Financial Ratios

PDF generated using the open source mwlib toolkit. See http://code.pediapress.com/ for more information.
PDF generated at: Sat, 29 Jan 2011 16:48:11 UTC
Business Administration
Financial Ratios
Contents
Articles
Financial ratio 1
Gross margin 9
Operating margin 11
Profit margin 12
Return on equity 13
Rate of return 15
Return on assets 25
Return on assets Du Pont 26
Return on net assets 28
Return on capital 28
Risk adjusted return on capital 29
Cash flow return on investment 30
Current ratio 30
Cash ratio 31
Operating cash flow 37
Net present value 38
Internal rate of return 43
References
Article Sources and Contributors 49
Image Sources, Licenses and Contributors 51
Article Licenses
License 52
Financial ratio
1
Financial ratio
Accountancy
Key concepts
Accountant € Bookkeeping € Cash and accrual basis € Constant Item Purchasing Power Accounting € Cost of goods sold € Debits and
credits € Double-entry system € Fair value accounting € FIFO & LIFO € GAAP / International Financial Reporting Standards € General
ledger € Historical cost € Matching principle € Revenue recognition € Trial balance
Fields of accounting
Cost € Financial € Forensic € Fund € Management € Tax
Financial statements
Statement of Financial Position € Statement of cash flows € Statement of changes in equity € Statement of comprehensive income €
Notes € MD&A
Auditing
Auditor's report € Financial audit € GAAS / ISA € Internal audit € Sarbanes€Oxley Act
Accounting qualifications
CA € CGA € CMA  € CPA
A financial ratio (or accounting ratio) is a relative magnitude of two selected numerical values taken from an
enterprise's financial statements. Often used in accounting, there are many standard ratios used to try to evaluate the
overall financial condition of a corporation or other organization. Financial ratios may be used by managers within a
firm, by current and potential shareholders (owners) of a firm, and by a firm's creditors. Security analysts use
financial ratios to compare the strengths and weaknesses in various companies.
[1]
If shares in a company are traded
in a financial market, the market price of the shares is used in certain financial ratios.
Ratios can be expressed as a decimal value, such as 0.10, or given as an equivalent percent value, such as 10%.
Some ratios are usually quoted as percentages, especially ratios that are usually or always less than 1, such as
earnings yield, while others are usually quoted as decimal numbers, especially ratios that are usually more than 1,
such as P/E ratio; these latter are also called multiples. Given any ratio, one can take its reciprocal; if the ratio was
above 1, the reciprocal will be below 1, and conversely. The reciprocal expresses the same information, but may be
more understandable: for instance, the earnings yield can be compared with bond yields, while the P/E ratio cannot
be: for example, a P/E ratio of 20 corresponds to an earnings yield of 5%.
Sources of data for financial ratios
Values used in calculating financial ratios are taken from the balance sheet, income statement, statement of cash
flows or (sometimes) the statement of retained earnings. These comprise the firm's "accounting statements" or
financial statements. The statements' data is based on the accounting method and accounting standards used by the
organization.
Purpose and types of ratios
Financial ratios quantify many aspects of a business and are an integral part of the financial statement analysis.
Financial ratios are categorized according to the financial aspect of the business which the ratio measures. Liquidity
ratios measure the availability of cash to pay debt.
[2]
Activity ratios measure how quickly a firm converts non-cash
assets to cash assets.
[3]
Debt ratios measure the firm's ability to repay long-term debt.
[4]
Profitability ratios
measure the firm's use of its assets and control of its expenses to generate an acceptable rate of return.
[5]
Market
ratios measure investor response to owning a company's stock and also the cost of issuing stock.
[6]
Financial ratio
2
Financial ratios allow for comparisons
• between companies
• between industries
• between different time periods for one company
• between a single company and its industry average
Ratios generally hold no meaning unless they are benchmarked against something else, like past performance or
another company. Thus, the ratios of firms in different industries, which face different risks, capital requirements,
and competition are usually hard to compare.
Accounting methods and principles
Financial ratios may not be directly comparable between companies that use different accounting methods or follow
various standard accounting practices. Most public companies are required by law to use generally accepted
accounting principles for their home countries, but private companies, partnerships and sole proprietorships may not
use accrual basis accounting. Large multi-national corporations may use International Financial Reporting Standards
to produce their financial statements, or they may use the generally accepted accounting principles of their home
country.
There is no international standard for calculating the summary data presented in all financial statements, and the
terminology is not always consistent between companies, industries, countries and time periods.
Abbreviations and terminology
Various abbreviations may be used in financial statements, especially financial statements summarized on the
Internet. Sales reported by a firm are usually net sales, which deduct returns, allowances, and early payment
discounts from the charge on an invoice. Net income is always the amount after taxes, depreciation, amortization,
and interest, unless otherwise stated. Otherwise, the amount would be EBIT, or EBITDA (see below).
Companies that are primarily involved in providing services with labour do not generally report "Sales" based on
hours. These companies tend to report "revenue" based on the monetary value of income that the services provide.
Note that Shareholder's Equity and Owner's Equity are not the same thing, Shareholder's Equity represents the total
number of shares in the company multiplied by each share's book value; Owner's Equity represents the total number
of shares that an individual shareholder owns (usually the owner with controlling interest), multiplied by each share's
book value. It is important to make this distinction when calculating ratios.
Other abbreviations
(Note: These are not ratios, but values in currency.)
• COGS = Cost of goods sold, or cost of sales.
• EBIT = Earnings before interest and taxes
• EBITDA = Earnings before interest, taxes, depreciation, and amortization
• EPS = Earnings per share
Financial ratio
3
Ratios
Profitability ratios
Profitability ratios measure the company's use of its assets and control of its expenses to generate an acceptable rate
of return
Gross margin, Gross profit margin or Gross Profit Rate
[7]

[8]
OR
Operating margin, Operating Income Margin, Operating profit margin or Return on sales (ROS)
[8]

[9]
Note: Operating income is the difference between operating revenues and operating expenses, but it is also
sometimes used as a synonym for EBIT and operating profit.
[10]
This is true if the firm has no non-operating
income. (Earnings before interest and taxes / Sales
[11]

[12]
)
Profit margin, net margin or net profit margin
[13]
Return on equity (ROE)
[13]
Return on investment (ROI ratio or Du Pont Ratio)
[6]
Return on assets (ROA)
[14]
Return on assets Du Pont (ROA Du Pont)
[15]
Return on Equity Du Pont (ROE Du Pont)
Return on net assets (RONA)
Return on capital (ROC)
Risk adjusted return on capital (RAROC)
Financial ratio
4
OR
Return on capital employed (ROCE)
Note: this is somewhat similar to (ROI), which calculates Net Income per Owner's Equity
Cash flow return on investment (CFROI)
Efficiency ratio
Net gearing
Basic Earnings Power Ratio
[16]
Liquidity ratios
Liquidity ratios measure the availability of cash to pay debt.
Current ratio (Working Capital Ratio)
[17]
Acid-test ratio (Quick ratio)
[17]
Cash ratio
[17]
Operation cash flow ratio
Financial ratio
5
Activity ratios (Efficiency Ratios)
Activity ratios measure the effectiveness of the firms use of resources.
Average collection period
[3]
Degree of Operating Leverage (DOL)
DSO Ratio.
[18]
Average payment period
[3]
Asset turnover
[19]
Stock turnover ratio
[20]

[21]
Receivables Turnover Ratio
[22]
Inventory conversion ratio
[4]
Inventory conversion period (essentially same thing as above)
Receivables conversion period
Payables conversion period
Cash Conversion Cycle
Financial ratio
6
Debt ratios (leveraging ratios)
Debt ratios measure the firm's ability to repay long-term debt. Debt ratios measure financial leverage.
Debt ratio
[23]
Debt to equity ratio
[24]
Long-term Debt to equity (LT Debt to Equity)
[24]
Times interest-earned ratio / Interest Coverage Ratio
[24]
OR
Debt service coverage ratio
Market ratios
Market ratios measure investor response to owning a company's stock and also the cost of issuing stock.
Earnings per share (EPS)
[25]
Payout ratio
[25]

[26]
OR
Dividend cover (the inverse of Payout Ratio)
P/E ratio
Dividend yield
Cash flow ratio or Price/cash flow ratio
[27]
Financial ratio
7
Price to book value ratio (P/B or PBV)
[27]
Price/sales ratio
PEG ratio
Other Market Ratios
EV/EBITDA
EV/Sales
Cost/Income ratio
Sector-specific ratios
EV/capacity
EV/output
Capital Budgeting Ratios
In addition to assisting management and owners in diagnosing the financial health of their company, ratios can also
help managers make decisions about investments or projects that the company is considering to take, such as
acquisitions, or expansion.
Many formal methods are used in capital budgeting, including the techniques such as
• Net present value
• Profitability index
• Internal rate of return
• Modified Internal Rate of Return
• Equivalent annuity
Financial ratio
8
References
[1] Groppelli, Angelico A.; Ehsan Nikbakht (2000). Finance, 4th ed. Barron's Educational Series, Inc.. pp. 433. ISBN 0764112759.
[2] Groppelli, p. 434.
[3] Groppelli, p. 436.
[4] Groppelli, p. 439.
[5] Groppelli, p. 442.
[6] Groppelli, p. 445.
[7] Williams, P. 265.
[8] Williams, p. 1094.
[9] Williams, Jan R.; Susan F. Haka, Mark S. Bettner, Joseph V. Carcello (2008). Financial & Managerial Accounting. McGraw-Hill Irwin.
pp. 266. ISBN 9780072996500.
[10] http:/ / www.investorwords.com/ 3460/ operating_income. html Operating income definition
[11] Groppelli, p. 443.
[12] Bodie, Zane; Alex Kane and Alan J. Marcus (2004). Essentials of Investments, 5th ed. McGraw-Hill Irwin. pp. 459. ISBN 0072510773.
[13] Groppelli, p. 444.
[14] Professor Cram. "Ratios of Profitability: Return on Assets" College-Cram.com. 14 May 2008
<http://www.college-cram.com/study/finance/ratios-of-profitability/return-on-assets/> (http:/ / www. college-cram. com/ study/ finance/
ratios-of-profitability/ return-on-assets/ )
[15] Professor Cram. "Ratios of Profitability: Return on Assets Du Pont" College-Cram.com. 14 May 2008
<http://www.college-cram.com/study/finance/ratios-of-profitability/return-on-assets-du-pont/> (http:/ / www. college-cram. com/ study/
finance/ ratios-of-profitability/ return-on-assets-du-pont/ )
[16] Weston, J. (1990). Essentials of Managerial Finance. Hinsdale: Dryden Press. p. 295. ISBN 0030307333.
[17] Groppelli, p. 435.
[18] Houston, Joel F.; Brigham, Eugene F. (2009). Fundamentals of Financial Management. [Cincinnati, Ohio]: South-Western College Pub.
p. 90. ISBN 0-324-59771-1.
[19] Bodie, p. 459.
[20] Groppelli, p. 438.
[21] Weygandt, J. J., Kieso, D. E., & Kell, W. G. (1996). Accounting Principles (4th ed.). New York, Chichester, Brisbane, Toronto, Singapore:
John Wiley & Sons, Inc. p. 801-802.
[22] Weygandt, J. J., Kieso, D. E., & Kell, W. G. (1996). Accounting Principles (4th ed.). New York, Chichester, Brisbane, Toronto, Singapore:
John Wiley & Sons, Inc. p. 800.
[23] Groppelli, p. 440; Williams, p. 640.
[24] Groppelli, p. 441.
[25] Groppelli, p. 446.
[26] Groppelli, p. 449.
[27] Groppelli, p. 447.
External links
• Stock Valuation Metrics (http:/ / www. retailinvestor. org/ valuemetrics. html)
• A Review of Financial Ratio Analysis (http:/ / lipas. uwasa. fi/ ~ts/ ejre/ ejre. html)
• On the Classification of Financial Ratios (http:/ / lipas. uwasa. fi/ ~ts/ sera/ sera. html)
Gross margin
9
Gross margin
Gross margin, gross profit margin or gross profit rate is the difference between the sales and the production costs
excluding overhead, payroll, taxation, and interest payments. Gross margin can be defined as the amount of
contribution to the business enterprise, after paying for direct-fixed and direct-variable unit costs, required to cover
overheads (fixed commitments) and provide a buffer for unknown items. It expresses the relationship between gross
profit and sales revenue. It is a measure of how well each dollar of a company's revenue is utilized to cover the costs
of goods sold.
[1]
It can be expressed in absolute terms:
Gross margin = net sales - cost of goods sold + annual sales return
or as the ratio of gross profit to sales revenue, usually in the form of a percentage:
Cost of sales (also known as cost of goods (CoGs)) includes variable costs and fixed costs directly linked to the sale,
such as material costs, labor, supplier profit, shipping costs, etc. It does not include indirect fixed costs like office
expenses, rent, administrative costs, etc.
Higher gross margins for a manufacturer reflect greater efficiency in turning raw materials into income. For a retailer
it will be their markup over wholesale. Larger gross margins are generally good for companies, with the exception of
discount retailers. They need to show that operations efficiency and financing allows them to operate with tiny
margins.
How gross margin is used in sales
Retailers can measure their profit by using two basic methods, markup and margin, both of which give a description
of the gross profit of the sale. The markup expresses profit as a percentage of the retailer's cost for the product. The
margin expresses profit as a percentage of the retailer's sales price for the product. These two methods give different
percentages as results, but both percentages are valid descriptions of the retailer's profit. It is important to specify
which method you are using when you refer to a retailer's profit as a percentage.
Some retailers use margins because you can easily calculate profits from a sales total. If your margin is 30%, then
30% of your sales total is profit. If your markup is 30%, the percentage of your daily sales that are profit will not be
the same percentage.
Some retailers use markups because it is easier to calculate a sales price from a cost using markups. If your markup
is 40%, then your sales price will be 40% above the item cost. If your margin is 40%, your sales price will not be
equal to 40% over cost (indeed it will be 60% above the item cost).
Markup
Markup can be expressed either as a decimal or as a percentage, but is used as a multiplier. Here is an example:
If a product costs the company $100 to make and they wish to make a 50% profit on the sale of the product (sale
dollars) they would have to use a markup of 100%. To calculate the price to the customer, you simply take the
product cost of $100 and multiply it by (1 + the markup), e.g.: 1+1=2, arriving at the selling price of $200.
