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 company sells 10 000 units at €12 each. The variable cost is €4 per unit and fixed costs are €40 000. Find the degree of operating leverage DOL at this sales level.
Q = 10 000p = €12v = €4F = €40 000
DOL =
2.Break-even analysisHard
A company sells 3 750 units at €26 each, with a variable cost of €6 per unit and fixed costs of €50 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 12%?
Q = 3 750p = €26v = €6F = €50 000%ΔQ = +12%
%ΔΠ = %
3.Financial accountingMedium
A company finds that a machine will last 8 years instead of the 5 originally estimated. Under IAS 8, how is this change applied?
- AProspectively, by spreading the remaining carrying amount over the new remaining life
- BBy changing the original cost of the machine
- CRetrospectively, by restating all prior years
- DBy recognising a large gain in the current year
4.Financial accountingHard
Two firms have the same operating profit, but one is financed mostly by debt. When operating profit falls by 20%, the highly geared firm's net profit:
- AFalls by a larger percentage
- BFalls by exactly 20% as well
- CRises because interest is fixed
- DFalls by a smaller percentage
3Solutions
1.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 = 10 000·(12 − 4) = €80 000
Operating profit
Π = 80 000 − 40 000 = €40 000
DOL
DOL = 80 000/40 000 = 2
Answer
DOL = 2
2.Break-even analysis
Answer: %ΔΠ = 36 %
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 = 3 750·20 = €75 000
Π = 75 000 − 50 000 = €25 000
DOL
DOL = 75 000/25 000 = 3
Change in profit
%ΔΠ = 3·(+12%) = +36%
Answer
%ΔΠ = +36%
Check: new profit = 4 200·20 − 50 000 = €34 000.00.
3.Financial accounting
Answer: A · Prospectively, by spreading the remaining carrying amount over the new remaining life
Why this is the answer
Changes in estimates affect the current and future periods only. Prior-period restatement is for changes in policy and corrections of errors.
Answer
A · Prospectively, by spreading the remaining carrying amount over the new remaining life
4.Financial accounting
Answer: A · Falls by a larger percentage
Why this is the answer
Fixed interest stays the same, so any change in operating profit causes a bigger percentage change in profit for shareholders. This is financial risk.
Answer
A · Falls by a larger percentage
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