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 €20 000 per year and a variable cost of €25 per unit. Method B, more automated, has fixed costs of €24 000 per year and a variable cost of €23 per unit. At what yearly volume Q do both methods cost the same?
FA = €20 000vA = €25FB = €24 000vB = €23
Q = units
2.Break-even analysisHard
A company sells 3 750 units at €30 each, with a variable cost of €20 per unit and fixed costs of €15 000. By what percentage %ΔΠ does operating profit change if sales volume falls by 10%?
Q = 3 750p = €30v = €20F = €15 000%ΔQ = −10%
%ΔΠ = %
3.Financial accountingMedium
Cost of sales is €600,000 and average inventory is €100,000. What is the inventory turnover?
- A0.17 times a year
- B16 times a year
- C6 times a year
- D60 times a year
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:
- AA change in accounting policy
- BA non-adjusting event, disclosed only
- CAn adjusting event, so receivables are reduced
- DIgnored, because it happened after the year end
3Solutions
1.Break-even analysis
Answer: Q = 2000 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
20 000 + 25Q = 24 000 + 23Q
Solve for Q
Q = (24 000 − 20 000)/(25 − 23) = 2 000
Answer
Q = 2 000 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
2.Break-even analysis
Answer: %ΔΠ = −16.67 %
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 = 3 750·10 = €37 500
Π = 37 500 − 15 000 = €22 500
DOL
DOL = 37 500/22 500 = 1.667
Change in profit
%ΔΠ = 1.667·(−10%) = −16.67%
Answer
%ΔΠ = −16.67%
Check: new profit = 3 375·10 − 15 000 = €18 750.00.
3.Financial accounting
Answer: C · 6 times a year
Why this is the answer
€600,000 ÷ €100,000 = 6, so inventory is replaced about every 61 days (365 ÷ 6).
Answer
C · 6 times a year
4.Financial accounting
Answer: C · 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
C · An adjusting event, so receivables are reduced
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