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
Why do many firms invest in customer retention and relationship marketing?
- ARetention removes the need for any advertising
- BLoyal customers always accept any price rise
- CNew customers are never profitable
- DKeeping existing customers is usually cheaper than winning new ones
2.Marketing principlesHard
In Rogers' diffusion curve, roughly what share of adopters are laggards?
- A16%
- B2.5%
- C34%
- D13.5%
3.Economics conceptsMedium
The marginal cost curve cuts the average total cost curve:
- ANever, as the two curves are parallel
- BAt the maximum point of average total cost
- CWhere average total cost equals zero
- DAt the minimum point of average total cost
4.Economics conceptsHard
Ricardian equivalence suggests that a debt-financed tax cut will:
- AReduce interest rates sharply
- BHave little effect on spending, because households save to pay expected future taxes
- CStrongly increase consumption, because households spend most of the tax cut through the multiplier
- DAlways cause inflation
5.Financial accountingMedium
Which ratio measures a company's ability to pay its short-term obligations?
- AThe current ratio
- BThe gross margin
- CReturn on equity
- DEarnings per share
6.Financial accountingHard
The going concern assumption means financial statements are prepared assuming the entity:
- AWill make a profit every year
- BHas no debts
- CWill continue to operate for the foreseeable future
- DWill be sold within one year
7.Break-even analysisMedium
A product sells for €22 per unit with a variable cost of €18 per unit. Fixed costs are €2 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €2 000p = €22v = €18profit = €2 000
Q = units
8.Break-even analysisHard
A product sells for €29 per unit, with a variable cost of €25 per unit and fixed costs of €4 800 per year. Budgeted sales are 1 800 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €4 800p = €29v = €25budget = 1 800
MS = %
3Solutions
1.Marketing principles
Answer: D · Keeping existing customers is usually cheaper than winning new ones
Why this is the answer
Acquiring customers is often more expensive than keeping them, and loyal customers tend to buy more and recommend the firm, raising lifetime value.
Answer
D · Keeping existing customers is usually cheaper than winning new ones
2.Marketing principles
Answer: A · 16%
Why this is the answer
Innovators 2.5%, early adopters 13.5%, early majority 34%, late majority 34% and laggards 16%, based on a normal distribution of adoption time.
Answer
A · 16%
3.Economics concepts
Answer: D · At the minimum point of average total cost
Why this is the answer
When MC is below ATC it pulls the average down, and when it is above it pushes the average up, so MC crosses ATC at its minimum.
Answer
D · At the minimum point of average total cost
4.Economics concepts
Answer: B · Have little effect on spending, because households save to pay expected future taxes
Why this is the answer
If consumers are forward-looking and see that government borrowing means higher taxes later, they save the tax cut, so aggregate demand barely changes.
Answer
B · Have little effect on spending, because households save to pay expected future taxes
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 · Will continue to operate for the foreseeable future
Why this is the answer
Unless management intends or must liquidate, assets and liabilities are measured assuming continued operations; material doubts must be disclosed.
Answer
C · Will continue to operate for the foreseeable future
7.Break-even analysis
Answer: Q = 1000 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 = 22 − 18 = €4
Units for the target profit
Q = (F + profit)/(p − v) = (2 000 + 2 000)/4 = 1 000
Answer
Q = 1 000 units
8.Break-even analysis
Answer: MS = 33.33 %
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).
Break-even quantity
Q = F/(p − v) = 4 800/4 = 1 200
Margin of safety
MS = (1 800 − 1 200)/1 800·100 = 33.33%
Answer
MS = 33.33%
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