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
Soft drinks are sold in supermarkets, petrol stations, vending machines and kiosks. Which distribution strategy is this?
- AIntensive distribution
- BSelective distribution
- CExclusive distribution
- DDirect distribution only
2.Marketing principlesHard
Which metric best shows the efficiency of acquiring customers through online advertising?
- ATotal impressions only
- BCustomer acquisition cost compared with customer lifetime value
- CThe number of employees in marketing
- DThe number of likes on posts
3.Economics conceptsMedium
The price of petrol rises sharply. What happens to the demand curve for large cars?
- AIt shifts to the right
- BThere is a movement along it
- CIt becomes vertical
- DIt shifts to the left
4.Economics conceptsHard
A Giffen good is one where:
- AQuantity demanded rises when its price rises, because a strong income effect outweighs the substitution effect
- BDemand rises because the good is a status symbol
- CThe price never changes
- DDemand rises with income, like most 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
Two firms have the same operating profit, but one is financed mostly by debt. When operating profit falls by 20%, the highly geared firm's net profit:
- AFalls by exactly 20% as well
- BFalls by a smaller percentage
- CRises because interest is fixed
- DFalls by a larger percentage
7.Break-even analysisMedium
A product sells for €14 per unit with a variable cost of €4 per unit. Fixed costs are €25 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €25 000p = €14v = €4profit = €5 000
Q = units
8.Break-even analysisHard
A company sells 1 500 units per month at €20 each, with a variable cost of €18 per unit and fixed costs of €2 400 per month. The variable cost rises by €1 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 1 500p = €20v = €18 → €19F = €2 400
Q = units
3Solutions
1.Marketing principles
Answer: A · Intensive distribution
Why this is the answer
Intensive distribution suits convenience products that customers buy on impulse and will not search for.
Answer
A · Intensive distribution
2.Marketing principles
Answer: B · Customer acquisition cost compared with customer lifetime value
Why this is the answer
CAC relative to CLV shows whether acquisition is profitable; vanity metrics like likes do not measure business value.
Answer
B · Customer acquisition cost compared with customer lifetime value
3.Economics concepts
Answer: D · It shifts to the left
Why this is the answer
Petrol and cars are complements, so a higher petrol price lowers demand for cars at every car price, shifting the demand curve left.
Answer
D · It shifts to the left
4.Economics concepts
Answer: A · 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
A · Quantity demanded rises when its price rises, because a strong income effect outweighs the substitution effect
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: D · Falls by a larger percentage
Why this is the answer
Fixed interest stays the same, so any change in operating profit causes a bigger percentage change in profit for shareholders. This is financial risk.
Answer
D · Falls by a larger percentage
7.Break-even analysis
Answer: Q = 3000 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 = 14 − 4 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (25 000 + 5 000)/10 = 3 000
Answer
Q = 3 000 units
8.Break-even analysis
Answer: Q = 3000 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 = 1 500·(20 − 18) − 2 400 = €600
New contribution margin per unit
20 − 19 = €1
Units for the same profit
Q = (2 400 + 600)/1 = 3 000
Answer
Q = 3 000 units
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