The equation for calculating gross margin is: gross margin = sales - cost of goods sold
A simple way to keep markup and gross margin factors straight is to remember that:
1. Percent of markup is 100 times the price difference divided by the cost.
2. Percent of gross margin is 100 times the price difference divided by the selling price.
Gross margin
10
Gross margin (as a percentage of sales)
Most people find it easier to work with gross margin because it directly tells you how many of the sale dollars are
profit. In reference to the two examples above:
The $200 price that includes a 100% markup represents a 50% gross margin. Gross margin is just the percentage of
the selling price that is profit. In this case 50% of the price is profit, or $100.
In the more complex example of selling price $339, a markup of 66% represents approximately a 40% gross margin.
This means that 40% of the $339 is profit. Again, gross margin is just the direct percentage of profit in the sale price.
In accounting, the gross margin refers to sales minus cost of goods sold. It is not necessarily profit as other expenses
such as sales, administrative, and financial must be deducted.And it means company are reducing their cost of
production or passing their cost to customers. the higher ratio is better
Converting between gross margin and markup
The formula to convert a markup to gross margin is:
Examples:
• Markup = 100%; GM = [1 / (1 + 1)] = 0.5 = 50%
• Markup = 66%; GM = [0.66 / (1 + 0.66)] = 0.39759036 = 39.759036%
The formula to convert a gross margin to markup is:
Examples:
• Gross margin = 0.5 = 50%; markup = [0.5 / (1 - 0.5)] = 1 = 100%
• Gross margin = 0.39759036 = 39.759036%; markup = [0.39759036 / (1 - 0.39759036)] = 0.659999996 = 66%
Using gross margin to calculate selling price
Given the cost of an item, one can compute the selling price required to achieve a specific gross margin. For
example, if your product costs $100 and the required gross margin is 40%, then
Selling price = $100 / (1 - 40%) = $100 / 0.60 = $166.67
Differences between industries
In some industries, like clothing for example, profit margins are expected to be near the 40% mark, as the goods
need to be bought from suppliers at a certain rate before they are resold. In other industries such as software product
development, since the cost of duplication is negligible, the gross profit margin can be higher than 80% in many
cases.
Gross margin
11
References
[1] Berman, Karen (2006). Financial Intelligence. Boston: Harvard Business School Press. p. 152. ISBN 1591397642.
Operating margin
In business, operating margin, operating income margin, operating profit margin or return on sales (ROS) is
the ratio of operating income (operating profit in the UK) divided by net sales, usually presented in percent.
Example
The Coca Cola Company
Consolidated Statements of Income
[1]
(In millions)
Net Operating Revenues $ 20,088
Gross Profit $ 15,924
Operating Income $ 6,318
Income Before Income Taxes $ 6,578
Net Income $ 5,080
(Relevant figures in italics)
It is a measurement of what proportion of a company's revenue is left over, before taxes and other indirect costs
(such as rent, bonus, interest, etc.), after paying for variable costs of production as wages, raw materials, etc. A good
operating margin is needed for a company to be able to pay for its fixed costs, such as interest on debt. A higher
operating margin means that the company has less financial risk.
http:/ / www. moneychimp. com/ articles/ financials/ income. htm
Operating margin can be considered total revenue from product sales less all costs before adjustment for taxes,
dividends to shareholders, and interest on debt
References
[1] The Coca Cola Company Form 10-K SEC Filing 2006, p 67
Profit margin
12
Profit margin
Profit margin, net margin, net profit margin or net profit ratio all refer to a measure of profitability. It is
calculated by finding the net profit as a percentage of the revenue.
[1]
The profit margin is mostly used for internal comparison. It is difficult to accurately compare the net profit ratio for
different entities. Individual businesses' operating and financing arrangements vary so much that different entities are
bound to have different levels of expenditure, so that comparison of one with another can have little meaning. A low
profit margin indicates a low margin of safety: higher risk that a decline in sales will erase profits and result in a net
loss, or a negative margin.
Profit margin is an indicator of a company's pricing strategies and how well it controls costs. Differences in
competitive strategy and product mix cause the profit margin to vary among different companies.
[2]
Confusion
Profit margin is frequently confused with markup. It's not uncommon for entrepreneurs to erroneously claim profit
margins over 100%. Most likely these entrepreneurs are referring to the markup on a product as a percentage of
product cost.
References
[1] "profit margin Definition" (http:/ / www.investorwords. com/ 3885/ profit_margin. html). InvestorWords. InvestorGuide.com. . Retrieved
December 17, 2009.
[2] "profit margin" (http:/ / financial-dictionary.thefreedictionary. com/ profit+ margin). The Free Dictionary. Farlex. . Retrieved December 17,
2009.
Return on equity
13
Return on equity
Accountancy
Key concepts
Accountant € Bookkeeping € Cash and accrual basis € Constant Item Purchasing Power Accounting € Cost of goods sold € Debits and
credits € Double-entry system € Fair value accounting € FIFO & LIFO € GAAP / International Financial Reporting Standards € General
ledger € Historical cost € Matching principle € Revenue recognition € Trial balance
Fields of accounting
Cost € Financial € Forensic € Fund € Management € Tax
Financial statements
Statement of Financial Position € Statement of cash flows € Statement of changes in equity € Statement of comprehensive income €
Notes € MD&A
Auditing
Auditor's report € Financial audit € GAAS / ISA € Internal audit € Sarbanes€Oxley Act
Accounting qualifications
CA € CGA € CMA  € CPA
Return on equity (ROE) measures the rate of return on the ownership interest (shareholders' equity) of the common
stock owners. It measures a firm's efficiency at generating profits from every unit of shareholders' equity (also
known as net assets or assets minus liabilities). ROE shows how well a company uses investment funds to generate
earnings growth. ROEs between 15% and 20% are considered desirable.
[1]
The formula

[2]
ROE is equal to a fiscal year's net income (after preferred stock dividends but before common stock dividends)
divided by total equity (excluding preferred shares), expressed as a percentage. As with many financial ratios, ROE
is best used to compare companies in the same industry.
High ROE yields no immediate benefit. Since stock prices are most strongly determined by earnings per share (EPS),
you will be paying twice as much (in Price/Book terms) for a 20% ROE company as for a 10% ROE company.
The benefit comes from the earnings reinvested in the company at a high ROE rate, which in turn gives the company
a high growth rate. The benefit can also come as a dividend on common shares or as a combination of dividends and
reinvestment in the company. ROE is presumably irrelevant if the earnings are not reinvested.
• The sustainable growth model shows us that when firms pay dividends, earnings growth lowers. If the dividend
payout is 20%, the growth expected will be only 80% of the ROE rate.
• The growth rate will be lower if the earnings are used to buy back shares. If the shares are bought at a multiple of
book value (say 3 times book), the incremental earnings returns will be only 'that fraction' of ROE (ROE/3).
• New investments may not be as profitable as the existing business. Ask "what is the company doing with its
earnings?"
• Remember that ROE is calculated from the company's perspective, on the company as a whole. Since much
financial manipulation is accomplished with new share issues and buyback, always recalculate on a 'per share'
basis, i.e., earnings per share/book value per share.
Return on equity
14
The DuPont formula
The DuPont formula, also known as the strategic profit model, is a common way to break down ROE into three
important components. Essentially, ROE will equal the net margin multiplied by asset turnover multiplied by
financial leverage. Splitting return on equity into three parts makes it easier to understand changes in ROE over time.
For example, if the net margin increases, every sale brings in more money, resulting in a higher overall ROE.
Similarly, if the asset turnover increases, the firm generates more sales for every unit of assets owned, again resulting
in a higher overall ROE. Finally, increasing financial leverage means that the firm uses more debt financing relative
to equity financing. Interest payments to creditors are tax deductible, but dividend payments to shareholders are not.
Thus, a higher proportion of debt in the firm's capital structure leads to higher ROE.
[1]
Financial leverage benefits
diminish as the risk of defaulting on interest payments increases. So if the firm takes on too much debt, the cost of
debt rises as creditors demand a higher risk premium, and ROE decreases.
[3]
Increased debt will make a positive
contribution to a firm's ROE only if the matching Return on assets (ROA) of that debt exceeds the interest rate on the
debt.
[4]
Notes
[1] " Profitability Indicator Ratios: Return On Equity (http:/ / www. investopedia. com/ university/ ratios/ profitability-indicator/ ratio4. asp)",
Richard Loth Investopedia
[2] http:/ / www. answers.com/ topic/ return-on-equity Answers.com Return on Equity
[3] Woolridge, J. Randall and Gray, Gary; Applied Principles of Finance (2006)
[4] Bodie, Kane, Markus, "Investments"
External links
• Annual Ratio Definitions (http:/ / gold. globeinvestor. com/ public/ help/ flat/ help_financials_report_ratios. html)
Rate of return
15
Rate of return
In finance, rate of return (ROR), also known as return on investment (ROI), rate of profit or sometimes just
return, is the ratio of money gained or lost (whether realized or unrealized) on an investment relative to the amount
of money invested. The amount of money gained or lost may be referred to as interest, profit/loss, gain/loss, or net
income/loss. The money invested may be referred to as the asset, capital, principal, or the cost basis of the
investment. ROI is usually expressed as a percentage.
Calculation
The initial value of an investment, , does not always have a clearly defined monetary value, but for purposes of
measuring ROI, the expected value must be clearly stated along with the rationale for this initial value. Similarly, the
final value of an investment, , also does not always have a clearly defined monetary value, but for purposes of
measuring ROI, the final value must be clearly stated along with the rationale for this final value.
The rate of return can be calculated over a single period, or expressed as an average over multiple periods of time.
Single-period
Arithmetic return
The arithmetic return is:
is sometimes referred to as the yield. See also: effective interest rate, effective annual rate (EAR) or annual
percentage yield (APY).
Logarithmic or continuously compounded return
The logarithmic return or continuously compounded return, also known as force of interest, is defined as:
It is the reciprocal of the e-folding time.
Multiperiod average returns
Arithmetic average rate of return
The arithmetic average rate of return over n periods is defined as:
Rate of return
16
Geometric average rate of return
The geometric average rate of return, also known as the True Time-Weighted Rate of Return, over n periods is
defined as:
The geometric average rate of return calculated over n years is also known as the annualized return.
Internal rate of return
The internal rate of return (IRR), also known as the dollar-weighted rate of return, is defined as the value(s) of
that satisfies the following equation:
where:
• NPV = net present value of the investment
• = cashflow at time
When the cost of capital is smaller than the IRR rate , the investment is profitable, i.e., .
Otherwise, the investment is not profitable.
Comparisons between various rates of return
Arithmetic and logarithmic return
The value of an investment is doubled over a year if the annual ROR = +100%, that is, if = ln(200% /
100%) = ln(2) = 69.3%. The value falls to zero when = -100%, that is, if = -•.
Arithmetic and logarithmic returns are not equal, but are approximately equal for small returns. The difference
between them is large only when percent changes are high. For example, an arithmetic return of +50% is equivalent
to a logarithmic return of 40.55%, while an arithmetic return of -50% is equivalent to a logarithmic return of
-69.31%.
Logarithmic returns are often used by academics in their research. The main advantage is that the continuously
compounded return is symmetric, while the arithmetic return is not: positive and negative percent arithmetic returns
are not equal. This means that an investment of $100 that yields an arithmetic return of 50% followed by an
arithmetic return of -50% will result in $75, while an investment of $100 that yields a logarithmic return of 50%
followed by an logarithmic return of -50% it will remain $100.
Comparison of arithmetic and logarithmic returns for initial investment of $100
Initial investment, $100 $100 $100 $100 $100
Final investment,
$0 $50 $100 $150 $200
Profit/loss,
‚$100 ‚$50 $0 $50 $100
Arithmetic return, ‚100% ‚50% 0% 50% 100%
Logarithmic return, ‚• ‚69.31% 0% 40.55% 69.31%
Rate of return
17
Arithmetic average and geometric average rates of return
Both arithmetic and geometric average rates of returns are averages of periodic percentage returns. Neither will
accurately translate to the actual dollar amounts gained or lost if percent gains are averaged with percent losses.
[1]
A
10% loss on a $100 investment is a $10 loss, and a 10% gain on a $100 investment is a $10 gain. When percentage
returns on investments are calculated, they are calculated for a period of time € not based on original investment
dollars, but based on the dollars in the investment at the beginning and end of the period. So if an investment of $100
loses 10% in the first period, the investment amount is then $90. If the investment then gains 10% in the next period,
the investment amount is $99.
A 10% gain followed by a 10% loss is a 1% loss. The order in which the loss and gain occurs does not affect the
result. A 50% gain and a 50% loss is a 25% loss. An 80% gain plus an 80% loss is a 64% loss. To recover from a
50% loss, a 100% gain is required. The mathematics of this are beyond the scope of this article, but since investment
returns are often published as "average returns", it is important to note that average returns do not always translate
into dollar returns.
Example #1 Level Rates of Return
Year 1 Year 2 Year 3 Year 4
Rate of Return 5% 5% 5% 5%
Geometric Average at End of Year 5% 5% 5% 5%
Capital at End of Year $105.00 $110.25 $115.76 $121.55
Dollar Profit/(Loss) $5.00 $10.25 $15.76 $21.55
Compound Yield 5% 5.4%
Example #2 Volatile Rates of Return, including losses
Year 1 Year 2 Year 3 Year 4
Rate of Return 50% -20% 30% -40%
Geometric Average at End of Year 50% 9.5% 16% -1.6%
Capital at End of Year $150.00 $120.00 $156.00 $93.60
Dollar Profit/(Loss) ($6.40)
Compound Yield -1.6%
Example #3 Highly Volatile Rates of Return, including losses
Year 1 Year 2 Year 3 Year 4
Rate of Return -95% 0% 0% 115%
Geometric Average at End of Year -95% -77.6% -63.2% -42.7%
Capital at End of Year $5.00 $5.00 $5.00 $10.75
Dollar Profit/(Loss) ($89.25)
Compound Yield -22.3%
Rate of return
18
Annual returns and annualized returns
Care must be taken not to confuse annual and annualized returns. An annual rate of return is a single-period return,
while an annualized rate of return is a multi-period, geometric average return.
An annual rate of return is the return on an investment over a one-year period, such as January 1 through December
31, or June 3, 2006 through June 2, 2007. Each ROI in the cash flow example above is an annual rate of return.
An annualized rate of return is the return on an investment over a period other than one year (such as a month, or two
years) multiplied or divided to give a comparable one-year return. For instance, a one-month ROI of 1% could be
stated as an annualized rate of return of 12%. Or a two-year ROI of 10% could be stated as an annualized rate of
return of 5%. **For GIPS compliance: you do not annualize portfolios or composites for periods of less than one
year. You start on the 13th month.
