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
Ansoff's matrix strategy of selling existing products in new markets is called:
- AMarket development
- BDiversification
- CMarket penetration
- DProduct development
2.Marketing principlesHard
When is price skimming most suitable?
- AFor a commodity product in a crowded market
- BFor an innovative product with few rivals and early buyers willing to pay a premium
- CWhen the firm wants the largest market share at launch
- DWhen customers are very sensitive to price
3.Economics conceptsMedium
The law of diminishing marginal returns states that:
- ALong-run average costs always fall as output rises
- BAdding more of a variable input to a fixed input eventually lowers the extra output per unit added
- CConsumers get less satisfaction as prices rise
- DTotal output always falls as more workers are hired
4.Economics conceptsHard
In the Solow growth model, sustained long-run growth in output per worker comes from:
- AA higher saving rate alone
- BGovernment budget deficits
- CTechnological progress
- DPopulation growth
5.Financial accountingMedium
Which ratio measures a company's ability to pay its short-term obligations?
- AThe current ratio
- BEarnings per share
- CThe gross margin
- DReturn on equity
6.Financial accountingHard
Inventory days are 60, receivable days 45 and payable days 30. What is the cash conversion (operating) cycle?
- A105 days
- B135 days
- C75 days
- D15 days
7.Break-even analysisMedium
A product sells for €18 per unit with a variable cost of €15 per unit. Fixed costs are €6 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €6 000p = €18v = €15profit = €6 000
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €11 with a variable cost of €8; product B sells for €38 with a variable cost of €30. They sell in a fixed mix of 3 units of A for every 1 of B. Fixed costs are €3 400 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €11, vA = €8pB = €38, vB = €30A : B = 3 : 1F = €3 400
Q = units
3Solutions
1.Marketing principles
Answer: A · Market development
Why this is the answer
Market penetration: existing products, existing markets; market development: existing products, new markets; product development: new products, existing markets; diversification: new products, new markets.
Answer
A · Market development
2.Marketing principles
Answer: B · For an innovative product with few rivals and early buyers willing to pay a premium
Why this is the answer
Skimming works when the product is distinctive, entry barriers protect it for a while, and some customers value being first enough to pay more.
Answer
B · For an innovative product with few rivals and early buyers willing to pay a premium
3.Economics concepts
Answer: B · Adding more of a variable input to a fixed input eventually lowers the extra output per unit added
Why this is the answer
In the short run, with at least one fixed factor, marginal product eventually falls, which makes marginal cost rise.
Answer
B · Adding more of a variable input to a fixed input eventually lowers the extra output per unit added
4.Economics concepts
Answer: C · Technological progress
Why this is the answer
A higher saving rate raises the steady-state level of output per worker but not its long-run growth rate; only technological progress produces continuous growth.
Answer
C · Technological progress
5.Financial accounting
Answer: A · The current ratio
Why this is the answer
The current ratio (current assets/current liabilities) indicates liquidity; a value below 1 can signal problems paying short-term debts.
Answer
A · The current ratio
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 = 4000 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 = 18 − 15 = €3
Units for the target profit
Q = (F + profit)/(p − v) = (6 000 + 6 000)/3 = 4 000
Answer
Q = 4 000 units
8.Break-even analysis
Answer: Q = 800 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 = €8
Weighted contribution margin
(3·3 + 1·8)/4 = €4.25
Break-even units
Q = 3 400/4.25 = 800
A: 600, B: 200
Answer
Q = 800 units
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