Goodwill (accounting)

Goodwill (accounting)

For other uses, see Goodwill.

Goodwill is an accounting term used to reflect the portion of the book value of a business entity not directly attributable to its assets and liabilities; it normally arises only in case of an acquisition. It reflects the ability of the entity to make a higher profit than would be derived from selling the tangible assets. Goodwill is considered an intangible asset.

Contents





1 Original sense

 2 Modern meaning

3 Basic goodwill formula





4 History and purchase vs. pooling-of-interests

 5 Amortization and adjustments to carrying value

6 See also

 7 External links

 8 References

Original sense

Goodwill as a term was originally used to reflect the fact that an ongoing business had some

"intrinsic value" beyond its assets, such as the reputation the firm enjoyed with its clients. Likewise, a buyer may agree to "overpay" because he sees potential synergy with his own business. The accounting sense of goodwill followed as a plausible explanation of why a firm sells for more than the value of its net assets.

Modern meaning

Goodwill in financial statements arises when a company is purchased for more than the book value of the company. The difference between the purchase price and the sum of the fair value of the net assets is by definition the value of the "goodwill" of the purchased company. The acquiring company must recognize goodwill as an asset in its financial statements and present it as a separate line item on the balance sheet, according to the current purchase accounting method. In this sense, goodwill serves as the balancing sum that allows one firm to provide accounting information regarding its purchase of another firm for a price substantially different from its book value.

Goodwill can be negative, arising where the net assets at the date of acquisition, fairly valued, exceed the cost of acquisition.

[1]

Negative goodwill is recognized as a liability.

For example, a software company may have net assets (consisting primarily of miscellaneous equipment, and assuming no debt) valued at $1 million, but the company's overall value (including brand, customers, intellectual capital) is valued at $10 million. Anybody buying that company would book $10 million in total assets acquired, comprising $1 million physical assets, and $9 million in goodwill. Goodwill has no predetermined value prior to the acquisition; its magnitude depends on the two other variables by definition .

The carrying value of an asset with associated goodwill may subsequently be adjusted by management, either by amortization or by means of occasional adjustments of the estimated value of the associated assets (primarily based upon their ability to generate cashflow and profits). The exact

treatment and other details, particularly amortization, will depend on the accounting standards applied.

There is a distinction between two types of goodwill depending upon the type of business enterprise: institutional goodwill and professional practice goodwill. Furthermore, goodwill in a professional practice entity may be attributed to the practice itself and to the professional practitioner.

[ citation needed ]

It should also be noted that while goodwill is technically an intangible asset, the two are usually listed as separate items on a company's balance sheet.

[2][3

Basic goodwill formula





Goodwill = Purchase Price – Fair Market Value of Net Assets

 Fair Market Value of Net Assets = Net Tangible Assets + Write-up of Net Assets

Net Tangible Assets = Assets – Target's Existing Goodwill – Liabilities

As can be seen, a merger destroys the target's "old" goodwill and creates "new" goodwill to appear in consolidated books. Net assets write-up is prepared through a qualified appraisal in a process known as a Purchase Price Allocation.

History and purchase vs. pooling-of-interests

Previously, companies could structure many acquisition transactions to determine the choice between two accounting methods to record a business combination: purchase accounting or poolingof-interests accounting. Pooling-of-interests method combined the book value of assets and liabilities of the two companies to create the new balance sheet of the combined companies. It therefore did not distinguish between who is buying whom. It also did not record the price the acquiring company had to pay for the acquisition. U.S. Generally Accepted Accounting Principles

(FAS 141) no longer allows pooling-of-interests method.

Amortization and adjustments to carrying value

Goodwill is no longer amortized under U.S. GAAP (FAS 142).

[4]

Companies objected to the removal of the option to use pooling-of-interests, so amortization was removed by Financial

Accounting Standards Board as a concession. As of 2005-01-01, it is also forbidden under

International Accounting Standards. Goodwill can now only be impaired.

[5]

Instead of deducting the value of goodwill annually over a period of maximal 40 years, companies are now required to value fair value of the reporting units, using present value of future cash flow, and compare it to their carrying value (booked value of assets plus goodwill minus liabilities.) If the fair value is less than carrying value (impaired), the goodwill value needs to be reduced so the fair value is equal to carrying value. The impairment loss is reported as a separate line item on the income statement, and new adjusted value of goodwill is reported in the balance sheet.

[6]

Since, in general, intellectual property (IP) is part of goodwill—in its lay, not accounting sense—one of the most important assets of knowledge-based companies does not appear at all on formal balance sheets. As for these companies, it is the IP that generates profit, not the buildings or the cash they hold; this may lead to a misleading valuation, discouraging investors who do not understand the company's value.

When the business is in trouble, with the threat of insolvency, investors will deduct the goodwill from any calculation of residual equity because it will likely have no resale value.

See also





Intangible asset

 Business valuation

Consolidation (business)

 Control premium

 Divestment

 Enterprise value

 Mergers and acquisitions

 Subsidiary

External links

 Definition of business goodwill

 Goodwill definition via Wikinvest

 Intangible Assets definition via Wikinvest

References

1.

ACCOUNTING TERMS — ACCOUNTING DICTIONARY — ACCOUNTING

GLOSSARY

2.

Intangible Assets Definition at Wikinvest

3.

Goodwill Definition at Wikinvest

4.

Summary of Statement No. 142

5.

A Primer on Calculating Goodwill Impairment: Valuation Issues Raised by Financial

Accounting Statement 142

6.

Focus on Goodwill, Intangible Assets v

Capital structure

Transactions

(terms / conditions)

Corporate finance and investment banking

Senior secured debt

·

Senior debt

·

Second lien debt

·

Subordinated debt

·

Mezzanine debt

·

Convertible debt

·

Exchangeable debt

·

Preferred equity

·

Shareholder loan

·

Common equity

·

Pari passu

Initial public offering (IPO) ·

Secondary Market Offering

Equity offerings (SEO)

·

Follow-on offering

·

Greenshoe (Reverse)

·

Book building

Takeover · Reverse takeover ·

Mergers and Tender offer

·

Poison pill

· acquisitions

Freeze-out merger

·

Tag-along right

·

Drag-along right

·

Control

Valuation premium · Divestment ·

Demerger

Leveraged buyout

·

Leveraged

Leverage recap

·

Financial sponsor

·

Private equity

·

Bond offering

·

Highyield debt

·

DIP financing

Financial modeling

·

APV

·

DCF

·

Net present value (NPV)

·

Cost of capital

(Weighted average)

·

Comparable company analysis

·

Enterprise value

·

Tax shield

·

Minority interest

·

EVA

·

MVA

Discounted cash flow

In finance, the discounted cash flow (or DCF) approach describes a method of valuing a project, company, or asset using the concepts of the time value of money. All future cash flows are estimated and discounted to give their present values. The discount rate used is generally the appropriate cost of capital and may incorporate judgments of the uncertainty (riskiness) of the future cash flows.

Discounted cash flow analysis is widely used in investment finance, real estate development, and corporate financial management.

Very similar is the net present value.

Contents

 1 Mathematics o 1.1 Discrete cash flows

 o 1.2 Continuous cash flows

 2 Example DCF

3 Methods of appraisal of a company or project





4 History

 5 See also

6 References


 8 Further reading

Mathematics

Discrete cash flows

The discounted cash flow formula is derived from the future value formula for calculating the time value of money and compounding returns.

Thus the discounted present value (for one cash flow in one future period) is expressed as: where

 DPV is the discounted present value of the future cash flow ( FV ), or FV adjusted for the delay in receipt;

 FV is the nominal value of a cash flow amount in a future period;

 i is the interest rate, which reflects the cost of tying up capital and may also allow for the risk that the payment may not be received in full;

 d is the discount rate, which is i /(1+ i ), ie the interest rate expressed as a deduction at the beginning of the year instead of an addition at the end of the year;

 n is the time in years before the future cash flow occurs.

Where multiple cash flows in multiple time periods are discounted, it is necessary to sum them as follows: for each future cash flow ( FV ) at any time period ( t ) in years from the present time, summed over all time periods. The sum can then be used as a net present value figure. If the amount to be paid at time

0 (now) for all the future cash flows is known, then that amount can be substituted for DPV and the equation can be solved for i , that is the internal rate of return.

All the above assumes that the interest rate remains constant throughout the whole period.

(1+i)^(-t) can of course also be expressed as exp(-it).

Continuous cash flows

With continuous cash flows, the summation in the above formula is replaced by an integration - nothing else changes:

DPV= integral over the required time period of FV(t) * (1-exp(-it)) dt where FV(t) is now the rate of cash flow.

Example DCF

To show how discounted cash flow analysis is performed, consider the following simplified example.

 John Doe buys a house for $100,000. Three years later, he expects to be able to sell this house for $150,000.

Simple subtraction suggests that the value of his profit on such a transaction would be $150,000 −

$100,000 = $50,000, or 50%. If that $50,000 is amortized over the three years, his implied annual return (known as the internal rate of return) would be about 14.5%. Looking at those figures, he might be justified in thinking that the purchase looked like a good idea.

