2467:
prior to 1990). This restriction from active trading, which amounts to a lack of marketability, is the only distinction between the restricted stock and its freely traded counterpart. Restricted stock can be traded in private transactions and usually do so at a discount. The restricted stock studies attempt to verify the difference in price at which the restricted shares trade versus the price at which the same unrestricted securities trade in the open market as of the same date. The underlying data by which these studies arrived at their conclusions has not been made public. Consequently, it is not possible when valuing a particular company to compare the characteristics of that company to the study data. Still, the existence of a marketability discount has been recognized by valuation professionals and the courts, and the restricted stock studies are frequently cited as empirical evidence. Notably, the lowest average discount reported by these studies was 26% and the highest average discount was 40%.
231:
The 2004 and 2007 SCF indicate a growing trend in stock ownership, with 51% of households indicating a direct or indirect ownership of stocks, with the majority of those respondents indicating indirect ownership through mutual funds. Few indications are available on the value of privately held firms. Anderson (2009) recently estimated the market value of U.S. privately held and publicly traded firms, using
Internal Revenue Service and SCF data. He estimates that privately held firms produced more income for investors, and had more value than publicly held firms, in 2004.
227:). A far larger number of firms are privately held. Normally, equity interests in these firms (which include corporations, partnerships, limited-liability companies, and some other organizational forms) are traded privately, and often irregularly. As a result, previous transactions provide limited evidence as to the current value of a private company primarily because business value changes over time, and the share price is associated with considerable uncertainty due to limited market exposure and high transaction costs.
1214:
generally different, too. Where a privately held company can be shown to be sufficiently similar to a public company, the CAPM may be suitable. However, it requires the knowledge of market stock prices for calculation. For private companies that do not sell stock on the public capital markets, this information is not readily available. Therefore, calculation of beta for private firms is problematic. The build-up cost of capital model, discussed below, is the typical choice in such cases.
2010:
companies. Such comparison often reveals useful insights which help business analysts better understand performance relationship between the subject company and its downstream industry. For example, if a growing subject company is in an industry more concentrated than its downstream industry with a high degree of interdependence, one should logically expect the subject company performs better than the downstream industry in terms of growth, margins and risk.
1713:, on the other hand, frequently fail for a variety of reasons too numerous to name. There are no federal guarantees. The risk of investing in a private company cannot be reduced through diversification, and most businesses do not own the type of hard assets that can ensure capital appreciation over time. This is why investors demand a much higher return on their investment in closely held businesses; such investments are inherently much more risky.
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holding stock in a private company. The difference in value can be quantified by applying a discount for lack of marketability. This discount is determined by studying prices paid for shares of ownership in private companies that eventually offer their stock in a public offering. Alternatively, the lack of marketability can be assessed by comparing the prices paid for restricted shares to fully marketable shares of stock of public companies.
459:
1819:
corporation. A controlling shareholder may have the authority to direct the corporation to sell all or part of the assets it owns and to distribute the proceeds to the shareholders. The non-controlling shareholder, however, lacks this authority and cannot access the value of the assets. As a result, the value of a corporation's assets is not the true indicator of value to a shareholder who cannot avail himself of that value.
2284:
grown more liquid in the past decade due to rapid electronic trading, reduced commissions, and governmental deregulation. These developments have not improved the liquidity of interests in private companies, however. Valuation discounts are multiplicative, so they must be considered in order. Control premiums and their inverse, minority interest discounts, are considered before marketability discounts are applied.
2363:. Mergerstat defines the "control premium" as the percentage difference between the acquisition price and the share price of the freely traded public shares five days prior to the announcement of the M&A transaction. While it is not without valid criticism, Mergerstat control premium data (and the minority interest discount derived therefrom) is widely accepted within the valuation profession.
1262:. However, the method of incomplete replication and risk covering come along without the need of capital market data and thus being more solid. Additionally, the existence of investment-based approaches, considering different investment opportunities and determining an investment program by means of linear optimization. Among them the approximative decomposition valuation approach can be found.
2666:
2584:
2481:
2406:
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2024:
1916:
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1276:
1130:
1011:
865:
649:
559:
346:
264:
25:
2549:. The offshore buyers may resell these shares in the United States, still without having to register the shares, after holding them for just 40 days. Typically, these shares are sold for 20% to 30% below the publicly traded share price. Some of these transactions have been reported with discounts of more than 30%, resulting from the lack of marketability. These discounts are similar to the
1703:, is a relatively new concept. It is, however, gaining acceptance in the business valuation consultancy community since it is based on modern portfolio theory (although see ). Total beta can help appraisers develop a cost of capital who were content to use their intuition alone when previously adding a purely subjective company-specific risk premium in the build-up approach.
2359:
data regarding control premiums is the
Control Premium Study, published annually by Mergerstat since 1972. Mergerstat compiles data regarding publicly announced mergers, acquisitions and divestitures involving 10% or more of the equity interests in public companies, where the purchase price is $ 1 million or more and at least one of the parties to the transaction is a
2106:. If the guideline public companies are sufficiently similar to each other and the subject company to permit a meaningful comparison, then their multiples should be similar. The public companies identified for comparison purposes should be similar to the subject company in terms of industry, product lines, market, growth, margins and risk.
2268:
These interests are generally traded on the New York Stock
Exchange, AMEX, NASDAQ, and other exchanges where there is a ready market for equity securities. These values represent a minority interest in the subject companies—small blocks of stock that represent less than 50% of the company's equity, and usually much less than 50%.
2648:(IPOs) to transactions in the same company's stocks prior to the IPO. Companies that are going public are required to disclose all transactions in their stocks for a period of three years prior to the IPO. The pre-IPO studies are the leading alternative to the restricted stock stocks in quantifying the marketability discount.
627:(liquidity, turnover, profitability, etc.), trend analysis and industry comparative analysis. This permits the valuation analyst to compare the subject company to other businesses in the same or similar industry, and to discover trends affecting the company and/or the industry over time. By comparing a company's
1991:. The market price of the stocks of publicly traded companies engaged in the same or a similar line of business, whose shares are actively traded in a free and open market, can be a valid indicator of value when the transactions in which stocks are traded are sufficiently similar to permit meaningful comparison.
