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 small firm makes premium climbing gear and targets only serious climbers. Which targeting strategy is this?
- ADifferentiated marketing
- BMicromarketing for each individual
- CUndifferentiated (mass) marketing
- DConcentrated (niche) marketing
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 falls, because quantity falls proportionally more than price rises
- BRevenue stays exactly the same
- CRevenue rises, because quantity falls proportionally less than price rises
- DRevenue falls to zero, because customers stop buying
3.Economics conceptsMedium
A country has 950 employed people and 50 unemployed people seeking work. Its unemployment rate is:
- A5.3%
- B50%
- C5%
- D95%
4.Economics conceptsHard
In the "Battle of the Sexes" coordination game, how many pure-strategy Nash equilibria are there?
- AOne
- BFour
- CTwo
- DNone
5.Financial accountingMedium
Which costs are relevant when making a business decision?
- AFuture cash flows that differ between the alternatives
- BAll costs in last year's income statement
- CAllocated fixed overheads that do not change with the decision
- DCosts already paid for the project
6.Financial accountingHard
An investor holds 30% of a company's shares and has significant influence but not control. How is the investment usually accounted for in group accounts?
- AAs a joint operation with line-by-line sharing
- BAt cost with no changes ever
- CUsing the equity method as an associate
- DBy full consolidation as a subsidiary
7.Break-even analysisMedium
A product sells for €21 with a variable cost of €6 per unit. Fixed costs are €15 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €6 000 after tax?
p = €21v = €6F = €15 000T = 20%after-tax profit = €6 000
Q = units
8.Break-even analysisHard
A product sells for €19 per unit, with a variable cost of €4 per unit and fixed costs of €30 000 per year. Budgeted sales are 2 800 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €30 000p = €19v = €4budget = 2 800
MS = %
3Solutions
1.Marketing principles
Answer: D · Concentrated (niche) marketing
Why this is the answer
Concentrated marketing focuses resources on one segment. It builds deep expertise but makes the firm dependent on that segment.
Answer
D · Concentrated (niche) marketing
2.Marketing principles
Answer: C · 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
C · Revenue rises, because quantity falls proportionally less than price rises
3.Economics concepts
Answer: C · 5%
Why this is the answer
The labour force is 950 + 50 = 1,000, so the rate is 50 / 1,000 = 5%.
Answer
C · 5%
4.Economics concepts
Answer: C · Two
Why this is the answer
Both outcomes where the players choose the same activity are Nash equilibria, so the problem is coordinating on one of them rather than avoiding defection.
Answer
C · Two
5.Financial accounting
Answer: A · Future cash flows that differ between the alternatives
Why this is the answer
Relevant costs are future, incremental cash flows. Sunk costs, committed costs and unchanged allocated overheads are ignored.
Answer
A · Future cash flows that differ between the alternatives
6.Financial accounting
Answer: C · Using the equity method as an associate
Why this is the answer
Under IAS 28 the investment starts at cost and is adjusted for the investor's share of the associate's profits or losses, less dividends received.
Answer
C · Using the equity method as an associate
7.Break-even analysis
Answer: Q = 1500 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
6 000/(1 − 0.2) = €7 500
Units needed
Q = (15 000 + 7 500)/15 = 1 500
Answer
Q = 1 500 units
8.Break-even analysis
Answer: MS = 28.57 %
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) = 30 000/15 = 2 000
Margin of safety
MS = (2 800 − 2 000)/2 800·100 = 28.57%
Answer
MS = 28.57%
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