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Business AdministrationFinancial Ratios

ContentsArticles

Financial ratio 1Gross margin 9Operating margin 11Profit margin 12Return on equity 13Rate of return 15Return on assets 25Return on assets Du Pont 26Return on net assets 28Return on capital 28Risk adjusted return on capital 29Cash flow return on investment 30Current ratio 30Cash ratio 31Operating cash flow 37Net present value 38Internal rate of return 43

ReferencesArticle Sources and Contributors 49Image Sources, Licenses and Contributors 51

Article LicensesLicense 52

Financial ratio 1

Financial ratio

AccountancyKey concepts

Accountant · Bookkeeping · Cash and accrual basis · Constant Item Purchasing Power Accounting · Cost of goods sold · Debits andcredits · 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 anenterprise's financial statements. Often used in accounting, there are many standard ratios used to try to evaluate theoverall financial condition of a corporation or other organization. Financial ratios may be used by managers within afirm, by current and potential shareholders (owners) of a firm, and by a firm's creditors. Security analysts usefinancial ratios to compare the strengths and weaknesses in various companies.[1] If shares in a company are tradedin 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 asearnings 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 wasabove 1, the reciprocal will be below 1, and conversely. The reciprocal expresses the same information, but may bemore understandable: for instance, the earnings yield can be compared with bond yields, while the P/E ratio cannotbe: for example, a P/E ratio of 20 corresponds to an earnings yield of 5%.

Sources of data for financial ratiosValues used in calculating financial ratios are taken from the balance sheet, income statement, statement of cashflows or (sometimes) the statement of retained earnings. These comprise the firm's "accounting statements" orfinancial statements. The statements' data is based on the accounting method and accounting standards used by theorganization.

Purpose and types of ratiosFinancial 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. Liquidityratios measure the availability of cash to pay debt.[2] Activity ratios measure how quickly a firm converts non-cashassets to cash assets.[3] Debt ratios measure the firm's ability to repay long-term debt.[4] Profitability ratiosmeasure the firm's use of its assets and control of its expenses to generate an acceptable rate of return.[5] Marketratios 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 averageRatios generally hold no meaning unless they are benchmarked against something else, like past performance oranother 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 principlesFinancial ratios may not be directly comparable between companies that use different accounting methods or followvarious standard accounting practices. Most public companies are required by law to use generally acceptedaccounting principles for their home countries, but private companies, partnerships and sole proprietorships may notuse accrual basis accounting. Large multi-national corporations may use International Financial Reporting Standardsto produce their financial statements, or they may use the generally accepted accounting principles of their homecountry.There is no international standard for calculating the summary data presented in all financial statements, and theterminology is not always consistent between companies, industries, countries and time periods.

Abbreviations and terminologyVarious abbreviations may be used in financial statements, especially financial statements summarized on theInternet. Sales reported by a firm are usually net sales, which deduct returns, allowances, and early paymentdiscounts 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 onhours. 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 totalnumber of shares in the company multiplied by each share's book value; Owner's Equity represents the total numberof shares that an individual shareholder owns (usually the owner with controlling interest), multiplied by each share'sbook 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 ratiosProfitability ratios measure the company's use of its assets and control of its expenses to generate an acceptable rateof returnGross 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 alsosometimes used as a synonym for EBIT and operating profit.[10] This is true if the firm has no non-operatingincome. (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 EquityCash flow return on investment (CFROI)

Efficiency ratio

Net gearing

Basic Earnings Power Ratio[16]

Liquidity ratiosLiquidity 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 ratiosMarket 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 RatiosEV/EBITDA

EV/Sales

Cost/Income ratioSector-specific ratiosEV/capacityEV/output

Capital Budgeting RatiosIn addition to assisting management and owners in diagnosing the financial health of their company, ratios can alsohelp managers make decisions about investments or projects that the company is considering to take, such asacquisitions, 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 marginGross margin, gross profit margin or gross profit rate is the difference between the sales and the production costsexcluding overhead, payroll, taxation, and interest payments. Gross margin can be defined as the amount ofcontribution to the business enterprise, after paying for direct-fixed and direct-variable unit costs, required to coveroverheads (fixed commitments) and provide a buffer for unknown items. It expresses the relationship between grossprofit and sales revenue. It is a measure of how well each dollar of a company's revenue is utilized to cover the costsof goods sold.[1]

It can be expressed in absolute terms:Gross margin = net sales - cost of goods sold + annual sales returnor 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 officeexpenses, rent, administrative costs, etc.Higher gross margins for a manufacturer reflect greater efficiency in turning raw materials into income. For a retailerit will be their markup over wholesale. Larger gross margins are generally good for companies, with the exception ofdiscount retailers. They need to show that operations efficiency and financing allows them to operate with tinymargins.

How gross margin is used in salesRetailers can measure their profit by using two basic methods, markup and margin, both of which give a descriptionof the gross profit of the sale. The markup expresses profit as a percentage of the retailer's cost for the product. Themargin expresses profit as a percentage of the retailer's sales price for the product. These two methods give differentpercentages as results, but both percentages are valid descriptions of the retailer's profit. It is important to specifywhich 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%, then30% of your sales total is profit. If your markup is 30%, the percentage of your daily sales that are profit will not bethe same percentage.Some retailers use markups because it is easier to calculate a sales price from a cost using markups. If your markupis 40%, then your sales price will be 40% above the item cost. If your margin is 40%, your sales price will not beequal to 40% over cost (indeed it will be 60% above the item cost).

