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 raises its price by 10% and the quantity sold falls by 20%. What is the price elasticity of demand, and what happens to revenue?
- A−2, inelastic, so revenue rises
- B−2, elastic, so revenue falls
- C−0.5, inelastic, so revenue rises
- D−0.5, elastic, so revenue falls
2.Marketing principlesHard
A company launches a product that is easy to copy, with highly price-sensitive buyers and strong economies of scale. Which launch pricing strategy fits best?
- ACaptive product pricing
- BPrestige pricing
- CPenetration pricing
- DPrice skimming
3.Economics conceptsMedium
Rising consumer confidence would most likely:
- AShift aggregate demand to the right
- BHave no effect on the economy
- CShift aggregate demand to the left
- DShift aggregate supply to the left
4.Economics conceptsHard
Price discrimination by a firm requires that:
- AIt operates in perfect competition
- BIts costs differ for each customer
- CAll consumers have identical elasticity of demand and buy the same amount
- DIt has market power, can separate markets and prevent resale
5.Financial accountingMedium
Current assets are €300,000 and current liabilities are €150,000. What is the current ratio?
- A0.5
- B4.5
- C2.0
- D1.5
6.Financial accountingHard
Production exceeds sales this period, so inventory rises. How does absorption costing profit compare with marginal costing profit?
- AAbsorption costing profit is higher
- BThey are always equal
- CAbsorption costing shows a loss
- DMarginal costing profit is higher this period
7.Break-even analysisMedium
A product sells for €14 with a variable cost of €4 per unit. Fixed costs are €12 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €6 000 after tax?
p = €14v = €4F = €12 000T = 20%after-tax profit = €6 000
Q = units
8.Break-even analysisHard
A company sells 10 000 units per month at €12 each, with a variable cost of €6 per unit and fixed costs of €24 000 per month. The variable cost rises by €3 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 10 000p = €12v = €6 → €9F = €24 000
Q = units
3Solutions
1.Marketing principles
Answer: B · −2, elastic, so revenue falls
Why this is the answer
PED = −20% ÷ 10% = −2. Because its size is above 1, demand is elastic and the price rise reduces total revenue.
Answer
B · −2, elastic, so revenue falls
2.Marketing principles
Answer: C · Penetration pricing
Why this is the answer
Low prices build share quickly, lower unit costs through scale and discourage imitators. Skimming suits unique products with buyers who are less sensitive to price.
Answer
C · Penetration pricing
3.Economics concepts
Answer: A · Shift aggregate demand to the right
Why this is the answer
Higher confidence raises consumption at every price level, shifting AD right and raising output and, possibly, prices in the short run.
Answer
A · Shift aggregate demand to the right
4.Economics concepts
Answer: D · It has market power, can separate markets and prevent resale
Why this is the answer
To charge different prices for the same good, the firm needs market power, the ability to identify groups with different elasticities and to prevent arbitrage.
Answer
D · It has market power, can separate markets and prevent resale
5.Financial accounting
Answer: C · 2.0
Why this is the answer
€300,000 ÷ €150,000 = 2.0, so current assets cover short-term obligations twice.
Answer
C · 2.0
6.Financial accounting
Answer: A · Absorption costing profit is higher
Why this is the answer
Under absorption costing part of this period's fixed overhead sits in closing inventory instead of being expensed, so reported profit is higher when inventory rises.
Answer
A · Absorption costing profit is higher
7.Break-even analysis
Answer: Q = 1950 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 = (12 000 + 7 500)/10 = 1 950
Answer
Q = 1 950 units
8.Break-even analysis
Answer: Q = 20000 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).
Current profit
Π = 10 000·(12 − 6) − 24 000 = €36 000
New contribution margin per unit
12 − 9 = €3
Units for the same profit
Q = (24 000 + 36 000)/3 = 20 000
Answer
Q = 20 000 units
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