In the cash flow example below, the dollar returns for the four years add up to $265. The annualized rate of return for
the four years is: $265 ‚ ($1,000 x 4 years) = 6.625%.
Uses
• ROI is a measure of cash generated by or lost due to the investment. It measures the cash flow or income stream
from the investment to the investor, relative to the amount invested. Cash flow to the investor can be in the form
of profit, interest, dividends, or capital gain/loss. Capital gain/loss occurs when the market value or resale value of
the investment increases or decreases. Cash flow here does not include the return of invested capital.
Cash Flow Example on $1,000 Investment
Year 1 Year 2 Year 3 Year 4
Dollar Return $100 $55 $60 $50
ROI 10% 5.5% 6% 5%
• ROI values typically used for personal financial decisions include Annual Rate of Return and Annualized Rate
of Return. For nominal risk investments such as savings accounts or Certificates of Deposit, the personal investor
considers the effects of reinvesting/compounding on increasing savings balances over time. For investments in
which capital is at risk, such as stock shares, mutual fund shares and home purchases, the personal investor
considers the effects of price volatility and capital gain/loss on returns.
• Profitability ratios typically used by financial analysts to compare a company€s profitability over time or
compare profitability between companies include Gross Profit Margin, Operating Profit Margin, ROI ratio,
Dividend yield, Net profit margin, Return on equity, and Return on assets.
[2]
• During capital budgeting, companies compare the rates of return of different projects to select which projects to
pursue in order to generate maximum return or wealth for the company's stockholders. Companies do so by
considering the average rate of return, payback period, net present value, profitability index, and internal rate of
return for various projects.
[3]
• A return may be adjusted for taxes to give the after-tax rate of return. This is done in geographical areas or
historical times in which taxes consumed or consume a significant portion of profits or income. The after-tax rate
of return is calculated by multiplying the rate of return by the tax rate, then subtracting that percentage from the
rate of return.
• A return of 5% taxed at 15% gives an after-tax return of 4.25%
0.05 x 0.15 = 0.0075
0.05 - 0.0075 = 0.0425 = 4.25%
• A return of 10% taxed at 25% gives an after-tax return of 7.5%
Rate of return
19
0.10 x 0.25 = 0.025
0.10 - 0.025 = 0.075 = 7.5%
Investors usually seek a higher rate of return on taxable investment returns than on non-taxable investment returns.
• A return may be adjusted for inflation to better indicate its true value in purchasing power. Any investment with a
nominal rate of return less than the annual inflation rate represents a loss of value, even though the nominal rate
of return might well be greater than 0%. When ROI is adjusted for inflation, the resulting return is considered an
increase or decrease in purchasing power. If an ROI value is adjusted for inflation, it is stated explicitly, such as
ƒThe return, adjusted for inflation, was 2%.„
• Many online poker tools include ROI in a player's tracked statistics, assisting users in evaluating an opponent's
profitability.
Cash or potential cash returns
Time value of money
Investments generate cash flow to the investor to compensate the investor for the time value of money.
Except for rare periods of significant deflation where the opposite may be true, a dollar in cash is worth less today
than it was yesterday, and worth more today than it will be worth tomorrow. The main factors that are used by
investors to determine the rate of return at which they are willing to invest money include:
• estimates of future inflation rates
• estimates regarding the risk of the investment (e.g. how likely it is that investors will receive regular
interest/dividend payments and the return of their full capital)
• whether or not the investors want the money available (•liquid‚) for other uses.
The time value of money is reflected in the interest rates that banks offer for deposits, and also in the interest rates
that banks charge for loans such as home mortgages. The ƒrisk-free„ rate is the rate on U.S. Treasury Bills, because
this is the highest rate available without risking capital.
The rate of return which an investor expects from an investment is called the Discount Rate. Each investment has a
different discount rate, based on the cash flow expected in future from the investment. The higher the risk, the higher
the discount rate (rate of return) the investor will demand from the investment.
Compounding or reinvesting
Compound interest or other reinvestment of cash returns (such as interest and dividends) does not affect the discount
rate of an investment, but it does affect the Annual Percentage Yield, because compounding/reinvestment increases
the capital invested.
For example, if an investor put $1,000 in a 1-year Certificate of Deposit (CD) that paid an annual interest rate of 4%,
compounded quarterly, the CD would earn 1% interest per quarter on the account balance. The account balance
includes interest previously credited to the account.
Rate of return
20
Compound Interest Example
1st Quarter 2nd Quarter 3rd Quarter 4th Quarter
Capital at the beginning of the period $1,000 $1,010 $1,020.10 $1,030.30
Dollar return for the period $10 $10.10 $10.20 $10.30
Account Balance at end of the period $1,010.00 $1,020.10 $1,030.30 $1,040.60
Quarterly ROI 1% 1% 1% 1%
The concept of 'income stream' may express this more clearly. At the beginning of the year, the investor took $1,000
out of his pocket (or checking account) to invest in a CD at the bank. The money was still his, but it was no longer
available for buying groceries. The investment provided a cash flow of $10.00, $10.10, $10.20 and $10.30. At the
end of the year, the investor got $1,040.60 back from the bank. $1,000 was return of capital.
Once interest is earned by an investor it becomes capital. Compound interest involves reinvestment of capital; the
interest earned during each quarter is reinvested. At the end of the first quarter the investor had capital of $1,010.00,
which then earned $10.10 during the second quarter. The extra dime was interest on his additional $10 investment.
The Annual Percentage Yield or Future value for compound interest is higher than for simple interest because the
interest is reinvested as capital and earns interest. The yield on the above investment was 4.06%.
Bank accounts offer contractually guaranteed returns, so investors cannot lose their capital. Investors/Depositors lend
money to the bank, and the bank is obligated to give investors back their capital plus all earned interest. Because
investors are not risking losing their capital on a bad investment, they earn a quite low rate of return. But their capital
steadily increases.
Returns when capital is at risk
Capital gains and losses
Many investments carry significant risk that the investor will lose some or all of the invested capital. For example,
investments in company stock shares put capital at risk. The value of a stock share depends on what someone is
willing to pay for it at a certain point in time. Unlike capital invested in a savings account, the capital value (price) of
a stock share constantly changes. If the price is relatively stable, the stock is said to have ƒlow volatility.„ If the price
often changes a great deal, the stock has ƒhigh volatility.„ All stock shares have some volatility, and the change in
price directly affects ROI for stock investments.
Stock returns are usually calculated for holding periods such as a month, a quarter or a year.
Reinvestment when capital is at risk: rate of return and yield
Example: Stock with low volatility and a regular quarterly dividend, reinvested
End of: 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter
Dividend $1 $1.01 $1.02 $1.03
Stock Price $98 $101 $102 $99
Shares Purchased 0.010204 0.01 0.01 0.010404
Total Shares Held 1.010204 1.020204 1.030204 1.040608
Investment Value $99 $103.04 $105.08 $103.02
Quarterly ROI -1% 4.08% 1.98% -1.96%
Rate of return
21
Yield is the compound rate of return that includes the effect of reinvesting interest or dividends.
To the right is an example of a stock investment of one share purchased at the beginning of the year for $100.
• The quarterly dividend is reinvested at the quarter-end stock price.
• The number of shares purchased each quarter = ($ Dividend)/($ Stock Price).
• The final investment value of $103.02 is a 3.02% Yield on the initial investment of $100. This is the compound
yield, and this return can be considered to be the return on the investment of $100.
To calculate the rate of return, the investor includes the reinvested dividends in the total investment. The investor
received a total of $4.06 in dividends over the year, all of which were reinvested, so the investment amount increased
by $4.06.
• Total Investment = Cost Basis = $100 + $4.06 = $104.06.
• Capital gain/loss = $103.02 - $104.06 = -$1.04 (a capital loss)
• ($4.06 dividends - $1.04 capital loss ) / $104.06 total investment = 2.9% ROI
The disadvantage of this ROI calculation is that it does not take into account the fact that not all the money was
invested during the entire year (the dividend reinvestments occurred throughout the year). The advantages are: (1) it
uses the cost basis of the investment, (2) it clearly shows which gains are due to dividends and which gains/losses are
due to capital gains/losses, and (3) the actual dollar return of $3.02 is compared to the actual dollar investment of
$104.06.
For U.S. income tax purposes, if the shares were sold at the end of the year, dividends would be $4.06, cost basis of
the investment would be $104.06, sale price would be $103.02, and the capital loss would be $1.04.
Since all returns were reinvested, the ROI might also be calculated as a continuously compounded return or
logarithmic return. The effective continuously compounded rate of return is the natural log of the final investment
value divided by the initial investment value:
• is the initial investment ($100)
• is the final value ($103.02)
.
Mutual fund and investment company returns
Mutual funds, exchange-traded funds (ETFs), and other equitized investments (such as unit investment trusts or
UITs, insurance separate accounts and related variable products such as variable universal life insurance policies and
variable annuity contracts, and bank-sponsored commingled funds, collective benefit funds or common trust funds)
are essentially portfolios of various investment securities such as stocks, bonds and money market instruments which
are equitized by selling shares or units to investors. Investors and other parties are interested to know how the
investment has performed over various periods of time.
Performance is usually quantified by a fund's total return. In the 1990s, many different fund companies were
advertising various total returns…some cumulative, some averaged, some with or without deduction of sales loads or
commissions, etc. To level the playing field and help investors compare performance returns of one fund to another,
the U.S. Securities and Exchange Commission (SEC) began requiring funds to compute and report total returns
based upon a standardized formula…so called "SEC Standardized total return" which is the average annual total
return assuming reinvestment of dividends and distributions and deduction of sales loads or charges. Funds may
compute and advertise returns on other bases (so-called "non-standardized" returns), so long as they also publish no
less prominently the "standardized" return data.
Subsequent to this, apparently investors who'd sold their fund shares after a large increase in the share price in the
late 1990s and early 2000s were ignorant of how significant the impact of income/capital gain taxes was on their
fund "gross" returns. That is, they had little idea how significant the difference could be between "gross" returns
Rate of return
22
(returns before federal taxes) and "net" returns (after-tax returns). In reaction to this apparent investor ignorance, and
perhaps for other reasons, the SEC made further rule-making to require mutual funds to publish in their annual
prospectus, among other things, total returns before and after the impact of U.S federal individual income taxes. And
further, the after-tax returns would include 1) returns on a hypothetical taxable account after deducting taxes on
dividends and capital gain distributions received during the illustrated periods and 2) the impacts of the items in #1)
as well as assuming the entire investment shares were sold at the end of the period (realizing capital gain/loss on
liquidation of the shares). These after-tax returns would apply of course only to taxable accounts and not to
tax-deferred or retirement accounts such as IRAs.
Lastly, in more recent years, "personalized" investment returns have been demanded by investors. In other words,
investors are saying more or less the fund returns may not be what their actual account returns are based upon the
actual investment account transaction history. This is because investments may have been made on various dates and
additional purchases and withdrawals may have occurred which vary in amount and date and thus are unique to the
particular account. More and more fund and brokerage firms have begun providing personalized account returns on
investor's account statements in response to this need.
With that out of the way, here's how basic earnings and gains/losses work on a mutual fund. The fund records
income for dividends and interest earned which typically increases the value of the mutual fund shares, while
expenses set aside have an offsetting impact to share value. When the fund's investments increase in market value, so
too does the value of the fund shares (or units) owned by the investors. When investments increase (decrease) in
market value, so too the fund shares value increases (or decreases). When the fund sells investments at a profit, it
turns or reclassifies that paper profit or unrealized gain into an actual or realized gain. The sale has no affect on the
value of fund shares but it has reclassified a component of its value from one bucket to another on the fund
books…which will have future impact to investors. At least annually, a fund usually pays dividends from its net
income (income less expenses) and net capital gains realized out to shareholders as an IRS requirement. This way,
the fund pays no taxes but rather all the investors in taxable accounts do. Mutual fund share prices are typically
valued each day the stock or bond markets are open and typically the value of a share is the net asset value of the
fund shares investors own.
Total returns
This section addresses only total returns without the impact of U.S. federal individual income and capital gains taxes.
Mutual funds report total returns assuming reinvestment of dividend and capital gain distributions. That is, the
dollar amounts distributed are used to purchase additional shares of the funds as of the reinvestment/ex-dividend
date. Reinvestment rates or factors are based on total distributions (dividends plus capital gains) during each period.
•
•
•
•
•
•
Rate of return
23
Average annual total return (geometric)
US mutual funds are to compute average annual total return as prescribed by the U.S. Securities and Exchange
Commission (SEC) in instructions to form N-1A (the fund prospectus) as the average annual compounded rates of
return for 1-year, 5-year and 10-year periods (or inception of the fund if shorter) as the "average annual total return"
for each fund. The following formula is used:
[4]
Where:
P = a hypothetical initial payment of $1,000.
T = average annual total return.
n = number of years.
ERV = ending redeemable value of a hypothetical $1,000 payment made at the beginning of the 1-, 5-, or 10-year
periods at the end of the 1-, 5-, or 10-year periods (or fractional portion).
Solving for T gives
Example
Example: Balanced mutual fund during boom times with regular annual dividends,
reinvested at time of distribution, initial investment $1,000 at end of Year 0, share price
$14.21
Year 1 Year 2 Year 3 Year 4 Year 5
Dividend Per Share $0.26 $0.29 $0.30 $0.50 $0.53
Capital Gain Distribution Per Share $0.06 $0.39 $0.47 $1.86 $1.12
Total Distribution Per Share $0.32 $0.68 $0.77 $2.36 $1.65
Share Price At End Of Year $17.50 $19.49 $20.06 $20.62 $19.90
Reinvestment Factor 1.01829 1.03553 1.03975 1.11900 1.09278
Shares Owned Before Distribution 70.373 71.676 74.125 76.859 84.752
Total Distribution $22.52 $48.73 $57.10 $181.73 $141.60
Share Price At Distribution $17.28 $19.90 $20.88 $22.98 $21.31
Shares Purchased 1.303 2.449 2.734 7.893 6.562
Shares Owned After Distribution 71.676 74.125 76.859 84.752 91.314
• Total Return = (($19.90 x 1.09278) / $14.21) - 1 = 53.04%
• Average Annual Total Return (geometric) = ((($19.90 x 91.314) / $1,000) ^ (1 / 5)) - 1 = 12.69%
Using a Holding Period Return calculation, after 5 years, an investor who reinvested owned 91.314 shares valued at
$19.90 per share. ((($19.90 x 91.314) / $1,000) - 1) / 5 = 16.34% return. An investor who did not reinvest received
total cash payments of $5.78 per share. ((($19.90 + $5.78) / $14.21) - 1) / 5 = 16.14% return.
