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
Management Accounting: cram pack
Formula sheets, the key method steps for every topic and 4 practice problems, with full solutions at the back.
1Formulas and methods
2Practice problems
1.Break-even analysisMedium
A product sells for €24 per unit with a variable cost of €4 per unit. Fixed costs are €40 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €40 000p = €24v = €4profit = €5 000
Q = units
2.Break-even analysisHard
A company sells 7 500 units at €30 each, with a variable cost of €15 per unit and fixed costs of €75 000. By what percentage %ΔΠ does operating profit change if sales volume falls by 10%?
Q = 7 500p = €30v = €15F = €75 000%ΔQ = −10%
%ΔΠ = %
3.Financial accountingMedium
A project costs €100,000 and brings in €25,000 cash per year. What is its payback period?
- A5 years
- B2.5 years
- C4 years
- D25 years
4.Financial accountingHard
An investor holds 30% of a company's shares and has significant influence but not control. How is the investment usually accounted for in group accounts?
- ABy full consolidation as a subsidiary
- BAs a joint operation with line-by-line sharing
- CUsing the equity method as an associate
- DAt cost with no changes ever
3Solutions
1.Break-even analysis
Answer: Q = 2250 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 = 24 − 4 = €20
Units for the target profit
Q = (F + profit)/(p − v) = (40 000 + 5 000)/20 = 2 250
Answer
Q = 2 250 units
2.Break-even analysis
Answer: %ΔΠ = −30 %
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 = 7 500·15 = €112 500
Π = 112 500 − 75 000 = €37 500
DOL
DOL = 112 500/37 500 = 3
Change in profit
%ΔΠ = 3·(−10%) = −30%
Answer
%ΔΠ = −30%
Check: new profit = 6 750·15 − 75 000 = €26 250.00.
3.Financial accounting
Answer: C · 4 years
Why this is the answer
€100,000 ÷ €25,000 = 4 years. Payback is simple but ignores the time value of money and cash flows after payback.
Answer
C · 4 years
4.Financial accounting
Answer: C · Using the equity method as an associate
Why this is the answer
Under IAS 28 the investment starts at cost and is adjusted for the investor's share of the associate's profits or losses, less dividends received.
Answer
C · Using the equity method as an associate
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