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 brand runs heavy consumer advertising so that shoppers ask retailers to stock its product. Which strategy is this?
- AA pull strategy
- BA diversification strategy
- CA penetration strategy
- DA push strategy
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 falls to zero, because customers stop buying
- CRevenue falls, because quantity falls proportionally more than price rises
- DRevenue rises, because quantity falls proportionally less than price rises
3.Economics conceptsMedium
If the ECB raises its main interest rate, the most likely short-term effect is:
- AHigher borrowing and spending, which adds to inflationary pressure
- BLower borrowing and spending, reducing inflationary pressure
- CAn immediate rise in GDP
- DA fall in the value of the euro
4.Economics conceptsHard
A Giffen good is one where:
- ADemand rises with income, like most goods
- BQuantity demanded rises when its price rises, because a strong income effect outweighs the substitution effect
- CDemand rises because the good is a status symbol
- DThe price never changes
5.Financial accountingMedium
Which error will NOT be revealed by a trial balance?
- AA sale left out of the books entirely
- BA balance copied to the wrong column
- CA debit posted without a matching credit
- DA wrongly added ledger column
6.Financial accountingHard
Operating profit is €200,000 and capital employed (equity plus non-current liabilities) is €1,000,000. What is ROCE?
- A50%
- B2%
- C5%
- D20%
7.Break-even analysisMedium
A product sells for €29 per unit with a variable cost of €25 per unit. Fixed costs are €8 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €8 000p = €29v = €25profit = €6 000
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €14 with a variable cost of €8; product B sells for €28 with a variable cost of €20. They sell in a fixed mix of 5 units of A for every 2 of B. Fixed costs are €36 800 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €14, vA = €8pB = €28, vB = €20A : B = 5 : 2F = €36 800
Q = units
3Solutions
1.Marketing principles
Answer: A · A pull strategy
Why this is the answer
A pull strategy builds consumer demand that pulls the product through the channel. A push strategy targets intermediaries with trade promotions and personal selling.
Answer
A · A pull strategy
2.Marketing principles
Answer: D · 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
D · Revenue rises, because quantity falls proportionally less than price rises
3.Economics concepts
Answer: B · 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
B · Lower borrowing and spending, reducing inflationary pressure
4.Economics concepts
Answer: B · 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
B · Quantity demanded rises when its price rises, because a strong income effect outweighs the substitution effect
5.Financial accounting
Answer: A · A sale left out of the books entirely
Why this is the answer
An error of omission leaves both sides unrecorded, so totals still agree. Single-sided postings and addition errors make the trial balance differ.
Answer
A · A sale left out of the books entirely
6.Financial accounting
Answer: D · 20%
Why this is the answer
ROCE = €200,000 ÷ €1,000,000 = 20%. It measures returns on all long-term finance, so it can be compared with the cost of borrowing.
Answer
D · 20%
7.Break-even analysis
Answer: Q = 3500 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 = 29 − 25 = €4
Units for the target profit
Q = (F + profit)/(p − v) = (8 000 + 6 000)/4 = 3 500
Answer
Q = 3 500 units
8.Break-even analysis
Answer: Q = 5600 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
(5·6 + 2·8)/7 = €6.57
Break-even units
Q = 36 800/6.571 = 5 600
A: 4 000, B: 1 600
Answer
Q = 5 600 units
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