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 company publishes articles on its own blog. In the paid, owned and earned media model, this is:
- AEarned media
- BPaid media
- COwned media
- DShared paid media
2.Marketing principlesHard
Under the EU General Data Protection Regulation (GDPR), sending marketing emails based on consent requires consent that is:
- AGiven once for all future purposes by any company
- BImplied by pre-ticked boxes
- CFreely given, specific, informed and unambiguous
- DAssumed when a customer visits the website
3.Economics conceptsMedium
When a central bank buys government bonds from banks in open market operations, it usually:
- ARaises tax revenue for the government
- BHas no effect on the money supply
- CIncreases bank reserves and the money supply
- DReduces bank reserves and so shrinks the money supply
4.Economics conceptsHard
The Laffer curve illustrates that:
- ABeyond some point, raising tax rates can reduce total tax revenue
- BLower tax rates always reduce tax revenue, whatever the starting rate
- CTax revenue is unrelated to tax rates
- DHigher tax rates always increase tax revenue
5.Financial accountingMedium
A project has a positive net present value (NPV) at the company's cost of capital. This means:
- AIts reported accounting profit will be positive in every year
- BIt recovers its cost within one year
- CIt has no risk at all
- DIt earns more than the required return and should add value
6.Financial accountingHard
Making a part costs €10 materials, €6 labour and €4 variable overhead, plus €5 of fixed overhead that continues anyway. A supplier offers it at €22. What should the firm do on cost grounds?
- ABuy it, because fixed costs are always relevant
- BMake it, because the full cost of €25 is below €22
- CMake it, because the relevant cost of €20 is below €22
- DBuy it, because the full cost of €25 per unit is above €22
7.Break-even analysisMedium
A company sells 1 200 units at €8 each. The variable cost is €6 per unit and fixed costs are €1 600. Find the degree of operating leverage DOL at this sales level.
Q = 1 200p = €8v = €6F = €1 600
DOL =
8.Break-even analysisHard
A product sells for €50 per unit, with a variable cost of €45 per unit and fixed costs of €5 000 per year. Budgeted sales are 1 400 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €5 000p = €50v = €45budget = 1 400
MS = %
3Solutions
1.Marketing principles
Answer: C · Owned media
Why this is the answer
Owned media are channels the brand controls, such as its website and blog. Paid media are bought ads; earned media are free coverage, shares and reviews.
Answer
C · Owned media
2.Marketing principles
Answer: C · Freely given, specific, informed and unambiguous
Why this is the answer
Consent must be a clear affirmative act; pre-ticked boxes or silence are not valid, and it must be as easy to withdraw as to give.
Answer
C · Freely given, specific, informed and unambiguous
3.Economics concepts
Answer: C · Increases bank reserves and the money supply
Why this is the answer
Buying bonds injects reserves into the banking system, which tends to increase the money supply and lower interest rates.
Answer
C · Increases bank reserves and the money supply
4.Economics concepts
Answer: A · 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
A · Beyond some point, raising tax rates can reduce total tax revenue
5.Financial accounting
Answer: D · It earns more than the required return and should add value
Why this is the answer
A positive NPV means the present value of inflows exceeds the investment at the required rate, so the project increases shareholder wealth.
Answer
D · It earns more than the required return and should add value
6.Financial accounting
Answer: C · Make it, because the relevant cost of €20 is below €22
Why this is the answer
Only the €20 of variable cost is avoided by buying; the €5 fixed overhead stays. Making costs €20 versus €22 to buy, so making saves €2 per unit.
Answer
C · Make it, because the relevant cost of €20 is below €22
7.Break-even analysis
Answer: DOL = 3
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 = 1 200·(8 − 6) = €2 400
Operating profit
Π = 2 400 − 1 600 = €800
DOL
DOL = 2 400/800 = 3
Answer
DOL = 3
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) = 5 000/5 = 1 000
Margin of safety
MS = (1 400 − 1 000)/1 400·100 = 28.57%
Answer
MS = 28.57%
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