137:
gift taxation, divorce litigation, allocate business purchase price among business assets, establish a formula for estimating the value of partners' ownership interest for buy-sell agreements, and many other business and legal purposes such as in shareholders deadlock, divorce litigation and estate contest.
2565:
is equal to the marketability discount. The range of marketability discounts derived by this study was 32% to 49%. However, ascribing the entire value of a put option to marketability is misleading, because the primary source of put value comes from the downside price protection. A correct economic
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Certain business situations, and the parent firms in those cases, are also logically analysed under an options framework. Just as a financial option gives its owner the right, but not the obligation, to buy or sell a security at a given price, companies that make strategic investments have the right,
1982:
The market approach to business valuation is rooted in the economic principle of competition: that in a free market the supply and demand forces will drive the price of business assets to a certain equilibrium. Buyers would not pay more for the business, and the sellers will not accept less, than the
748:
Three different approaches are commonly used in business valuation: the income approach, the asset-based approach, and the market approach. Within each of these approaches, there are various techniques for determining the value of a business using the definition of value appropriate for the appraisal
2391:
Several empirical studies have been published that attempt to quantify the discount for lack of marketability. These studies include the restricted stock studies and the pre-IPO studies. The aggregate of these studies indicate average discounts of 35% and 50%, respectively. Some experts believe the
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All other factors being equal, an interest in a publicly traded company is worth more because it is readily marketable. Conversely, an interest in a private-held company is worth less because no established market exists. "The IRS Valuation Guide for Income, Estate and Gift Taxes, Valuation
Training
2374:
Another factor to be considered in valuing closely held companies is the marketability of an interest in such businesses. Marketability is defined as the ability to convert the business interest into cash quickly, with minimum transaction and administrative costs, and with a high degree of certainty
1706:
This capitalization rate for small, privately held companies is significantly higher than the return that an investor might expect to receive from other common types of investments, such as money market accounts, mutual funds, or even real estate. Those investments involve substantially lower levels
249:
The standard of value is the hypothetical conditions under which the business will be valued. The premise of value relates to the assumptions, such as assuming that the business will continue forever in its current form (going concern), or that the value of the business lies in the proceeds from the
214:
The evidence on the market value of specific businesses varies widely, largely depending on reported market transactions in the equity of the firm. A fraction of businesses are publicly traded, meaning that their equity can be purchased and sold by investors in stock markets available to the general
2466:
Restricted stocks are equity securities of public companies that are similar in all respects to the freely traded stocks of those companies except that they carry a restriction that prevents them from being traded on the open market for a certain period of time, which is usually one year (two years
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The first discount that must be considered is the discount for lack of control, which in this instance is also a minority interest discount. Minority interest discounts are the inverse of control premiums, to which the following mathematical relationship exists: MID = 1 – The most common source of
2109:
However, if the subject company is privately owned, its value must be adjusted for lack of marketability. This is usually represented by a discount, or a percentage reduction in the value of the company when compared to its publicly traded counterparts. This reflects the higher risk associated with
738:
Discretionary adjustments. The owners of private companies may be paid at variance from the market level of compensation that similar executives in the industry might command. In order to determine fair market value, the owner's compensation, benefits, perquisites and distributions must be adjusted
709:
The key objective of normalization is to identify the ability of the business to generate income for its owners. A measure of the income is the amount of cash flow that the owners can remove from the business without adversely affecting its operations. The most common normalization adjustments fall
516:
A business valuation report generally begins with a summary of the purpose and scope of business appraisal as well as its date and stated audience. Following is then a description of national, regional and local economic conditions existing as of the valuation date, as well as the conditions of the
431:
Business valuation results can vary considerably depending upon the choice of both the standard and premise of value. In an actual business sale, it would be expected that the buyer and seller, each with an incentive to achieve an optimal outcome, would determine the fair market value of a business
1826:
may be the most relevant standard of value where liquidation is imminent or ongoing; where a company earnings or cash flow are nominal, negative or worth less than its assets; or where net book value is standard in the industry in which the company operates. The adjusted net book value may also be
718:
to facilitate a comparison between the subject company and other businesses in the same industry or geographic location. These adjustments are intended to eliminate differences between the way that published industry data is presented and the way that the subject company's data is presented in its
230:
A number of stock market indicators in the United States and other countries provide an indication of the market value of publicly traded firms. The Survey of
Consumer Finance in the U.S. also includes an estimate of household ownership of stocks, including indirect ownership through mutual funds.
965:
On the other hand, a capitalization rate is applied in methods of business valuation that are based on business data for a single period of time. For example, in real estate valuations for properties that generate cash flows, a capitalization rate may be applied to the net operating income (NOI)
734:
Non-recurring adjustments. The subject company's financial statements may be affected by events that are not expected to recur, such as the purchase or sale of assets, a lawsuit, or an unusually large revenue or expense. These non-recurring items are adjusted so that the financial statements will
631:
in different time periods, the valuation expert can view growth or decline in revenues or expenses, changes in capital structure, or other financial trends. How the subject company compares to the industry will help with the risk assessment and ultimately help determine the discount rate and the
136:
are used by financial market participants to determine the price they are willing to pay or receive to effect a sale of the business. In addition to estimating the selling price of a business, the same valuation tools are often used by business appraisers to resolve disputes related to estate and
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The discount for lack of control is separate and distinguishable from the discount for lack of marketability. It is the valuation professional's task to quantify the lack of marketability of an interest in a privately held company. Because, in this case, the subject interest is not a controlling
2283:
Despite a growing inclination of the IRS and tax courts to challenge valuation discounts, Shannon Pratt suggested in a scholarly presentation recently that valuation discounts are actually increasing as the differences between public and private companies is widening. Publicly traded stocks have
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The intermediate level, marketable minority interest, is less than the controlling interest level and higher than the non-marketable minority interest level. The marketable minority interest level represents the perceived value of equity interests that are freely traded without any restrictions.
