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 chocolate brand launches an ice cream under the same brand name. This is an example of:
- ALine extension
- BPrivate labelling
- CBrand extension
- DCo-branding
2.Marketing principlesHard
In 1985 Coca-Cola replaced its formula with "New Coke", then brought back the original within months. What is the main marketing lesson?
- AAdvertising cannot influence soft drink sales
- BBrands should change their formula every year
- CBlind taste tests can miss consumers' emotional attachment to a brand
- DConsumers always prefer the cheapest product
3.Economics conceptsMedium
When a central bank buys government bonds from banks in open market operations, it usually:
- AHas no effect on the money supply
- BRaises tax revenue for the government
- CReduces bank reserves and so shrinks the money supply
- DIncreases bank reserves and the money supply
4.Economics conceptsHard
The "paradox of thrift" suggests that if all households try to save more during a recession:
- AInterest rates will rise sharply
- BInvestment and growth will rise immediately
- CTotal income may fall, so total saving does not rise
- DInflation will increase
5.Financial accountingMedium
Operating profit is €120,000 and interest expense is €30,000. What is interest cover?
- A0.25 times
- B90,000 times
- C3 times
- D4 times
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?
- AShow one equity-method investment line for its 70% share of S
- BConsolidate 100% of S line by line and show a non-controlling interest
- CKeep the investment at cost and report only the dividends received from S
- DAdd only 70% of each of S's assets, liabilities, income and expenses
7.Break-even analysisMedium
A product sells for €35 with a variable cost of €30 per unit. Fixed costs are €7 500 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €1 500 after tax?
p = €35v = €30F = €7 500T = 20%after-tax profit = €1 500
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €16 with a variable cost of €10; product B sells for €33 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 €10 800 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €16, vA = €10pB = €33, vB = €25A : B = 2 : 3F = €10 800
Q = units
3Solutions
1.Marketing principles
Answer: C · Brand extension
Why this is the answer
A brand extension uses an existing brand name in a new category. A line extension adds variants in the same category, such as new flavours.
Answer
C · Brand extension
2.Marketing principles
Answer: C · Blind taste tests can miss consumers' emotional attachment to a brand
Why this is the answer
Taste tests favoured the new formula, but loyal customers felt something meaningful had been taken away. Brand equity includes emotional and symbolic meaning, not just product attributes.
Answer
C · Blind taste tests can miss consumers' emotional attachment to a brand
3.Economics concepts
Answer: D · Increases bank reserves and the money supply
Why this is the answer
Buying bonds injects reserves into the banking system, which tends to increase the money supply and lower interest rates.
Answer
D · Increases bank reserves and the money supply
4.Economics concepts
Answer: C · 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
C · Total income may fall, so total saving does not rise
5.Financial accounting
Answer: D · 4 times
Why this is the answer
€120,000 ÷ €30,000 = 4. The company earns its interest four times over; low cover signals a risk of not meeting interest payments.
Answer
D · 4 times
6.Financial accounting
Answer: B · 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
B · Consolidate 100% of S line by line and show a non-controlling interest
7.Break-even analysis
Answer: Q = 1875 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
1 500/(1 − 0.2) = €1 875
Units needed
Q = (7 500 + 1 875)/5 = 1 875
Answer
Q = 1 875 units
8.Break-even analysis
Answer: Q = 1500 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 = €6, cmB = €8
Weighted contribution margin
(2·6 + 3·8)/5 = €7.20
Break-even units
Q = 10 800/7.2 = 1 500
A: 600, B: 900
Answer
Q = 1 500 units
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