Mutual funds include capital gains as well as dividends in their return calculations. Since the market price of a
mutual fund share is based on net asset value, a capital gain distribution is offset by an equal decrease in mutual fund
share value/price. From the shareholder's perspective, a capital gain distribution is not a net gain in assets, but it is a
realized capital gain.
Rate of return
24
Summary: overall rate of return
Rate of Return and Return on Investment indicate cash flow from an investment to the investor over a specified
period of time, usually a year.
ROI is a measure of investment profitability, not a measure of investment size. While compound interest and
dividend reinvestment can increase the size of the investment (thus potentially yielding a higher dollar return to the
investor), Return on Investment is a percentage return based on capital invested.
In general, the higher the investment risk, the greater the potential investment return, and the greater the potential
investment loss.
References
[1] Damato,Karen. Doing the Math: Tech Investors' Road to Recovery is Long. Wall Street Journal, pp.C1-C19, May 18, 2001
[2] A. A. Groppelli and Ehsan Nikbakht (2000). Barron's Finance, 4th Edition. New York. pp. 442€456. ISBN 0-7641-1275-9.
[3] Barron's Finance. pp. 151€163.
[4] U.S. Securities and Exchange Commission (1998). "Final Rule: Registration Form Used by Open-End Management Investment Companies:
Sample Form and instructions" (http:/ / www.sec.gov/ rules/ final/ 33-7512f. htm#E12E2). .
Further reading
• A. A. Groppelli and Ehsan Nikbakht. Barron€s Finance, 4th Edition. New York: Barron†s Educational Series, Inc.,
2000. ISBN 0-7641-1275-9
• Zvi Bodie, Alex Kane and Alan J. Marcus. Essentials of Investments, 5th Edition. New York: McGraw-Hill/Irwin,
2004. ISBN 0-07-251077-3
• Richard A. Brealey, Stewart C. Myers and Franklin Allen. Principles of Corporate Finance, 8th Edition.
McGraw-Hill/Irwin, 2006
• Walter B. Meigs and Robert F. Meigs. Financial Accounting, 4th Edition. New York: McGraw-Hill Book
Company, 1970. ISBN 0-07-041534-X
• Bruce J. Feibel. Investment Performance Measurement. New York: Wiley, 2003. ISBN 0471268496
External links
• ROR Nomenclature and usage by different products (http:/ / www. retailinvestor. org/ return. html)
Return on assets
25
Return on assets
The return on assets (ROA) percentage shows how profitable a company's assets are in generating revenue.
ROA can be computed as:
[1]
This number tells you what the company can do with what it has, i.e. how many dollars of earnings they derive from
each dollar of assets they control. It's a useful number for comparing competing companies in the same industry. The
number will vary widely across different industries. Return on assets gives an indication of the capital intensity of
the company, which will depend on the industry; companies that require large initial investments will generally have
lower return on assets.
Usage
Return on assets is an indicator of how profitable a company is before leverage, and is compared with companies in
the same industry. Since the figure for total assets of the company depends on the carrying value of the assets, some
caution is required for companies whose carrying value may not correspond to the actual market value. Return on
assets is a common figure used for comparing performance of financial institutions (such as banks), because the
majority of their assets will have a carrying value that is close to their actual market value. Return on assets is not
useful for comparisons between industries because of factors of scale and peculiar capital requirements (such as
reserve requirements in the insurance and banking industries).
Return on assets is one of the elements used in financial analysis using the Du Pont Identity.
References
[1] Susan V. Crosson; Belverd E., Jr Needles; Needles, Belverd E.; Powers, Marian (2008). Principles of accounting. Boston: Houghton Mifflin.
p. 209. ISBN 0-618-73661-1.
External links
• Return On Assets - ROA (http:/ / www. investopedia. com/ terms/ r/ returnonassets. asp)
Return on assets Du Pont
26
Return on assets Du Pont
DuPont analysis (also known as the DuPont identity, DuPont equation, DuPont Model or the DuPont method)
is an expression which breaks ROE (Return On Equity) into three parts.
The name comes from the DuPont Corporation that started using this formula in the 1920s.
Basic formula
ROE = (Profit margin)*(Asset turnover)*(Equity multiplier) = (Net
profit/Sales)*(Sales/Assets)*(Assets/Equity)= (Net Profit/Equity)
• Operating efficiency (measured by profit margin)
• Asset use efficiency (measured by asset turnover)
• Financial leverage (measured by equity multiplier)
ROE analysis
The Du Pont identity breaks down Return on Equity (that is, the returns that investors receive from the firm) into
three distinct elements. This analysis enables the analyst to understand the source of superior (or inferior) return by
comparison with companies in similar industries (or between industries).
The Du Pont identity, however, is less useful for some industries, such as investment banking, that do not use certain
concepts or for which the concepts are less meaningful. Variations may be used in certain industries, as long as they
also respect the underlying structure of the Du Pont identity.
Du Pont analysis relies upon the accounting identity, that is, a statement (formula) that is by definition true.
Examples
High turnover industries
Certain types of retail operations, particularly stores, may have very low profit margins on sales, and relatively
moderate leverage. In contrast, though, groceries may have very high turnover, selling a significant multiple of their
assets per year. The ROE of such firms may be particularly dependent on performance of this metric, and hence asset
turnover may be studied extremely carefully for signs of under-, or, over-performance. For example, same store sales
of many retailers is considered important as an indication that the firm is deriving greater profits from existing stores
(rather than showing improved performance by continually opening new stores).
High margin industries
Other industries, such as fashion, may derive a substantial portion of their competitive advantage from selling at a
higher margin, rather than higher sales. For high-end fashion brands, increasing sales without sacrificing margin may
be critical. The Du Pont identity allows analysts to determine which of the elements is dominant in any change of
ROE.
High leverage industries
Some sectors, such as the financial sector, rely on high leverage to generate acceptable ROE. In contrast, however,
many other industries would see high levels of leverage as unacceptably risky. Du Pont analysis enables the third
party (relying primarily on the financial statements) to compare leverage with other financial elements that determine
ROE among similar companies.
Return on assets Du Pont
27
ROI and ROE ratio
The return on investment (ROI) ratio developed by DuPont for its own use is now used by many firms to evaluate
how effectively assets are used. It measures the combined effects of profit margins and asset turnover.
[1]
The return on equity (ROE) ratio is a measure of the rate of return to stockholders.
[2]
Decomposing the ROE into
various factors influencing company performance is often called the Du Pont system.
[3]
Where
• Net profit = net profit after taxes
• Equity = shareholders' equity
• EBIT = Earnings before interest and taxes
• Sales = Net sales
This decomposition presents various ratios used in fundamental analysis.
• The company's tax burden is (Net profit ‚ Pretax profit). This is the proportion of the company's profits retained
after paying income taxes.
• The company's interest burden is (Pretax profit ‚ EBIT). This will be 1.00 for a firm with no debt or financial
leverage.
• The company's operating profit margin or return on sales (ROS) is (EBIT ‚ Sales). This is the operating profit
per dollar of sales.
• The company's asset turnover (ATO) is (Sales ‚ Assets).
• The company's leverage ratio is (Assets ‚ Equity), which is equal to the firm's debt to equity ratio + 1. This is a
measure of financial leverage.
• The company's return on assets (ROA) is (Return on sales x Asset turnover).
• The company's compound leverage factor is (Interest burden x Leverage).
ROE can also be stated as:
[4]
ROE = Tax burden x Interest burden x Margin x Turnover x Leverage
ROE = Tax burden x ROA x Compound leverage factor
Profit margin is (Net profit ‚ Sales), so the ROE equation can be restated:
References
[1] Groppelli, Angelico A.; Ehsan Nikbakht (2000). Finance, 4th ed. Barron's Educational Series, Inc.. pp. 444€445. ISBN 0764112759.
[2] Groppelli, Angelico A.; Ehsan Nikbakht (2000). Finance, 4th ed. Barron's Educational Series, Inc.. p. 444. ISBN 0764112759.
[3] Bodie, Zane; Alex Kane and Alan J. Marcus (2004). Essentials of Investments, 5th ed. McGraw-Hill Irwin. pp. 458€459. ISBN 0072510773.
[4] Bodie, Zane; Alex Kane and Alan J. Marcus (2004). Essentials of Investments, 5th ed. McGraw-Hill Irwin. p. 460. ISBN 0072510773.
External links
• Decoding DuPont Analysis (http:/ / www. investopedia. com/ articles/ fundamental-analysis/ 08/ dupont-analysis.
asp)
Return on net assets
28
Return on net assets
The return on net assets (RONA) is a measure of financial performance of a company which takes the use of assets
into account.
Formula
Return on net assets = Profit after tax ( also known as net income) / ( Fixed assets + working capital )
In a manufacturing sector this is also calculated as:
Return on net assets = (plant revenue - costs) / net assets
Return on capital
Return on capital (ROC) is a ratio used in finance, valuation, and accounting. The ratio is estimated by dividing the
after-tax operating income (NOPAT) by the book value of invested capital.
Formula
•
This differs from ROIC. Return on invested capital (ROIC) is a financial measure that quantifies how well a
company generates cash flow relative to the capital it has invested in its business. It is defined as net operating profit
less adjusted taxes divided by invested capital and is usually expressed as a percentage. In this calculation, capital
invested includes all monetary capital invested: long-term debt, common and preferred shares.
When the return on capital is greater than the cost of capital (usually measured as the weighted average cost of
capital), the company is creating value; when it is less than the cost of capital, value is destroyed.
ROIC formula
•
Note that the numerator in the ROIC fraction does not subtract interest expense, because denominator includes debt
capital.
See also
• Cash flow return on investment (CFROI)
• Profitability
• Rate of profit
• Profit maximization
• Tendency of the rate of profit to fall
• Return of capital
• Return on investment (ROI)
• Return on net assets (RONA)
• Return on revenue (ROR), also Return on sales (ROS)
• Risk adjusted return on capital (RAROC)
Return on capital
29
References
Risk adjusted return on capital
Risk adjusted return on capital (RAROC) is a risk-based profitability measurement framework for analysing
risk-adjusted financial performance and providing a consistent view of profitability across businesses. The concept
was developed by Bankers Trust and principal designer Dan Borge in the late 1970s.
[1]
Note, however, that more and
more Return on risk Adjusted Capital (RORAC) is used as a measure, whereby the risk adjustment of Capital is
based on the capital adequacy guidelines as outlined by the Basel Committee, currently Basel II.
Basic formula
• RAROC = (Expected Return)/(Economic Capital)
[2]
or
• RAROC = (Expected Return)/(Value at risk)
[2]
Broadly speaking, in business enterprises, risk is traded off against benefit. RAROC is defined as the ratio of risk
adjusted return to economic capital. The economic capital is the amount of money which is needed to secure the
survival in a worst case scenario, it is a buffer against expected shocks in market values. Economic capital is a
function of market risk, credit risk, and operational risk, and is often calculated by VaR. This use of capital based on
risk improves the capital allocation across different functional areas of banks, insurance companies, or any business
in which capital is placed at risk for an expected return above the risk-free rate.
RAROC system allocates capital for 2 basic reasons:
1. Risk management
2. Performance evaluation
For risk management purposes, the main goal of allocating capital to individual business units is to determine the
bank's optimal capital structure…that is economic capital allocation is closely correlated with individual business
risk. As a performance evaluation tool, it allows banks to assign capital to business units based on the economic
value added of each unit.
References
[1] Herring, Richard; Diebold, Francis X.; Doherty, Neil A. (2010). The Known, the Unknown, and the Unknowable in Financial Risk
Management: Measurement and Theory Advancing Practice. Princeton, N.J: Princeton University Press. p. 347.
[2] Quantifying Risk in the Electricity Business: A RAROC-based Approach (http:/ / www. pstat. ucsb. edu/ research/ papers/ report10_2004[1].
pdf)
• "An Introduction to Broad Based Credit Engineering" By Morton Glantz
External links
• RAROC & Economic Capital (http:/ / www. teradata. com/ tdmo/ v07n01/ pdf/ AR5210. pdf)
• Between RAROC and a hard place (http:/ / www. erisk. com/ ResourceCenter/ Features/ raroc. pdf)
Cash flow return on investment
30
Cash flow return on investment
Cash flow return on investment is a valuation model that assumes the stock market sets prices based on cash flow,
not on corporate performance and earnings.
CFROI = Cash Flow / Market Recapitalization
For the corporation, it is essentially internal rate of return (IRR). CFROI is compared to a hurdle rate to determine if
investment/product is performing adequately. The hurdle rate is the total cost of capital for the corporation calculated
by a mix of cost of debt financing plus investors `expected return on equity investments. The CFROI must exceed
the hurdle rate to satisfy both the debt financing and the investors expected return.
CFROI = Gross Cash Flow / Gross Investment
Michael J. Maubossin, in his 2006 book 'MORE THAN YOU KNOW', quoted an analysis by CSFB, that, measured
by CFROI, performance of companies tend to converge after five years in terms of their survival rates.
The CFROI for a firm or a division can then be written as follows:
CFROI = (Gross Cash Flow - Economic Depreciation) / Gross Investment
This annuity is called the economic depreciation.
Economic Depreciation = (Replacement Cost in Current dollars (Kc)) / ((1+ Kc )^n - 1)
where n is the expected life of the asset.
Current ratio
The current ratio is a financial ratio that measures whether or not a firm has enough resources to pay its debts over
the next 12 months. It compares a firm's current assets to its current liabilities. It is expressed as follows:
For example, if WXY Company's current assets are $50,000,000 and its current liabilities are $40,000,000, then its
current ratio would be $50,000,000 divided by $40,000,000, which equals 1.25. It means that for every dollar the
company owes it has $1.25 available in current assets. A current ratio of assets to liabilities of 2:1 is usually
considered to be acceptable (ie., your current assets are twice your current liabilities).
[1]
The current ratio is an indication of a firm's market liquidity and ability to meet creditor's demands. Acceptable
current ratios vary from industry to industry. If a company's current ratio is in this range, then it is generally
considered to have good short-term financial strength. If current liabilities exceed current assets (the current ratio is
below 1), then the company may have problems meeting its short-term obligations. If the current ratio is too high,
then the company may not be efficiently using its current assets or its short-term financing facilities. This may also
indicate problems in working capital management.
