?
- AProfitable companies never pay taxes
- BCash is not recorded in accounting
- CProfit always equals cash
- DProfit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
6.Financial accountingHard
A company borrows at 5% interest to invest in assets that earn 12%. What is the likely effect on return on equity?
- AROE stays the same, because debt is not equity
- BROE rises and financial risk falls
- CROE falls, because interest is an expense
- DROE rises, but financial risk also increases
7.Break-even analysisMedium
A company sells 3 200 units at €20 each. The variable cost is €15 per unit and fixed costs are €10 000. Find the degree of operating leverage DOL at this sales level.
Q = 3 200p = €20v = €15F = €10 000
DOL =
8.Break-even analysisHard
A product sells for €35 per unit, with a variable cost of €15 per unit and fixed costs of €40 000 per year. Budgeted sales are 2 500 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €40 000p = €35v = €15budget = 2 500
MS = %
3Solutions
1.Marketing principles
Answer: A · To explore customers' motives and feelings in detail
Why this is the answer
In-depth interviews give rich, qualitative insight into why people behave as they do. Questionnaires suit measuring how many people think or do something.
Answer
A · To explore customers' motives and feelings in detail
2.Marketing principles
Answer: C · 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
C · 0.5
3.Economics concepts
Answer: C · 5%
Why this is the answer
The labour force is 950 + 50 = 1,000, so the rate is 50 / 1,000 = 5%.
Answer
C · 5%
4.Economics concepts
Answer: B · Beyond some point, raising tax rates can reduce total tax revenue
Why this is the answer
Very high rates discourage taxed activity or encourage avoidance, so revenue peaks at some rate between 0 and 100%; where that peak lies is debated.
Answer
B · Beyond some point, raising tax rates can reduce total tax revenue
5.Financial accounting
Answer: D · Profit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
Why this is the answer
Profit is measured on an accrual basis; growth can tie up cash in inventory and receivables, so cash flow can be negative despite profits.
Answer
D · Profit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
6.Financial accounting
Answer: D · ROE rises, but financial risk also increases
Why this is the answer
Positive financial leverage: assets earn more than the debt costs, so profit per euro of equity rises. If returns drop below 5%, leverage works against shareholders.
Answer
D · ROE rises, but financial risk also increases
7.Break-even analysis
Answer: DOL = 2.667
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.
Total contribution margin
CM = 3 200·(20 − 15) = €16 000
Operating profit
Π = 16 000 − 10 000 = €6 000
DOL
DOL = 16 000/6 000 = 2.667
Answer
DOL = 2.667
8.Break-even analysis
Answer: MS = 20 %
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) = 40 000/20 = 2 000
Margin of safety
MS = (2 500 − 2 000)/2 500·100 = 20%
Answer
MS = 20%
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