MarkupMarkup 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 (saledollars) they would have to use a markup of 100%. To calculate the price to the customer, you simply take theproduct 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 soldA 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 areprofit. 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 ofthe 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 expensessuch as sales, administrative, and financial must be deducted.And it means company are reducing their cost ofproduction or passing their cost to customers. the higher ratio is better

Converting between gross margin and markupThe 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 priceGiven the cost of an item, one can compute the selling price required to achieve a specific gross margin. Forexample, if your product costs $100 and the required gross margin is 40%, thenSelling price = $100 / (1 - 40%) = $100 / 0.60 = $166.67

Differences between industriesIn some industries, like clothing for example, profit margins are expected to be near the 40% mark, as the goodsneed to be bought from suppliers at a certain rate before they are resold. In other industries such as software productdevelopment, since the cost of duplication is negligible, the gross profit margin can be higher than 80% in manycases.

Gross margin 11

References[1] Berman, Karen (2006). Financial Intelligence. Boston: Harvard Business School Press. p. 152. ISBN 1591397642.

Operating marginIn business, operating margin, operating income margin, operating profit margin or return on sales (ROS) isthe 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 goodoperating margin is needed for a company to be able to pay for its fixed costs, such as interest on debt. A higheroperating margin means that the company has less financial risk.http:/ / www. moneychimp. com/ articles/ financials/ income. htmOperating 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 marginProfit margin, net margin, net profit margin or net profit ratio all refer to a measure of profitability. It iscalculated 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 fordifferent entities. Individual businesses' operating and financing arrangements vary so much that different entities arebound to have different levels of expenditure, so that comparison of one with another can have little meaning. A lowprofit margin indicates a low margin of safety: higher risk that a decline in sales will erase profits and result in a netloss, or a negative margin.Profit margin is an indicator of a company's pricing strategies and how well it controls costs. Differences incompetitive strategy and product mix cause the profit margin to vary among different companies.[2]

ConfusionProfit margin is frequently confused with markup. It's not uncommon for entrepreneurs to erroneously claim profitmargins over 100%. Most likely these entrepreneurs are referring to the markup on a product as a percentage ofproduct 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

AccountancyKey concepts

Accountant · Bookkeeping · Cash and accrual basis · Constant Item Purchasing Power Accounting · Cost of goods sold · Debits andcredits · 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 commonstock owners. It measures a firm's efficiency at generating profits from every unit of shareholders' equity (alsoknown as net assets or assets minus liabilities). ROE shows how well a company uses investment funds to generateearnings 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, ROEis 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 companya high growth rate. The benefit can also come as a dividend on common shares or as a combination of dividends andreinvestment 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 formulaThe DuPont formula, also known as the strategic profit model, is a common way to break down ROE into threeimportant components. Essentially, ROE will equal the net margin multiplied by asset turnover multiplied byfinancial 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 resultingin a higher overall ROE. Finally, increasing financial leverage means that the firm uses more debt financing relativeto 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 benefitsdiminish as the risk of defaulting on interest payments increases. So if the firm takes on too much debt, the cost ofdebt rises as creditors demand a higher risk premium, and ROE decreases. [3] Increased debt will make a positivecontribution to a firm's ROE only if the matching Return on assets (ROA) of that debt exceeds the interest rate on thedebt. [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 returnIn finance, rate of return (ROR), also known as return on investment (ROI), rate of profit or sometimes justreturn, is the ratio of money gained or lost (whether realized or unrealized) on an investment relative to the amountof money invested. The amount of money gained or lost may be referred to as interest, profit/loss, gain/loss, or netincome/loss. The money invested may be referred to as the asset, capital, principal, or the cost basis of theinvestment. ROI is usually expressed as a percentage.