Low values for the current or quick ratios (values less than 1) indicate that a firm may have difficulty meeting
current obligations. Low values, however, do not indicate a critical problem. If an organization has good long-term
prospects, it may be able to borrow against those prospects to meet current obligations. Some types of businesses
usually operate with a current ratio less than one. For example, if inventory turns over much more rapidly than the
accounts payable become due, then the current ratio will be less than one (this is true for McDonalds). This can
allow a firm to operate with a low current ratio.
If all other things were equal, a creditor, who is expecting to be paid in the next 12 months, would consider a high
current ratio to be better than a low current ratio, because a high current ratio means that the company is more likely
to meet its liabilities which fall due in the next 12 months.
Current ratio
31
Notes
[1] Yahoo Money Matters (http:/ / au. pfinance. yahoo.com/ small-business/ financial_techniques. html)
Cash ratio
The Reserve Requirements (or Cash Reserve Ratio) is a Central bank regulation that sets the minimum reserves
each Commercial bank must hold to customer deposits and notes i.e the amount that the bank surrenders with the
central bank. It would normally be in the form of fiat currency stored in a bank vault (vault cash), or with a central
bank.
The reserve ratio is sometimes used as a tool in the monetary policy, influencing the country's economy, borrowing,
and interest rates
[1]
. Western central banks rarely alter the reserve requirements because it would cause immediate
liquidity problems for banks with low excess reserves; they prefer to use open market operations to implement their
monetary policy. The People's Bank of China uses changes in reserve requirements as an inflation-fighting tool,
[2]
and raised the reserve requirement nine times in 2007. As of 2006 the required reserve ratio in the United States was
10% on transaction deposits (component of money supply "M1"), and zero on time deposits and all other deposits.
An institution that holds reserves in excess of the required amount is said to hold excess reserves.
Effects on money supply
MS = Money Supply
Mb = Monetary base
mm = money multiplier
c = rate at which people hold cash (as opposed to depositing it)
R = the reserve requirement (the percent of deposits that banks are not allowed to lend)
If banks only have to hold 10% of deposits,they will lend the other 90% of deposits. The person with that loan will
then choose to deposit the money from the loan back into the bank at a rate of 'c' (for simplicity say c=0%.) then the
bank can again loan 90% of the second deposit which was 90% of the first deposit.
Reserve requirements affect the potential of the banking system to create transaction deposits. If the reserve
requirement is 10%, for example, a bank that receives a $100 deposit may lend out $90 of that deposit. If the
borrower then writes a check to someone who deposits the $90, the bank receiving that deposit can lend out $81. As
the process continues, the banking system can expand the change in excess reserves of $90 into a maximum of
$1,000 of money ($100+$90+81+$72.90+...=$1,000), e.g.$100/0.10=$1,000. In contrast, with a 20% reserve
requirement, the banking system would be able to expand the initial $100 deposit into a maximum of
($100+$80+$64+$51.20+...=$500), e.g.$100/0.20=$500. Thus, higher reserve requirements reduce money creation
and help maintain the purchasing power of the currency previously in use.
Reserve requirements in the US apply only to transaction accounts, which are components of M1, a narrowly defined
measure of money. Deposits that are components of M2 and M3 (but not M1), such as savings accounts and time
deposits such as CDs, have no reserve requirements and therefore can expand without regard to reserve levels.
Because of the exponential impact that reserve requirements have on the money supply, and the large time lag
between their implementation and the corresponding effect of inflation, the Federal reserve does not frequently
change reserve requirements for the purpose of affecting monetary policy.
Cash ratio
32
Reserve ratios
A cash reserve ratio (or CRR) is the percentage of bank reserves to deposits and notes. The cash reserve ratio is also
known as the cash asset ratio or liquidity ratio. , the Board of Governors of the Federal Reserve System requires
zero percent (0%) fractional reserves from depository institutions having net transactions accounts of up to $10.7
million.
[3]
Depository institutions having over $10.7 million, and up to $55.2 million in net transaction accounts
must have fractional reserves totaling three percent (3%) of that amount.
[3]
Finally, depository institutions having
over $55.2 million in net transaction accounts must have fractional reserves totaling ten percent (10%) of that
amount.
[3]
However, under current policy, these numbers do not apply to time deposits from domestic corporations,
or deposits from foreign corporations or governments, called "nonpersonal time deposits" and "eurocurrency
liabilities," respectively. For these account classes, the fractional reserve requirement is one percent (1%) regardless
of net account value.
[3]
The Bank of England holds to a voluntary reserve ratio system. In 1998 the average cash reserve ratio across the
entire United Kingdom banking system was 3.1%. Countries that do this, listed as 'None' in the table below, allow
effectively an infinite amount of credit money creation. While this can happen, it doesn't, and it would mean average
reserves tend to zero. The reported average ratio of 3.1% implies an average maximum total deposits of ƒ3,225.80
from ƒ100 of base money.
Other countries have required reserve ratios (or RRRs) that are statutorily enforced (sourced from Lecture 8, Slide
4: Central Banking and the Money Supply, by Dr. Pinar Yesin, University of Zurich, based on 2003 survey of CBC
participants at the Study Center Gerzensee
[4]
):
Country Required reserve (in %) Note
Australia None
Statutory Reserve Deposits abolished in 1988,
replaced with 1% Non-callable Deposits
[5]
Canada None
Mexico None
New Zealand None
1999 [6]
Sweden None
Hong Kong None
United Kingdom None
Czech Republic 2.00 Since 7 October 2009
Eurozone 2.00
Since 1999
[7]
Hungary 2.00 Since November 2008
South Africa 2.50
Switzerland 2.50
Latvia 3.00
Just after the Parex Bank bailout (24.12.2008), Latvian Central Bank
decreased the RRR from 7% (?) down to 3%
[8]
Poland 3.00
Chile 4.50
India 6.00 as per RBI.
Bangladesh 6.00 Raised from 5.50. Effective from 15 December 2010
Lithuania 6.00
Pakistan 5.00 Since 1 November 2008
Cash ratio
33
Taiwan 7.00
[9]
Jordan 8.00
Zambia 8.00
Burundi 8.50
Ghana 9.00
Israel 9.00
the Required Reserve Ratio is called Minimum Capital Ratio
[10]
United States 10.00
No reserve required on savings accounts since 1990
[11]
Sri Lanka 10.00
Bulgaria 10.00
Croatia 14.00
Down from 17%, effective from 2009-01-14
[12]
Costa Rica 15.00
Brazil 20.00
Up from 15%, effective from 2010-12-06 - Ratio is for requirement on term deposits
[13]
.
RRR for currency positions increased to 43.00 on 2010 July 15th[14]
Malawi 15.00
China 19.50
Rate is for major Chinese Banks on 2011-01-20; it was 15.5% beginning of 2010
[15]
.
Small and medium-size banks have a lower rate of 17%
Tajikistan 20.00
Suriname 25.00
Down from 27%, effective from 2007-01-01
[16]
Lebanon 30.00
[17]
In some countries, the cash reserve ratios have decreased over time (sourced from IMF Financial Statistic
Yearbook):
Country 1968 1978 1988 1998
United Kingdom 20.5 15.9 5.0 3.1
Turkey 58.3 62.7 30.8 18.0
Germany 19.0 19.3 17.2 11.9
United States 12.3 10.1 8.5 10.3
(Ratios are expressed in percentage points.)
Capital adequacy ratio (CAR), also called Capital to Risk (Weighted) Assets Ratio (CRAR)
[18]
, is a ratio of a
bank's capital to its risk. National regulators track a bank's CAR to ensure that it can absorb a reasonable amount of
loss
[19]
and are complying with their statutory capital requirements.
Cash ratio
34
Formula
Capital adequacy ratios ("CAR") are a measure of the amount of a bank's capital expressed as a percentage of its risk
weighted credit exposures.
Capital adequacy ratio is defined as
where Risk can either be weighted assets ( ) or the respective national regulator's minimum total capital
requirement. If using risk weighted assets,
‡ 8%.
[18]
The percent threshold (8% in this case, a common requirement for regulators conforming to the Basel Accords) is set
by the national banking regulator.
Two types of capital are measured: tier one capital ( above), which can absorb losses without a bank being
required to cease trading, and tier two capital ( above), which can absorb losses in the event of a winding-up and
so provides a lesser degree of protection to depositors.
Use
Capital adequacy ratio is the ratio which determines the capacity of the bank in terms of meeting the time liabilities
and other risk such as credit risk, operational risk, etc. In the most simple formulation, a bank's capital is the
"cushion" for potential losses, which protect the bank's depositors or other lenders. Banking regulators in most
countries define and monitor CAR to protect depositors, thereby maintaining confidence in the banking system.
[18]
CAR is similar to leverage; in the most basic formulation, it is comparable to the inverse of debt-to-equity leverage
formulations: CAR uses equity divided by assets instead of debt-to-equity (total debt divided by shareholder's equity
or other invested capital). It is important to note that the assets of a bank are its outstanding loans (not the deposits it
has taken in). In accounting generally, total assets are by definition equal to debt plus equity. Therefore the capital
adequacey ratio is equivalent to the proportion of Capital (generally what shareholders paid to the bank to purchase
common stock, but Capital may also include other types of securities issuances) to the "assets" it hold on its books
(i.e. the loans that bank customers have to pay back to the bank…such as a home mortgage). Unlike traditional
leverage, however, CAR recognizes that assets can have different levels of risk. The "safer" the asset the more the
bank is allowed to discount that asset in its CAR calculation; in other words, banks do not have to hold so much in
reserves if their "assets" (the loan dollars owed to them) are very safe (i.e. highly likely to be paid back). For
example, if the bank buys and holds a bond from a corporation, there is a better likelihood the corporation will pay
off its bond than that a homeowner will pay off his mortgage.
Risk weighting
Since different types of assets have different risk profiles, CAR primarily adjusts for assets that are less risky by
allowing banks to "discount" lower-risk assets. The specifics of CAR calculation vary from country to country, but
general approaches tend to be similar for countries that apply the Basel Accords. In the most basic application,
government debt is allowed a 0% "risk weighting" - that is, they are subtracted from total assets for purposes of
calculating the CAR.
Cash ratio
35
Risk weighting example
Local regulations establish that cash and government bonds have a 0% risk weighting, and residential mortgage
loans have a 50% risk weighting. All other types of assets (loans to customers) have a 100% risk weighting.
Bank "A" has assets totaling 100 units, consisting of:
• Cash: 10 units.
• Government bonds: 15 units.
• Mortgage loans: 20 units.
• Other loans: 50 units.
• Other assets: 5 units.
Bank "A" has deposits of 95 units, all of which are deposits (remember: "deposits" to a bank are its "debt"). By
definition, equity is equal to assets minus debt, or 5 units.
Bank A's risk-weighted assets are calculated as follows:
Cash
Government bonds
Mortgage loans
Other loans
Other assets
Total risk
Weighted assets 65
Equity 5
CAR (Equity/RWA) 7.69%
Even though Bank "A" would appear to have a debt-to-equity ratio of 95:5, or equity-to-assets of only 5%, its CAR is
substantially higher. It is considered less risky because some of its assets are less risky than others.
Types of capital
The Basel rules recognize that different types of equity are more important than others. To recognize this, different
adjustments are made:
1. Tier I Capital: Actual contributed equity plus retained earnings.
2. Tier II Capital: Preferred shares plus 50% of subordinated debt.
Different minimum CAR ratios are applied: minimum Tier I equity to risk-weighted assets may be 4%, while
minimum CAR including Tier II capital may be 8%.
There is usually a maximum of Tier II capital that may be "counted" towards CAR, depending on the jurisdiction.
Cash ratio
36
References
[1] http:/ / www. cbr. ru/ eng/ analytics/ standart_system/ print. asp?file=policy_e. html
[2] "China moves to cool its inflation" (http:/ / news.bbc. co. uk/ 1/ hi/ business/ 7089307. stm). BBC News. 2007-11-11. .
[3] Reserve Requirements of Depository Institutions in February 2008 Statistical Supplement to the Federal Reserve Bulletin, Table 1.15 (http:/ /
www.federalreserve.gov/ pubs/ supplement/ 2008/ 02/ table1_15. htm)
[4] Monetary Macroeconomics by Dr. Pinar Yesin (http:/ / www. iew. unizh. ch/ study/ courses/ downloads/ lecture8_467. pdf)
[5] "Inquiry into the Australian Banking Industry, Reserve Bank of Australia, January 1991
[6] http:/ / www. cnb. cz/ m2export/ sites/ www.cnb.cz/ cs/ menova_politika/ mp_nastroje/ download/ menove_nastroje. xls
[7] <en> European Central Bank, minimum reserve requirements (https:/ / www. ecb. europa. eu/ mopo/ implement/ mr/ html/ calc. en. html)
[8] "Minimum Reserve Ratio" (http:/ / www.bank. lv/ eng/ main/ all/ noract/ mon_oper/ reserve/ reserve_ratio_n21). Bank of Latvia. . Retrieved
2010-12-29.
[9] Liquidity ratio and liquid reserves of deposit money banks (http:/ / www. cbc. gov. tw/ public/ data/ EBOOKXLS/ P077. pdf). Data released
by Taiwan's central bank in October 2010.
[10] "Minimum capital ratio" (http:/ / www. bankisrael. gov. il/ deptdata/ pikuah/ nihul_takin/ eng/ 311_et. pdf). Bank of Israel. . Retrieved
2010-12-29.
[11] "Are Reserve Requirements Still Binding?" (http:/ / www. ny. frb. org/ research/ epr/ 02v08n1/ 0205benn/ 0205benn. html). Federal Bank of
New York. . Retrieved 2010-12-27.
[12] (http:/ / www. hnb.hr/ propisi/ odluke-centralno/ h-obvezna rezerva. pdf) (in Croatian)
[13] Busines week - Brazil reserve requirement raise (http:/ / www. businessweek. com/ news/ 2010-12-03/
brazil-banks-stocks-drop-on-reserve-requirement-raise. html)
[14] http:/ / www.businessweek.com/ news/ 2010-07-22/ brazil-signals-rate-increases-to-end-as-growth-cools. html
[15] "China raises bank reserves again" (http:/ / www.reuters. com/ article/ idUSTRE70D1WY20110114). Reuters. . Retrieved 2011-01-19.
[16] "Reserve base en Kasreserve" (http:/ / www. cbvs. sr/ english/ publicaties-reserve. htm). Centrale Bank van Suriname. . Retrieved
2009-12-21.
[17] http:/ / news. bbc. co. uk/ 2/ hi/ middle_east/ 7764657. stm
[18] "Capital Adequacy Ratio - CAR" (http:/ / www.investopedia. com/ terms/ c/ capitaladequacyratio. asp). Investopedia. . Retrieved
2007-07-10.
