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 €30 with a variable cost of €20 per unit. Fixed costs are €5 000 per month and profit is taxed at 25%. How many units Q must be sold per month to earn €1 500 after tax?
p = €30v = €20F = €5 000T = 25%after-tax profit = €1 500
Q = units
2.Break-even analysisHard
A product sells for €42 per unit, with a variable cost of €30 per unit and fixed costs of €60 000 per year. Budgeted sales are 6 500 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €60 000p = €42v = €30budget = 6 500
MS = %
3.Financial accountingMedium
A machine costs €10,000 and is depreciated at 20% a year on the reducing balance. What is the depreciation charge in year 2?
- A€4,000
- B€1,800
- C€1,600
- D€2,000
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
- BIgnored completely
- CShown in financing activities
- DSubtracted from net profit
3Solutions
1.Break-even analysis
Answer: Q = 700 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).
Pre-tax profit needed
1 500/(1 − 0.25) = €2 000
Units needed
Q = (5 000 + 2 000)/10 = 700
Answer
Q = 700 units
2.Break-even analysis
Answer: MS = 23.08 %
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) = 60 000/12 = 5 000
Margin of safety
MS = (6 500 − 5 000)/6 500·100 = 23.08%
Answer
MS = 23.08%
3.Financial accounting
Answer: C · €1,600
Why this is the answer
Year 1: 20% × €10,000 = €2,000, leaving €8,000. Year 2: 20% × €8,000 = €1,600. Reducing balance charges less each year.
Answer
C · €1,600
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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