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 do many firms invest in customer retention and relationship marketing?
- AKeeping existing customers is usually cheaper than winning new ones
- BLoyal customers always accept any price rise
- CNew customers are never profitable
- DRetention removes the need for any advertising
2.Marketing principlesHard
Which conditions are needed for price discrimination (charging different groups different prices) to work?
- AThe product must be sold only in one shop
- BThe firm must have no fixed costs
- CSegments with different price sensitivity that can be separated, and little reselling between them
- DAll customers must have identical price sensitivity
3.Economics conceptsMedium
A sharp rise in world oil prices leading to higher inflation is an example of:
- ACost-push inflation
- BDisinflation
- CDeflation
- DDemand-pull inflation
4.Economics conceptsHard
Which is a key difference between the CPI and the GDP deflator?
- AThey always give exactly the same inflation rate
- BThe GDP deflator includes imported goods; the CPI does not
- CThe CPI covers investment goods; the GDP deflator does not
- DThe CPI includes prices of imported consumer goods; the GDP deflator covers only domestically produced goods
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 IFRS, how is purchased goodwill treated after acquisition?
- AIt is amortised over 20 years
- BIt is revalued upwards every year
- CIt is not amortised but tested for impairment at least annually
- DIt is written off against equity immediately
7.Break-even analysisMedium
A product sells for €25 per unit with a variable cost of €15 per unit. Fixed costs are €10 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €10 000p = €25v = €15profit = €6 000
Q = units
8.Break-even analysisHard
A product sells for €11 per unit, with a variable cost of €6 per unit and fixed costs of €20 000 per year. Budgeted sales are 6 400 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €20 000p = €11v = €6budget = 6 400
MS = %
3Solutions
1.Marketing principles
Answer: A · Keeping existing customers is usually cheaper than winning new ones
Why this is the answer
Acquiring customers is often more expensive than keeping them, and loyal customers tend to buy more and recommend the firm, raising lifetime value.
Answer
A · Keeping existing customers is usually cheaper than winning new ones
2.Marketing principles
Answer: C · Segments with different price sensitivity that can be separated, and little reselling between them
Why this is the answer
The firm must identify segments with different elasticities, keep them apart (for example with ID or timing) and prevent low-price buyers reselling to others.
Answer
C · Segments with different price sensitivity that can be separated, and little reselling between them
3.Economics concepts
Answer: A · Cost-push inflation
Why this is the answer
Higher input costs shift aggregate supply to the left, raising prices and possibly lowering output; demand-pull inflation comes from excess aggregate demand.
Answer
A · Cost-push inflation
4.Economics concepts
Answer: D · The CPI includes prices of imported consumer goods; the GDP deflator covers only domestically produced goods
Why this is the answer
The CPI uses a fixed basket of consumer goods, including imports, while the deflator covers all domestically produced output with changing weights.
Answer
D · The CPI includes prices of imported consumer goods; the GDP deflator covers only domestically produced goods
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: C · It is not amortised but tested for impairment at least annually
Why this is the answer
Goodwill has an indefinite life under IFRS. It is allocated to cash-generating units and tested for impairment yearly, or more often if there are signs of impairment.
Answer
C · It is not amortised but tested for impairment at least annually
7.Break-even analysis
Answer: Q = 1600 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 = 25 − 15 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (10 000 + 6 000)/10 = 1 600
Answer
Q = 1 600 units
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) = 20 000/5 = 4 000
Margin of safety
MS = (6 400 − 4 000)/6 400·100 = 37.5%
Answer
MS = 37.5%
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