1.145

3

x 100000 = 150000 approximately.

However, since three years have passed between the purchase and the sale, any cash flow from the sale must be discounted accordingly. At the time John Doe buys the house, the 3-year US Treasury

Note rate is 5% per annum. Treasury Notes are generally considered to be inherently less risky than real estate, since the value of the Note is guaranteed by the US Government and there is a liquid market for the purchase and sale of T-Notes. If he hadn't put his money into buying the house, he could have invested it in the relatively safe T-Notes instead. This 5% per annum can therefore be regarded as the risk-free interest rate for the relevant period (3 years).

Using the DPV formula above, that means that the value of $150,000 received in three years actually has a present value of $129,576 (rounded off). Those future dollars aren't worth the same as the dollars we have now.

Subtracting the purchase price of the house ($100,000) from the present value results in the net present value of the whole transaction, which would be $29,576 or a little more than 29% of the purchase price.

Another way of looking at the deal as the excess return achieved (over the risk-free rate) is (14.5%-

5.0%)/(100%+5%) or approximately 9.0% (still very respectable). (As a check, 1.050 x 1.090 =

1.145 approximately.)

But what about risk?

We assume that the $150,000 is John's best estimate of the sale price that he will be able to achieve in 3 years time (after deducting all expenses, of course). There is of course a lot of uncertainty about house prices, and the outturn may end up higher or lower than this estimate.

(The house John is buying is in a "good neighborhood", but market values have been rising quite a lot lately and the real estate market analysts in the media are talking about a slow-down and higher interest rates. There is a probability that John might not be able to get the full $150,000 he is expecting in three years due to a slowing of price appreciation, or that loss of liquidity in the real estate market might make it very hard for him to sell at all.)

Under normal circumstances, people entering into such transactions are risk-averse, that is to say that they are prepared to accept a lower expected return for the sake of avoiding risk. See Capital asset pricing model for a further discussion of this. For the sake of the example (and this is a gross simplification), let's assume that he values this particular risk at 5% per annum (we could perform a more precise probabilistic analysis of the risk, but that is beyond the scope of this article). Therefore, allowing for this risk, his expected return is now 9.0% per annum (the arithmetic is the same as above).

And the excess return over the risk-free rate is now (9.0%-5.0%)/(100% + 5%) which comes to approximately 3.8% per annum.

That return rate may seem low, but it is still positive after all of our discounting, suggesting that the investment decision is probably a good one: it produces enough profit to compensate for tying up capital and incurring risk with a little extra left over. When investors and managers perform DCF analysis, the important thing is that the net present value of the decision after discounting all future cash flows at least be positive (more than zero). If it is negative, that means that the investment decision would actually lose money even if it appears to generate a nominal profit. For instance, if the expected sale price of John Doe's house in the example above was not $150,000 in three years, but $130,000 in three years or $150,000 in five years, then on the above assumptions buying the house would actually cause John to lose money in present-value terms (about $3,000 in the first case, and about $8,000 in the second). Similarly, if the house was located in an undesirable neighborhood and the Federal Reserve Bank was about to raise interest rates by five percentage points, then the risk factor would be a lot higher than 5%: it might not be possible for him to make a profit in discounted terms even if he could sell the house for $200,000 in three years.

In this example, only one future cash flow was considered. For a decision which generates multiple cash flows in multiple time periods, all the cash flows must be discounted and then summed into a single net present value.

Methods of appraisal of a company or project

This is necessarily a simple treatment of a complex subject: more detail is beyond the scope of this article.

For these valuation purposes, a number of different DCF methods are distinguished today, some of which are outlined below. The details are likely to vary depending on the capital structure of the company. However the assumptions used in the appraisal (especially the equity discount rate and the projection of the cash flows to be achieved) are likely to be at least as important as the precise model used.

Both the income stream selected and the associated cost of capital model determine the valuation result obtained with each method. This is one reason these valuation methods are formally referred to as the Discounted Future Economic Income methods.

 Equity-Approach o Flows to equity approach (FTE)

Discount the cash flows available to the holders of equity capital, after allowing for cost of servicing debt capital

Advantages: Makes explicit allowance for the cost of debt capital

Disadvantages: Requires judgement on choice of discount rate

 Entity-Approach: o Adjusted present value approach (APV)

Discount the cash flows before allowing for the debt capital (but allowing for the tax relief obtained on the debt capital)

Advantages: Simpler to apply if a specific project is being valued which does not have earmarked debt capital finance

Disadvantages: Requires judgement on choice of discount rate; no explicit allowance for cost of debt capital, which may be much higher than a "risk-free" rate

 o Weighted average cost of capital approach (WACC)

Derive a weighted cost of the capital obtained from the various sources and use that discount rate to discount the cash flows from the project

Advantages: Overcomes the requirement for debt capital finance to be earmarked to particular projects

Disadvantages: Care must be exercised in the selection of the appropriate income stream. The net cash flow to total invested capital is the generally accepted choice.

 o Total cash flow approach (TCF)

[ clarification needed ]

This distinction illustrates that the Discounted Cash Flow method can be used to determine the value of various business ownership interests. These can include equity or debt holders.

Alternatively, the method can be used to value the company based on the value of total invested capital. In each case, the differences lie in the choice of the income stream and discount rate. For example, the net cash flow to total invested capital and WACC are appropriate when valuing a company based on the market value of all invested capital.

[1]

History

Discounted cash flow calculations have been used in some form since money was first lent at interest in ancient times. As a method of asset valuation it has often been opposed to accounting book value, which is based on the amount paid for the asset. Following the stock market crash of

1929, discounted cash flow analysis gained popularity as a valuation method for stocks. Irving

Fisher in his 1930 book "The Theory of Interest" and John Burr Williams's 1938 text 'The Theory of

Investment Value' first formally expressed the DCF method in modern economic terms.

See also

 Adjusted present value

 Capital budgeting





Cost of capital

 Economic value added

Enterprise value

 Internal rate of return

 Financial modeling





 Net present value





Flows to equity

Market value added

Valuation using discounted cash flows

Time value of money

References

1.

^ Pratt, Shannon; Robert F. Reilly, Robert P. Schweihs (2000). Valuing a Business .

McGraw-Hill Professional. McGraw Hill. ISBN 0071356150. http://books.google.com/books?id=WO6wd8O8dsUC&printsec=frontcover&dq=shannon+pr

att&ei=fcfUR6q-

F4TCyQSrxfWABA&sig=Fpqt8pGRjbLPZJ9e_QEQGFzQ7y0#PPA913,M1.

External links

 Continuous compounding/cash flows

 The Theory of Interest at the Library of Economics and Liberty.





Monography about DCF (including some lectures on DCF). Wacc.biz

 Foolish Use of DCF. Motley Fool .

DCF web calculator. Sporkforge.com

 Getting Started With Discounted Cash Flows. The Street .

 International Good Practice: Guidance on Project Appraisal Using Discounted Cash Flow ,

International Federation of Accountants, June 2008, ISBN 978-1-934779-39-2

Further reading

 International Federation of Accountants (2007). Project Appraisal Using Discounted Cash

Flow .

 Copeland, Thomas E.; Tim Koller, Jack Murrin (2000). Valuation: Measuring and

Managing the Value of Companies . New York: John Wiley & Sons. ISBN 0-471-36190-9.

 Damodaran, Aswath (1996). Investment Valuation: Tools and Techniques for Determining

 the Value of Any Asset . New York: John Wiley & Sons. ISBN 0-471-13393-0.

Rosenbaum, Joshua; Joshua Pearl (2009). Investment Banking: Valuation, Leveraged

Buyouts, and Mergers & Acquisitions . Hoboken, NJ: John Wiley & Sons. ISBN 0-470-

44220-4. v • d • e


Transactions



Senior secured debt

·

Senior debt

·

Second lien debt

·

Subordinated debt

·

Mezzanine debt · Convertible debt · Exchangeable debt · Preferred equity ·

Shareholder loan

·

Common equity

·

Pari passu

Initial public offering (IPO)

·


Equity offerings (SEO) · Follow-on offering ·

Greenshoe (Reverse)

·

Book building

Takeover

·

Reverse takeover

·

Mergers and Tender offer

·

Poison pill

· acquisitions

Freeze-out merger · Tag-along right · Drag-along right ·

Valuation

Control premium

·

Divestment

·

Demerger

Leveraged buyout

·

Leveraged

Leverage recap · Financial sponsor ·

Private equity · Bond offering ·

High-yield debt

·

DIP financing

Financial modeling

·

APV

·

DCF

·


·

Cost of capital (Weighted average)

·


·

Enterprise value · Tax shield · Minority interest · EVA · MVA

P/E ratio

The P/E ratio ( price-to-earnings ratio ) of a stock (also called its "P/E", "PER", "earnings multiple," or simply "multiple") is a measure of the price paid for a share relative to the annual net income or profit earned by the firm per share.

