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 2 400 units at €12 each. The variable cost is €6 per unit and fixed costs are €4 800. Find the degree of operating leverage DOL at this sales level.
Q = 2 400p = €12v = €6F = €4 800
DOL =
2.Break-even analysisHard
A product sells for €32 per unit, with a variable cost of €12 per unit and fixed costs of €80 000 per year. Budgeted sales are 4 600 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €80 000p = €32v = €12budget = 4 600
MS = %
3.Financial accountingMedium
Profit for ordinary shareholders is €500,000 and there are 1,000,000 ordinary shares. What are basic earnings per share?
- A€2.00
- B€0.05
- C€0.50
- D€5.00
4.Financial accountingHard
In the indirect method of the cash flow statement, depreciation is:
- AAdded back to net profit because it is a non-cash expense
- BShown in financing activities
- CIgnored completely
- DSubtracted from net profit
3Solutions
1.Break-even analysis
Answer: DOL = 1.5
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 = 2 400·(12 − 6) = €14 400
Operating profit
Π = 14 400 − 4 800 = €9 600
DOL
DOL = 14 400/9 600 = 1.5
Answer
DOL = 1.5
2.Break-even analysis
Answer: MS = 13.04 %
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) = 80 000/20 = 4 000
Margin of safety
MS = (4 600 − 4 000)/4 600·100 = 13.04%
Answer
MS = 13.04%
3.Financial accounting
Answer: C · €0.50
Why this is the answer
Basic EPS = €500,000 ÷ 1,000,000 = €0.50 per share. Dividing the share price by EPS gives the P/E ratio.
Answer
C · €0.50
4.Financial accounting
Answer: A · Added back to net profit because it is a non-cash expense
Why this is the answer
Starting from profit, non-cash charges like depreciation are added back, and changes in working capital are adjusted.
Answer
A · Added back to net profit because it is a non-cash expense
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