CalculationThe initial value of an investment, , does not always have a clearly defined monetary value, but for purposes ofmeasuring ROI, the expected value must be clearly stated along with the rationale for this initial value. Similarly, thefinal value of an investment, , also does not always have a clearly defined monetary value, but for purposes ofmeasuring 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 annualpercentage 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 isdefined 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) ofthat 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 returnThe 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 differencebetween them is large only when percent changes are high. For example, an arithmetic return of +50% is equivalentto 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 continuouslycompounded return is symmetric, while the arithmetic return is not: positive and negative percent arithmetic returnsare not equal. This means that an investment of $100 that yields an arithmetic return of 50% followed by anarithmetic 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 returnBoth arithmetic and geometric average rates of returns are averages of periodic percentage returns. Neither willaccurately translate to the actual dollar amounts gained or lost if percent gains are averaged with percent losses.[1] A10% loss on a $100 investment is a $10 loss, and a 10% gain on a $100 investment is a $10 gain. When percentagereturns on investments are calculated, they are calculated for a period of time – not based on original investmentdollars, but based on the dollars in the investment at the beginning and end of the period. So if an investment of $100loses 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 theresult. 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 a50% loss, a 100% gain is required. The mathematics of this are beyond the scope of this article, but since investmentreturns are often published as "average returns", it is important to note that average returns do not always translateinto 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 returnsCare 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 December31, 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 twoyears) multiplied or divided to give a comparable one-year return. For instance, a one-month ROI of 1% could bestated as an annualized rate of return of 12%. Or a two-year ROI of 10% could be stated as an annualized rate ofreturn of 5%. **For GIPS compliance: you do not annualize portfolios or composites for periods of less than oneyear. 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 forthe 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 formof profit, interest, dividends, or capital gain/loss. Capital gain/loss occurs when the market value or resale value ofthe 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 Rateof Return. For nominal risk investments such as savings accounts or Certificates of Deposit, the personal investorconsiders the effects of reinvesting/compounding on increasing savings balances over time. For investments inwhich capital is at risk, such as stock shares, mutual fund shares and home purchases, the personal investorconsiders 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 orcompare 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 topursue in order to generate maximum return or wealth for the company's stockholders. Companies do so byconsidering the average rate of return, payback period, net present value, profitability index, and internal rate ofreturn 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 orhistorical times in which taxes consumed or consume a significant portion of profits or income. The after-tax rateof return is calculated by multiplying the rate of return by the tax rate, then subtracting that percentage from therate of return.

• A return of 5% taxed at 15% gives an after-tax return of 4.25%0.05 x 0.15 = 0.00750.05 - 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 = 0.0250.10 - 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 rateof return might well be greater than 0%. When ROI is adjusted for inflation, the resulting return is considered anincrease or decrease in purchasing power. If an ROI value is adjusted for inflation, it is stated explicitly, such as“The return, adjusted for inflation, was 2%.”

• Many online poker tools include ROI in a player's tracked statistics, assisting users in evaluating an opponent'sprofitability.

Cash or potential cash returns

Time value of moneyInvestments 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 todaythan it was yesterday, and worth more today than it will be worth tomorrow. The main factors that are used byinvestors 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 ratesthat banks charge for loans such as home mortgages. The “risk-free” rate is the rate on U.S. Treasury Bills, becausethis 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 adifferent discount rate, based on the cash flow expected in future from the investment. The higher the risk, the higherthe discount rate (rate of return) the investor will demand from the investment.

Compounding or reinvestingCompound interest or other reinvestment of cash returns (such as interest and dividends) does not affect the discountrate of an investment, but it does affect the Annual Percentage Yield, because compounding/reinvestment increasesthe 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 balanceincludes 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 $1,000out of his pocket (or checking account) to invest in a CD at the bank. The money was still his, but it was no longeravailable for buying groceries. The investment provided a cash flow of $10.00, $10.10, $10.20 and $10.30. At theend 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; theinterest 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 theinterest 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 lendmoney to the bank, and the bank is obligated to give investors back their capital plus all earned interest. Becauseinvestors are not risking losing their capital on a bad investment, they earn a quite low rate of return. But their capitalsteadily increases.

Returns when capital is at risk

Capital gains and lossesMany 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 iswilling to pay for it at a certain point in time. Unlike capital invested in a savings account, the capital value (price) ofa stock share constantly changes. If the price is relatively stable, the stock is said to have “low volatility.” If the priceoften changes a great deal, the stock has “high volatility.” All stock shares have some volatility, and the change inprice 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 investorreceived a total of $4.06 in dividends over the year, all of which were reinvested, so the investment amount increasedby $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 wasinvested during the entire year (the dividend reinvestments occurred throughout the year). The advantages are: (1) ituses the cost basis of the investment, (2) it clearly shows which gains are due to dividends and which gains/losses aredue 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 ofthe 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 orlogarithmic return. The effective continuously compounded rate of return is the natural log of the final investmentvalue divided by the initial investment value:• is the initial investment ($100)• is the final value ($103.02)

.