[2]

It is a financial ratio used for valuation: a higher P/E ratio means that investors are paying more for each unit of net income, so the stock is more expensive compared to one with lower P/E ratio. The P/E ratio has units of years,

[note 1]

which can be interpreted as "number of years of earnings to pay back purchase price", ignoring the time value of money. In other words, P/E ratio shows current investor demand for a company share. The reciprocal of the PE ratio is known as the earnings yield.

[3]

The earnings yield is an estimate of expected return to be earned from holding the stock if we accept certain restrictive assumptions (see

T-Model).

Robert Shiller's plot of the S&P Composite Real Price-Earnings Ratio and Interest Rates (1871–

2008), from Irrational Exuberance , 2d ed.

[1]

In the preface to this edition, Shiller warns that "[t]he stock market has not come down to historical levels: the price-earnings ratio as I define it in this book is still, at this writing [2005], in the mid-20s, far higher than the historical average. … People still place too much confidence in the markets and have too strong a belief that paying attention to the gyrations in their investments will someday make them rich, and so they do not make conservative preparations for possible bad outcomes."

Contents





1 Definition

 2 Determining share prices

3 Other related measures o o

3.1 Earnings yield

3.2 Price/Dividend Ratio o 3.3 Dividend Yield o 3.4 Relationship between measures





4 Interpretation

 5 The Market P/E

6 Inputs o 6.1 Accuracy and context o 6.2 Historical vs. Projected Earnings

 7 The P/E Concept in Business Culture





8 Recent historic values





9 See also

 10 Notes

11 References

12 External links

Definition

There are various P/E ratios, all defined as:

The price per share in the numerator is the market price of a single share of the stock. The earnings per share in the denominator depends on the type of P/E:

 "Trailing P/E" or "P/E ttm": Earnings per share is the net income of the company for the most recent 12 month period, divided by number of shares outstanding. This is the most common meaning of "P/E" if no other qualifier is specified. Monthly earning data for individual companies are not available, so the previous four quarterly earnings reports are used and earnings per share is updated quarterly. Note, companies individually choose their financial year so the schedule of updates will vary.

 "Trailing P/E from continued operations": Instead of net income, uses operating earnings which exclude earnings from discontinued operations, extraordinary items (e.g. one-off windfalls and writedowns), or accounting changes. Note, longer-term P/E data such as

Schiller's uses net earnings.

 "Forward P/E", "P/Ef", or "estimated P/E": Instead of net income, uses estimated net earnings over next 12 months. Estimates are typically derived as the mean of a select group of analysts (note, selection criteria is rarely cited). In times of rapid economic dislocation, such estimates become less relevant as "the situation changes" (e.g. new economic data is published and/or the basis of their forecasts become obsolete) more quickly than analysts adjust their forecasts.

The P/E ratio can alternatively be calculated by dividing the company's market capitalization by its total annual earnings.

For example, if a stock is trading at $24 and the earnings per share for the most recent 12 month period is $3, then stock A has a P/E ratio of 24/3 or 8. Put another way, the purchaser of the stock is paying $8 for every dollar of earnings. Companies with losses (negative earnings) or no profit have an undefined P/E ratio (usually shown as Not applicable or "N/A"); sometimes, however, a negative

P/E ratio may be shown.

By comparing price and earnings per share for a company, one can analyze the market's stock valuation of a company and its shares relative to the income the company is actually generating.

Stocks with higher (and/or more certain) forecast earnings growth will usually have a higher P/E, and those expected to have lower (and/or riskier) earnings growth will in most cases have a lower

P/E. Investors can use the P/E ratio to compare the value of stocks: if one stock has a P/E twice that of another stock, all things being equal (especially the earnings growth rate), it is a less attractive investment. Companies are rarely equal, however, and comparisons between industries, companies, and time periods may be misleading.

Since 1900, the average P/E ratio for the S&P 500 index has ranged from 4.78 in Dec 1920 to 44.20 in Dec 1999

[4]

. The average P/E of the market varies in relation with, among other factors, expected growth of earnings, expected stability of earnings, expected inflation, and yields of competing investments. For example, when US treasuries yield high returns, investors pay less for a given earnings per share and P/E's fall.

Determining share prices

Share prices in a publicly traded company are determined by market supply and demand, and thus depend upon the expectations of buyers and sellers. Among these are:

 The company's future and recent performance, including potential growth;

 Perceived risk, including risk due to high leverage;

 Prospects for companies of this type, the market sector.

By dividing the price of one share in a company by the profits earned by the company per share, you arrive at the P/E ratio. If earnings per share move proportionally with share prices the ratio stays the same. But if stock prices gain in value and earnings remain the same or go down, the P/E rises.

The earnings figure used is the most recently available, although this figure may be out of date and may not necessarily reflect the current position of the company. This is often referred to as a 'trailing

P/E', because it involves taking earnings from the last four quarters

Price-Earnings ratios as a predictor of twenty-year returns based upon the plot by Robert Shiller

(Figure 10.1

[1]

, source). The horizontal axis shows the real price-earnings ratio of the S&P

Composite Stock Price Index as computed in Irrational Exuberance (inflation adjusted price divided by the prior ten-year mean of inflation-adjusted earnings). The vertical axis shows the geometric average real annual return on investing in the S&P Composite Stock Price Index, reinvesting dividends, and selling twenty years later. Data from different twenty year periods is color-coded as shown in the key. See also ten-year returns. Shiller states that this plot "confirms that long-term investors—investors who commit their money to an investment for ten full years—did do well when prices were low relative to earnings at the beginning of the ten years. Long-term investors would be well advised, individually, to lower their exposure to the stock market when it is high, as it has been recently, and get into the market when it is low."

[1]

Other related measures

The forward P/E uses the estimated earnings going forward twelve months.

P/E10 uses average earnings for the past 10 years. There is a view that the average earnings for a 20 year period remains largely constant

[5]

, thus using P/E10 will reduce the noise in the data.

The P/E ratio relates to the equity value. A similar measure can be defined for real estate, see

Case-

Shiller index .

PEG ratio is obtained by dividing the P/E ratio by the annual earnings growth rate. It is considered a form of normalization because higher growth rate should cause higher P/E.

The similar ratio on the enterprise value level is EV/EBITDA Enterprise value divided by the

EBITDA .

Present Value of Growth Opportunities (PVGO) is another alternative method for stock valuation. Present value of growth opportunities is calculated by finding the difference between price of equity with constant growth and price of equity with no growth.

PVGO = P(Growth) - P(No growth) = [D1/(r-g)] - E/r

where

P = Price of equity

D1 = Dividend for next period r = Cost of Capital or the capitalization rate of the company

E = Earning on equity g = The growth rate of the company

Since the Price/Earnings (P/E) Multiple is 'Price per share / Earnings per share' it can be written as

P0 / E1 = 1/r [ 1+ (PVGO/(E1/r))]

Thus, as PVGO rises, the P/E ratio rises.

Earnings yield

Main article: Earnings yield

The reverse (or reciprocal) of the P/E is the E/P, also known as the earnings yield. The earnings yield is quoted as a percentage, and is useful in comparing a stock, sector, or the market's valuation relative to bonds.

The earnings yield is also the cost to a publicly traded company of raising expansion capital through the issuance of stock.

Price/Dividend Ratio

Publicly traded companies often make periodic quarterly or yearly cash payments to their owners, the shareholders, in direct proportion to the number of shares held. According to US law, such payments can only be made out of current earnings or out of reserves (earnings retained from previous years). The company decides on the total payment and this is divided by the number of shares. The resulting dividend is an amount of cash per share.

Just as P/E is the ratio of price to earnings, the Price/Dividend ratio is the ratio of price to dividend.

Dividend Yield

Main article: Dividend yield

The dividend yield is the dividend paid in the last accounting year divided by the current share price: it is the reciprocal of the Price/Dividend ratio.

If a stock paid out $5 per share in cash dividends to its shareholders last year, and its price is currently $50, then it has a dividend yield of 10%.

Historically, at severely high P/E ratios (such as over 100x), a stock has NO (0.0%) or negligible dividend yield. With a P/E ratio over 100x, and supposing a portion of earnings is paid as dividend, it would take over a century to earn back the purchase price. Such stocks are extremely overvalued, unless a huge growth of earnings in the next years is expected.

Relationship between measures

Several of these measures are related to each other: given price, earnings, and dividend, there are 6 possible ratios, which come in reciprocal pairs:







P/E ratio and earnings yield are reciprocals;

P/D ratio and dividend yield are reciprocals;

Dividend payout ratio (DPR) = Dividend/EPS, while the reciprocal is dividend cover (DC) =

EPS/Dividend.

They are related by the following equations:

 P/E = P/D * DPR and P/D = P/E * DC;

 taking reciprocals, earnings yield = dividend yield * DC and dividend yield = earnings yield

* DPR.