791:
In determining which of these approaches to use, the valuation professional must exercise discretion. Each technique has advantages and drawbacks, which must be considered when applying those techniques to a particular subject company. Most treatises and court decisions encourage the valuator to
2279:
Non-marketable, minority level is the lowest level on the chart, representing the level at which non-controlling equity interests in private companies are generally valued or traded. This level of value is discounted because no ready market exists in which to purchase or sell interests. Private
2009:
When there is a lack of comparison with direct competition, a meaningful alternative could be a vertical value-chain approach where the subject company is compared with, for example, a known downstream industry to have a good feel of its value by building useful correlations with its downstream
1901:
Besides mathematical approaches for the valuation of companies a rather unknown method includes also the cultural aspect. The so-called "cultural valuation method" (cultural due diligence) seeks to combine existing knowledge, motivation and internal culture with the results of a net-asset-value
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to a level which brings risk-reward back into balance. The referenced studies establish a reasonable range of valuation discounts from the mid-30%s to the low 50%s. The more recent studies appeared to yield a more conservative range of discounts than older studies, which may have suffered from
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Controlling interest level is the value that an investor would be willing to pay to acquire more than 50% of a company's stock, thereby gaining the attendant prerogatives of control. Some of the prerogatives of control include: electing directors, hiring and firing the company's management and
1576:
is a widely recognized method of determining the after-tax net cash flow discount rate, which in turn yields the capitalization rate. The figures used in the build-Up method are derived from various sources. This method is called a build-up method because it is the sum of risks associated with
1213:
One of the criticisms of the CAPM is that beta is derived from volatility of prices of publicly traded companies, which differ from non-publicly companies in liquidity, marketability, capital structures and control. Other aspects such as access to credit markets, size, and management depth are
439:
These assumptions might not, and probably do not, reflect the actual conditions of the market in which the subject business might be sold. However, these conditions are assumed because they yield a uniform standard of value, after applying generally accepted valuation techniques, which allows
992:
Careful matching of the discount rate to the appropriate measure of economic income is critical to the accuracy of the business valuation results. Net cash flow is a frequent choice in professionally conducted business appraisals. The rationale behind this choice is that this earnings basis
1818:
In considering an asset-based approach, the valuation professional must consider whether the shareholder whose interest is being valued would have any authority to access the value of the assets directly. Shareholders own shares in a corporation, but not its assets, which are owned by the
1649:
representing that portion of total investment risk that can be avoided through diversification. Public capital markets do not provide evidence of unsystematic risk since investors that fail to diversify cannot expect additional returns. Unsystematic risk falls into one of two categories.
1807:). For this reason, the asset-based approach is not the most probative method of determining the value of going business concerns. In these cases, the asset-based approach yields a result that is probably less than the fair market value of the business. The asset based approach is the
850:
However, income valuation methods can also be used to establish the value of a severable business asset as long as an income stream can be attributed to it. An example is licensable intellectual property whose value needs to be established to arrive at a supportable royalty structure.
989:, after tax net income, excess earnings, projected cash flow, etc. The result of this formula is the indicated value before discounts. Before moving on to calculate discounts, however, the valuation professional must consider the indicated value under the asset and market approaches.
2173:
but not the obligation, to exploit opportunities in the future; management will of course only exercise where this makes economic sense. Thus, for companies facing uncertainty of this type, the stock price may be seen as the sum of the value of existing businesses (i.e., the
1707:
of risk than an investment in a closely held company. Depository accounts are insured by the federal government (up to certain limits); mutual funds are composed of publicly traded stocks, for which risk can be substantially minimized through portfolio diversification.
1596:, require a greater return, so the next element of the build-up method is the equity risk premium. In determining a company's value, the long-horizon equity risk premium is used because the Company's life is assumed to be infinite. The sum of the risk-free rate and the
978:
that compensates an investor for the relative level of risk associated with a particular investment in excess of the risk-free rate. Most importantly, the selected discount or capitalization rate must be consistent with stream of benefits to which it is to be applied.
250:
sale of all of its assets minus the related debt (sum of the parts or assemblage of business assets). When done correctly, a valuation should reflect the capacity of the business to match a certain market demand, as it is the only true predictor of future cash flows.
2651:
The pre-IPO studies are sometimes criticized because the sample size is relatively small, the pre-IPO transactions may not be arm's length, and the financial structure and product lines of the studied companies may have changed during the three year pre-IPO window.
1631:
By adding the first three elements of a build-up discount rate, we can determine the rate of return that investors would require on their investments in small public company stocks. These three elements of the build-up discount rate are known collectively as the
2228:
sectors—can similarly be viewed as the sum of the value of products in place and the portfolio of patents yet to be deployed. As regards the option analysis, since the patent provides the firm with the right to develop the product, it will do so only if the
2383:
interest in the company, and the owner of that interest cannot compel liquidation to convert the subject interest to cash quickly, and no established market exists on which that interest could be sold, the discount for lack of marketability is appropriate.
945:
are closely related to each other, but distinguishable. Generally speaking, the discount rate or capitalization rate may be defined as the yield necessary to attract investors to a particular investment, given the risks associated with that investment.
2375:
as to the amount of net proceeds. There is usually a cost and a time lag associated with locating interested and capable buyers of interests in privately held companies, because there is no established market of readily available buyers and sellers.
2280:
companies are less "liquid" than publicly traded companies, and transactions in private companies take longer and are more uncertain. Between the intermediate and lowest levels of the chart, there are restricted shares of publicly traded companies.
2184:
investments. Here, the value of the asset is a function of both quantity of resource available and the price of the resource in question. The value of the resource is then the difference between the value of the asset and the cost associated with
730:
standard), the seller would retain any assets which were not related to the production of earnings or price those non-operating assets separately. For this reason, non-operating assets (such as excess cash) are usually eliminated from the balance
2726:
The studies confirm what the marketplace knows intuitively: Investors covet liquidity and loathe obstacles that impair liquidity. Prudent investors buy illiquid investments only when there is a sufficient discount in the price to increase the
842:
of a controlling, marketable interest in the subject company, since the entire benefit stream of the subject company is most often valued, and the capitalization and discount rates are derived from statistics concerning public companies.
1662:
and can be observed by studying the returns of a group of companies operating in the same industry sector. Morningstar's yearbooks contain empirical data to quantify the risks associated with various industries, grouped by SIC industry
432:
asset that would compete in the market for such an acquisition. If the synergies are specific to the company being valued, they may not be considered. Fair value also does not incorporate discounts for lack of control or marketability.
