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 company publishes articles on its own blog. In the paid, owned and earned media model, this is:
- AOwned media
- BPaid media
- CEarned media
- DShared paid media
2.Marketing principlesHard
Under the EU General Data Protection Regulation (GDPR), sending marketing emails based on consent requires consent that is:
- AGiven once for all future purposes by any company
- BAssumed when a customer visits the website
- CFreely given, specific, informed and unambiguous
- DImplied by pre-ticked boxes
3.Economics conceptsMedium
Crowding out refers to:
- AOvercrowded public services
- BHigher government borrowing raising interest rates and reducing private investment
- CImports replacing domestic production
- DToo many firms entering a market
4.Economics conceptsHard
Which is a key difference between the CPI and the GDP deflator?
- AThey always give exactly the same inflation rate
- BThe CPI includes prices of imported consumer goods; the GDP deflator covers only domestically produced goods
- CThe GDP deflator includes imported goods; the CPI does not
- DThe CPI covers investment goods; the GDP deflator does not
5.Financial accountingMedium
Current assets are €300,000, including inventory of €100,000. Current liabilities are €200,000. What is the quick (acid-test) ratio?
- A1.0
- B1.5
- C0.5
- D2.0
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 lease with a term of 12 months or less
- BAny lease of land and buildings
- CAny lease with monthly payments
- DA ten-year lease of a large production machine
7.Break-even analysisMedium
A product sells for €20 with a variable cost of €15 per unit. Fixed costs are €6 000 per month and profit is taxed at 25%. How many units Q must be sold per month to earn €3 000 after tax?
p = €20v = €15F = €6 000T = 25%after-tax profit = €3 000
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €8 with a variable cost of €5; product B sells for €35 with a variable cost of €25. They sell in a fixed mix of 2 units of A for every 3 of B. Fixed costs are €18 000 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €8, vA = €5pB = €35, vB = €25A : B = 2 : 3F = €18 000
Q = units
3Solutions
1.Marketing principles
Answer: A · Owned media
Why this is the answer
Owned media are channels the brand controls, such as its website and blog. Paid media are bought ads; earned media are free coverage, shares and reviews.
Answer
A · Owned media
2.Marketing principles
Answer: C · Freely given, specific, informed and unambiguous
Why this is the answer
Consent must be a clear affirmative act; pre-ticked boxes or silence are not valid, and it must be as easy to withdraw as to give.
Answer
C · Freely given, specific, informed and unambiguous
3.Economics concepts
Answer: B · Higher government borrowing raising interest rates and reducing private investment
Why this is the answer
When government borrowing raises interest rates, some private investment is no longer profitable, reducing the net effect of fiscal expansion.
Answer
B · Higher government borrowing raising interest rates and reducing private investment
4.Economics concepts
Answer: B · 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
B · The CPI includes prices of imported consumer goods; the GDP deflator covers only domestically produced goods
5.Financial accounting
Answer: A · 1.0
Why this is the answer
Quick ratio = (current assets − inventory) ÷ current liabilities = €200,000 ÷ €200,000 = 1.0. Inventory is excluded because it may be slow to turn into cash.
Answer
A · 1.0
6.Financial accounting
Answer: A · 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
A · A lease with a term of 12 months or less
7.Break-even analysis
Answer: Q = 2000 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
3 000/(1 − 0.25) = €4 000
Units needed
Q = (6 000 + 4 000)/5 = 2 000
Answer
Q = 2 000 units
8.Break-even analysis
Answer: Q = 2500 units
Break-even with a sales mix: when products sell in a fixed ratio, use the weighted average contribution margin: weight each product's p − v by its share of units. Break-even units = F/(weighted contribution margin), split again in the mix ratio.
Contribution margins
cmA = €3, cmB = €10
Weighted contribution margin
(2·3 + 3·10)/5 = €7.20
Break-even units
Q = 18 000/7.2 = 2 500
A: 1 000, B: 1 500
Answer
Q = 2 500 units
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