Mutual fund and investment company returnsMutual funds, exchange-traded funds (ETFs), and other equitized investments (such as unit investment trusts orUITs, insurance separate accounts and related variable products such as variable universal life insurance policies andvariable 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 whichare equitized by selling shares or units to investors. Investors and other parties are interested to know how theinvestment has performed over various periods of time.Performance is usually quantified by a fund's total return. In the 1990s, many different fund companies wereadvertising various total returns—some cumulative, some averaged, some with or without deduction of sales loads orcommissions, 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 returnsbased upon a standardized formula—so called "SEC Standardized total return" which is the average annual totalreturn assuming reinvestment of dividends and distributions and deduction of sales loads or charges. Funds maycompute and advertise returns on other bases (so-called "non-standardized" returns), so long as they also publish noless 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 thelate 1990s and early 2000s were ignorant of how significant the impact of income/capital gain taxes was on theirfund "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, andperhaps for other reasons, the SEC made further rule-making to require mutual funds to publish in their annualprospectus, among other things, total returns before and after the impact of U.S federal individual income taxes. Andfurther, the after-tax returns would include 1) returns on a hypothetical taxable account after deducting taxes ondividends 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 onliquidation of the shares). These after-tax returns would apply of course only to taxable accounts and not totax-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 theactual investment account transaction history. This is because investments may have been made on various dates andadditional purchases and withdrawals may have occurred which vary in amount and date and thus are unique to theparticular account. More and more fund and brokerage firms have begun providing personalized account returns oninvestor'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 recordsincome for dividends and interest earned which typically increases the value of the mutual fund shares, whileexpenses set aside have an offsetting impact to share value. When the fund's investments increase in market value, sotoo does the value of the fund shares (or units) owned by the investors. When investments increase (decrease) inmarket value, so too the fund shares value increases (or decreases). When the fund sells investments at a profit, itturns or reclassifies that paper profit or unrealized gain into an actual or realized gain. The sale has no affect on thevalue of fund shares but it has reclassified a component of its value from one bucket to another on the fundbooks—which will have future impact to investors. At least annually, a fund usually pays dividends from its netincome (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 typicallyvalued each day the stock or bond markets are open and typically the value of a share is the net asset value of thefund 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, thedollar amounts distributed are used to purchase additional shares of the funds as of the reinvestment/ex-dividenddate. 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 ExchangeCommission (SEC) in instructions to form N-1A (the fund prospectus) as the average annual compounded rates ofreturn 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-yearperiods 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 receivedtotal 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 amutual fund share is based on net asset value, a capital gain distribution is offset by an equal decrease in mutual fundshare value/price. From the shareholder's perspective, a capital gain distribution is not a net gain in assets, but it is arealized capital gain.

Rate of return 24

Summary: overall rate of returnRate of Return and Return on Investment indicate cash flow from an investment to the investor over a specifiedperiod of time, usually a year.ROI is a measure of investment profitability, not a measure of investment size. While compound interest anddividend reinvestment can increase the size of the investment (thus potentially yielding a higher dollar return to theinvestor), 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 potentialinvestment 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 assetsThe 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 fromeach dollar of assets they control. It's a useful number for comparing competing companies in the same industry. Thenumber will vary widely across different industries. Return on assets gives an indication of the capital intensity ofthe company, which will depend on the industry; companies that require large initial investments will generally havelower return on assets.

UsageReturn on assets is an indicator of how profitable a company is before leverage, and is compared with companies inthe same industry. Since the figure for total assets of the company depends on the carrying value of the assets, somecaution is required for companies whose carrying value may not correspond to the actual market value. Return onassets is a common figure used for comparing performance of financial institutions (such as banks), because themajority of their assets will have a carrying value that is close to their actual market value. Return on assets is notuseful for comparisons between industries because of factors of scale and peculiar capital requirements (such asreserve 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 PontDuPont 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 formulaROE = (Profit margin)*(Asset turnover)*(Equity multiplier) = (Netprofit/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 analysisThe Du Pont identity breaks down Return on Equity (that is, the returns that investors receive from the firm) intothree distinct elements. This analysis enables the analyst to understand the source of superior (or inferior) return bycomparison 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 certainconcepts or for which the concepts are less meaningful. Variations may be used in certain industries, as long as theyalso 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 industriesCertain types of retail operations, particularly stores, may have very low profit margins on sales, and relativelymoderate leverage. In contrast, though, groceries may have very high turnover, selling a significant multiple of theirassets per year. The ROE of such firms may be particularly dependent on performance of this metric, and hence assetturnover may be studied extremely carefully for signs of under-, or, over-performance. For example, same store salesof 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 industriesOther industries, such as fashion, may derive a substantial portion of their competitive advantage from selling at ahigher margin, rather than higher sales. For high-end fashion brands, increasing sales without sacrificing margin maybe critical. The Du Pont identity allows analysts to determine which of the elements is dominant in any change ofROE.

High leverage industriesSome 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 thirdparty (relying primarily on the financial statements) to compare leverage with other financial elements that determineROE among similar companies.

Return on assets Du Pont 27

ROI and ROE ratioThe return on investment (ROI) ratio developed by DuPont for its own use is now used by many firms to evaluatehow 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 intovarious 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 LeverageROE = 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 assetsThe return on net assets (RONA) is a measure of financial performance of a company which takes the use of assetsinto account.

FormulaReturn 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 capitalReturn on capital (ROC) is a ratio used in finance, valuation, and accounting. The ratio is estimated by dividing theafter-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 acompany generates cash flow relative to the capital it has invested in its business. It is defined as net operating profitless adjusted taxes divided by invested capital and is usually expressed as a percentage. In this calculation, capitalinvested 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 ofcapital), 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 debtcapital.

