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−0.5, elastic, so revenue falls
- B−2, inelastic, so revenue rises
- C−0.5, inelastic, so revenue rises
- D−2, elastic, so revenue falls
2.Marketing principlesHard
A survey asks: "Don't you agree that our excellent staff are very helpful?" What is the main problem?
- AIt is too short to be understood
- BIt is a leading question that pushes respondents towards agreement
- CIt is an open question that is hard to analyse
- DIt asks about two unrelated products
3.Economics conceptsMedium
Nominal GDP grew by 5% and the GDP deflator rose by 2%. Real GDP grew by approximately:
- A3%
- B10%
- C7%
- D2.5%
4.Economics conceptsHard
The Laffer curve illustrates that:
- ATax revenue is unrelated to tax rates
- BBeyond some point, raising tax rates can reduce total tax revenue
- CHigher tax rates always increase tax revenue
- DLower tax rates always reduce tax revenue, whatever the starting rate
5.Financial accountingMedium
When preparing a bank reconciliation, which item explains why the bank statement balance is higher than the cash book balance?
- ACash deposited but not yet credited on the bank statement
- BCheques issued but not yet presented to the bank
- CBank charges not yet entered in the cash book
- DA direct debit not yet entered in the cash book
6.Financial accountingHard
A company borrows at 5% interest to invest in assets that earn 12%. What is the likely effect on return on equity?
- AROE rises, but financial risk also increases
- BROE stays the same, because debt is not equity
- CROE rises and financial risk falls
- DROE falls, because interest is an expense
7.Break-even analysisMedium
A product sells for €50 with a variable cost of €45 per unit. Fixed costs are €25 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €7 500 after tax?
p = €50v = €45F = €25 000T = 20%after-tax profit = €7 500
Q = units
8.Break-even analysisHard
A company sells 2 000 units at €18 each, with a variable cost of €8 per unit and fixed costs of €8 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 10%?
Q = 2 000p = €18v = €8F = €8 000%ΔQ = +10%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: D · −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
D · −2, elastic, so revenue falls
2.Marketing principles
Answer: B · It is a leading question that pushes respondents towards agreement
Why this is the answer
Leading questions bias answers through wording. A neutral version would be "How helpful were our staff?" with a balanced rating scale.
Answer
B · It is a leading question that pushes respondents towards agreement
3.Economics concepts
Answer: A · 3%
Why this is the answer
Subtracting the rise in prices from nominal growth gives real growth of roughly 5% − 2% = 3%.
Answer
A · 3%
4.Economics concepts
Answer: B · Beyond some point, raising tax rates can reduce total tax revenue
Why this is the answer
Very high rates discourage taxed activity or encourage avoidance, so revenue peaks at some rate between 0 and 100%; where that peak lies is debated.
Answer
B · Beyond some point, raising tax rates can reduce total tax revenue
5.Financial accounting
Answer: B · Cheques issued but not yet presented to the bank
Why this is the answer
Unpresented cheques have reduced the cash book but not the bank balance. Outstanding deposits, bank charges and unrecorded direct debits work the other way.
Answer
B · Cheques issued but not yet presented to the bank
6.Financial accounting
Answer: A · ROE rises, but financial risk also increases
Why this is the answer
Positive financial leverage: assets earn more than the debt costs, so profit per euro of equity rises. If returns drop below 5%, leverage works against shareholders.
Answer
A · ROE rises, but financial risk also increases
7.Break-even analysis
Answer: Q = 6875 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
7 500/(1 − 0.2) = €9 375
Units needed
Q = (25 000 + 9 375)/5 = 6 875
Answer
Q = 6 875 units
8.Break-even analysis
Answer: %ΔΠ = 16.67 %
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 = 2 000·10 = €20 000
Π = 20 000 − 8 000 = €12 000
DOL
DOL = 20 000/12 000 = 1.667
Change in profit
%ΔΠ = 1.667·(+10%) = +16.67%
Answer
%ΔΠ = +16.67%
Check: new profit = 2 200·10 − 8 000 = €14 000.00.
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