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 laptop comes with a two-year warranty, free delivery and online support. In Kotler's product levels, these belong to the:
- ACore customer value
- BActual product
- CAugmented product
- DPotential product only
2.Marketing principlesHard
A firm uses different prices for the same seat on a flight depending on demand and booking time. This is:
- ACaptive product pricing
- BDynamic pricing (yield management)
- CCost-plus pricing
- DPsychological pricing with .99 endings
3.Economics conceptsMedium
In an oligopoly, firms are typically:
- AFew and interdependent in their decisions
- BCompletely unregulated by competition law
- CMany and too small to affect the price
- DA single seller in the market
4.Economics conceptsHard
A monopolist faces demand P = 100 − Q and has constant marginal cost of 20. What are its profit-maximising output and price?
- AQ = 80, P = 20
- BQ = 50, P = 50
- CQ = 40, P = 60
- DQ = 40, P = 20
5.Financial accountingMedium
Profit for ordinary shareholders is €500,000 and there are 1,000,000 ordinary shares. What are basic earnings per share?
- A€0.50
- B€5.00
- C€2.00
- D€0.05
6.Financial accountingHard
Under IFRS, how is purchased goodwill treated after acquisition?
- AIt is written off against equity immediately
- BIt is not amortised but tested for impairment at least annually
- CIt is amortised over 20 years
- DIt is revalued upwards every year
7.Break-even analysisMedium
A company sells 1 880 units at €24 each. The variable cost is €4 per unit and fixed costs are €30 000. Find the degree of operating leverage DOL at this sales level.
Q = 1 880p = €24v = €4F = €30 000
DOL =
8.Break-even analysisHard
A product sells for €49 per unit, with a variable cost of €45 per unit and fixed costs of €8 000 per year. Budgeted sales are 3 000 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €8 000p = €49v = €45budget = 3 000
MS = %
3Solutions
1.Marketing principles
Answer: C · Augmented product
Why this is the answer
The core value is the benefit sought, the actual product is the item with its features and brand, and the augmented product adds services such as warranties and support.
Answer
C · Augmented product
2.Marketing principles
Answer: B · Dynamic pricing (yield management)
Why this is the answer
Dynamic pricing adjusts prices to demand, time and capacity to maximise revenue, common in airlines and hotels.
Answer
B · Dynamic pricing (yield management)
3.Economics concepts
Answer: A · Few and interdependent in their decisions
Why this is the answer
Oligopolies have a few large firms whose pricing and output decisions affect each other, often analysed with game theory.
Answer
A · Few and interdependent in their decisions
4.Economics concepts
Answer: C · Q = 40, P = 60
Why this is the answer
Setting MR = MC gives 100 − 2Q = 20, so Q = 40; the price from the demand curve is 100 − 40 = 60.
Answer
C · Q = 40, P = 60
5.Financial accounting
Answer: A · €0.50
Why this is the answer
Basic EPS = €500,000 ÷ 1,000,000 = €0.50 per share. Dividing the share price by EPS gives the P/E ratio.
Answer
A · €0.50
6.Financial accounting
Answer: B · It is not amortised but tested for impairment at least annually
Why this is the answer
Goodwill has an indefinite life under IFRS. It is allocated to cash-generating units and tested for impairment yearly, or more often if there are signs of impairment.
Answer
B · It is not amortised but tested for impairment at least annually
7.Break-even analysis
Answer: DOL = 4.947
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.
Total contribution margin
CM = 1 880·(24 − 4) = €37 600
Operating profit
Π = 37 600 − 30 000 = €7 600
DOL
DOL = 37 600/7 600 = 4.947
Answer
DOL = 4.947
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) = 8 000/4 = 2 000
Margin of safety
MS = (3 000 − 2 000)/3 000·100 = 33.33%
Answer
MS = 33.33%
ExamProblems · examproblems.com/courses/business-fundamentals