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 capitalRisk adjusted return on capital (RAROC) is a risk-based profitability measurement framework for analysingrisk-adjusted financial performance and providing a consistent view of profitability across businesses. The conceptwas developed by Bankers Trust and principal designer Dan Borge in the late 1970s.[1] Note, however, that more andmore Return on risk Adjusted Capital (RORAC) is used as a measure, whereby the risk adjustment of Capital isbased 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 riskadjusted return to economic capital. The economic capital is the amount of money which is needed to secure thesurvival in a worst case scenario, it is a buffer against expected shocks in market values. Economic capital is afunction of market risk, credit risk, and operational risk, and is often calculated by VaR. This use of capital based onrisk improves the capital allocation across different functional areas of banks, insurance companies, or any businessin 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 management2. Performance evaluationFor risk management purposes, the main goal of allocating capital to individual business units is to determine thebank's optimal capital structure—that is economic capital allocation is closely correlated with individual businessrisk. As a performance evaluation tool, it allows banks to assign capital to business units based on the economicvalue 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 investmentCash 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 RecapitalizationFor the corporation, it is essentially internal rate of return (IRR). CFROI is compared to a hurdle rate to determine ifinvestment/product is performing adequately. The hurdle rate is the total cost of capital for the corporation calculatedby a mix of cost of debt financing plus investors `expected return on equity investments. The CFROI must exceedthe hurdle rate to satisfy both the debt financing and the investors expected return.CFROI = Gross Cash Flow / Gross InvestmentMichael J. Maubossin, in his 2006 book 'MORE THAN YOU KNOW', quoted an analysis by CSFB, that, measuredby 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 InvestmentThis 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 ratioThe current ratio is a financial ratio that measures whether or not a firm has enough resources to pay its debts overthe 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 itscurrent ratio would be $50,000,000 divided by $40,000,000, which equals 1.25. It means that for every dollar thecompany owes it has $1.25 available in current assets. A current ratio of assets to liabilities of 2:1 is usuallyconsidered 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. Acceptablecurrent ratios vary from industry to industry. If a company's current ratio is in this range, then it is generallyconsidered to have good short-term financial strength. If current liabilities exceed current assets (the current ratio isbelow 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 alsoindicate problems in working capital management.Low values for the current or quick ratios (values less than 1) indicate that a firm may have difficulty meetingcurrent obligations. Low values, however, do not indicate a critical problem. If an organization has good long-termprospects, it may be able to borrow against those prospects to meet current obligations. Some types of businessesusually operate with a current ratio less than one. For example, if inventory turns over much more rapidly than theaccounts payable become due, then the current ratio will be less than one (this is true for McDonalds). This canallow 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 highcurrent ratio to be better than a low current ratio, because a high current ratio means that the company is more likelyto 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 ratioThe Reserve Requirements (or Cash Reserve Ratio) is a Central bank regulation that sets the minimum reserveseach Commercial bank must hold to customer deposits and notes i.e the amount that the bank surrenders with thecentral bank. It would normally be in the form of fiat currency stored in a bank vault (vault cash), or with a centralbank.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 immediateliquidity problems for banks with low excess reserves; they prefer to use open market operations to implement theirmonetary 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 was10% 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 SupplyMb = Monetary basemm = money multiplierc = 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 willthen choose to deposit the money from the loan back into the bank at a rate of 'c' (for simplicity say c=0%.) then thebank 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 reserverequirement is 10%, for example, a bank that receives a $100 deposit may lend out $90 of that deposit. If theborrower then writes a check to someone who deposits the $90, the bank receiving that deposit can lend out $81. Asthe 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% reserverequirement, 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 creationand 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 definedmeasure of money. Deposits that are components of M2 and M3 (but not M1), such as savings accounts and timedeposits 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 lagbetween their implementation and the corresponding effect of inflation, the Federal reserve does not frequentlychange reserve requirements for the purpose of affecting monetary policy.

Cash ratio 32

Reserve ratiosA cash reserve ratio (or CRR) is the percentage of bank reserves to deposits and notes. The cash reserve ratio is alsoknown as the cash asset ratio or liquidity ratio. , the Board of Governors of the Federal Reserve System requireszero percent (0%) fractional reserves from depository institutions having net transactions accounts of up to $10.7million.[3] Depository institutions having over $10.7 million, and up to $55.2 million in net transaction accountsmust have fractional reserves totaling three percent (3%) of that amount.[3] Finally, depository institutions havingover $55.2 million in net transaction accounts must have fractional reserves totaling ten percent (10%) of thatamount.[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 "eurocurrencyliabilities," respectively. For these account classes, the fractional reserve requirement is one percent (1%) regardlessof net account value.[3]

The Bank of England holds to a voluntary reserve ratio system. In 1998 the average cash reserve ratio across theentire United Kingdom banking system was 3.1%. Countries that do this, listed as 'None' in the table below, alloweffectively an infinite amount of credit money creation. While this can happen, it doesn't, and it would mean averagereserves tend to zero. The reported average ratio of 3.1% implies an average maximum total deposits of £3,225.80from £100 of base money.Other countries have required reserve ratios (or RRRs) that are statutorily enforced (sourced from Lecture 8, Slide4: Central Banking and the Money Supply, by Dr. Pinar Yesin, University of Zurich, based on 2003 survey of CBCparticipants 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 Bankdecreased 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 StatisticYearbook):

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 abank's capital to its risk. National regulators track a bank's CAR to ensure that it can absorb a reasonable amount ofloss [19] and are complying with their statutory capital requirements.

Cash ratio 34

FormulaCapital adequacy ratios ("CAR") are a measure of the amount of a bank's capital expressed as a percentage of its riskweighted credit exposures.Capital adequacy ratio is defined as

where Risk can either be weighted assets ( ) or the respective national regulator's minimum total capitalrequirement. 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 setby the national banking regulator.Two types of capital are measured: tier one capital ( above), which can absorb losses without a bank beingrequired to cease trading, and tier two capital ( above), which can absorb losses in the event of a winding-up andso provides a lesser degree of protection to depositors.