997:, models: the returns obtained from investments in publicly traded companies can easily be represented in terms of net cash flows. At the same time, the discount rates are generally also derived from the public capital markets data.
245:
Before the value of a business can be measured, the valuation assignment must specify the reason for and circumstances surrounding the business valuation. These are formally known as the business value standard and premise of value.
1691:
The only unknown in the two equations is the company specific risk premium. While it is possible to isolate the company-specific risk premium as shown above, many appraisers just key in on the TCOE provided by the first equation.
818:
The income approach relies upon the economic principle of expectation: the value of business is based on the expected economic benefit and level of risk associated with the investment. Income based valuation methods determine
2272:
determining their compensation; declaring dividends and distributions, determining the company's strategy and line of business, and acquiring, selling or liquidating the business. This level of value generally contains a
1673:
Historically, no published data has been available to quantify specific company risks. However, as of late 2006, new research has been able to quantify, or isolate, this risk for publicly traded stocks through the use of
962:
of a series of projected cash flows. The discount rate can also be viewed as the required rate of return the investors expect to receive from the business enterprise, given the level of risk they undertake.
325:
Fair market value – a value of a business enterprise determined between a willing buyer and a willing seller both in full knowledge of all the relevant facts and neither compelled to conclude a transaction.
1983:
price of a comparable business enterprise. The buyers and sellers are assumed to be equally well informed and acting in their own interests to conclude a transaction. It is similar in many respects to the
767:
A number of business valuation models can be constructed that utilize various methods under the three business valuation approaches. Venture
Capitalists and Private Equity professionals have long used the
435:
However, it is possible to achieve the fair market value for a business asset that is being liquidated in its secondary market. This underscores the difference between the standard and premise of value.
2164:
options which nevertheless have value, equity may have value even if the value of the firm falls well below the face value of the outstanding debt—and this value can be determined using the appropriate
1441:
2257:
of the company as a whole. In valuing a minority, non-controlling interest in a business, however, the valuation professional must consider the applicability of discounts that affect such interests.
1116:
Since the WACC captures the risk of the subject business itself, the existing or contemplated capital structures, rather than industry averages, are the appropriate choices for business valuation.
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inferred from the restricted and pre-IPO studies, despite the holding period being just 40 days. Studies based on the prices paid for options have also confirmed similar discounts. If one holds
3258:
635:
It is important to mention that among the financial statements, the primary statement to show the liquidity of the company is cash flow. Cash flow shows the company's cash in and out flow.
823:
by dividing the benefit stream generated by the subject or target company times a discount or capitalization rate. The discount or capitalization rate converts the stream of benefits into
183:. This distinction derives mainly from the use of the results: stock investors intend to profit from price movement, whereas a business owner is focused on the enterprise as a total,
3117:
1695:
It is similar to using the market approach in the income approach instead of adding separate (and potentially redundant) measures of risk in the build-up approach. The use here of
792:
consider more than one technique, which must be reconciled with each other to arrive at a value conclusion. A measure of common sense and a good grasp of mathematics is helpful.
2276:
over the intermediate level of value, which typically ranges from 25% to 50%. An additional premium may be paid by strategic investors who are motivated by synergistic motives.
2102:. The comparison is generally based on published data regarding the public companies' stock prices and earnings, sales, or revenues, which is expressed as a fraction known as a
2939:
Bucks, Kennickell, Mach, & Moore, "Changes in US Family
Finances from 2004 to 2007: Evidence from the Survey of Consumer Finances," Federal Reserve Bulletin, February 2009
2201:
may therefore also be analysed using the options approach. Specifically, the value of the firm comprises the value of already active projects determined via DCF valuation (or
2148:
protects equity investors, shareholders would choose not to repay the firm's debt where the value of the firm as perceived is less than the value of the outstanding debt; see
517:
industry in which the subject business operates. A common source of economic information for the first section of the business valuation report is the
Federal Reserve Board's
2392:
lack of control and marketability discounts can aggregate discounts for as much as ninety percent of a company's fair market value, specifically with family-owned companies.
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on the firm, and this allows for the valuation of troubled firms which may otherwise be difficult to analyse. The classic application of this approach is to the valuation of
772:
which essentially combines the income approach with the market approach. In certain cases equity may also be valued by applying the techniques and frameworks developed for
1642:. It arises from external factors and affect every type of investment in the economy. As a result, investors taking systematic risk are rewarded by an additional premium.
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of the expected cash flows from the product exceeds the cost of development, and the patent rights thus correspond to a call option. Similar analysis may be applied to
469:
3534:
2910:
1222:
With regard to capital market-oriented valuation approaches there are numerous valuation approaches besides the traditional CAPM model. They include, for example, the
985:
Once the capitalization rate or discount rate is determined, it must be applied to an appropriate economic income stream: pretax cash flow, aftertax cash flow, pretax
3376:
Anderson, Patrick L., "New
Developments in Business Valuation." Developments in Litigation Economics. Eds P.A. Gaughan and R.J. Thornton, Burlington: Elsevier, 2005.
1498:
1210:, a measure of stock price volatility. Beta is compiled by various researchers for particular industries and companies, and measures systematic risks of investment.
1556:
1527:
1472:
838:"), and the excess earnings method (which is a hybrid of asset and income approaches). The result of a value calculation under the income approach is generally the
763:
and the market approaches determine value by comparing the subject company to other companies in the same industry, of the same size, and/or within the same region.
2379:
for
Appeals Officers" acknowledges the relationship between value and marketability, stating: "Investors prefer an asset which is easy to sell, that is, liquid."
164:
doing the business valuation. Here, attorneys should always be prepared to have their expert's report withstand the scrutiny of cross-examination and criticism.
1227:
219:
that is a direct estimate of the market value of the firm's equity. Some publicly traded firms have relatively few recorded trades (including many firms traded
982:
Capitalization and discounting valuation calculations become mathematically equivalent under the assumption that the business income grows at a constant rate.