Interpretation

The average U.S. equity P/E ratio from 1900 to 2005 is 14 (or 16, depending on whether the geometric mean or the arithmetic mean, respectively, is used to average). An oversimplified interpretation would conclude that it takes about 14 years of dividends to recoup the price paid for a stock [not including any additional income from the reinvestment of those dividends].

Normally, stocks with high earning growth are traded at higher P/E values. From the previous example, stock A, trading at $24 per share, may be expected to earn $6 per share the next year. Then the forward P/E ratio is $24/6 = 4. So, you are paying $4 for every one dollar of earnings, which makes the stock more attractive than it was the previous year.

The P/E ratio implicitly incorporates the perceived risk of a given company's future earnings. For a stock purchaser, this risk includes the possibility of bankruptcy. For companies with high leverage

(that is, high levels of debt), the risk of bankruptcy will be higher than for other companies.

Assuming the effect of leverage is positive, the earnings for a highly-leveraged company will also be higher. In principle, the P/E ratio incorporates this information, and different P/E ratios may reflect the structure of the balance sheet.

Variations on the standard trailing and forward P/E ratios are common. Generally, alternative P/E measures substitute different measures of earnings, such as rolling averages over longer periods of time (to "smooth" volatile earnings, for example), [6] or "corrected" earnings figures that exclude certain extraordinary events or one-off gains or losses. The definitions may not be standardized.

Various interpretations of a particular P/E ratio are possible, and the historical table below is just indicative and cannot be a guide, as current P/E ratios should be compared to current real interest rates (see Fed model):

A company with no earnings has an undefined P/E ratio. By convention, companies with

N/A losses (negative earnings) are usually treated as having an undefined P/E ratio, although a negative P/E ratio can be mathematically determined.

0–10

Either the stock is undervalued or the company's earnings are thought to be in decline.

Alternatively, current earnings may be substantially above historic trends or the company may have profited from selling assets.

10–17 For many companies a P/E ratio in this range may be considered fair value.

17–25

Either the stock is overvalued or the company's earnings have increased since the last earnings figure was published. The stock may also be a growth stock with earnings expected to increase substantially in future.

25+

A company whose shares have a very high P/E may have high expected future growth in earnings or the stock may be the subject of a speculative bubble.

It is usually not enough to look at the P/E ratio of one company and determine its status. Usually, an analyst will look at a company's P/E ratio compared to the industry the company is in, the sector the company is in, as well as the overall market (for example the S&P 500 if it is listed in a US exchange). Sites such as Reuters offer these comparisons in one table. Example of RHT Often, comparisons will also be made between quarterly and annual data. Only after a comparison with the industry, sector, and market can an analyst determine whether a P/E ratio is high or low with the above mentioned distinctions (i.e., undervaluation, over valuation, fair valuation, etc).

Using Discounted cash flow analysis, the impact of earnings growth and inflation can be evaluated.

The on-line calculator at Moneychimp

[7]

allows one to evaluate the "fair P/E ratio". Using constant historical earnings growth rate of 3.8 and post-war S&P 500 returns of 11% (including 4% inflation) as the discount rate, the fair P/E is obtained as 14.42. A stock growing at 10% for next 5 years would have a fair P/E of 18.65.

The Market P/E

To calculate the P/E ratio of a market index such as the S&P 500, it is not accurate to take the

"simple average" of the P/Es of all stock constituents. The preferred and accurate method is to calculate the weighted average. In this case, each stock's underlying market cap (price multiplied by number of shares in issue) is summed to give the total value in terms of market capitalization for the whole market index. The same method is computed for each stock's underlying net earnings

(earnings per share multiplied by number of shares in issue). In this case, the total of all net earnings is computed and this gives the total earnings for the whole market index. The final stage is to divide the total market capitalization by the total earnings to give the market P/E ratio. The reason for using the weighted average method rather than 'simple' average can best be described by the fact that the smaller constituents have less of an impact on the overall market index. For example, if a market index is composed of companies X and Y, both of which have the same P/E ratio (which causes the market index to have the same ratio as well) but X has a 9 times greater market cap than Y, then a percentage drop in earnings per share in Y should yield a much smaller effect in the market index than the same percentage drop in earnings per share in X.

A variation that is often used is to exclude companies with negative earnings from the sample - especially when looking at sub-indices with a lower number of stocks where companies with negative earnings will distort the figures.

In Stocks for the Long Run, Jeremy Siegel argues that the earnings yield is a good indicator of the market performance on the long run. The average P/E for the past 130 years has been 12.1 (i.e. earnings yield 5.3 percent). Shiller has argued that the mean P/E has risen from 12 to about 21 during 1920 to 2003

[8]

.

Inputs

Accuracy and context

In practice, decisions must be made as to how to exactly specify the inputs used in the calculations.

















Does the current market price accurately value the organization?

How is income to be calculated and for what periods? How do we calculate total capitalization?

Can these values be trusted?

What are the revenue and earnings growth prospects over the time frame one is investing in?

Were there special one-time charges which artificially lowered (or artificially raised) the earnings used in the calculation, and did those charges cause a drop in stock price or were they ignored?

Were these charges truly one-time, or is the company trying to manipulate us into thinking so?

What kind of P/E ratios is the market giving to similar companies, and also the P/E ratio of the entire market?

Are P/E ratios an accurate measure?

Historical vs. Projected Earnings

A distinction has to be made between the fundamental (or intrinsic) P/E and the way we actually compute P/Es. The fundamental or intrinsic P/E examines earnings forecasts. That is what was done in the analogy above. In reality, we actually compute P/Es using the latest 12 month corporate earnings. Using past earnings introduces a temporal mismatch, but it is felt that having this mismatch is better than using future earnings, since future earnings estimates are notoriously inaccurate and susceptible to deliberate manipulation.

On the other hand, just because a stock is trading at a low fundamental P/E is not an indicator that the stock is undervalued. A stock may be trading at a low P/E because the investors are less optimistic about the future earnings from the stock. Thus, one way to get a fair comparison between stocks is to use their primary P/E . This primary P/E is based on the earnings projections made for the next years to which a discount calculation is applied.

The P/E Concept in Business Culture

The P/E ratio of a company is a significant focus for management in many companies and industries. This is because management is primarily paid with their company's stock (a form of payment that is supposed to align the interests of management with the interests of other stock holders), in order to increase the stock price. The stock price can increase in one of two ways: either through improved earnings or through an improved multiple that the market assigns to those

earnings. As mentioned earlier, a higher P/E ratio is the result of a sustainable advantage that allows a company to grow earnings over time (i.e., investors are paying for their peace of mind). Efforts by management to convince investors that their companies do have a sustainable advantage have had profound effects on business:





The primary motivation for building conglomerates is to diversify earnings so that they go up steadily over time

[ citation needed ]

.

The choice of businesses which are enhanced or closed down or sold within these conglomerates is often made based on their perceived volatility, regardless of the absolute level of profits or profit margins [ citation needed ] .

 One of the main genres of financial fraud, "slush fund accounting" (hiding excess earnings in good years to cover for losses in lean years), is designed to create the image that the company always slowly but steadily increases profits, with the goal to increase the P/E ratio.

These and many other actions used by companies to structure themselves to be perceived as commanding a higher P/E ratio can seem counterintuitive to some, because while they may decrease the absolute level of profits they are designed to increase the stock price. Thus, in this situation, maximizing the stock price acts as a perverse incentive.

Recent historic values

There is no theoretically ideal P/E ratio for a company. For instance, the Alternative Investment

Market in London comprises mining companies like Talvivaara with P/E ratio exceeding 9,262 in late November 2008.

Here are the recent year end values of the S&P 500 index and the associated P/E as reported.

[9]

For a list of recent contractions (recessions) and expansions see US Business Cycle Expansions and

Contractions.

Date Index P/E EPS growth %

2007-12-31 1468.36 22.19 1.4

2006-12-31 1418.30 17.40 14.7

2005-12-31 1248.29 17.85 13.0

2004-12-31 1211.92 20.70 23.8

2003-12-31 1111.92 22.81 18.8

Comment

2002-12-31 879.82 31.89 18.5

2001-12-31 1148.08 46.50 -30.8

2000-12-31 1320.28 26.41 8.6

1999-12-31 1469.25 30.50 16.7

1998-12-31 1229.23 32.60 0.6

1997-12-31 970.43 24.43 8.3

1996-12-31 740.74 19.13 7.3

1995-12-31 615.93 18.14 18.7

1994-12-31 459.27 15.01 18.0

1993-12-31 466.45 21.31 28.9

1992-12-31 435.71 22.82 8.1

1991-12-31 417.09 26.12 -14.8

1990-12-31 330.22 15.47 -6.9

1989-12-31 353.40 15.45 .

1988-12-31 277.72 11.69 .

2001 contraction resulting in P/E Peak

Dot-com bubble burst: March 10, 2000

Low P/E due to high recent earnings growth.

July 1990-March 1991 contraction.