UseCapital adequacy ratio is the ratio which determines the capacity of the bank in terms of meeting the time liabilitiesand 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 mostcountries 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 leverageformulations: CAR uses equity divided by assets instead of debt-to-equity (total debt divided by shareholder's equityor other invested capital). It is important to note that the assets of a bank are its outstanding loans (not the deposits ithas taken in). In accounting generally, total assets are by definition equal to debt plus equity. Therefore the capitaladequacey ratio is equivalent to the proportion of Capital (generally what shareholders paid to the bank to purchasecommon 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 traditionalleverage, however, CAR recognizes that assets can have different levels of risk. The "safer" the asset the more thebank is allowed to discount that asset in its CAR calculation; in other words, banks do not have to hold so much inreserves if their "assets" (the loan dollars owed to them) are very safe (i.e. highly likely to be paid back). Forexample, if the bank buys and holds a bond from a corporation, there is a better likelihood the corporation will payoff its bond than that a homeowner will pay off his mortgage.

Risk weightingSince different types of assets have different risk profiles, CAR primarily adjusts for assets that are less risky byallowing banks to "discount" lower-risk assets. The specifics of CAR calculation vary from country to country, butgeneral 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 ofcalculating the CAR.

Cash ratio 35

Risk weighting exampleLocal regulations establish that cash and government bonds have a 0% risk weighting, and residential mortgageloans 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"). Bydefinition, 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 issubstantially higher. It is considered less risky because some of its assets are less risky than others.

Types of capitalThe Basel rules recognize that different types of equity are more important than others. To recognize this, differentadjustments 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%, whileminimum 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 flowIn financial accounting, operating cash flow (OCF), cash flow provided by operations or cash flow fromoperating activities, refers to the amount of cash a company generates from the revenues it brings in, excludingcosts associated with long-term investment on capital items or investment in securities.[1] The International FinancialReporting 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 generatedfrom operations, one must calculate cash generated from customers and cash paid to suppliers. The differencebetween the two reflects cash generated from operations.

CalculationsCash 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 relatedCash 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 EBITDAInterest is an operating flow. Since it adjusts for liabilities, receivables, and depreciation, operating cash flow is amore accurate measure of how much cash a company has generated (or used) than traditional measures ofprofitability 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 anon-cash expense[3] the operating cash flow would provide a more accurate picture of the company's current cashholdings than the artificially low net income.[4]

Earnings before interest, taxes, depreciation and amortization (EBITDA) is a non-GAAP metric that can be used toevaluate a company's profitability based on net working capital. The difference between EBITDA and OCF wouldthen reflect how the entity finances its net working capital in the short term. OCF is not a measure of free cash flowand 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 valueIn finance, the net present value (NPV) or net present worth (NPW)[1] of a time series of cash flows, bothincoming and outgoing, is defined as the sum of the present values (PVs) of the individual cash flows. In the casewhen all future cash flows are incoming (such as coupons and principal of a bond) and the only outflow of cash isthe 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 ofmoney to appraise long-term projects. Used for capital budgeting, and widely throughout economics, finance, andaccounting, 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 outputsa price; the converse process in DCF analysis - taking a sequence of cash flows and a price as input and inferring asoutput a discount rate (the discount rate which would yield the given price as NPV) - is called the yield, and is morewidely used in bond trading.

FormulaEach cash inflow/outflow is discounted back to its present value (PV). Then they are summed. Therefore NPV is thesum of all terms,

wheret - the time of the cash flowi - the discount rate (the rate of return that could be earned on an investment in the financial markets withsimilar risk.)

- the net cash flow (the amount of cash, inflow minus outflow) at time t. For educational purposes, iscommonly 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 bethe present value but in case where the cash flows are not equal in amount then the previous formula will be used todetermine the present value of each cash flow separately. Any cash flow within 12 months will not be discounted forNPV purpose.[2]

Net present value 39

The discount rateThe 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 touse higher discount rates to adjust for risk or other factors. A variable discount rate with higher rates applied to cashflows 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 projectcould return if invested in an alternative venture. If, for example, the capital required for Project A can earn fivepercent elsewhere, use this discount rate in the NPV calculation to allow a direct comparison to be made betweenProject A and the alternative. Related to this concept is to use the firm's Reinvestment Rate. Reinvestment rate canbe defined as the rate of return for the firm's investments on average. When analyzing projects in a capitalconstrained environment, it may be appropriate to use the reinvestment rate rather than the firm's weighted averagecost of capital as the discount factor. It reflects opportunity cost of investment, rather than the possibly lower cost ofcapital.An NPV calculated using variable discount rates (if they are known for the duration of the investment) better reflectsthe real situation than one calculated from a constant discount rate for the entire investment duration. Refer to thetutorial article written by Samuel Baker[3] for more detailed relationship between the NPV value and the discountrate.For some professional investors, their investment funds are committed to target a specified rate of return. In suchcases, that rate of return should be selected as the discount rate for the NPV calculation. In this way, a directcomparison 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 issimply to determine whether a project will add value to the company, using the firm's weighted average cost ofcapital may be appropriate. If trying to decide between alternative investments in order to maximize the value of thefirm, 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 asuperior methodology, but is seldom used in practice. Using the discount rate to adjust for risk is often difficult to doin practice (especially internationally), and is difficult to do well. An alternative to using discount factor to adjust forrisk is to explicitly correct the cash flows for the risk elements using rNPV or a similar method, then discount at thefirm's rate.

