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
A car maker offers separate models and campaigns for students, families and luxury buyers. Which targeting strategy is this?
- ADifferentiated marketing
- BConcentrated marketing
- CMass customisation of one model
- DUndifferentiated marketing
2.Marketing principlesHard
A customer sees a social ad, later reads a review, then clicks a search ad and buys. What is the main weakness of last-click attribution here?
- AIt gives all credit to the search ad and ignores earlier touchpoints
- BIt cannot record online purchases
- CIt counts the same sale three times
- DIt gives too much credit to the social ad
3.Economics conceptsMedium
If demand for a product is price inelastic, a price increase will:
- ALeave total revenue unchanged
- BReduce quantity demanded to zero
- CIncrease total revenue
- DDecrease total revenue
4.Economics conceptsHard
A Giffen good is one where:
- AThe price never changes
- BQuantity demanded rises when its price rises, because a strong income effect outweighs the substitution effect
- CDemand rises with income, like most goods
- DDemand rises because the good is a status symbol
5.Financial accountingMedium
Which ratio measures a company's ability to pay its short-term obligations?
- AReturn on equity
- BThe current ratio
- CThe gross margin
- DEarnings per share
6.Financial accountingHard
Company P buys 70% of the voting shares of S and gains control. How does P report S in its group accounts?
- AAdd only 70% of each of S's assets, liabilities, income and expenses
- BShow one equity-method investment line for its 70% share of S
- CConsolidate 100% of S line by line and show a non-controlling interest
- DKeep the investment at cost and report only the dividends received from S
7.Break-even analysisMedium
A company sells 1 600 units at €21 each. The variable cost is €6 per unit and fixed costs are €12 000. Find the degree of operating leverage DOL at this sales level.
Q = 1 600p = €21v = €6F = €12 000
DOL =
8.Break-even analysisHard
A company sells 3 000 units per month at €16 each, with a variable cost of €6 per unit and fixed costs of €12 000 per month. The variable cost rises by €2 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 3 000p = €16v = €6 → €8F = €12 000
Q = units
3Solutions
1.Marketing principles
Answer: A · Differentiated marketing
Why this is the answer
Differentiated marketing targets several segments with different products or messages. It can raise sales but also costs.
Answer
A · Differentiated marketing
2.Marketing principles
Answer: A · It gives all credit to the search ad and ignores earlier touchpoints
Why this is the answer
Last-click models undervalue channels that create awareness early in the journey. Multi-touch attribution or experiments give a fairer picture of each channel's contribution.
Answer
A · It gives all credit to the search ad and ignores earlier touchpoints
3.Economics concepts
Answer: C · Increase total revenue
Why this is the answer
With inelastic demand the percentage fall in quantity is smaller than the percentage price rise, so price × quantity rises.
Answer
C · Increase total revenue
4.Economics concepts
Answer: B · Quantity demanded rises when its price rises, because a strong income effect outweighs the substitution effect
Why this is the answer
For a Giffen good the income effect of a price rise (feeling poorer, buying more of the cheap staple) dominates the substitution effect, so demand slopes upward.
Answer
B · Quantity demanded rises when its price rises, because a strong income effect outweighs the substitution effect
5.Financial accounting
Answer: B · The current ratio
Why this is the answer
The current ratio (current assets/current liabilities) indicates liquidity; a value below 1 can signal problems paying short-term debts.
Answer
B · The current ratio
6.Financial accounting
Answer: C · Consolidate 100% of S line by line and show a non-controlling interest
Why this is the answer
A subsidiary is consolidated line by line at 100%. The 30% owned by others is shown as a non-controlling interest within equity.
Answer
C · Consolidate 100% of S line by line and show a non-controlling interest
7.Break-even analysis
Answer: DOL = 2
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 = 1 600·(21 − 6) = €24 000
Operating profit
Π = 24 000 − 12 000 = €12 000
DOL
DOL = 24 000/12 000 = 2
Answer
DOL = 2
8.Break-even analysis
Answer: Q = 3750 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).
Current profit
Π = 3 000·(16 − 6) − 12 000 = €18 000
New contribution margin per unit
16 − 8 = €8
Units for the same profit
Q = (12 000 + 18 000)/8 = 3 750
Answer
Q = 3 750 units
ExamProblems · examproblems.com/courses/business-fundamentals