Bottom (Black Monday was Oct 19, 1987)

Note that at the height of the Dot-com bubble P/E had risen to 32. The collapse in earnings caused

P/E to rise to 46.50 in 2001. It has declined to a more sustainable region of 17. Its decline in recent years has been due to higher earnings growth.

During 1920-1990, the P/E ratio was mostly between 10 and 20, except for some brief periods.

[10]

Jeremy Siegel has suggested that the average P/E ratio of about 15 (or earnings yield of about 6.6%) arises due to the long term returns for stocks of about 6.8%.

Jeremy Siegel in Stocks for the Long Run , (2002 edition) had argued that with the favorable developments like the lower capital gains tax rates and transaction costs, P/E ratio in "low twenties" is sustainable, although higher than the historic average.

[11]

See also

 Fundamental analysis

 Stock valuation





Dividend yield

 Stock market

Stock market bubble





Stock market crash

 Value investing

List of finance topics

Notes

1.

Price is in currency or currency/share, while earnings are in currency/year, or currency/share/year.

References

1.

Shiller, Robert (2005). Irrational Exuberance (2d ed.) . Princeton University Press. ISBN 0-

691-12335-7.

2.

"Price-Earnings Ratio (P/E Ratio)". Investopedia. http://www.investopedia.com/terms/p/price-earningsratio.asp.

3.

Stocks for the Long Run, by Jeremy J. Siegel, McGraw-Hill Companies; 2nd edition (March

1, 1998) (Old edition) New edition is Siegel, Jeremy J. (2007). Stocks for the Long Run, 4th

Edition . New York: McGraw-Hill. unknown pages for citation. ISBN 978-0071494700.

4.

http://seekingalpha.com/article/124295-s-p-p-e-ratio-is-low-but-has-been-lower Seeking

Alpha blog comment...more authoritative citation needed

5.

11% Solution - Overvalued Stock Market - Adam Barth in Barron's - Generational Dynamics

6.

Anderson, K.; Brooks, C. (2006). The Long-Term Price-Earnings Ratio . http://papers.ssrn.com/sol3/papers.cfm?abstract_id=739664.

7.

P/E: Price to Earnings Ratio

8.

http://www.investopedia.com/articles/technical/04/020404.asp Is the P/E Ratio a Good

Market-Timing Indicator?

9.

http://www2.standardandpoors.com/spf/xls/index/SP500EPSEST.XLS S&P 500

EARNINGS AND ESTIMATE REPORT

10.

Is the P/E Ratio a Good Market-Timing Indicator?

11.

NAREIT - Capital Markets

External links













Is P/E Ratio a useful valuation measure?

Hussman Funds — Popup: Why We Use Price to Peak Earnings

Crestmont Research — Relationship of Inflation & Price/Earnings Ratios (1900—2005)

P/E Ratio: A Quick and Dirty Way to Determine Relative Value

How to Use the P/E

Way2invest: P/E Ratio

Types of stocks

Participants

Exchanges

Stock market

Stock · Common stock · Preferred stock · Outstanding stock · Treasury stock · Authorised stock · Restricted stock · Concentrated stock · Golden share

Investor · Stock trader/investor · Market maker · Floor trader · Floor broker ·

Broker-dealer

Stock exchange · List of stock exchanges · Over-the-counter · Electronic

Communication Network

Stock valuation

Gordon model · Dividend yield · Earnings per share · Book value · Earnings yield · Beta · Alpha · CAPM · Arbitrage pricing theory

Financial ratios

P/CF ratio · P/E · PEG · Price/sales ratio · P/B ratio · D/E ratio · Dividend payout ratio · Dividend cover · SGR · ROIC · ROCE · ROE · ROA ·

EV/EBITDA · RSI · Sharpe ratio · Treynor ratio · Cap rate

Trading theories Efficient market hypothesis · Fundamental analysis · Technical analysis ·

Related terms

Modern portfolio theory · Post-modern portfolio theory · Mosaic theory

Dividend · Stock split · Reverse stock split · Growth stock · Speculation ·

Trade · IPO · Market trends · Short Selling · Momentum · Day trading ·

Swing trading · DuPont Model · Dark liquidity · Market depth · Margin ·

Rally

The Income Method

By Michelle Collins & Julie King

Formulas for putting a value on a business: The Income Method

Looking at the asset value of a business can be complicated, as the numbers on the balance sheet may not accurately reflect the actual value of things like building and equipment after depreciation, or land value if the business is more than a few years old.

For this reason, some valuators prefer to use the company's income before depreciation, interest and tax (IBDIT) are deducted to predict future earnings and the overall value of the company. IBDIT should reflect the true nature of the business, and as such should be based on the financial records averaged over the last 5 years, 3 years, or current year if that is more appropriate.

Calculating Interest Before Depreciation, Interest and Taxes (IBDIT)

When using this method, it is important to study the overall business, and adjust the value assigned to IBDIT for considerations that can be found both on and off the balance sheet.

For example, upcoming building or equipment maintenance will not be found on the balance sheet, but if your analysis shows that there will be an increase in costs of this nature, then you should reduce IBDIT by a reasonable estimate of maintenance costs. Similarily, unusual profits or losses, such as the sale of a major asset, should be removed from your calculation of IBDIT. When doing the calculations you may also want to replace the current owner's salary on the operating expense section of the seller's income statement with the salary that you feel would be reasonable for the new management of the company.

When calculating IBDIT, you should not factor in possible growth of income due to further investment in or expansion of the business; you only pay the seller for the business performance as it exists now.

Coming up with a Capitalization Rate

Once you have determined IBDIT, you need to come up with an appropriate capitalization rate, which you will use as a multiplier. Here are the key factors that go into this equation:







Current interest rate on any loans or mortgages used to purchase the business.

The amount of cash you put into the business, also known as your equity investment, is another factor. Since you are making an investment in the company, you should consider what return you expect to get on your investment (ROI), in percentage.

A risk factor should also be added, as this investment will likely be much riskier than purchasing treasury bills or other securities. Combing these three percentages, you should weigh each one accordingly to come up with an overall average.

Capitalization rate: sample calculation

Here is a sample calculation for someone purchasing a business for $100,000:

Bank loan: $60,000 @ 8.9% per annum

Equity investment: $40,000 @ 15% per annum (the return you want to get on your investment)

Risk factor: 3%

Investment Weight Interest Rate Weighted Capitalization Rate (weight x interest rate)

Bank Loan 60% 8.9% 0.60 x 8.9% = 5.34%

Equity investment 40%

Sub-total --

15%

--

0.40 x 15% = 6.0%

5.34 + 6.0 = 11.34%

Plus risk factor --

Total 100%

-- 3%

11.34% + 3% = 14.34%

Process of calculating a company's value using the Capitalized Earnings Method:

1.

Use the seller's income statements to estimate Income before Depreciation, Interest and Tax

(IBDIT).

2.

Adjust IBDIT for potential increases in expenses after the business is purchased due to building, equipment and fixtures/furniture maintenance and replacements.

3.

Now that a final value for IBDIT has been calculated you need to calculate a capitalization rate. This rate is based on the interest you must pay to the bank, the return on investment you want to see from your original investment, and a risk factor that you feel is appropriate for the purchase of this business. (see above example) Once you have the IBDIT and a capitalization rate, you determine the purchase value of the business by dividing IBDIT by the capitalization rate: IBDIT

Capitalization rate

Continuing with the example above:

IBDIT = $100,000

Capitalization rate = 14.34% or 0.1434

The value of the business in this example, therefore, would be:

$100,000 = $697,350.00

0.1434

Valuation Formulas: a) The Book & Adjusted Book Value b)

The Liquidation Value

Valuation Formulas: Owner Benefit

Valuation

Capitalization rate

Capitalization rate (or "cap rate") is a measure of the ratio between the net operating income produced by an asset (usually real estate) and its capital cost (the original price paid to buy the asset) or alternatively its current market value. The rate is calculated in a simple fashion as follows:

 annual net operating income / cost (or value) = Capitalization Rate

For example, if a building is purchased for $1,000,000 sale price and it produces $100,000 in positive net operating income (the amount left over after fixed costs and variable costs are subtracted from gross lease income) during one year, then:

 $100,000 / $1,000,000 = 0.10 = 10%

The asset's capitalization rate is ten percent.

Capitalization rates are an indirect measure of how fast an investment will pay for itself. In the example above, the purchased building will be fully capitalized (pay for itself) after ten years (100% divided by 10%). If the capitalization rate were 5%, the payback period would be twenty years. Note that a real estate appraisal in the U.S. uses net operating income. Cash flow equals net operating income minus debt service. Where sufficiently detailed information is not available, the capitalization rate will be derived or estimated from net operating income to determine cost, value or required annual income.