NPV in decision makingNPV is an indicator of how much value an investment or project adds to the firm. With a particular project, if isa positive value, the project is in the status of discounted cash inflow in the time of t. If is a negative value, theproject is in the status of discounted cash outflow in the time of t. Appropriately risked projects with a positive NPVcould be accepted. This does not necessarily mean that they should be undertaken since NPV at the cost of capitalmay not account for opportunity cost, i.e. comparison with other available investments. In financial theory, if there isa 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 addvalue to the firm

the project may be accepted

NPV< 0

the investment would subtractvalue from the firm

the project should be rejected

NPV= 0

the investment would neithergain nor lose value for the firm

We should be indifferent in the decision whether to accept or reject the project. This project adds nomonetary value. Decision should be based on other criteria, e.g. strategic positioning or other factors notexplicitly included in the calculation.

ExampleA 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 areexpected to be $5,000 per year. Cash inflows are expected to be $30,000 each for years 1–6. All cash flows areafter-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 thanzero, it would be better to invest in the project than to do nothing, and the corporation should invest in this project ifthere 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, unevencash 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 cautiousbut too optimistic. Some people see this as a problem with NPV. A way to avoid this problem is to includeexplicit provision for financing any losses after the initial investment, that is, explicitly calculate the cost offinancing such losses.

• Another common pitfall is to adjust for risk by adding a premium to the discount rate. Whilst a bank might chargea higher rate of interest for a risky project, that does not mean that this is a valid approach to adjusting a netpresent value for risk, although it can be a reasonable approximation in some specific cases. One reason such anapproach 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 rigorousapproach to risk requires identifying and valuing risks explicitly, e.g. by actuarial or Monte Carlo techniques, andexplicitly 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 andthe risk premium. As a result, future cash flows are discounted by both the risk-free rate as well as the riskpremium and this effect is compounded by each subsequent cash flow. This compounding results in a much lowerNPV than might be otherwise calculated. The certainty equivalent model can be used to account for the riskpremium 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 acertain project. To see a percentage gain relative to the investments for the project, usually, Internal rate of returnor other efficiency measures are used as a complement to NPV.

Net present value 42

HistoryNet present value as a valuation methodology dates at least to the 19th century. Karl Marx refers to NPV as fictitiouscapital, and the calculation as capitalising, writing:[4]

The forming of a fictitious capital is called capitalising. Every periodically repeated income is capitalised bycalculating it on the average rate of interest, as an income which would be realised by a capital at this rate ofinterest.

In mainstream neo-classical economics, NPV was formalized and popularized by Irving Fisher, in his 1907 The Rateof 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 ofhistory 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 returnThe internal rate of return (IRR) is a rate of return used in capital budgeting to measure and compare theprofitability of investments. It is also called the discounted cash flow rate of return (DCFROR) or simply the rate ofreturn (ROR).[1] In the context of savings and loans the IRR is also called the effective interest rate. The terminternal refers to the fact that its calculation does not incorporate environmental factors (e.g., the interest rate orinflation).

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 thatmakes the net present value (NPV) of all cash flows (both positive andnegative) from a particular investment equal to zero.

In more specific terms, the IRR of an investment is the interest rate atwhich the net present value of costs (negative cash flows) of theinvestment equals the net present value of the benefits (positive cashflows) of the investment.

Internal rates of return are commonly used to evaluate the desirabilityof investments or projects. The higher a project's internal rate of return,the more desirable it is to undertake the project. Assuming all otherfactors are equal among the various projects, the project with the highest IRR would probably be considered the bestand undertaken first.A firm (or individual) should, in theory, undertake all projects or investments available with IRRs that exceed thecost of capital. Investment may be limited by availability of funds to the firm and/or by the firm's capacity or abilityto manage numerous projects.

UsesImportant: Because the internal rate of return is a rate quantity, it is an indicator of the efficiency, quality, or yield ofan investment. This is in contrast with the net present value, which is an indicator of the value or magnitude of aninvestment.An investment is considered acceptable if its internal rate of return is greater than an established minimumacceptable rate of return or cost of capital. In a scenario where an investment is considered by a firm that has equityholders, this minimum rate is the cost of capital of the investment (which may be determined by the risk-adjustedcost of capital of alternative investments). This ensures that the investment is supported by equity holders since, ingeneral, an investment whose IRR exceeds its cost of capital adds value for the company (i.e., it is economicallyprofitable).