726:
Non-operating adjustments. It is reasonable to assume that if a business were sold in a hypothetical sales transaction (which is the underlying premise of the
525:. State governments and industry associations also publish useful statistics describing regional and industry conditions. Valuators use these as well as other
739:
to industry standards. Similarly, the rent paid by the subject business for the use of property owned by the company's owners individually may be scrutinized.
2838:
1206:. The method derives the discount rate by adding risk premium to the risk-free rate. The risk premium is derived by multiplying the equity risk premium with
1075:(WACC) is an approach to determining a discount rate that incorporates both equity and debt financing; the method determines the subject company's actual
328:
Investment value – a value the company has to a particular investor. The effect of synergy is included in valuation under the investment standard of value.
3105:
424:
In use – if the asset would provide maximum value to the market participants principally through its use in combination with other assets as a group.
413:
Orderly disposition – value of business assets in exchange, where the assets are to be disposed of individually and not used for business operations.
974:, which is the return that an investor would expect from a secure, practically risk-free investment, such as a high quality government bond; plus a
844:
3458:
Wolpin, Jeffrey; "Mythbusting – Discrediting Appraisal Myths Through Properly Applied Statistical Reasoning," Valuation Strategies, Jan./Feb 2008
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various classes of assets. It is based on the principle that investors would require a greater return on classes of assets that are more risky.
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smaller sample sizes. Another method of quantifying the lack of marketability discount is the quantifying marketability discounts model (QMDM).
2570:, demonstrating that marketability of restricted stock is of low value because it is easy to hedge using unrestricted stock or futures trades.
3449:
Pratt, Reilly, and Schweihs, Valuing A Business, The Analysis and Appraisal of Closely Held Companies, 3rd ed., New York, McGraw-Hill, 1996,
3403:
2869:
2828:
1994:
The difficulty lies in identifying public companies that are sufficiently comparable to the subject company for this purpose. Also, as for a
1194:(CAPM) provides one method of determining a discount rate in business valuation. The CAPM originated from the Nobel Prize-winning studies of
813:
3346:
Abudy M. and Benninga S., (2016). Valuing Restricted Stock Grants to Non-Executive Employees, Journal of Economics and Business 86, 33-51.
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method. Especially during a company takeover uncovering hidden problems is of high importance for a later success of the business venture.
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2687:
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2502:
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2319:
2045:
1937:
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1297:
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886:
670:
580:
367:
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Intrinsic value – the measure of business value that reflects the investor's in-depth understanding of the company's economic potential.
285:
42:
1244:
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3493:
2546:
970:
There are several different methods of determining the appropriate discount rates. The discount rate is composed of two elements: the
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3414:
3392:
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3370:
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1963:
1888:
1774:
1323:
1177:
1058:
912:
696:
606:
503:
393:
311:
108:
3198:
1787:
In asset-based analysis the value of a business is equal to the sum of its assets. The values of these assets must be adjusted to
1113:, or the optimal capital structure. Such discretion detracts from the objectivity of this approach, in the minds of some critics.
1105:
One of the problems with this method is that the valuator may elect to calculate WACC according to the subject company's existing
3409:
Campbell Ian R., and Johnson, Howard E., The Valuation of Business Interests, Canadian Institute of Chartered Accountants, 2001.
2371:
A "discount for lack of marketability" (DLOM) may be applied to a minority block of stock to alter the valuation of that block.
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1072:
89:
1341:
61:
2541:
In addition to the restricted stock studies, U.S. publicly traded companies are able to sell stock to offshore investors (SEC
3573:
3568:
3330:
Abudy M., Benninga S., and Shust E., (2016). The Cost of Equity for Private Firms, Journal of Corporate Finance 37, 431-443.
2691:
2609:
2506:
2431:
2323:
2186:
2049:
1941:
1866:
1752:
1301:
1155:
1036:
890:
674:
584:
371:
289:
145:
46:
1091:; the cost of equity, as discussed below, is typically calculated via the CAPM, but often employing an alternative method.
3093:
2221:
68:
2193:", management will undertake the development, and will not do so otherwise, and a resource project is thus effectively a
202:, whereas in other contexts, the valuation and subsequent transactions are generally handled by a business valuator and
3563:
3558:
620:
1230:(CCAPM). Furthermore, alternative capital market models were developed, having in common that expected return hinge on
2095:
2085:
1191:
994:
240:
153:
149:
2676:
2594:
2491:
2416:
2308:
2034:
1926:
1851:
1737:
1286:
1140:
1021:
875:
659:
569:
485:
427:
In exchange – if the asset would provide maximum value to the market participants principally on a stand-alone basis.
356:
274:
75:
3455:
Trout, Robert, "Business Valuations," chapter 8 in Patrick Gaughan, ed., Measuring Commercial Damages, Wiley, 2000.
2992:
2695:
2680:
2613:
2598:
2510:
2495:
2435:
2420:
2327:
2312:
2264:. There are three common levels of value: controlling interest, marketable minority, and non-marketable minority.
2053:
2038:
1945:
1930:
1870:
1855:
1756:
1741:
1305:
1290:
1159:
1144:
1040:
1025:
894:
879:
678:
663:
588:
573:
375:
360:
293:
278:
35:
3214:
2833:
2818:
2198:
2099:
1977:
1639:
1249:
3031:
Zhang, Chu (2009). "On the explanatory power of firm-specific variables in cross-sections of expected returns".
2948:
Anderson, Patrick L., "Value of Private Businesses in the United States," Business Economics (2009) 44, 87–108.
1827:
used as a "sanity check" when compared to other methods of valuation, such as the income and market approaches.
1811:
and should preferably be used in businesses having mature or declining growth cycle, and is more suitable for a
3191:
3010:
2928:
2823:
2798:
2750:
2742:
2645:
1678:
calculations. Butler and Pinkerton have outlined a procedure which sets the following two equations together:
1608:
1223:
1099:
195:
57:
2141:
3431:
Fishman, Pratt, Morrison, Standards of Value: Theory and Applications, John Wiley & Sons, Inc., NJ, 2007.
2550:
3446:
Pratt, Shannon H. Valuing Small Businesses and Professional Practices. 3rd ed., New York, McGraw-Hill, 1998.