Contents





1 Use for valuation o 1.1 Cash flow defined

2 Use for comparison

 3 Reversionary

 4 Change in asset value

 5 Recent trends

 6 See also


 8 References

Use for valuation

In real estate investment, real property is often valued according to projected capitalization rates used as investment criteria. This is done by algebraic manipulation of the formula below:

 Capital Cost (asset price) = Cash flow / Capitalization Rate

For example, in valuing the projected sale price of an apartment building that produces an annual net cash flow of $10,000, if we set a projected capitalization rate at 7%, then the asset value (or price we would pay to own it) is $142,857.

This is often referred to as direct capitalization, and is commonly used for valuing income generating property in a real estate appraisal.

One advantage of capitalization rate valuation is that it is separate from a "market-comparables" approach to an appraisal (which compares 3 valuations: what other similar properties have sold for based on a comparison of physical, location and economic characteristics, actual replacement cost to re-build the structure in addition to the cost of the land and capitalization rates). Given the inefficiency of real estate markets, multiple approaches are generally preferred when valuing a real estate asset. Capitalization rates for similar properties, and particularly for "pure" income properties, are usually compared to ensure that estimated revenue is being properly valued.

Cash flow defined

The capitalization rate is calculated using a measure of cash flow called net operating income (NOI), not net income. Generally, NOI is defined as income (earnings) before depreciation and interest expenses:

 Cash flow = Net income + depreciation + interest expense + profit tax - reserves for repairs =

Gross income - non-interest expenses

Interest expenses are excluded so that the valuation of the property does not depend on the amount of debt used to purchase the property; in financial terms, the cap rate is a capital structure-neutral valuation measure. Similarly, profit taxes (or other similar taxes) are usually excluded, as they will depend on the interest and depreciation expenses charged; most other taxes, and specifically property taxes, are treated as part of non-interest expenses.

Depreciation in the tax and accounting sense is excluded from the valuation of the asset, because it does not directly affect the cash generated by the asset. To arrive at a more careful and realistic definition, however, estimated annual maintenance expenses or capital expenditures will be included in the non-interest expenses.

Although cash flow is the generally-accepted figure used for calculating cap rates, this is often referred to under various terms, including simply income.

Use for comparison

Capitalization rates, or cap rates, provide a tool for investors to use for roughly valuing a property based on its income. For example, if a real estate investment provides $160,000 a year in cash flow and similar properties have sold based on 8% cap rates, the subject property can be roughly valued at $2,000,000 because $160,000 divided by 8% (0.08) equals $2,000,000.

Reversionary

Property values based on capitalization rates are calculated on an "in-place" or "passing rent" basis, i.e. given the rental income generated from current tenancy agreements. In addition, a valuer also provides an Estimated Rental Value (ERV). The ERV states the valuer’s opinion as to the open market rent which could reasonably be expected to be achieved on the subject property at the time of valuation.

The difference between the in-place rent and the ERV is the reversionary value of the property. For example, with passing rent of $160,000, and an ERV of $200,000, the property is $40,000 reversionary. Holding the valuers cap rate constant at 8%, we could consider the property as having a current value of $2,000,000 based on passing rent, or $2,500,000 based on ERV.

Finally, if the passing rent payable on a property is equivalent to its ERV, it is said to be "Rack

Rented".

Change in asset value

The cap rate only recognizes the cash flow a real estate investment produces and not the change in value of the property.

To get the unlevered rate of return on an investment the real estate investor adds (or subtracts) the price change percentage from the cap rate. For example, a property delivering an 8% capitalization, or cap rate, that increases in value by 2% delivers a 10% overall rate of return. The actual realised rate of return will depend on the amount of borrowed funds, or leverage, used to purchase the asset.

In Europe, the term Yield is more frequently used in connection with real estate than capitalization rate. Yield is a more general term that refers to income in relation to the price of an asset.

Recent trends

The National Council of Real Estate Investment Fiduciaries in a Sept 30, 2007 report reported that for the prior year, for all properties income return was 5.7% and the appreciation return was 11.1%.

A Wall Street Journal report using data from Real Capital Analytics and Federal Reserve

[1]

showed that since the beginning of 2001 to end of 2007, the cap rate for offices and apartments have dropped from about 10% to 5.5%, and from about 8.5% to 6% respectively. In May 2008, the cap rates 5.98% for the offices and 6.28% for the apartments. By comparison, 10-year treasury yields have remained largely between 4% and 5%.

The cap rates for apartments have been stable at around 6% since late 2005.

See also

 Real estate investing

 Internal rate of return

 Yield (finance)

External links

 CAP rate calculation considering cost of repairs





Visulate Property Investment Worksheet

 Forbes Cap Rate Calculator

Historical Cap rate index for several categories of real-estate

 Cap Rate as a valuation tool for Commercial Real Estate

 Vacancy and Cap rate

References

1.

^ http://www.wsj.com/article/SB121436232049002445.html?mod=residential_real_estate

Capitalization Rates Were Mixed in May, June 25, 2008 v • d • e

Types of stocks

Participants

Exchanges

Stock valuation


Trading theories

Related terms

Stock market



Broker-dealer





EV/EBITDA · RSI · Sharpe ratio · Treynor ratio · Cap rate

Efficient market hypothesis · Fundamental analysis · Technical analysis ·


Dividend · Stock split · Reverse stock split · Growth stock · Speculation ·


Swing trading · DuPont Model · Dark liquidity · Market depth · Margin ·

Rally

Capital asset pricing model

In finance, the capital asset pricing model (CAPM) is used to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk. The model takes into account the asset's sensitivity to nondiversifiable risk (also known as systemic risk or market risk), often represented by the quantity beta

(β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset.

The model was introduced by Jack Treynor (1961, 1962) [1] , William Sharpe (1964), John Lintner

(1965a,b) and Jan Mossin (1966) independently, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory. Sharpe received the Nobel Memorial Prize in

Economics (jointly with Markowitz and Merton Miller) for this contribution to the field of financial economics.

An estimation of the CAPM and the Security Market Line (purple) for the Dow Jones Industrial

Average over the last 3 years for monthly data.

Contents

 1 The formula

 2 Asset pricing





3 Asset-specific required return

 4 Risk and diversification

5 The efficient frontier





6 The market portfolio

 7 Assumptions of CAPM

8 Shortcomings of CAPM

 9 See also

 10 References


The formula

The Security Market Line, seen here in a graph, describes a relation between the beta and the asset's expected rate of return.

The CAPM is a model for pricing an individual security or a portfolio. For individual securities, we made use of the security market line (SML) and its relation to expected return and systemic risk

(beta) to show how the market must price individual securities in relation to their security risk class.

The SML enables us to calculate the reward-to-risk ratio for any security in relation to that of the overall market. Therefore, when the expected rate of return for any security is deflated by its beta coefficient, the reward-to-risk ratio for any individual security in the market is equal to the market reward-to-risk ratio, thus:

The market reward-to-risk ratio is effectively the market risk premium and by rearranging the above equation and solving for E(Ri), we obtain the Capital Asset Pricing Model (CAPM). where:





 is the expected return on the capital asset is the risk-free rate of interest such as interest arising from government bonds

(the beta coefficient ) is the sensitivity of the asset returns to market returns, or also





, is the expected return of the market is sometimes known as the market premium or risk premium (the difference between the expected market rate of return and the risk-free rate of return).

Restated, in terms of risk premium, we find that:

which states that the individual risk premium equals the market premium times

β

.

Note 1: the expected market rate of return is usually estimated by measuring the Geometric Average of the historical returns on a market portfolio (i.e. S&P 500).

Note 2: the risk free rate of return used for determining the risk premium is usually the arithmetic average of historical risk free rates of return and not the current risk free rate of return.

For the full derivation see Modern portfolio theory.

Asset pricing

Once the expected return, E ( R i

), is calculated using CAPM, the future cash flows of the asset can be discounted to their present value using this rate ( E ( R i

)), to establish the correct price for the asset.

In theory, therefore, an asset is correctly priced when its observed price is the same as its value calculated using the CAPM derived discount rate. If the observed price is higher than the valuation, then the asset is overvalued (and undervalued when the observed price is below the CAPM valuation).

Alternatively, one can "solve for the discount rate" for the observed price given a particular valuation model and compare that discount rate with the CAPM rate. If the discount rate in the model is lower than the CAPM rate then the asset is overvalued (and undervalued for a too high discount rate).

Asset-specific required return

The CAPM returns the asset-appropriate required return or discount rate - i.e. the rate at which future cash flows produced by the asset should be discounted given that asset's relative riskiness.

Betas exceeding one signify more than average "riskiness"; betas below one indicate lower than average. Thus a more risky stock will have a higher beta and will be discounted at a higher rate; less sensitive stocks will have lower betas and be discounted at a lower rate. Given the accepted concave utility function, the CAPM is consistent with intuition - investors (should) require a higher return for holding a more risky asset.

Since beta reflects asset-specific sensitivity to non-diversifiable, i.e. market risk, the market as a whole, by definition, has a beta of one. Stock market indices are frequently used as local proxies for the market - and in that case (by definition) have a beta of one. An investor in a large, diversified portfolio (such as a mutual fund) therefore expects performance in line with the market.

