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 €19 per unit with a variable cost of €15 per unit. Fixed costs are €10 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €10 000p = €19v = €15profit = €5 000
Q = units
2.Break-even analysisHard
A company sells 2 000 units per month at €16 each, with a variable cost of €8 per unit and fixed costs of €6 400 per month. The variable cost rises by €3 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 2 000p = €16v = €8 → €11F = €6 400
Q = units
3.Financial accountingMedium
Which ratio measures a company's ability to pay its short-term obligations?
- AEarnings per share
- BThe current ratio
- CThe gross margin
- DReturn on equity
4.Financial accountingHard
In the indirect method of the cash flow statement, depreciation is:
- AIgnored completely
- BSubtracted from net profit
- CShown in financing activities
- DAdded back to net profit because it is a non-cash expense
3Solutions
1.Break-even analysis
Answer: Q = 3750 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).
Contribution margin per unit
p − v = 19 − 15 = €4
Units for the target profit
Q = (F + profit)/(p − v) = (10 000 + 5 000)/4 = 3 750
Answer
Q = 3 750 units
2.Break-even analysis
Answer: Q = 3200 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).
Current profit
Π = 2 000·(16 − 8) − 6 400 = €9 600
New contribution margin per unit
16 − 11 = €5
Units for the same profit
Q = (6 400 + 9 600)/5 = 3 200
Answer
Q = 3 200 units
3.Financial accounting
Answer: B · The current ratio
Why this is the answer
The current ratio (current assets/current liabilities) indicates liquidity; a value below 1 can signal problems paying short-term debts.
Answer
B · The current ratio
4.Financial accounting
Answer: D · 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
D · Added back to net profit because it is a non-cash expense
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