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
In the BCG matrix, what are the usual options for a "question mark"?
- AAlways close it immediately
- BHarvest cash with minimal investment
- CInvest heavily to build market share, or divest
- DKeep it unchanged because it is the market leader
2.Marketing principlesHard
When is price skimming most suitable?
- AFor an innovative product with few rivals and early buyers willing to pay a premium
- BWhen the firm wants the largest market share at launch
- CFor a commodity product in a crowded market
- DWhen customers are very sensitive to price
3.Economics conceptsMedium
A savings account pays a nominal interest rate of 6% and inflation is 4%. The approximate real interest rate is:
- A1.5%
- B10%
- C2%
- D24%
4.Economics conceptsHard
According to the quantity theory of money (MV = PY), if velocity and real output are constant, a 5% rise in the money supply leads to:
- AA 5% fall in velocity
- BNo change in prices
- CAbout a 5% rise in the price level
- DAbout a 5% rise in real output
5.Financial accountingMedium
Budgeted sales are 1,500 units and the break-even point is 1,000 units. What is the margin of safety?
- A1,500 units
- B500 units
- C2,500 units
- D1,000 units
6.Financial accountingHard
Under IFRS 15, revenue is recognised:
- AAt the end of the financial year
- BWhen (or as) the entity satisfies a performance obligation by transferring control to the customer
- COnly when cash is received
- DWhen the contract is signed
7.Break-even analysisMedium
A company sells 5 000 units at €31 each. The variable cost is €25 per unit and fixed costs are €15 000. Find the degree of operating leverage DOL at this sales level.
Q = 5 000p = €31v = €25F = €15 000
DOL =
8.Break-even analysisHard
A product sells for €16 per unit, with a variable cost of €12 per unit and fixed costs of €10 000 per year. Budgeted sales are 3 500 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €10 000p = €16v = €12budget = 3 500
MS = %
3Solutions
1.Marketing principles
Answer: C · Invest heavily to build market share, or divest
Why this is the answer
Question marks need cash to grow. Managers must decide whether they can become stars; if not, it may be better to sell or drop them.
Answer
C · Invest heavily to build market share, or divest
2.Marketing principles
Answer: A · For an innovative product with few rivals and early buyers willing to pay a premium
Why this is the answer
Skimming works when the product is distinctive, entry barriers protect it for a while, and some customers value being first enough to pay more.
Answer
A · For an innovative product with few rivals and early buyers willing to pay a premium
3.Economics concepts
Answer: C · 2%
Why this is the answer
The real interest rate is approximately the nominal rate minus inflation: 6% − 4% = 2%.
Answer
C · 2%
4.Economics concepts
Answer: C · About a 5% rise in the price level
Why this is the answer
With V and Y constant, M and P move proportionally, so prices rise about 5%. This is the classical view of money neutrality in the long run.
Answer
C · About a 5% rise in the price level
5.Financial accounting
Answer: B · 500 units
Why this is the answer
Margin of safety = budgeted sales − break-even sales = 500 units, or one third of budgeted sales.
Answer
B · 500 units
6.Financial accounting
Answer: B · When (or as) the entity satisfies a performance obligation by transferring control to the customer
Why this is the answer
The steps: identify the contract, identify performance obligations, determine the price, allocate it, and recognise revenue as each obligation is satisfied.
Answer
B · When (or as) the entity satisfies a performance obligation by transferring control to the customer
7.Break-even analysis
Answer: DOL = 2
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 = 5 000·(31 − 25) = €30 000
Operating profit
Π = 30 000 − 15 000 = €15 000
DOL
DOL = 30 000/15 000 = 2
Answer
DOL = 2
8.Break-even analysis
Answer: MS = 28.57 %
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) = 10 000/4 = 2 500
Margin of safety
MS = (3 500 − 2 500)/3 500·100 = 28.57%
Answer
MS = 28.57%
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