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
Which of these is one of Porter's five competitive forces?
- AThe firm's brand awareness
- BThe political stability of a country
- CThe level of inflation
- DThe threat of substitute products
2.Marketing principlesHard
A company sells printers cheaply but charges high prices for ink cartridges. This is:
- ABundle pricing
- BPsychological pricing
- CPenetration pricing for both products
- DCaptive product pricing
3.Economics conceptsMedium
A firm has spent €1 million on research for a product that now looks unprofitable. When deciding whether to continue, the €1 million should be:
- ATreated as the opportunity cost of stopping
- BRecovered by raising prices
- CIgnored, because it is a sunk cost
- DAdded to the expected future costs
4.Economics conceptsHard
The time-inconsistency problem in monetary policy (Kydland and Prescott) is a key argument for:
- AIndependent central banks with a credible commitment to low inflation
- BGovernments setting interest rates directly, especially before elections
- CAbolishing central banks entirely
- DFixing the money supply at zero growth
5.Financial accountingMedium
Return on equity (ROE) is calculated as:
- ANet profit / shareholders' equity
- BCurrent assets / current liabilities
- CNet profit / total revenue
- DTotal assets / equity
6.Financial accountingHard
A company records routine repair costs as additions to non-current assets instead of expenses. What is the effect this year?
- AProfit is understated and assets are overstated
- BOnly cash is affected
- CProfit and assets are overstated
- DProfit and assets are understated
7.Break-even analysisMedium
A product sells for €32 per unit with a variable cost of €12 per unit. Fixed costs are €80 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €80 000p = €32v = €12profit = €6 000
Q = units
8.Break-even analysisHard
A product sells for €38 per unit, with a variable cost of €30 per unit and fixed costs of €4 000 per year. Budgeted sales are 650 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €4 000p = €38v = €30budget = 650
MS = %
3Solutions
1.Marketing principles
Answer: D · The threat of substitute products
Why this is the answer
The five forces are rivalry among competitors, threat of new entrants, threat of substitutes, and the bargaining power of buyers and of suppliers.
Answer
D · The threat of substitute products
2.Marketing principles
Answer: D · Captive product pricing
Why this is the answer
Captive product pricing sets a low price for the main product and earns margins on necessary consumables.
Answer
D · Captive product pricing
3.Economics concepts
Answer: C · Ignored, because it is a sunk cost
Why this is the answer
Sunk costs cannot be recovered and do not change with the decision, so rational choices compare only future costs and benefits.
Answer
C · Ignored, because it is a sunk cost
4.Economics concepts
Answer: A · Independent central banks with a credible commitment to low inflation
Why this is the answer
If the public expects policymakers to inflate later, expectations and inflation rise; delegating policy to an independent, credible central bank reduces this bias.
Answer
A · Independent central banks with a credible commitment to low inflation
5.Financial accounting
Answer: A · Net profit / shareholders' equity
Why this is the answer
ROE shows how much profit the company generates for each euro of equity invested by shareholders.
Answer
A · Net profit / shareholders' equity
6.Financial accounting
Answer: C · Profit and assets are overstated
Why this is the answer
Capitalising expenses moves cost out of profit into assets, so both are overstated now. Later depreciation spreads the cost over future years.
Answer
C · Profit and assets are overstated
7.Break-even analysis
Answer: Q = 4300 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 = 32 − 12 = €20
Units for the target profit
Q = (F + profit)/(p − v) = (80 000 + 6 000)/20 = 4 300
Answer
Q = 4 300 units
8.Break-even analysis
Answer: MS = 23.08 %
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) = 4 000/8 = 500
Margin of safety
MS = (650 − 500)/650·100 = 23.08%
Answer
MS = 23.08%
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