3223:
2924:
971:
760:
the asset-based approaches determine value by adding the sum of the parts of the business (net asset value);
481:
3303:
175:, which is about calculating theoretical values of listed companies and their stocks, for the purposes of
3304:"The Discount for Lack of Marketability: Update on Current Studies and Analysis of Current Controversies,
3058:
GleiĂźner Werner, Gregor Dorfleitner (2016). "Valuing streams of risky cash flows with risk-value models".
2003:
1804:
1095:
3398:
Brining, Brian P., JD, CPA, Finance & Accounting for Lawyers, BV Resources, LLC, Portland, OR, 2011.
3553:
2783:
2238:
2137:
1988:
1796:
966:(i.e., income before depreciation and interest expenses) of the property for the trailing twelve months.
180:
140:
Specialized business valuation credentials include the Chartered Business Valuator (CBV) offered by the
3014:
3443:
Mercer, Christopher, "Fair Market Value vs. The Real World," Valuation Strategies, March 1999; reprint
3018:
2966:
2768:
2567:
2360:
2174:
1710:
951:
926:
835:
769:
720:
715:
628:
526:
522:
2887:"Withstand the Scrutiny of Cross-Examination and Criticism of your Business Valuation Expert Report"
2644:
Another approach to measure the marketability discount is to compare the prices of stock offered in
3434:
Gaughan, Patrick A., Measuring Business Interruption Losses, John Wiley & Sons, Inc., NJ, 2004.
2234:
2216:
may also be valued as options, and the value of firms holding these patents—typically firms in the
1597:
942:
930:
801:
785:
538:
416:
Liquidation – value in exchange when business assets are to be disposed of in a forced liquidation.
157:
133:
125:
3387:
Greg Beech and Dave Thayser, Valuations, Mergers and Acquisitions, Oxford University Press, 2015.
3174:
1336:
The cost of equity (Ke) is computed by using the modified capital asset pricing model (Mod. CAPM)
3528:
3240:
3187:
3154:
2793:
2202:
2153:
2121:, in certain cases equity may be valued by applying the techniques and frameworks developed for
1998:, the equity is less liquid (in other words its stocks are less easy to buy or sell) than for a
82:
3514:
3489:
3421:
3410:
3399:
3388:
3377:
3366:
3262:
2972:
2904:
2865:
2813:
2755:
2254:
2145:
1812:
1792:
1788:
1646:
1620:
1616:
1203:
1110:
1106:
959:
839:
820:
754:
727:
534:
191:
3486:
Financial Modeling and Valuation: A Practical Guide to Investment Banking and Private Equity
3347:
3331:
3232:
3218:
3146:
3040:
3006:
2949:
2803:
2788:
2778:
2554:
2181:
2166:
2152:. Where firm value is greater than debt value, the shareholders would choose to repay (i.e.
2122:
1808:
1800:
1700:
1685:= risk-free rate + beta * equity risk premium + size premium + company-specific risk premium
1624:
1604:
1593:
1589:
1483:
1259:
773:
530:
410:
Assemblage of assets – value of assets in place but not used to conduct business operations.
1534:
1505:
1450:
847:
states that earnings are preeminent for the valuation of closely held operating companies.
3259:
The real options component of firm market value: The case of the technological corporation
3202:
3137:
Black, Fischer; Myron Scholes (1973). "The Pricing of Options and Corporate Liabilities".
3074:
Using Total Beta and the Butler Pinkerton Calculator to Solve the CAPM Credibility Problem
2886:
2273:
1995:
1633:
1475:
1195:
1076:
955:
938:
624:
203:
199:
194:: when two corporates are involved, the valuation and transaction is within the realm of "
172:
3118:
Why Total Beta Produces Arbitrary Valuations: A Violation of the 'No-Arbitrage' Principle
3195:
2728:
2561:), the holder has, in effect, purchased marketability for the shares. The price of the
2149:
1999:
1582:
1102:—and is thus applied to the subject company's net cash flow to total invested capital.
1084:
537:(NPV) for similar companies may vary depending on the country because of the different
161:
3547:
3158:
2230:
2161:
1088:
934:
824:
800:
The various approaches to valuation are detailed in the following sections. See also
184:
176:
141:
3365:
Anderson, Patrick L., Business Economics and Finance, Chapman & Hall/CRC, 2005.
3094:
The Butler Pinkerton Model - Empirical Support for Company for Company-specific Risk
830:
There are several different income methods, including capitalization of earnings or
3351:
3335:
2542:
2206:
2190:
2126:
1659:
1612:
1080:
975:
777:
542:
407:
Going concern – value in continued use as an ongoing operating business enterprise.
215:
public. Publicly traded companies on major stock markets have an easily calculated
3044:
2177:) plus any real option value. Equity valuations here, may thus proceed likewise.
1600:
yields the long-term average market rate of return on large public company stocks.
1239:
2859:
3440:
Hughes, David, The Business Value Myth, Canopy Law Books, 2012. ASIN: B009XB91CU
2665:
2583:
2480:
2405:
2297:
2242:
2194:
2133:
2023:
1915:
1840:
1726:
1682:
Total cost of equity (TCOE) = risk-free rate + total beta * equity risk premium
1275:
1199:
1129:
1010:
864:
648:
558:
345:
263:
24:
2763:
2562:
2558:
1823:
986:
518:
1258:
Nevertheless, even these models are not wholly consistent, as they also show
2808:
2773:
2260:
Discussions of discounts and premiums frequently begin with a review of the
2157:
831:
3274:
129:
1799:, is generally impossible to determine apart from the company's overall
3244:
3163:
2213:
757:
of the benefit stream generated by the business (discounted cash flow);
714:
Comparability adjustments. The valuer may adjust the subject company's
440:
meaningful comparison between businesses which are similarly situated.
3261: ; A. Buckley, K. Tse, H. Rijken and H. Eijgenhuijsen. (2002).
2953:
993:
corresponds to the equity discount rate derived from the build-up, or
1500:= Beta value (sensitivity of the stock returns to market returns)
3236:
3150:
735:
better reflect the management's expectations of future performance.
2993:
Economic Principles behind the Market, Asset and Income Approaches
2557:
and purchases an option to sell that stock at the market price (a
3116:
Dominica Canefield, Lutz Kruschwitz, and Andreas Löffler (2014).
