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 firm competes across a broad market by having the lowest costs in its industry and passing savings on as low prices. Which Porter generic strategy is this?
- ADifferentiation
- BMarket development
- CDifferentiation focus
- DCost leadership
2.Marketing principlesHard
Brand equity in Keller's customer-based model comes mainly from:
- AThe lowest possible price
- BThe number of factories a company owns
- CThe size of the marketing department
- DBrand awareness and strong, favourable and unique brand associations
3.Economics conceptsMedium
Using the expenditure approach, GDP equals:
- AC − I + G − (X + M)
- BC + I + G + (X − M)
- CWages + profits − taxes
- DC + I + G + X + M
4.Economics conceptsHard
For a normal good, when its price falls, the substitution effect and income effect:
- ABoth decrease the quantity demanded
- BBoth increase the quantity demanded
- CCancel out exactly
- DWork in opposite directions
5.Financial accountingMedium
A firm buys 200 units at €5 and 300 units at €6, then sells 400 units. Using weighted average cost, what is closing inventory?
- A€550
- B€500
- C€600
- D€560
6.Financial accountingHard
Closing inventory this year is overstated by €10,000 by mistake. What is the effect on profit, if not corrected?
- AThis year's profit is overstated and next year's understated by €10,000
- BOnly this year's profit is understated
- CProfit is unaffected; only the balance sheet changes
- DBoth years' profits are overstated
7.Break-even analysisMedium
A product sells for €35 per unit with a variable cost of €25 per unit. Fixed costs are €20 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €20 000p = €35v = €25profit = €6 000
Q = units
8.Break-even analysisHard
A product sells for €51 per unit, with a variable cost of €45 per unit and fixed costs of €4 800 per year. Budgeted sales are 920 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €4 800p = €51v = €45budget = 920
MS = %
3Solutions
1.Marketing principles
Answer: D · Cost leadership
Why this is the answer
Cost leadership seeks the lowest cost position in a broad market. Differentiation offers unique value at a premium; focus strategies target a narrow segment.
Answer
D · Cost leadership
2.Marketing principles
Answer: D · Brand awareness and strong, favourable and unique brand associations
Why this is the answer
Customer-based brand equity is the differential effect of brand knowledge (awareness and image) on consumer response to marketing.
Answer
D · Brand awareness and strong, favourable and unique brand associations
3.Economics concepts
Answer: B · C + I + G + (X − M)
Why this is the answer
GDP is consumption plus investment plus government purchases plus net exports (exports minus imports).
Answer
B · C + I + G + (X − M)
4.Economics concepts
Answer: B · Both increase the quantity demanded
Why this is the answer
The substitution effect always favours the cheaper good, and for a normal good the higher real income also raises demand, so both effects reinforce each other.
Answer
B · Both increase the quantity demanded
5.Financial accounting
Answer: D · €560
Why this is the answer
Average cost = (€1,000 + €1,800) ÷ 500 = €5.60. Closing inventory = 100 × €5.60 = €560.
Answer
D · €560
6.Financial accounting
Answer: A · This year's profit is overstated and next year's understated by €10,000
Why this is the answer
Higher closing inventory reduces cost of sales, raising this year's profit. Next year opening inventory is too high, increasing cost of sales and lowering profit by the same amount.
Answer
A · This year's profit is overstated and next year's understated by €10,000
7.Break-even analysis
Answer: Q = 2600 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 = 35 − 25 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (20 000 + 6 000)/10 = 2 600
Answer
Q = 2 600 units
8.Break-even analysis
Answer: MS = 13.04 %
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) = 4 800/6 = 800
Margin of safety
MS = (920 − 800)/920·100 = 13.04%
Answer
MS = 13.04%
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