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
In the BCG matrix, what are the usual options for a "question mark"?
- AHarvest cash with minimal investment
- BKeep it unchanged because it is the market leader
- CInvest heavily to build market share, or divest
- DAlways close it immediately
2.Marketing principlesHard
Research shows young consumers see a long-established brand as old-fashioned, although product quality is good. What is the most suitable strategy?
- AWithdrawing the product immediately
- BCutting the price to the lowest in the market
- CRepositioning the brand through new communication and image
- DChanging the distribution to exclusive dealers only
3.Economics conceptsMedium
If the ECB raises its main interest rate, the most likely short-term effect is:
- ALower borrowing and spending, reducing inflationary pressure
- BAn immediate rise in GDP
- CHigher borrowing and spending, which adds to inflationary pressure
- DA fall in the value of the euro
4.Economics conceptsHard
For a normal good, when its price falls, the substitution effect and income effect:
- AWork in opposite directions
- BBoth increase the quantity demanded
- CBoth decrease the quantity demanded
- DCancel out exactly
5.Financial accountingMedium
Why can a profitable company run out of cash?
- ACash is not recorded in accounting
- BProfitable companies never pay taxes
- CProfit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
- DProfit always equals cash
6.Financial accountingHard
Under IFRS 16, which lease may a lessee choose to expense on a straight-line basis instead of recognising a right-of-use asset?
- AA ten-year lease of a large production machine
- BAny lease of land and buildings
- CAny lease with monthly payments
- DA lease with a term of 12 months or less
7.Break-even analysisMedium
A product sells for €35 with a variable cost of €20 per unit. Fixed costs are €30 000 per month and profit is taxed at 25%. How many units Q must be sold per month to earn €9 000 after tax?
p = €35v = €20F = €30 000T = 25%after-tax profit = €9 000
Q = units
8.Break-even analysisHard
A company sells 1 000 units at €18 each, with a variable cost of €12 per unit and fixed costs of €3 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 8%?
Q = 1 000p = €18v = €12F = €3 000%ΔQ = +8%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: C · Invest heavily to build market share, or divest
Why this is the answer
Question marks need cash to grow. Managers must decide whether they can become stars; if not, it may be better to sell or drop them.
Answer
C · Invest heavily to build market share, or divest
2.Marketing principles
Answer: C · Repositioning the brand through new communication and image
Why this is the answer
Repositioning changes how the target segment sees the brand, for example with updated design, new messages and channels the younger audience uses.
Answer
C · Repositioning the brand through new communication and image
3.Economics concepts
Answer: A · Lower borrowing and spending, reducing inflationary pressure
Why this is the answer
Higher rates make credit more expensive and saving more attractive, reducing demand and inflation; they also tend to strengthen the currency.
Answer
A · Lower borrowing and spending, reducing inflationary pressure
4.Economics concepts
Answer: B · Both increase the quantity demanded
Why this is the answer
The substitution effect always favours the cheaper good, and for a normal good the higher real income also raises demand, so both effects reinforce each other.
Answer
B · Both increase the quantity demanded
5.Financial accounting
Answer: C · Profit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
Why this is the answer
Profit is measured on an accrual basis; growth can tie up cash in inventory and receivables, so cash flow can be negative despite profits.
Answer
C · Profit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
6.Financial accounting
Answer: D · A lease with a term of 12 months or less
Why this is the answer
Lessees may elect not to recognise short-term leases (12 months or less) and leases of low-value assets, expensing the payments instead.
Answer
D · A lease with a term of 12 months or less
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).
Pre-tax profit needed
9 000/(1 − 0.25) = €12 000
Units needed
Q = (30 000 + 12 000)/15 = 2 800
Answer
Q = 2 800 units
8.Break-even analysis
Answer: %ΔΠ = 16 %
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.
Contribution margin and profit
CM = 1 000·6 = €6 000
Π = 6 000 − 3 000 = €3 000
DOL
DOL = 6 000/3 000 = 2
Change in profit
%ΔΠ = 2·(+8%) = +16%
Answer
%ΔΠ = +16%
Check: new profit = 1 080·6 − 3 000 = €3 480.00.
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