[19] "Capital adequacy ratios for banks - simplified explanation and example of calculation" (http:/ / web. archive. org/ web/ 20070614200030/
http:/ / www.rbnz. govt.nz/ finstab/ banking/ regulation/ 0091769. html). Reserve Bank of New Zealand. Archived from the original (http:/ /
www.rbnz.govt.nz/ finstab/ banking/ regulation/ 0091769. html) on 14 June 2007. . Retrieved 2007-07-10.
External links
• Title 12 of the Code of Federal Regulations (12CFR) PART 204--RESERVE REQUIREMENTS OF
DEPOSITORY INSTITUTIONS (REGULATION D) (http:/ / ecfr. gpoaccess. gov/ cgi/ t/ text/ text-idx?c=ecfr&
tpl=/ ecfrbrowse/ Title12/ 12cfr204_main_02. tpl) (See Section „204.4 for current reserve requirements.)
• Capital Adequacy Ratio (http:/ / www. investopedia. com/ terms/ c/ capitaladequacyratio. asp) at Investopedia.
• Capital Adequacy Ratio (http:/ / www. rbnz. govt. nz/ finstab/ banking/ regulation/ 0091769. html) at The Reserve
Bank of New Zealand's website.
• Reserve Requirements - Fedpoints - Federal Reserve Bank of New York (http:/ / www. newyorkfed. org/
aboutthefed/ fedpoint/ fed45. html)
• Reserve Requirements - The Federal Reserve Board (http:/ / www. federalreserve. gov/ monetarypolicy/
reservereq. htm)
• Hussman Funds - Why the Federal Reserve is Irrelevant - August 2001 (http:/ / www. hussmanfunds. com/ html/
fedirrel. htm)
• Don't mention the reserve ratio (http:/ / www. islamic-finance. com/ item113_f. htm)
Operating cash flow
37
Operating cash flow
In financial accounting, operating cash flow (OCF), cash flow provided by operations or cash flow from
operating activities, refers to the amount of cash a company generates from the revenues it brings in, excluding
costs associated with long-term investment on capital items or investment in securities.
[1]
The International Financial
Reporting Standards defines operating cash flow as cash generated from operations less taxation and interest paid,
investment income received and less dividends paid gives rise to operating cash flows.
[2]
To calculate cash generated
from operations, one must calculate cash generated from customers and cash paid to suppliers. The difference
between the two reflects cash generated from operations.
Calculations
Cash generated from operating customers
• revenue as reported
• - increase (decrease) in operating trade receivables (1)
• - investment income (Profit on asset Sales, disclosed separately in Investment Cash Flow)
• - other income that is non cash and/or non sales related
Cash paid to operating suppliers
• costs of sales- Stock Variation = Purchase of goods. (2)
• + all other expenses
• - increase (decrease) in operating trade payables (1)
• - non cash expense items such as depreciation, provisioning, impairments, bad debts, etc.
• - financing expenses (disclosed separately in Finance Cash Flow)
(1): operating: Variations of Assets Suppliers and Clients accounts will be disclosed in the Financial Cash Flow
(2): Cost of Sales = Stock Out for sales. It is Cash Neutral. Cost of Sales - Stock Variation = Stock out - (Stock out -
Stock In)= Stock In = Purchase of goods: Cash Out
Operating Cash Flow vs. Net Income, EBIT, and EBITDA
Interest is an operating flow. Since it adjusts for liabilities, receivables, and depreciation, operating cash flow is a
more accurate measure of how much cash a company has generated (or used) than traditional measures of
profitability such as net income or EBIT. For example, a company with numerous fixed assets on its books (e.g.
factories, machinery, etc.) would likely have decreased net income due to depreciation; however, as depreciation is a
non-cash expense
[3]
the operating cash flow would provide a more accurate picture of the company's current cash
holdings than the artificially low net income.
[4]
Earnings before interest, taxes, depreciation and amortization (EBITDA) is a non-GAAP metric that can be used to
evaluate a company's profitability based on net working capital. The difference between EBITDA and OCF would
then reflect how the entity finances its net working capital in the short term. OCF is not a measure of free cash flow
and the effect of investment activities would need to be considered to arrive at the free cash flow of the entity.
Operating cash flow
38
See also
• EBITDA
• Cash flow
• Cash flow statement
• Free cash flow
• Operating Cash Flow at Wikinvest
References
[1] Ross, Stephen, Randolf Westerfield and Bradford Jordan Fundamentals of Corporate Finance
[2] International Accounting Standards 7, Cash Flow Statements (January 2007)
[3] Definition of depreciation via Wikinvest
[4] Definition of OCF via Wikinvest
Net present value
In finance, the net present value (NPV) or net present worth (NPW)
[1]
of a time series of cash flows, both
incoming and outgoing, is defined as the sum of the present values (PVs) of the individual cash flows. In the case
when all future cash flows are incoming (such as coupons and principal of a bond) and the only outflow of cash is
the purchase price, the NPV is simply the PV of future cash flows minus the purchase price (which is its own PV).
NPV is a central tool in discounted cash flow (DCF) analysis, and is a standard method for using the time value of
money to appraise long-term projects. Used for capital budgeting, and widely throughout economics, finance, and
accounting, it measures the excess or shortfall of cash flows, in present value terms, once financing charges are met.
The NPV of a sequence of cash flows takes as input the cash flows and a discount rate or discount curve and outputs
a price; the converse process in DCF analysis - taking a sequence of cash flows and a price as input and inferring as
output a discount rate (the discount rate which would yield the given price as NPV) - is called the yield, and is more
widely used in bond trading.
Formula
Each cash inflow/outflow is discounted back to its present value (PV). Then they are summed. Therefore NPV is the
sum of all terms,
where
t - the time of the cash flow
i - the discount rate (the rate of return that could be earned on an investment in the financial markets with
similar risk.)
- the net cash flow (the amount of cash, inflow minus outflow) at time t. For educational purposes, is
commonly placed to the left of the sum to emphasize its role as (minus) the investment.
The result of this formula if multiplied with the Annual Net cash in-flows and reduced by Initial Cash outlay will be
the present value but in case where the cash flows are not equal in amount then the previous formula will be used to
determine the present value of each cash flow separately. Any cash flow within 12 months will not be discounted for
NPV purpose.
[2]
Net present value
39
The discount rate
The rate used to discount future cash flows to the present value is a key variable of this process.
A firm's weighted average cost of capital (after tax) is often used, but many people believe that it is appropriate to
use higher discount rates to adjust for risk or other factors. A variable discount rate with higher rates applied to cash
flows occurring further along the time span might be used to reflect the yield curve premium for long-term debt.
Another approach to choosing the discount rate factor is to decide the rate which the capital needed for the project
could return if invested in an alternative venture. If, for example, the capital required for Project A can earn five
percent elsewhere, use this discount rate in the NPV calculation to allow a direct comparison to be made between
Project A and the alternative. Related to this concept is to use the firm's Reinvestment Rate. Reinvestment rate can
be defined as the rate of return for the firm's investments on average. When analyzing projects in a capital
constrained environment, it may be appropriate to use the reinvestment rate rather than the firm's weighted average
cost of capital as the discount factor. It reflects opportunity cost of investment, rather than the possibly lower cost of
capital.
An NPV calculated using variable discount rates (if they are known for the duration of the investment) better reflects
the real situation than one calculated from a constant discount rate for the entire investment duration. Refer to the
tutorial article written by Samuel Baker
[3]
for more detailed relationship between the NPV value and the discount
rate.
For some professional investors, their investment funds are committed to target a specified rate of return. In such
cases, that rate of return should be selected as the discount rate for the NPV calculation. In this way, a direct
comparison can be made between the profitability of the project and the desired rate of return.
To some extent, the selection of the discount rate is dependent on the use to which it will be put. If the intent is
simply to determine whether a project will add value to the company, using the firm's weighted average cost of
capital may be appropriate. If trying to decide between alternative investments in order to maximize the value of the
firm, the corporate reinvestment rate would probably be a better choice.
Using variable rates over time, or discounting "guaranteed" cash flows differently from "at risk" cash flows may be a
superior methodology, but is seldom used in practice. Using the discount rate to adjust for risk is often difficult to do
in practice (especially internationally), and is difficult to do well. An alternative to using discount factor to adjust for
risk is to explicitly correct the cash flows for the risk elements using rNPV or a similar method, then discount at the
firm's rate.
NPV in decision making
NPV is an indicator of how much value an investment or project adds to the firm. With a particular project, if is
a positive value, the project is in the status of discounted cash inflow in the time of t. If is a negative value, the
project is in the status of discounted cash outflow in the time of t. Appropriately risked projects with a positive NPV
could be accepted. This does not necessarily mean that they should be undertaken since NPV at the cost of capital
may not account for opportunity cost, i.e. comparison with other available investments. In financial theory, if there is
a choice between two mutually exclusive alternatives, the one yielding the higher NPV should be selected.
Net present value
40
If... It means... Then...
NPV
> 0
the investment would add
value to the firm
the project may be accepted
NPV
< 0
the investment would subtract
value from the firm
the project should be rejected
NPV
= 0
the investment would neither
gain nor lose value for the firm
We should be indifferent in the decision whether to accept or reject the project. This project adds no
monetary value. Decision should be based on other criteria, e.g. strategic positioning or other factors not
explicitly included in the calculation.
Example
A corporation must decide whether to introduce a new product line. The new product will have startup costs,
operational costs, and incoming cash flows over six years. This project will have an immediate (t=0) cash outflow of
$100,000 (which might include machinery, and employee training costs). Other cash outflows for years 1€6 are
expected to be $5,000 per year. Cash inflows are expected to be $30,000 each for years 1€6. All cash flows are
after-tax, and there are no cash flows expected after year 6. The required rate of return is 10%. The present value
(PV) can be calculated for each year:
Year Cash flow Present value
T=0 -$100,000
T=1 $22,727
T=2 $20,661
T=3 $18,783
T=4 $17,075
T=5 $15,523
T=6 $14,112
The sum of all these present values is the net present value, which equals $8,881.52. Since the NPV is greater than
zero, it would be better to invest in the project than to do nothing, and the corporation should invest in this project if
there is no mutually exclusive alternative with a higher NPV.
The same example in Excel formulae:
• NPV(rate,net_inflow)+initial_investment
• PV(rate,year_number,yearly_net_inflow)
Net present value
41
More realistic problems would need to consider other factors, generally including the calculation of taxes, uneven
cash flows, and salvage values as well as the availability of alternate investment opportunities.
Common pitfalls
• If, for example, the are generally negative late in the project (e.g., an industrial or mining project might have
clean-up and restoration costs), then at that stage the company owes money, so a high discount rate is not cautious
but too optimistic. Some people see this as a problem with NPV. A way to avoid this problem is to include
explicit provision for financing any losses after the initial investment, that is, explicitly calculate the cost of
financing such losses.
• Another common pitfall is to adjust for risk by adding a premium to the discount rate. Whilst a bank might charge
a higher rate of interest for a risky project, that does not mean that this is a valid approach to adjusting a net
present value for risk, although it can be a reasonable approximation in some specific cases. One reason such an
approach may not work well can be seen from the following: if some risk is incurred resulting in some losses,
then a discount rate in the NPV will reduce the impact of such losses below their true financial cost. A rigorous
approach to risk requires identifying and valuing risks explicitly, e.g. by actuarial or Monte Carlo techniques, and
explicitly calculating the cost of financing any losses incurred.
• Yet another issue can result from the compounding of the risk premium. R is a composite of the risk free rate and
the risk premium. As a result, future cash flows are discounted by both the risk-free rate as well as the risk
premium and this effect is compounded by each subsequent cash flow. This compounding results in a much lower
NPV than might be otherwise calculated. The certainty equivalent model can be used to account for the risk
premium without compounding its effect on present value.
• Another issue with relying on NPV is that it does not provide an overall picture of the gain or loss of executing a
certain project. To see a percentage gain relative to the investments for the project, usually, Internal rate of return
or other efficiency measures are used as a complement to NPV.
Net present value
42
History
Net present value as a valuation methodology dates at least to the 19th century. Karl Marx refers to NPV as fictitious
capital, and the calculation as capitalising, writing:
[4]
The forming of a fictitious capital is called capitalising. Every periodically repeated income is capitalised by
calculating it on the average rate of interest, as an income which would be realised by a capital at this rate of
interest.
In mainstream neo-classical economics, NPV was formalized and popularized by Irving Fisher, in his 1907 The Rate
of Interest and became included in textbooks from the 1950s onwards, starting in finance texts.
[5]

[6]
Alternative capital budgeting methods
• Adjusted present value (APV): adjusted present value, is the net present value of a project if financed solely by
ownership equity plus the present value of all the benefits of financing.
• Payback period: which measures the time required for the cash inflows to equal the original outlay. It measures
risk, not return.
• Cost-benefit analysis: which includes issues other than cash, such as time savings.
• Real option method: which attempts to value managerial flexibility that is assumed away in NPV.
• Internal rate of return: which calculates the rate of return of a project while disregarding the absolute amount of
money to be gained.
• Modified internal rate of return (MIRR): similar to IRR, but it makes explicit assumptions about the reinvestment
of the cash flows. Sometimes it is called Growth Rate of Return.
• Accounting rate of return (ARR): a ratio similar to IRR and MIRR
References
[1] Lin, Grier C. I.; Nagalingam, Sev V. (2000). CIM justification and optimisation. London: Taylor & Francis. pp. 36. ISBN 0-7484-0858-4.
[2] Khan, M.Y. (1993). Theory & Problems in Financial Management. Boston: McGraw Hill Higher Education. ISBN 9780074636831.
[3] Baker, Samuel L. (2000). "Perils of the Internal Rate of Return" (http:/ / hspm. sph. sc. edu/ COURSES/ ECON/ invest/ invest. html). .
Retrieved January 12, 2007.
[4] Karl Marx, Capital, Volume 3, 1909 edition, p. 548
[5] Bichler, Shimshon; Nitzan, Jonathan (July 2010), Systemic Fear, Modern Finance and the Future of Capitalism (http:/ / bnarchives. yorku.
ca/ 289/ 03/ 20100700_bn_systemic_fear_modern_finance_future_of_capitalism. pdf), Jerusalem and Montreal, pp. 8€11 (for discussion of
history of use of NPV as "capitalisation"),
[6] Nitzan, Jonathan; Bichler, Shimshon (2009), Capital as Power. A Study of Order and Creorder., RIPE Series in Global Political Economy,
New York and London: Routledge
Internal rate of return
43
Internal rate of return
The internal rate of return (IRR) is a rate of return used in capital budgeting to measure and compare the
profitability of investments. It is also called the discounted cash flow rate of return (DCFROR) or simply the rate of
return (ROR).
