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
Which of these is one of Porter's five competitive forces?
- AThe firm's brand awareness
- BThe political stability of a country
- CThe threat of substitute products
- DThe level of inflation
2.Marketing principlesHard
Research shows young consumers see a long-established brand as old-fashioned, although product quality is good. What is the most suitable strategy?
- AWithdrawing the product immediately
- BCutting the price to the lowest in the market
- CRepositioning the brand through new communication and image
- DChanging the distribution to exclusive dealers only
3.Economics conceptsMedium
Overfishing in international waters is an example of:
- AThe tragedy of the commons
- BA Giffen good
- CA natural monopoly
- DPrice discrimination
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
- CAlways cause inflation
- DStrongly increase consumption, because households spend most of the tax cut through the multiplier
5.Financial accountingMedium
Why can a profitable company run out of cash?
- AProfit always equals cash
- BProfitable companies never pay taxes
- CProfit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
- DCash is not recorded in accounting
6.Financial accountingHard
Machine hours are scarce. Product X earns €20 contribution and needs 4 hours; product Y earns €15 and needs 2 hours. Which should be made first?
- AX, because it earns more contribution per unit
- BEither, because the total contribution is the same
- CX, because it uses more machine time
- DY, because it earns €7.50 per hour versus €5 for X
7.Break-even analysisMedium
A product sells for €18 per unit with a variable cost of €8 per unit. Fixed costs are €40 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €40 000p = €18v = €8profit = €6 000
Q = units
8.Break-even analysisHard
A product sells for €30 per unit, with a variable cost of €15 per unit and fixed costs of €7 500 per year. Budgeted sales are 800 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €7 500p = €30v = €15budget = 800
MS = %
3Solutions
1.Marketing principles
Answer: C · The threat of substitute products
Why this is the answer
The five forces are rivalry among competitors, threat of new entrants, threat of substitutes, and the bargaining power of buyers and of suppliers.
Answer
C · The threat of substitute products
2.Marketing principles
Answer: C · Repositioning the brand through new communication and image
Why this is the answer
Repositioning changes how the target segment sees the brand, for example with updated design, new messages and channels the younger audience uses.
Answer
C · Repositioning the brand through new communication and image
3.Economics concepts
Answer: A · The tragedy of the commons
Why this is the answer
When a common resource is rival but people cannot be excluded, each user ignores the cost they impose on others, leading to overuse.
Answer
A · The tragedy of the commons
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: C · Profit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
Why this is the answer
Profit is measured on an accrual basis; growth can tie up cash in inventory and receivables, so cash flow can be negative despite profits.
Answer
C · Profit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
6.Financial accounting
Answer: D · Y, because it earns €7.50 per hour versus €5 for X
Why this is the answer
X earns €20 ÷ 4 = €5 per hour, Y earns €15 ÷ 2 = €7.50 per hour. With a scarce resource, maximise contribution per scarce hour.
Answer
D · Y, because it earns €7.50 per hour versus €5 for X
7.Break-even analysis
Answer: Q = 4600 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 − 8 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (40 000 + 6 000)/10 = 4 600
Answer
Q = 4 600 units
8.Break-even analysis
Answer: MS = 37.5 %
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) = 7 500/15 = 500
Margin of safety
MS = (800 − 500)/800·100 = 37.5%
Answer
MS = 37.5%
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