Risk and diversification

The risk of a portfolio comprises systematic risk, also known as undiversifiable risk, and unsystematic risk which is also known as idiosyncratic risk or diversifiable risk. Systematic risk refers to the risk common to all securities - i.e. market risk. Unsystematic risk is the risk associated with individual assets. Unsystematic risk can be diversified away to smaller levels by including a greater number of assets in the portfolio (specific risks "average out"). The same is not possible for systematic risk within one market. Depending on the market, a portfolio of approximately 30-40 securities in developed markets such as UK or US will render the portfolio sufficiently diversified to limit exposure to systematic risk only. In developing markets a larger number is required, due to the higher asset volatilities.

A rational investor should not take on any diversifiable risk, as only non-diversifiable risks are rewarded within the scope of this model. Therefore, the required return on an asset, that is, the return that compensates for risk taken, must be linked to its riskiness in a portfolio context - i.e. its contribution to overall portfolio riskiness - as opposed to its "stand alone riskiness." In the CAPM context, portfolio risk is represented by higher variance i.e. less predictability. In other words the beta of the portfolio is the defining factor in rewarding the systematic exposure taken by an investor.

The efficient frontier

Main article: Efficient frontier

The (Markowitz) efficient frontier

The CAPM assumes that the risk-return profile of a portfolio can be optimized - an optimal portfolio displays the lowest possible level of risk for its level of return. Additionally, since each additional asset introduced into a portfolio further diversifies the portfolio, the optimal portfolio must comprise every asset, (assuming no trading costs) with each asset value-weighted to achieve the above

(assuming that any asset is infinitely divisible). All such optimal portfolios, i.e., one for each level of return, comprise the efficient frontier.

Because the unsystematic risk is diversifiable, the total risk of a portfolio can be viewed as beta.

The market portfolio

An investor might choose to invest a proportion of his or her wealth in a portfolio of risky assets with the remainder in cash - earning interest at the risk free rate (or indeed may borrow money to fund his or her purchase of risky assets in which case there is a negative cash weighting). Here, the ratio of risky assets to risk free asset does not determine overall return - this relationship is clearly linear. It is thus possible to achieve a particular return in one of two ways:

1.

By investing all of one's wealth in a risky portfolio,

2.

or by investing a proportion in a risky portfolio and the remainder in cash (either borrowed or invested).

For a given level of return, however, only one of these portfolios will be optimal (in the sense of lowest risk). Since the risk free asset is, by definition, uncorrelated with any other asset, option 2 will generally have the lower variance and hence be the more efficient of the two.

This relationship also holds for portfolios along the efficient frontier: a higher return portfolio plus cash is more efficient than a lower return portfolio alone for that lower level of return. For a given risk free rate, there is only one optimal portfolio which can be combined with cash to achieve the lowest level of risk for any possible return. This is the market portfolio.

Assumptions of CAPM

All Investors:

1.

Aim to maximize economic utility.

2.

Are rational risk-averse.

3.

Are price takers, i.e., they cannot influence prices.

4.

Can lend and borrow unlimited under the risk free rate of interest.

5.

Trade without transaction or taxation costs.

6.

Deal with securities that are all highly divisible into small parcels.

7.

Assume all information is at the same time available to all investors.

Shortcomings of CAPM

















The model assumes that asset returns are (jointly) normally distributed random variables. It is however frequently observed that returns in equity and other markets are not normally distributed. As a result, large swings (3 to 6 standard deviations from the mean) occur in the market more frequently than the normal distribution assumption would expect.

The model assumes that the variance of returns is an adequate measurement of risk. This might be justified under the assumption of normally distributed returns, but for general return distributions other risk measures (like coherent risk measures) will likely reflect the investors' preferences more adequately.

The model assumes that all investors have access to the same information and agree about the risk and expected return of all assets (homogeneous expectations assumption).

The model assumes that the probability beliefs of investors match the true distribution of returns. A different possibility is that investors' expectations are biased, causing market prices to be informationally inefficient. This possibility is studied in the field of behavioral finance, which uses psychological assumptions to provide alternatives to the CAPM such as the overconfidence-based asset pricing model of Kent Daniel, David Hirshleifer, and

Avanidhar Subrahmanyam (2001)

[2]

.

The model does not appear to adequately explain the variation in stock returns. Empirical studies show that low beta stocks may offer higher returns than the model would predict.

Some data to this effect was presented as early as a 1969 conference in Buffalo, New York in a paper by Fischer Black, Michael Jensen, and Myron Scholes. Either that fact is itself rational (which saves the Efficient Market Hypothesis but makes CAPM wrong), or it is irrational (which saves CAPM, but makes the EMH wrong – indeed, this possibility makes volatility arbitrage a strategy for reliably beating the market).

The model assumes that given a certain expected return investors will prefer lower risk

(lower variance) to higher risk and conversely given a certain level of risk will prefer higher returns to lower ones. It does not allow for investors who will accept lower returns for higher risk. Casino gamblers clearly pay for risk, and it is possible that some stock traders will pay for risk as well.

The model assumes that there are no taxes or transaction costs, although this assumption may be relaxed with more complicated versions of the model.

The market portfolio consists of all assets in all markets, where each asset is weighted by its market capitalization. This assumes no preference between markets and assets for individual

investors, and that investors choose assets solely as a function of their risk-return profile. It also assumes that all assets are infinitely divisible as to the amount which may be held or transacted.

 The market portfolio should in theory include all types of assets that are held by anyone as an investment (including works of art, real estate, human capital...) In practice, such a market portfolio is unobservable and people usually substitute a stock index as a proxy for the true market portfolio. Unfortunately, it has been shown that this substitution is not innocuous and can lead to false inferences as to the validity of the CAPM, and it has been said that due to the inobservability of the true market portfolio, the CAPM might not be empirically testable.

This was presented in greater depth in a paper by Richard Roll in 1977, and is generally

 referred to as Roll's critique.

The model assumes just two dates, so that there is no opportunity to consume and rebalance portfolios repeatedly over time. The basic insights of the model are extended and generalized in the intertemporal CAPM (ICAPM) of Robert Merton, and the consumption CAPM

(CCAPM) of Douglas Breeden and Mark Rubinstein.

See also

 Arbitrage pricing theory (APT)

 Efficient market hypothesis





Fama-French three-factor model

 Hamada's equation

Modern portfolio theory

 Roll's critique

 Valuation (finance)

References





Black, Fischer., Michael C. Jensen, and Myron Scholes (1972). The Capital Asset Pricing

Model: Some Empirical Tests , pp. 79-121 in M. Jensen ed., Studies in the Theory of Capital

Markets. New York: Praeger Publishers.

 Fama, Eugene F. (1968). Risk, Return and Equilibrium: Some Clarifying Comments . Journal of Finance Vol. 23, No. 1, pp. 29-40.

 Fama, Eugene F. and Kenneth French (1992). The Cross-Section of Expected Stock Returns .

Journal of Finance, June 1992, 427-466.

French, Craig W. (2003). The Treynor Capital Asset Pricing Model , Journal of Investment



Management, Vol. 1, No. 2, pp. 60-72. Available at http://www.joim.com/

French, Craig W. (2002). Jack Treynor's 'Toward a Theory of Market Value of Risky Assets'



(December). Available at http://ssrn.com/abstract=628187

Lintner, John (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets , Review of Economics and Statistics, 47 (1), 13-37.

 Markowitz, Harry M. (1999). The early history of portfolio theory: 1600-1960 , Financial

Analysts Journal, Vol. 55, No. 4

 Mehrling, Perry (2005). Fischer Black and the Revolutionary Idea of Finance. Hoboken:







John Wiley & Sons, Inc.

Mossin, Jan. (1966). Equilibrium in a Capital Asset Market , Econometrica, Vol. 34, No. 4, pp. 768-783.

Ross, Stephen A. (1977). The Capital Asset Pricing Model (CAPM), Short-sale Restrictions and Related Issues , Journal of Finance, 32 (177)

Rubinstein, Mark (2006). A History of the Theory of Investments. Hoboken: John Wiley &

Sons, Inc.

 Sharpe, William F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk , Journal of Finance, 19 (3), 425-442

 Stone, Bernell K. (1970) Risk, Return, and Equilibrium: A General Single-Period Theory of

Asset Selection and Capital-Market Equilibrium. Cambridge: MIT Press.

 Tobin, James (1958). Liquidity preference as behavior towards risk , The Review of



Economic Studies, 25

 Treynor, Jack L. (1961). Market Value, Time, and Risk . Unpublished manuscript.

Treynor, Jack L. (1962). Toward a Theory of Market Value of Risky Assets . Unpublished manuscript. A final version was published in 1999, in Asset Pricing and Portfolio



Performance: Models, Strategy and Performance Metrics. Robert A. Korajczyk (editor)

London: Risk Books, pp. 15-22.

Mullins, David W. (1982). Does the capital asset pricing model work?

, Harvard Business

Review, January-February 1982, 105-113.

