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 6 000 units at €8 each. The variable cost is €4 per unit and fixed costs are €16 000. Find the degree of operating leverage DOL at this sales level.
Q = 6 000p = €8v = €4F = €16 000
DOL =
2.Break-even analysisHard
A company sells two products. Product A sells for €12 with a variable cost of €8; product B sells for €27 with a variable cost of €15. They sell in a fixed mix of 2 units of A for every 1 of B. Fixed costs are €4 000 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €12, vA = €8pB = €27, vB = €15A : B = 2 : 1F = €4 000
Q = units
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€1,800
- B€4,000
- C€1,600
- D€2,000
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:
- ARises because interest is fixed
- BFalls by a smaller percentage
- CFalls by a larger percentage
- DFalls by exactly 20% as well
3Solutions
1.Break-even analysis
Answer: DOL = 3
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 = 6 000·(8 − 4) = €24 000
Operating profit
Π = 24 000 − 16 000 = €8 000
DOL
DOL = 24 000/8 000 = 3
Answer
DOL = 3
2.Break-even analysis
Answer: Q = 600 units
Break-even with a sales mix: when products sell in a fixed ratio, use the weighted average contribution margin: weight each product's p − v by its share of units. Break-even units = F/(weighted contribution margin), split again in the mix ratio.
Contribution margins
cmA = €4, cmB = €12
Weighted contribution margin
(2·4 + 1·12)/3 = €6.67
Break-even units
Q = 4 000/6.667 = 600
A: 400, B: 200
Answer
Q = 600 units
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: C · 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
C · Falls by a larger percentage
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