3437:
Hitchner, James R., ed., Financial Valuation, McGraw-Hill, 2003.
3420:
Damodaran, Aswath. Investment Valuation, New York, Wiley, 1996.
1645:
In addition to systematic risks, the discount rate must include
3511:
Investment Banking Workbook: Valuation, LBOs, M&A, and IPOs
3470:
Investment Banking Workbook: Valuation, LBOs, M&A, and IPOs
3263:
Stock Market Valuation with Real Options: lessons from Netscape
2659:
2577:
2474:
2399:
2291:
2017:
1909:
1834:
1720:
1615:". Size premium data is generally available from two sources:
1269:
1123:
1004:
858:
642:
552:
452:
339:
257:
18:
2965:
Pratt, Shannon; Robert F. Reilly; Robert P. Schweihs (2000).
1585:, which is the rate of return for long-term government bonds.
468:
deal primarily with the United States and do not represent a
1623:& Associates') Stocks, Bonds, Bills & Inflation and
2885:
Gottlieb, CPA/ABV/CFF, ASA, CVA, CBA, MST, Mark S. (2011).
2545:, enacted in 1990) without registering the shares with the
2002:, its value is considered to be slightly lower than such a
1581:
The first element of a build-up capitalization rate is the
3196:
How Do You Assess The Value of A Company's "Real Options"?
124:
is a process and a set of procedures used to estimate the
3015:
Applications Of Option Pricing Theory To Equity Valuation
2756:
Corporate finance § Investment and project valuation
1638:. This type of investment risk cannot be avoided through
1474:= Risk free rate of return (generally taken as 10-year
1436:{\displaystyle k_{e}=R_{f}+\beta (R_{m}-R_{f})+SCRP+CSRP}
753:
the income approaches determine value by calculating the
3509:
Joshua Rosenbaum, Joshua Pearl, Joseph Gasparro (2021).
1094:
The resultant discount rate is used for cases where the
954:
valuations, the discount rate, often an estimate of the
150:
National Association of Certified Valuators and Analysts
1087:. The debt cost is essentially the company's after tax
477:
1537:
1508:
1486:
1453:
1344:
1079:
by calculating the weighted average of the company's
3090:
National Association of Certified Valuation Analysts
3257:P. Alonso, V. Azofra, and G. de la Fuente. (2006).
3221:(1985). "Evaluating Natural Resource Investments".
148:, and the Certified Valuation Analyst (CVA) by the
49:. Unsourced material may be challenged and removed.
3452:Pratt, Reilly, Cost of Capital, McGraw-Hill, 2002.
2751:Mergers and acquisitions § Business valuation
1550:
1521:
1492:
1466:
1435:
1218:Alternative valuation approaches and factor models
3468:Joshua Rosenbaum, Joshua Pearl, Joseph Gasparro,
2929:"Valuation Factors: The Top 9 Things To Consider"
2205:) and undeveloped reserves as analysed using the
1592:, which are inherently more risky than long-term
788:by industry and / or given the business context.
16:Determination of the economic value of a business
3132:
3130:
2925:"Business Valuation vs. Stock Market Valuation"
2566:analysis would use deeply in-the-money puts or
3173:Aswath Damodaran (Stern School of Business):
1234:risk sources and thus being less restrictive:
781:
1228:consumption-based capital asset pricing model
802:Valuation (finance) § Business valuation
466:The examples and perspective in this article
8:
3533:: CS1 maint: multiple names: authors list (
2909:: CS1 maint: multiple names: authors list (
2839:Valuation using the Market Penetration Model
1791:wherever possible. The value of a company's
420:Premise of value for fair value calculation
3302:Robert Reilly, and Aaron Rotkowski (2007).
3106:Total Beta: A review of theory and practice
3002:
3000:
2694:. Unsourced material may be challenged and
2612:. Unsourced material may be challenged and
2509:. Unsourced material may be challenged and
2434:. Unsourced material may be challenged and
2326:. Unsourced material may be challenged and
2052:. Unsourced material may be challenged and
1944:. Unsourced material may be challenged and
1869:. Unsourced material may be challenged and
1755:. Unsourced material may be challenged and
1304:. Unsourced material may be challenged and
1158:. Unsourced material may be challenged and
1039:. Unsourced material may be challenged and
958:for the business, is used to calculate the
893:. Unsourced material may be challenged and
677:. Unsourced material may be challenged and
587:. Unsourced material may be challenged and
374:. Unsourced material may be challenged and
292:. Unsourced material may be challenged and
156:. In some cases, the court would appoint a
2118:
2971:. McGraw-Hill Professional. McGraw Hill.
2714:Learn how and when to remove this message
2632:Learn how and when to remove this message
2529:Learn how and when to remove this message
2454:Learn how and when to remove this message
2346:Learn how and when to remove this message
2072:Learn how and when to remove this message
1964:Learn how and when to remove this message
1889:Learn how and when to remove this message
1775:Learn how and when to remove this message
1542:
1536:
1513:
1507:
1485:
1458:
1452:
1394:
1381:
1362:
1349:
1343:
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1178:Learn how and when to remove this message
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3019:Option Pricing Applications in Valuation
1611:, require a greater return, called the "
3476:
2850:
3526:
2902:
2132:In general, equity may be viewed as a
1098:are discounted—i.e. as opposed to the
521:, published eight times a year by the
152:; these professionals may be known as
2829:Valuation using discounted cash flows
1564:CSRP = Company specific risk premium
941:of a business. The discount rate and
814:Valuation using discounted cash flows
639:Normalization of financial statements
167:Business valuation takes a different
7:
3275:"Discount for Lack of Marketability"
2692:adding citations to reliable sources
2610:adding citations to reliable sources
2507:adding citations to reliable sources
2432:adding citations to reliable sources
2324:adding citations to reliable sources
2144:paper. Here, since the principle of
2140:, already discussed in the original
2050:adding citations to reliable sources
1942:adding citations to reliable sources
1867:adding citations to reliable sources
1753:adding citations to reliable sources
1302:adding citations to reliable sources
1266:Modified capital asset pricing model
1156:adding citations to reliable sources
1037:adding citations to reliable sources
891:adding citations to reliable sources
710:into the following four categories:
675:adding citations to reliable sources
585:adding citations to reliable sources
372:adding citations to reliable sources
290:adding citations to reliable sources
47:adding citations to reliable sources
3104:Correia, C & Gevers, J (2015).
