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 luxury watch brand sells only through a few carefully chosen dealers in each country. Which distribution strategy is this?
- ASelective distribution in all outlets
- BMass distribution
- CIntensive distribution
- DExclusive distribution
2.Marketing principlesHard
An ice cream brand finds that its sales and its advertising spend both peak in summer. Why can it not conclude that advertising caused the sales?
- ASales data is always unreliable
- BSummer sales are too small to measure
- CHot weather may drive both, so correlation does not prove causation
- DAdvertising never affects sales of food
3.Economics conceptsMedium
In perfect competition in the long run, firms earn:
- AZero economic profit
- BLarge economic profits
- CLosses forever
- DMonopoly profits
4.Economics conceptsHard
In the "Battle of the Sexes" coordination game, how many pure-strategy Nash equilibria are there?
- AFour
- BOne
- CTwo
- DNone
5.Financial accountingMedium
Trade receivables are €50,000 and annual credit sales are €365,000. What are the receivable days?
- A73 days
- B7.3 days
- C36.5 days
- D50 days
6.Financial accountingHard
Goodwill arises in a business combination when:
- AThe acquired company makes a loss
- BAssets are revalued upwards
- CThe consideration paid exceeds the fair value of identifiable net assets acquired
- DA company has a good reputation
7.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €10 000 per year and a variable cost of €10 per unit. Method B, more automated, has fixed costs of €12 000 per year and a variable cost of €6 per unit. At what yearly volume Q do both methods cost the same?
FA = €10 000vA = €10FB = €12 000vB = €6
Q = units
8.Break-even analysisHard
A company sells 3 200 units at €18 each, with a variable cost of €12 per unit and fixed costs of €12 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 5%?
Q = 3 200p = €18v = €12F = €12 000%ΔQ = +5%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: D · Exclusive distribution
Why this is the answer
Exclusive distribution uses very few outlets to keep control and a premium image. Intensive distribution places products in as many outlets as possible.
Answer
D · Exclusive distribution
2.Marketing principles
Answer: C · Hot weather may drive both, so correlation does not prove causation
Why this is the answer
A confounding factor, such as temperature, can create a correlation between two variables. Controlled tests or models that account for seasonality are needed to estimate the ad effect.
Answer
C · Hot weather may drive both, so correlation does not prove causation
3.Economics concepts
Answer: A · Zero economic profit
Why this is the answer
Profits attract entry and losses cause exit until price equals minimum average cost and economic profit is zero.
Answer
A · Zero economic profit
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: D · 50 days
Why this is the answer
€50,000 ÷ €365,000 × 365 = 50 days. This is the average time customers take to pay.
Answer
D · 50 days
6.Financial accounting
Answer: C · The consideration paid exceeds the fair value of identifiable net assets acquired
Why this is the answer
Goodwill = consideration − fair value of identifiable net assets. Under IFRS it is not amortised but tested for impairment annually.
Answer
C · The consideration paid exceeds the fair value of identifiable net assets acquired
7.Break-even analysis
Answer: Q = 500 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).
Equal total costs
10 000 + 10Q = 12 000 + 6Q
Solve for Q
Q = (12 000 − 10 000)/(10 − 6) = 500
Answer
Q = 500 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: %ΔΠ = 13.33 %
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Contribution margin and profit
CM = 3 200·6 = €19 200
Π = 19 200 − 12 000 = €7 200
DOL
DOL = 19 200/7 200 = 2.667
Change in profit
%ΔΠ = 2.667·(+5%) = +13.33%
Answer
%ΔΠ = +13.33%
Check: new profit = 3 360·6 − 12 000 = €8 160.00.
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