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 can be made in two ways. Method A has fixed costs of €10 000 per year and a variable cost of €15 per unit. Method B, more automated, has fixed costs of €12 500 per year and a variable cost of €10 per unit. At what yearly volume Q do both methods cost the same?
FA = €10 000vA = €15FB = €12 500vB = €10
Q = units
2.Break-even analysisHard
A company sells 8 000 units at €50 each, with a variable cost of €30 per unit and fixed costs of €100 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 15%?
Q = 8 000p = €50v = €30F = €100 000%ΔQ = +15%
%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?
- ABy recognising a large gain in the current year
- BRetrospectively, by restating all prior years
- CBy changing the original cost of the machine
- DProspectively, by spreading the remaining carrying amount over the new remaining life
4.Financial accountingHard
After the year end, but before the accounts are approved, a customer who owed money at year end goes bankrupt. Under IAS 10 this is:
- AIgnored, because it happened after the year end
- BAn adjusting event, so receivables are reduced
- CA change in accounting policy
- DA non-adjusting event, disclosed only
3Solutions
1.Break-even analysis
Answer: Q = 500 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).
Equal total costs
10 000 + 15Q = 12 500 + 10Q
Solve for Q
Q = (12 500 − 10 000)/(15 − 10) = 500
Answer
Q = 500 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
2.Break-even analysis
Answer: %ΔΠ = 40 %
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 = 8 000·20 = €160 000
Π = 160 000 − 100 000 = €60 000
DOL
DOL = 160 000/60 000 = 2.667
Change in profit
%ΔΠ = 2.667·(+15%) = +40%
Answer
%ΔΠ = +40%
Check: new profit = 9 200·20 − 100 000 = €84 000.00.
3.Financial accounting
Answer: D · 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
D · Prospectively, by spreading the remaining carrying amount over the new remaining life
4.Financial accounting
Answer: B · An adjusting event, so receivables are reduced
Why this is the answer
The customer's inability to pay existed at year end, so the accounts are adjusted. A fire after year end would be non-adjusting, because it is a new condition.
Answer
B · An adjusting event, so receivables are reduced
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