[1]
In the context of savings and loans the IRR is also called the effective interest rate. The term
internal refers to the fact that its calculation does not incorporate environmental factors (e.g., the interest rate or
inflation).
Definition
Showing the position of the IRR on the graph of
( is labelled 'i' in the graph)
The internal rate of return on an investment or project is the
"annualized effective compounded return rate" or discount rate that
makes the net present value (NPV) of all cash flows (both positive and
negative) from a particular investment equal to zero.
In more specific terms, the IRR of an investment is the interest rate at
which the net present value of costs (negative cash flows) of the
investment equals the net present value of the benefits (positive cash
flows) of the investment.
Internal rates of return are commonly used to evaluate the desirability
of investments or projects. The higher a project's internal rate of return,
the more desirable it is to undertake the project. Assuming all other
factors are equal among the various projects, the project with the highest IRR would probably be considered the best
and undertaken first.
A firm (or individual) should, in theory, undertake all projects or investments available with IRRs that exceed the
cost of capital. Investment may be limited by availability of funds to the firm and/or by the firm's capacity or ability
to manage numerous projects.
Uses
Important: Because the internal rate of return is a rate quantity, it is an indicator of the efficiency, quality, or yield of
an investment. This is in contrast with the net present value, which is an indicator of the value or magnitude of an
investment.
An investment is considered acceptable if its internal rate of return is greater than an established minimum
acceptable rate of return or cost of capital. In a scenario where an investment is considered by a firm that has equity
holders, this minimum rate is the cost of capital of the investment (which may be determined by the risk-adjusted
cost of capital of alternative investments). This ensures that the investment is supported by equity holders since, in
general, an investment whose IRR exceeds its cost of capital adds value for the company (i.e., it is economically
profitable).
Internal rate of return
44
Calculation
Given a collection of pairs (time, cash flow) involved in a project, the internal rate of return follows from the net
present value as a function of the rate of return. A rate of return for which this function is zero is an internal rate of
return.
Given the (period, cash flow) pairs ( , ) where is a positive integer, the total number of periods , and
the net present value , the internal rate of return is given by in:
Note that the period is usually given in years, but the calculation may be made simpler if is calculated using the
period in which the majority of the problem is defined (e.g., using months if most of the cash flows occur at monthly
intervals) and converted to a yearly period thereafter.
Note that any fixed time can be used in place of the present (e.g., the end of one interval of an annuity); the value
obtained is zero if and only if the NPV is zero.
In the case that the cash flows are random variables, such as in the case of a life annuity, the expected values are put
into the above formula.
Often, the value of cannot be found analytically. In this case, numerical methods or graphical methods must be
used.
Example
If an investment may be given by the sequence of cash flows
Year ( ) Cash Flow ( )
0 ‚4000
1 1200
2 1410
3 1875
4 1050
then the IRR is given by
.
In this case, the answer is 14.3%.
Numerical solution
Since the above is a manifestation of the general problem of finding the roots of the equation , there are
many numerical methods that can be used to estimate . For example, using the secant method, is given by
.
where is considered the
th
approximation of the IRR.
This can be found to an arbitrary degree of accuracy.
The convergence behaviour of the sequence is governed by the following:
• If the function has a single real root , then the sequence will converge reproducibly towards .
Internal rate of return
45
• If the function has real roots , then the sequence will converge to one of the roots and
changing the values of the initial pairs may change the root to which it converges.
• If function has no real roots, then the sequence will tend towards +•.
Having when or when may speed up convergence of to .
Numerical Solution for Single Outflow and Multiple Inflows
Of particular interest is the case where the stream of payments consists of a single outflow, followed by multiple
inflows occurring at equal periods. In the above notation, this corresponds to: < 0, ‡ 0 for ‡ 1. In this
case the NPV of the payment stream is a convex, strictly decreasing function of interest rate. There is always a single
unique solution for IRR.
Given two estimates and for IRR, the secant method equation (see above) with will always produce
an improved estimate . This is sometimes referred to as the Hit and Trial (or Trial and Error) method. There is
however a much more accurate estimation formula, given by:
where
.
In this equation, and refer to the NPV's of the inflows only (that is, set = 0 and compute
NPV). For example, using the stream of payments {-4000, 1200, 1410, 1875, 1050} and initial guesses
and gives and . The accurate formula estimates IRR as
14.35% (0.3% error) as compared to IRR = 14.7% (3% error) from the secant method.
If applied iteratively, either the secant method or the improved formula will always converge to the correct solution.
Both the secant method and the improved formula rely on initial guesses for IRR. The following initial guesses may
be used:
where
sum of inflows
.
Further discussion and a performance comparison of IRR estimation methods may be found in.
[2]
Internal rate of return
46
Problems with using internal rate of return
As an investment decision tool, the calculated IRR should not be used to rate mutually exclusive projects, but only to
decide whether a single project is worth investing in.
NPV vs discount rate comparison for two mutually exclusive projects. Project 'A' has a
higher NPV (for certain discount rates), even though its IRR (=x-axis intercept) is lower
than for project 'B' (click to enlarge)
In cases where one project has a higher
initial investment than a second
mutually exclusive project, the first
project may have a lower IRR
(expected return), but a higher NPV
(increase in shareholders' wealth) and
should thus be accepted over the
second project (assuming no capital
constraints).
IRR assumes reinvestment of interim
cash flows in projects with equal rates
of return (the reinvestment can be the
same project or a different project).
Therefore, IRR overstates the annual
equivalent rate of return for a project
whose interim cash flows are
reinvested at a rate lower than the
calculated IRR. This presents a
problem, especially for high IRR
projects, since there is frequently not another project available in the interim that can earn the same rate of return as
the first project.
When the calculated IRR is higher than the true reinvestment rate for interim cash flows, the measure
will overestimate … sometimes very significantly … the annual equivalent return from the project. The
formula assumes that the company has additional projects, with equally attractive prospects, in which to
invest the interim cash flows.
[3]
This makes IRR a suitable (and popular) choice for analyzing venture capital and other private equity investments, as
these strategies usually require several cash investments throughout the project, but only see one cash outflow at the
end of the project (e.g., via IPO or M&A).
Since IRR does not consider cost of capital, it should not be used to compare projects of different duration. Modified
Internal Rate of Return (MIRR) does consider cost of capital and provides a better indication of a project's efficiency
in contributing to the firm's discounted cash flow.
In the case of positive cash flows followed by negative ones (+ + - - -) the IRR may have multiple values. In this case
a discount rate may be used for the borrowing cash flow and the IRR calculated for the investment cash flow. This
applies for example when a customer makes a deposit before a specific machine is built.
In a series of cash flows like (-10, 21, -11), one initially invests money, so a high rate of return is best, but then
receives more than one possesses, so then one owes money, so now a low rate of return is best. In this case it is not
even clear whether a high or a low IRR is better. There may even be multiple IRRs for a single project, like in the
example 0% as well as 10%. Examples of this type of project are strip mines and nuclear power plants, where there
is usually a large cash outflow at the end of the project.
In general, the IRR can be calculated by solving a polynomial equation. Sturm's theorem can be used to determine if
that equation has a unique real solution. In general the IRR equation cannot be solved analytically but only
iteratively.
Internal rate of return
47
When a project has multiple IRRs it may be more convenient to compute the IRR of the project with the benefits
reinvestmented.
[3]
Accordingly, MIRR is used, which has an assumed reinvestment rate, usually equal to the
project's cost of capital.
Despite a strong academic preference for NPV, surveys indicate that executives prefer IRR over NPV.
[4]
Apparently,
managers find it easier to compare investments of different sizes in terms of percentage rates of return than by
dollars of NPV. However, NPV remains the "more accurate" reflection of value to the business. IRR, as a measure of
investment efficiency may give better insights in capital constrained situations. However, when comparing mutually
exclusive projects, NPV is the appropriate measure.
Mathematics
Mathematically the value of the investment is assumed to undergo exponential growth or decay according to some
rate of return (any value greater than -100%), with discontinuities for cash flows, and the IRR of a series of cash
flows is defined as any rate of return that results in a net present value of zero (or equivalently, a rate of return that
results in the correct value of zero after the last cash flow).
Thus internal rate(s) of return follow from the net present value as a function of the rate of return. This function is
continuous. Towards a rate of return of -100% the net present value approaches infinity with the sign of the last cash
flow, and towards a rate of return of positive infinity the net present value approaches the first cash flow (the one at
the present). Therefore, if the first and last cash flow have a different sign there exists an internal rate of return.
Examples of time series without an IRR:
• Only negative cash flows - the NPV is negative for every rate of return.
• (-1, 1, -1), rather small positive cash flow between two negative cash flows; the NPV is a quadratic function of
1/(1+r), where r is the rate of return, or put differently, a quadratic function of the discount rate r/(1+r); the
highest NPV is -0.75, for r = 100%.
In the case of a series of exclusively negative cash flows followed by a series of exclusively positive ones, consider
the total value of the cash flows converted to a time between the negative and the positive ones. The resulting
function of the rate of return is continuous and monotonically decreasing from positive infinity to negative infinity,
so there is a unique rate of return for which it is zero. Hence the IRR is also unique (and equal). Although the
NPV-function itself is not necessarily monotonically decreasing on its whole domain, it is at the IRR.
Similarly, in the case of a series of exclusively positive cash flows followed by a series of exclusively negative ones
the IRR is also unique.
• Extended Internal Rate of Return: The Internal rate of return calculates the rate at which the investment made will
generate cash flows. This method is convenient if the project has a short duration, but for projects which has an
outlay of many years this method is not practical as IRR ignores the time value of money. To take into
consideration the Time Value of Money Extended Internal Rate of Return was introduced where all the future
cash flows are first discounted at a discount rate and then the IRR is calculated. This method of calculation of IRR
is called Extended Internal Rate of Return or XIRR.
Internal rate of return
48
References
[1] Project Economics and Decision Analysis, Volume I: Deterministic Models, M.A.Main, Page 269
[2] Thron, C and Moten, J, "Easy, Accurate Methods for Estimating Internal Rate of Return" (http:/ / www. tarleton. edu/ faculty/ thron/
Simple_IRR_Estimation_Thron_Moten_5Nov10.pdf)
[3] Internal Rate of Return: A Cautionary Tale (http:/ / www. cfo. com/ article. cfm/ 3304945)
[4] Pogue, M.(2004). Investment Appraisal: A New Approach. Managerial Auditing Journal.Vol. 19 No. 4, 2004. pp. 565-570
Further reading
1. Bruce J. Feibel. Investment Performance Measurement. New York: Wiley, 2003. ISBN 0471268496