Internal rate of return 44

CalculationGiven a collection of pairs (time, cash flow) involved in a project, the internal rate of return follows from the netpresent value as a function of the rate of return. A rate of return for which this function is zero is an internal rate ofreturn.Given the (period, cash flow) pairs ( , ) where is a positive integer, the total number of periods , andthe 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 theperiod in which the majority of the problem is defined (e.g., using months if most of the cash flows occur at monthlyintervals) 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 valueobtained 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 putinto the above formula.Often, the value of cannot be found analytically. In this case, numerical methods or graphical methods must beused.

ExampleIf 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 aremany 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 andchanging 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 multipleinflows occurring at equal periods. In the above notation, this corresponds to: < 0, ≥ 0 for ≥ 1. In thiscase the NPV of the payment stream is a convex, strictly decreasing function of interest rate. There is always a singleunique solution for IRR.Given two estimates and for IRR, the secant method equation (see above) with will always producean improved estimate . This is sometimes referred to as the Hit and Trial (or Trial and Error) method. There ishowever 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 computeNPV). For example, using the stream of payments {-4000, 1200, 1410, 1875, 1050} and initial guesses and gives and . The accurate formula estimates IRR as14.35% (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 maybe 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 returnAs an investment decision tool, the calculated IRR should not be used to rate mutually exclusive projects, but only todecide whether a single project is worth investing in.

NPV vs discount rate comparison for two mutually exclusive projects. Project 'A' has ahigher 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 higherinitial investment than a secondmutually exclusive project, the firstproject may have a lower IRR(expected return), but a higher NPV(increase in shareholders' wealth) andshould thus be accepted over thesecond project (assuming no capitalconstraints).IRR assumes reinvestment of interimcash flows in projects with equal ratesof return (the reinvestment can be thesame project or a different project).Therefore, IRR overstates the annualequivalent rate of return for a projectwhose interim cash flows arereinvested at a rate lower than thecalculated IRR. This presents aproblem, especially for high IRRprojects, since there is frequently not another project available in the interim that can earn the same rate of return asthe first project.

When the calculated IRR is higher than the true reinvestment rate for interim cash flows, the measurewill overestimate — sometimes very significantly — the annual equivalent return from the project. Theformula assumes that the company has additional projects, with equally attractive prospects, in which toinvest the interim cash flows.[3]

This makes IRR a suitable (and popular) choice for analyzing venture capital and other private equity investments, asthese strategies usually require several cash investments throughout the project, but only see one cash outflow at theend 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. ModifiedInternal Rate of Return (MIRR) does consider cost of capital and provides a better indication of a project's efficiencyin 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 casea discount rate may be used for the borrowing cash flow and the IRR calculated for the investment cash flow. Thisapplies 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 thenreceives more than one possesses, so then one owes money, so now a low rate of return is best. In this case it is noteven clear whether a high or a low IRR is better. There may even be multiple IRRs for a single project, like in theexample 0% as well as 10%. Examples of this type of project are strip mines and nuclear power plants, where thereis 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 ifthat equation has a unique real solution. In general the IRR equation cannot be solved analytically but onlyiteratively.

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 benefitsreinvestmented.[3] Accordingly, MIRR is used, which has an assumed reinvestment rate, usually equal to theproject'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 bydollars of NPV. However, NPV remains the "more accurate" reflection of value to the business. IRR, as a measure ofinvestment efficiency may give better insights in capital constrained situations. However, when comparing mutuallyexclusive projects, NPV is the appropriate measure.

MathematicsMathematically the value of the investment is assumed to undergo exponential growth or decay according to somerate of return (any value greater than -100%), with discontinuities for cash flows, and the IRR of a series of cashflows is defined as any rate of return that results in a net present value of zero (or equivalently, a rate of return thatresults 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 iscontinuous. Towards a rate of return of -100% the net present value approaches infinity with the sign of the last cashflow, and towards a rate of return of positive infinity the net present value approaches the first cash flow (the one atthe 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); thehighest 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, considerthe total value of the cash flows converted to a time between the negative and the positive ones. The resultingfunction 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 theNPV-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 onesthe 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 anoutlay of many years this method is not practical as IRR ignores the time value of money. To take intoconsideration the Time Value of Money Extended Internal Rate of Return was introduced where all the futurecash flows are first discounted at a discount rate and then the IRR is calculated. This method of calculation of IRRis 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 reading1. 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 ContributorsFinancial 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, EwigerBesserwisser, 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, YahelGuhan, 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, AndrésDjordjalian, 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 NotBe, 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, 16anonymous edits

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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,

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Image Sources, Licenses and Contributors 51

Image Sources, Licenses and ContributorsFile:DiscreteCF.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:DiscreteCF.jpg  License: Public Domain  Contributors: Grochim, Kenckar, Yoshi122File:cumCF.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:CumCF.jpg  License: Public Domain  Contributors: Grochim, Kenckar, Yoshi122Image:IRR1 - Grieger.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:IRR1_-_Grieger.jpg  License: Public Domain  Contributors: Bkell, Grieger, 1 anonymous editsImage:exclusive investments.png  Source: http://en.wikipedia.org/w/index.php?title=File:Exclusive_investments.png  License: Public Domain  Contributors: Grieger

License 52

LicenseCreative Commons Attribution-Share Alike 3.0 Unportedhttp:/ / creativecommons. org/ licenses/ by-sa/ 3. 0/