1.

http://ssrn.com/abstract=447580

2.

Overconfidence, Arbitrage, and Equilibrium Asset Pricing,' Kent D. Daniel, David

Hirshleifer and Avanidhar Subrahmanyam, Journal of Finance, 56(3) (June, 2001), pp. 921-

965

External links





Yale Finance Lecture on the CAPM

 Two asset efficient frontier

Multiasset efficient frontier v • d • e

Types of stocks

Participants

Exchanges

Stock valuation


Stock market



Broker-dealer





EV/EBITDA · RSI · Sharpe ratio · Treynor ratio · Cap rate

Trading theories

Efficient market hypothesis · Fundamental analysis · Technical analysis ·


Related terms Dividend · Stock split · Reverse stock split · Growth stock · Speculation ·


Swing trading · DuPont Model ·

Weighted average cost of capital

The weighted average cost of capital (WACC) is the rate that a company is expected to pay to finance its assets. WACC is the minimum return that a company must earn on existing asset base to satisfy its creditors, owners, and other providers of capital. Companies raise money from a number of sources: common equity, preferred equity, straight debt, convertible debt, exchangeable debt, warrants, options, pension liabilities, executive stock options, governmental subsidies, and so on.

Different securities are expected to generate different returns. WACC is calculated taking into account the relative weights of each component of the capital structure. Calculation of WACC for a company with a complex capital structure is a laborious exercise.

Contents

 1 The formula for a simple case





2 How it works

 3 Sources of information

4 Effect on valuation





5 References

 6 See also

7 External links

The formula for a simple case

The weighted average cost of capital is defined by: where and the following table defines each symbol:

Symbol Meaning weighted average cost of capital required or expected rate of return on equity , or cost of equity" required or expected rate of return on borrowings , or cost of debt corporate tax rate

Units

%

%

%

%

total debt and leases (including current portion of long-term debt and notes payable) total market value of equity and equity equivalents total capital invested in the going concern currency currency currency

This equation describes only the situation with homogeneous equity and debt. If part of the capital consists, for example, of preferred stock (with different cost of equity y ), then the formula would include an additional term for each additional source of capital. or

WACC

[1]

= w d

(1-T) r d

+ w e

r e w d

= debt portion of value of corporation

T = tax rate r d

= cost of debt (rate) w e

= equity portion of value of corporation r e

= cost of internal equity (rate)

How it works

Since we are measuring expected cost of new capital, we should use the market values of the components, rather than their book values (which can be significantly different). In addition, other, more "exotic" sources of financing, such as convertible/callable bonds, convertible preferred stock, etc., would normally be included in the formula if they existed in any significant amounts - since the cost of those financing methods is usually different from the plain vanilla bonds and equity due to their extra features.

WACC is a special way to measure the capital discount of the firms gaining and spending.

A calculation of a firm's cost of capital in which each category of capital is proportionately weighted. All capital sources - common stock, preferred stock, bonds and any other long-term debt - are included in a WACC calculation.

WACC is calculated by multiplying the cost of each capital component by its proportional weight and then summing: Broadly speaking, a company’s assets are financed by either debt or equity.

WACC is the average of the costs of these sources of financing, each of which is weighted by its respective use in the given situation. By taking a weighted average, we can see how much interest the company has to pay for every dollar it finances.

A firm's WACC is the overall required return on the firm as a whole and, as such, it is often used internally by company directors to determine the economic feasibility of expansionary opportunities and mergers. It is the appropriate discount rate to use for cash flows with risk that is similar to that of the overall firm.

Sources of information

How do we find out the values of the components in the formula for WACC? First let us note that the "weight" of a source of financing is simply the market value of that piece divided by the sum of the values of all the pieces. For example, the weight of common equity in the above formula would be determined as follows:

Market value of common equity / (Market value of common equity + Market value of debt + Market value of preferred equity).

So, let us proceed in finding the market values of each source of financing (namely the debt, preferred stock, and common stock).

 The market value for equity for a publicly traded company is simply the price per share multiplied by the number of shares outstanding, and tends to be the easiest component to find.

 The market value of the debt is easily found if the company has publicly traded bonds.

Frequently, companies also have a significant amount of bank loans, whose market value is not easily found. However, since the market value of debt tends to be pretty close to the book value (for companies that have not experienced significant changes in credit rating, at least), the book value of debt is usually used in the WACC formula.

 The market value of preferred stock is again usually easily found on the market, and determined by multiplying the cost per share by number of shares outstanding.

Now, let us take care of the costs.

 Preferred equity is equivalent to a perpetuity, where the holder is entitled to fixed payments forever. Thus the cost is determined by dividing the periodic payment by the price of the preferred stock, in percentage terms.

 The cost of common equity is usually determined using the capital asset pricing model.

 The cost of debt is the yield to maturity on the publicly traded bonds of the company. Failing availability of that, the rates of interest charged by the banks on recent loans to the company would also serve as a good cost of debt. Since a corporation normally can write off taxes on the interest it pays on the debt, however, the cost of debt is further reduced by the tax rate that the corporation is subject to. Thus, the cost of debt for a company becomes (YTM on bonds or interest on loans) × (1 − tax rate). In fact, the tax deduction is usually kept in the formula for WACC, rather than being rolled up into cost of debt, as such:

WACC = weight of preferred equity × cost of preferred equity

+ weight of common equity × cost of common equity

+ weight of debt × cost of debt × (1 − tax rate).

And now we are ready to plug all our data into the WACC formula.

Effect on valuation

Economists Merton Miller and Franco Modigliani showed in the Modigliani-Miller theorem that in an economy with no transaction costs or taxes, financing decisions are irrelevant to the company's value: an all-equity financed company is worth the same as an all-debt financed one. However,

many governments allow a tax deduction on interest, thereby creating a bias towards debt financing.

However, there is a cost to financial distress (e.g. bankruptcy) which creates a bias towards equity financing. Therefore theoretically, the appropriate level of Debt to Equity in a company will then be the point at which the benefits of the tax shield provided by debt financing are outweighed by the costs of financial distress.

References

1.

http://faculty.smu.edu/ozerturk/pdf4368/4368-note11.pdf

This article includes a list of references or external links, but its sources remain unclear because it lacks inline citations.

Please improve this article by introducing more precise citations where appropriate. (November 2007)

 G. Bennet Stewart III (1991). The Quest for Value . HarperCollins.

 F. Modigliani and M. Miller, "The Cost of Capital, Corporation Finance and the Theory of



Investment," American Economic Review (June 1958).

M. Miller and F. Modigliani. "Corporate income taxes and the cost of capital: a correction."

American Economic Review , 53 (3) (1963), pp. 433-443.

 J. Miles und J. Ezzell. "The weighted average cost of capital, perfect capital markets and project life: a clarification." Journal of Financial and Quantitative Analysis , 15 (1980), S.

719-730.

See also

 Beta coefficient





Cost of capital

Discounted cash flow

 Economic Value Added





Internal rate of return

 Minimum acceptable rate of return

Modigliani-Miller theorem

 Net present value

 Opportunity cost

External links





Video about practical application of the WACC approach

Yee, Kenton K., "Earnings Quality and the Equity Risk Premium: A Benchmark Model" .

Contemporary Accounting Research , Vol. 23, No. 3, pp. 833-877, Fall 2006. Available at



SSRN: http://ssrn.com/abstract=921914.

Velez-Pareja, Ignacio and Tham, Joseph, "A Note on the Weighted Average Cost of Capital

WACC" (August 7, 2005). Available at SSRN: http://ssrn.com/abstract=254587.

Unpublished.

 calculate the WACC with your own values to understand the equation

 Find the WACC of any publicly traded company by entering the firm's stock ticker symbol

 Paper describing a method for generating the WACC curve when there is default risk - spreadsheet available

v • d • e



Senior secured debt

·

Senior debt

·

Second lien debt

·

Subordinated debt

·

Mezzanine debt

·

Convertible debt

·

Exchangeable debt

·

Preferred equity

·

Shareholder loan · Common equity · Pari passu

Transactions


Valuation

Initial public offering (IPO) ·


Equity offerings (SEO)

·

Follow-on offering

·

Greenshoe (Reverse)

·

Book building

Takeover

·

Reverse takeover

·

Tender offer

·

Poison pill

·

Mergers and Freeze-out merger

·

Tag-along acquisitions right

·

Drag-along right

·

Control premium ·

Divestment

·

Demerger

Leveraged buyout

·

Leveraged

Leverage recap

·

Financial sponsor

·

Private equity

·

Bond offering

·

High-yield debt · DIP financing

Financial modeling

·

APV

·

DCF

·


·

Cost of capital ( Weighted average )

·


·

Enterprise value

·

Tax shield

·

Minority interest

·

EVA

·

MVA

Goodwill (accounting)

Goodwill (accounting)

Discounted cash flow

P/E ratio

The Income Method

Capitalization rate

Capital asset pricing model

Weighted average cost of capital

Related documents

Products

Support

Goodwill (accounting)