External links
• Economics Interactive Lecture from University of South Carolina (http:/ / hspm. sph. sc. edu/ courses/ Econ/ irr/
irr. html)
Article Sources and Contributors
49
Article Sources and Contributors
Financial ratio  Source: http://en.wikipedia.org/w/index.php?oldid=410760009  Contributors: A. B., Alexius08, Andrew Reynolds, Andrewericoleman, Andycjp, Anna Lincoln, AnthonyUK,
Auntof6, Binary TSO, Blue Tie, Calvin 1998, Capricorn42, Catgut, Chessy999, Chrylis, David Chouinard, Deli nk, DocendoDiscimus, Doulos Christos, Ehrenkater, Ex nihil, Feco, Finnancier,
Fintor, Foggy Morning, Giftlite, Gilliam, Gregalton, GregorB, HenkvD, James Foye, James086, Jeanine Leuckel, Jerryseinfeld, Kbrose, KennethJ, Kortaggio, Kuru, Lamro, Laptop.graham, Md7t,
Mild Bill Hiccup, Mouse Nightshirt, Mrdashboard, My.toa.badz, Nbarth, Nifky?, Nwiggs, Octopus-Hands, Ohnoitsjamie, Paulkappelle, Pgreenfinch, PigFlu Oink, Queerkid2, RJN,
Ravensfan5252, Reconsider the static, Retail Investor, Rich Farmbrough, Rjanag, Rjwilmsi, Robertson-Glasgow, Rrburke, Saturnight, Sax888, Seaphoto, SirIsaacBrock, Sivikoo, Suidafrikaan,
Tbileth, Tide rolls, Trubadur, Vidhyasagarss, WikipedianYknOK, Xezbeth, Yankeerudy, 168 anonymous edits
Gross margin  Source: http://en.wikipedia.org/w/index.php?oldid=403492322  Contributors: Ahsq, Albedo, Ansgarjohn, Arthena, Bobo192, Calor, Dangelon, Dnieweg, DocendoDiscimus,
ESkog, Eeekster, ErikNilsson, Everyking, Feco, Fredi@wiki, Frodet, HamburgerRadio, Hans G. Oberlack, Hessamnia, Hu12, Hugh Mason, Ino5hiro, Javert, Jemappel1, Ktwombley, Lelkens,
Nbarth, NuclearWinner, Nurg, Octopus-Hands, Oroso, Pg133, Qwertythecat, Renata3, Rhobite, Rich Farmbrough, Rufous, Sebross, Semilemon, Shyam, SirIsaacBrock, Snoyes, Staffwaterboy,
Surajmohandas, TWCarlson, Teixant, Tesseran, Testaabb, TheParanoidOne, TheoClarke, Thingg, Thue, Tsotnekutalia, Underpants, VQuakr, WipedEven, Yudengdeng, 185 anonymous edits
Operating margin  Source: http://en.wikipedia.org/w/index.php?oldid=394766491  Contributors: Agaochen, Ashitagaarusa, Bryan Derksen, Bunnyhop11, CuandoCubango, DocendoDiscimus,
Geronimoslastand, Gloumouth1, Goodgerster, Happybp, Hu12, Iatrowvw, Jerryseinfeld, King of Hearts (old account 2), Lachambre, Lumidek, Madamd, Maurreen, Mydogategodshat, Nbarth,
Octopus-Hands, Piabelle, Sebross, SeptimusOrcinus, Shyam, SirIsaacBrock, TDaily, Tend birds, Timotheus Canens, Yonidebest, 27 anonymous edits
Profit margin  Source: http://en.wikipedia.org/w/index.php?oldid=410081222  Contributors: Comet Tuttle, DVD R W, December21st2012Freak, Deon, Difu Wu, Dreadstar, Enochlau, Ewiger
Besserwisser, Fluent aphasia, Goldendroplets, Goodgerster, Isfisk, Jack Daniel Adams, Jag123, Jeisenberg, Jerryseinfeld, KSU 83, Katalaveno, Katherine, KelleyCook, Kuru, Mac, Marcinbmach,
Maurreen, Medxdispensing, Mleader1, Mygerardromance, Nirvana2013, Novelo, Octopus-Hands, Ohms law, Ohnoitsjamie, Reedy, Retail Investor, Retiono Virginian, Ryan Norton, Sakletare,
Sebross, Shoffy, SirIsaacBrock, Skrock724, Svetovid, Tide rolls, Tothebarricades.tk, Unschool, UpstateNYer, Usual weeks, VMS Mosaic, Varow48, W.P. Norton, Wackymacs, Wiki.gcc, Yahel
Guhan, 103 anonymous edits
Return on equity  Source: http://en.wikipedia.org/w/index.php?oldid=404724441  Contributors: Aitias, Antiuser, Arthena, Ashitagaarusa, Ask123, Ayanpro, Bluemoose, Buschke,
Chrismcgoogey, DocendoDiscimus, Drmies, EnSamulili, Epbr123, Feco, Gary King, Giftlite, Gogo Dodo, Gregalton, Gurubrahma, Gzuckier, Infinity0, Kenckar, Kuru, Lamro, Lopeztoonen,
Michael Broquist, Mrdthree, Octopus-Hands, Pearle, Pinnecco, Pjetter, RJN, Ravensfan5252, Retail Investor, S-n-ushakov, Sarrus, Sebross, SirIsaacBrock, Spmcnamee, Tabletop, Tomas e,
Wiki.gcc, Wolf530, Zach425, 73 anonymous edits
Rate of return  Source: http://en.wikipedia.org/w/index.php?oldid=410674458  Contributors: 7ema7, Ahoerstemeier, AlbertaSunwapta, Alkarex, Altruistguy, Amirab, Amizzi, Andr…s
Djordjalian, AnnuitSophia, Aylad, BTLizard, Bluerasberry, CRoetzer, Chamal N, Chrisgil25, Clear memory, Closedmouth, Costkiller, Doronp, Drunken Pirate, Encyclops, Ewlyahoocom,
Feibels, Finnancier, Gabi S., Gary King, Giler, Glane23, GraemeL, Gregalton, GregorB, Ground Zero, Heirpixel, Hoegholm, Hubbardaie, Hydrogen Iodide, Ian Pitchford, Ilya Voyager,
IvanLanin, JMSwtlk, James086, Junming999, Kalbasa, Kameyama, Kuru, Levineps, Linuxerist, Lunchscale, Magator, Magister Mathematicae, MarceloB, Mark ok7, Marra, Mathdeveloper,
Mboverload, Michaelas10, Mindmatrix, MinorContributor, Miquonranger03, Mnmngb, Mrholybrain, Music Sorter, Musiphil, Namazu-tron, NoticeBored, Nschuma, Octopus-Hands,
Ohnoitsjamie, Patrick, Paul.Paquette, Plasticup, Pol098, Protonk, Psb777, Radagast83, Reedy, Rickhev1, Rjwilmsi, Robykiwi, Roy Fultun, Saurael, Secular mind, Shpleeurnck, Siktath,
SirIsaacBrock, Smallbones, Smee, SnakeType, South Bay, SueHay, Svetovid, TECH-NOIR, The Thing That Should Not Be, The Utahraptor, Thinktwins, Uncle Dick, UncleDouggie, Versus22,
Wgroth, White Trillium, Wikipelli, Wkbeh, 294 anonymous edits
Return on assets  Source: http://en.wikipedia.org/w/index.php?oldid=410008305  Contributors: Ahmed A. Hassan, Almirvargas, Andyjwagner, Ashitagaarusa, BlueNovember, Correogsk,
Earthlyreason, Feco, Giftlite, Gregalton, HeavyStorm, Hildey, Hu12, Jannex, Jerryseinfeld, Jhinman, John Doe45, Kortaggio, Kuru, Lamro, Longhair, MadMadDog, Mrdthree, NBA-Forum.net,
Natarajanganesan, Octopus-Hands, PTSE, Patrick, Scriberius, SirIsaacBrock, Swampyank, TigerShark, Tjic, WarthogDemon, Yankeerudy, Zain Ebrahim111, 55 anonymous edits
Return on assets Du Pont  Source: http://en.wikipedia.org/w/index.php?oldid=404870555  Contributors: Asocall, Boothy443, Ckatz, Epbr123, Feco, Foggy Morning, Gaius Cornelius, Gede,
Gregalton, Hectorthebat, ImperfectlyInformed, Lamro, Markaci, Octopus-Hands, Oparadoha, PhishNeslo, RevelationDirect, SergioBruno66, Tagishsimon, Tapir666, The Thing That Should Not
Be, ThinkBlue, Utcursch, 50 anonymous edits
Return on net assets  Source: http://en.wikipedia.org/w/index.php?oldid=409124953  Contributors: Diannaa, DrewMorris, Infinity0, Ixfd64, Mkoval, Mramsey68, Peter.Procenko, Ronz,
SirIsaacBrock, TexasAndroid, 8 anonymous edits
Return on capital  Source: http://en.wikipedia.org/w/index.php?oldid=399933923  Contributors: 1-is-blue, A papalexandris, Afa86, Aldo samulo, Ask123, Banknote, BenFrantzDale,
Bluefinancer, Bluemoose, Chakreshsinghai, Cherkash, Closedmouth, Dave6, DocendoDiscimus, EPM, Feco, Gregalton, Hu12, Infinity0, Jerryseinfeld, Jurriaan, Kingpin13, Kourii, Kuru, Lamro,
Mannafredo, Maurreen, MonideepGupta, Octopus-Hands, Pocopocopocopoco, Psantora, Sagaciousuk, Sam Hocevar, Shawnc, SirIsaacBrock, SpuriousQ, TheProject, UnitedStatesian,
Urbansuperstar, Verbum Veritas, 40 anonymous edits
Risk adjusted return on capital  Source: http://en.wikipedia.org/w/index.php?oldid=405694981  Contributors: Anwar saadat, Athaenara, Avraham, Brad101, Dchessar, Exeunt, Hu12, JJMcVey,
Jeepday, JimmyBlackwing, Johanvranken, Kuru, Lamro, MacGyverMagic, MarceloB, Michael Devore, NawlinWiki, Octopus-Hands, Pattrick, Pnm, Rjwilmsi, Sagarbiyani, Solarapex, Svick, 16
anonymous edits
Cash flow return on investment  Source: http://en.wikipedia.org/w/index.php?oldid=381568207  Contributors: Businessman332211, CXCV, Cantalamessa, Edward, GregorB, Jrockley,
Katharineamy, Kumioko, LilHelpa, Longhair, Mankind 2k, Octopus-Hands, Rjwilmsi, Shamoonanwar, Sicherlich, Thlthl3, 11 anonymous edits
Current ratio  Source: http://en.wikipedia.org/w/index.php?oldid=383204783  Contributors: -Midorihana-, Although, Alwang, Andrew Reynolds, Ashitagaarusa, Crzycheetah, J a pearson, James
Slezak, Jonathunder, Kuru, MadMadDog, Md7t, Mohammed sa'ad shaikh, Octopus-Hands, Pecos Jack, Savaria, Scott5114, SirIsaacBrock, Wiki.gcc, Yankeerudy, 36 anonymous edits
Cash ratio  Source: http://en.wikipedia.org/w/index.php?oldid=41230583  Contributors: ABACA, Abaniyuwe, Achshar, Addshore, Adimbait, Alberth2, Amyedunlop, Anuragpatil, Audacity,
Azhmbb, Bender235, Brian, Bsellis, Btyner, Can't sleep, clown will eat me, Cloak Reaver, Crosbiesmith, David Ja†a, Dialectric, Dthomsen8, E. Perkerson, EGeek, Ebinviswanath, Edward,
Embeee, Epbr123, Esp rus2, Ewlyahoocom, Fivemack, Gary King, Gjgjgj, Gonello, Gurch, Guy Peters, Headbomb, Iain99, JHP, Jerryseinfeld, Kaihsu, Karovd, Koustav dasgupta, Ladislav
Simko, Mickhlaw, Million Little Gods, Mouse Nightshirt, Mpt, Mydogategodshat, NaveenHooda, Nirvana2013, Nutcracker, Pakaran, Paul Gard, Paul Nollen, PaulHanson, R'n'B,
RAJJAISWAL1991, Radagast83, Rgoodermote, Rich Farmbrough, Rjwilmsi, Rlaager, Rusty, Ruziklan, Saif Tinku, Saif tinku, Salahuddin sultan, Sardanaphalus, Shivlund, Sidonuke, Simon123,
Sodamoeba, Surturz, The Random Editor, Trna.michal, Ttony21, Urbansuperstar, Utcursch, Vipinhari, Wikitanvir, Wjbiopat, Woohookitty, Z1derful, Zman241, 205 anonymous edits
Operating cash flow  Source: http://en.wikipedia.org/w/index.php?oldid=407057956  Contributors: Armcharles, Cavrdg, Ceyockey, Ctashian, DUBOIS DENIS, DocendoDiscimus, Gary King,
Grafen, Green Squares, Hebrides, Kneel17, Martin.kariuki, PaulHanson, RichardVeryard, Shawnc, Shyam, SirIsaacBrock, SueHay, Titocosta, 25 anonymous edits
Net present value  Source: http://en.wikipedia.org/w/index.php?oldid=410240251  Contributors: AdamNealis, Agbr, Ahoerstemeier, Altenmann, AlterFritz, Andy, Appraiser, Arichnad, Arishth,
Badgernet, Bcrounse, BenFrantzDale, Bfinn, Bhoola Pakistani, Can't sleep, clown will eat me, Capricorn42, Cedric dlb, Chakreshsinghai, Cheese Sandwich, Chris the speller, Chrisch, Cibergili,
Credema, Cs419 hewe, D3j4vu, DRogers, Daniel.gruno, Ddr, Diana.chripczuk, Djstreet, Docu, Doorjam, Ehrenkater, Ejjazaccountant, Erichiggs, Ertyqway, Euryalus, Ewiger Besserwisser,
EyeSerene, Fahad79, Fannemel, Farklethehippo, Feco, Fildon, Flowanda, Fsiler, Gabridelca, Garzo, Gaz Man, Ginsengbomb, Gregalton, Greudin, Grieger, Grochim, Guoguo12, Gurch, Guy M,
HelpSign, Here.it.comes.again, HolyT, Hu12, Hyteqsystems, IRP, Ixfd64, JHP, JamesBWatson, Jaredehansen, Javincy, Jerryseinfeld, Jgswikiname, Jhwheuer, Jic, Jmkim dot com, JohnDoe0007,
Jose77, Jovianeye, Jusdafax, KelleyCook, Kenckar, Kingpin13, Kinzlp, Kku, Kopaka649, Kruglick, Kuru, Lamro, Laptop.graham, Les boys, Loren.wilton, Mareino, Mark, Megalodon99,
Metagraph, Michael Hardy, Mild Bill Hiccup, Mindmatrix, MrOllie, MustangAficionado, Nbarth, Nickwilliams1975, Nirvana2013, Notinasnaid, Oxymoron83, Patrick, Pearle, Philip Trueman,
Pleasantville, ProductBox, Retail Investor, Rich Farmbrough, Rjwilmsi, Sam mishra, Schnell, Seaphoto, Sheitan, Simoes, Skysmith, Smallbones, SmilingBoy, Solarapex, Stathisgould,
Statisticsblog, Stewartjohnson, SueHay, Swanseaeu1, TNorthcutt, Terjepetersen, Tgeller, The Aviv, The Thing That Should Not Be, Thincat, Thomas Larsen, Timo Honkasalo, Tiredofscams,
Tobacman, Torch-r, Trainso, Urbanrenewal, Voidxor, Vssun, Wickethewok, Wmahan, Wohingenau, Xiaopo, YoavD, Zaphodtx, Zeiden, 391 anonymous edits
Internal rate of return  Source: http://en.wikipedia.org/w/index.php?oldid=409781098  Contributors: Adambro, Alireza824, Altruistguy, Amarsesh, Andonic, Anna2325a, B0mbrman, Barek,
Benjicharlton, Bhoola Pakistani, Btyner, CRGreathouse, CWenger, Calmer Waters, CanadianLinuxUser, Charles Matthews, Cheese Sandwich, Chokca, Chokoboii, Cibergili, Cs419 hewe,
Daniel.gruno, David7757, Dffgd, Djstreet, Dying, Edward, Ejjazaccountant, Ewlyahoocom, Excirial, FU2000, Financial-projections, Flowanda, Flyingidiot, Gabbe, Gijsdereeper, Gregalton,
Greudin, Grieger, Howardjacobson, Hu12, IstvanWolf, J.delanoy, JamesBWatson, Javincy, Jbryanscott, Jdpipe, Jeddawiiah, Jeff3000, Jerryseinfeld, Jic, Jitse Niesen, Jmkim dot com, Jose77,
Jujutacular, Kenckar, Kuru, Lamro, Laptop.graham, LeaveSleaves, LilHelpa, Longhair, Madcat87, Mahoroba, Managerarc, Markeet, Max power, Maximo.martinez, Mervyn, Mic, Mmccalpin,
Modi mode, MrOllie, Nakon, Nanjihea, Notinasnaid, Nyirenda, Oxymoron83, Parveson, Patrick, Pjetter, Pocopocopocopoco, Pondster123, Pontus, RJaguar3, Retail Investor, Romistrub,
Article Sources and Contributors
50
SHCarter, Sky Attacker, Smallbones, Sman9356, Stathisgould, Stefan heizmann, SueHay, TAMU-CT math, Tide rolls, Versageek, VisitLeast, Vssun, Wbhobbs, Yoenit, 309 anonymous edits
Image Sources, Licenses and Contributors
51
Image Sources, Licenses and Contributors
File:DiscreteCF.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:DiscreteCF.jpg  License: Public Domain  Contributors: Grochim, Kenckar, Yoshi122
File:cumCF.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:CumCF.jpg  License: Public Domain  Contributors: Grochim, Kenckar, Yoshi122
Image:IRR1 - Grieger.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:IRR1_-_Grieger.jpg  License: Public Domain  Contributors: Bkell, Grieger, 1 anonymous edits
Image:exclusive investments.png  Source: http://en.wikipedia.org/w/index.php?title=File:Exclusive_investments.png  License: Public Domain  Contributors: Grieger
License
52
License
Creative Commons Attribution-Share Alike 3.0 Unported
http:/ / creativecommons. org/ licenses/ by-sa/ 3. 0/