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 produce statistically representative percentages for the market
- BTo survey thousands of people cheaply
- CTo explore customers' motives and feelings in detail
- DTo avoid any interviewer influence
2.Marketing principlesHard
Geoffrey Moore's "chasm" in technology markets refers to the gap between which adopter groups?
- AEarly adopters and the early majority
- BLate majority and laggards
- CEarly majority and late majority
- DInnovators and early adopters
3.Economics conceptsMedium
Stagflation is a combination of:
- AHigh growth and falling prices
- BHigh inflation and high unemployment with low growth
- CDeflation and rapid growth
- DLow inflation and low unemployment
4.Economics conceptsHard
Why is the real-world government spending multiplier usually smaller than the simple 1/(1 − MPC)?
- ATaxes, imports and crowding out leak part of each round of spending
- BGovernments cannot borrow money
- CThe MPC is always above 1
- DConsumers never spend extra income
5.Financial accountingMedium
The prudence (conservatism) concept suggests that accountants should:
- AAvoid overstating assets and income under uncertainty
- BValue assets at their selling price
- CIgnore possible losses
- DAlways record the highest possible profit to attract investors
6.Financial accountingHard
Operating profit is €200,000 and capital employed (equity plus non-current liabilities) is €1,000,000. What is ROCE?
- A20%
- B50%
- C2%
- D5%
7.Break-even analysisMedium
A product sells for €32 per unit with a variable cost of €12 per unit. Fixed costs are €50 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €50 000p = €32v = €12profit = €6 000
Q = units
8.Break-even analysisHard
A product sells for €14 per unit, with a variable cost of €6 per unit and fixed costs of €4 000 per year. Budgeted sales are 900 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €4 000p = €14v = €6budget = 900
MS = %
3Solutions
1.Marketing principles
Answer: C · 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
C · To explore customers' motives and feelings in detail
2.Marketing principles
Answer: A · Early adopters and the early majority
Why this is the answer
Early adopters accept risk for advantage, while the early majority want proven, complete solutions and references. Many products fail to make this transition.
Answer
A · Early adopters and the early majority
3.Economics concepts
Answer: B · High inflation and high unemployment with low growth
Why this is the answer
Stagflation combines stagnant output, rising unemployment and high inflation, usually after supply shocks.
Answer
B · High inflation and high unemployment with low growth
4.Economics concepts
Answer: A · Taxes, imports and crowding out leak part of each round of spending
Why this is the answer
Income taxes, spending on imports, higher interest rates (crowding out) and saving reduce the extra spending in each round, so the multiplier shrinks.
Answer
A · Taxes, imports and crowding out leak part of each round of spending
5.Financial accounting
Answer: A · Avoid overstating assets and income under uncertainty
Why this is the answer
Prudence means exercising caution so that assets and income are not overstated and liabilities and expenses not understated.
Answer
A · Avoid overstating assets and income under uncertainty
6.Financial accounting
Answer: A · 20%
Why this is the answer
ROCE = €200,000 ÷ €1,000,000 = 20%. It measures returns on all long-term finance, so it can be compared with the cost of borrowing.
Answer
A · 20%
7.Break-even analysis
Answer: Q = 2800 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 = 32 − 12 = €20
Units for the target profit
Q = (F + profit)/(p − v) = (50 000 + 6 000)/20 = 2 800
Answer
Q = 2 800 units
8.Break-even analysis
Answer: MS = 44.44 %
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) = 4 000/8 = 500
Margin of safety
MS = (900 − 500)/900·100 = 44.44%
Answer
MS = 44.44%
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