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
Price elasticity matters for pricing because:
- AIf demand is elastic, a price cut can raise total revenue
- BIt has no effect on pricing decisions
- CIf demand is inelastic, a price rise will lower total revenue
- DElasticity only affects costs
2.Marketing principlesHard
A firm's research shows demand for its product is price inelastic. If costs and competitors stay the same, what does a price rise usually do to revenue?
- ARevenue stays exactly the same
- BRevenue rises, because quantity falls proportionally less than price rises
- CRevenue falls, because quantity falls proportionally more than price rises
- DRevenue falls to zero, because customers stop buying
3.Economics conceptsMedium
Comparative advantage means a country should specialise in goods it can produce:
- AMore cheaply in absolute terms than every other country
- BOnly for its own consumption
- CAt a lower opportunity cost than other countries
- DWith the most workers
4.Economics conceptsHard
The "paradox of thrift" suggests that if all households try to save more during a recession:
- AInvestment and growth will rise immediately
- BTotal income may fall, so total saving does not rise
- CInterest rates will rise sharply
- DInflation will increase
5.Financial accountingMedium
Under the accrual basis of accounting, revenue is recognised when:
- ACash is received
- BThe customer pays the invoice, even if goods were delivered earlier
- CThe tax return is filed
- DIt is earned, whether or not cash has been received
6.Financial accountingHard
Inventory days are 60, receivable days 45 and payable days 30. What is the cash conversion (operating) cycle?
- A15 days
- B135 days
- C75 days
- D105 days
7.Break-even analysisMedium
A product sells for €45 per unit with a variable cost of €30 per unit. Fixed costs are €18 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €18 000p = €45v = €30profit = €6 000
Q = units
8.Break-even analysisHard
A product sells for €15 per unit, with a variable cost of €12 per unit and fixed costs of €4 500 per year. Budgeted sales are 2 250 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €4 500p = €15v = €12budget = 2 250
MS = %
3Solutions
1.Marketing principles
Answer: A · If demand is elastic, a price cut can raise total revenue
Why this is the answer
With elastic demand, quantity responds strongly, so a lower price can increase revenue; with inelastic demand, a price rise increases revenue.
Answer
A · If demand is elastic, a price cut can raise total revenue
2.Marketing principles
Answer: B · Revenue rises, because quantity falls proportionally less than price rises
Why this is the answer
With inelastic demand, the percentage drop in quantity is smaller than the percentage price rise, so total revenue increases.
Answer
B · Revenue rises, because quantity falls proportionally less than price rises
3.Economics concepts
Answer: C · At a lower opportunity cost than other countries
Why this is the answer
Even a country that is less efficient at everything gains from trade by specialising where its opportunity cost is lowest.
Answer
C · At a lower opportunity cost than other countries
4.Economics concepts
Answer: B · Total income may fall, so total saving does not rise
Why this is the answer
Higher saving reduces consumption and aggregate demand, lowering income; with lower income, aggregate saving may end up no higher, as Keynes argued.
Answer
B · Total income may fall, so total saving does not rise
5.Financial accounting
Answer: D · It is earned, whether or not cash has been received
Why this is the answer
Accrual accounting records revenue when the performance obligation is satisfied and expenses when incurred, not when cash moves.
Answer
D · It is earned, whether or not cash has been received
6.Financial accounting
Answer: C · 75 days
Why this is the answer
60 + 45 − 30 = 75 days between paying suppliers and collecting cash from customers. A shorter cycle needs less working capital finance.
Answer
C · 75 days
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 = 45 − 30 = €15
Units for the target profit
Q = (F + profit)/(p − v) = (18 000 + 6 000)/15 = 1 600
Answer
Q = 1 600 units
8.Break-even analysis
Answer: MS = 33.33 %
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) = 4 500/3 = 1 500
Margin of safety
MS = (2 250 − 1 500)/2 250·100 = 33.33%
Answer
MS = 33.33%
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