2253:The valuation approaches yield the
1603:Similarly, investors who invest in
2547:Securities and Exchange Commission
2367:Discount for lack of marketability
1561:SCRP = Small company risk premium
14:
834:, discounted future cash flows ("
3463:Financial Modeling and Valuation
2664:
2582:
2479:
2404:
2296:
2022:
1914:
1839:
1725:
1274:
1128:
1073:weighted average cost of capital
1009:
1001:Weighted average cost of capital
863:
855:Discount or capitalization rates
647:
557:
457:
344:
262:
23:
2092:guideline public company method
2014:Guideline public company method
632:selection of market multiples.
34:needs additional citations for
3352:10.1016/j.jeconbus.2016.04.002
3336:10.1016/j.jcorpfin.2016.01.014
2923:See, e.g., these discussions:
1400:
1374:
1245:Fama–French three-factor model
146:American Society of Appraisers
1:
3045:10.1016/j.jempfin.2008.10.001
1254:Fama–French five-factor model
235:Standard and premise of value
3139:Journal of Political Economy
3033:Journal of Empirical Finance
2891:BusinessValuationNewYork.com
2864:(2nd ed.). LexisNexis.
2288:Discount for lack of control
621:financial statement analysis
134:various valuation techniques
128:of an owner's interest in a
2180:A common application is to
2086:Comparable company analysis
1558:= Market rate of return
1192:capital asset pricing model
1120:Capital asset pricing model
480:, discuss the issue on the
241:Business valuation standard
210:Estimates of business value
190:A second distinction is re
3590:
2858:Kwok, Benny K. B. (2008).
2175:discounted cash flow value
2167:option valuation technique
2098:of the subject company to
2083:
1975:
811:
238:
3513:. John Wiley & Sons.
3488:. John Wiley & Sons.
3175:Valuing Firms in Distress
3122:Business Valuation Review
3078:Business Valuation Review
2834:Valuation using multiples
2819:Residual income valuation
2203:other standard techniques
2114:Option pricing approaches
2100:publicly traded companies
1987:that is commonly used in
1978:Valuation using multiples
1831:Cultural valuation method
1640:portfolio diversification
1607:, which are riskier than
1250:Carhart four-factor model
933:is used to determine the
784:. The valuation approach
198:", and is managed by an
3192:Columbia Business School
3011:Stern School of Business
2824:Tax amortization benefit
2799:Mergers and acquisitions
2743:Consolidation (business)
2646:initial public offerings
2396:Restricted stock studies
1224:arbitrage pricing theory
845:IRS Revenue Ruling 59-60
780:framework, as discussed
749:assignment. Generally,
196:mergers and acquisitions
144:, ASA and CEIV from the
3484:Paul Pignataro (2013).
3224:The Journal of Business
3124:(2014) 33 (4): 131–135.
2551:marketability discounts
2241:) and the valuation of
2187:developing the resource
1985:comparable sales method
1590:large-cap equity stocks
1109:, the average industry
2249:Discounts and premiums
2004:market-based valuation
1805:tangible common equity
1717:Asset-based approaches
1711:Closely held companies
1658:. It is also known as
1627:' Risk Premium Report.
1552:
1523:
1494:
1493:{\displaystyle \beta }
1468:
1437:
3574:Administrative theory
3569:Corporate development
3186:Alfred Rappaport and
3080:(2010) 29 (3): 75–82.
2784:Goodwill (accounting)
2239:intellectual property
2154:exercise their option
2138:distressed securities
2084:Further information:
1989:real estate appraisal
1667:Company specific risk
1656:industry risk premium
1553:
1551:{\displaystyle R_{m}}
1524:
1522:{\displaystyle k_{e}}
1495:
1469:
1467:{\displaystyle R_{f}}
1438:
1226:(APT) as well as the
812:Further information:
744:Approach to valuation
217:market capitalization
181:investment management
3284:. September 25, 2009
3072:M. Mark Lee (2010).
2861:Forensic Accountancy
2769:Economic value added
2688:improve this section
2656:Applying the studies
2606:improve this section
2568:single-stock futures
2503:improve this section
2428:improve this section
2320:improve this section
2160:. Thus analogous to
2046:improve this section
1938:improve this section
1863:improve this section
1749:improve this section
1535:
1506:
1484:
1451:
1342:
1298:improve this section
1152:improve this section
1033:improve this section
887:improve this section
770:First Chicago Method
721:financial statements
716:financial statements
671:improve this section
629:financial statements
581:improve this section
545:and risk-free rate.
523:Federal Reserve Bank
486:create a new article
478:improve this article
368:improve this section
286:improve this section
58:"Business valuation"
43:improve this article
3564:Valuation (finance)
3559:Financial economics
2747:Corporate finance:
2237:(or other works of
2189:. Where positive, "
1809:entry barrier value
1598:equity risk premium
1529:= Cost of equity
1100:cashflows to equity
943:capitalization rate
931:capitalization rate
539:time-value of money
449:Economic conditions
158:forensic accountant
3201:2019-10-20 at the
3188:Michael Mauboussin
2968:Valuing a Business
2794:Market value added
1660:idiosyncratic risk
1588:Investors who buy
1548:
1519:
1490:
1464:
1433:
549:Financial analysis
254:Standards of value
154:business valuators
122:Business valuation
3461:Pignataro, Paul,
3404:978-1-935081-71-5
2954:10.1057/be.2009.4
2871:978-962-8972-76-0
2814:Price/sales ratio
2724:
2723:
2716:
2642:
2641:
2634:
2539:
2538:
2531:
2464:
2463:
2456:
2387:Empirical studies
2356:
2355:
2348:
2255:fair market value
2146:limited liability
2123:financial options
2082:
2081:
2074:
1974:
1973:
1966:
1906:Market approaches
1899:
1898:
1891:
1813:capital intensive
1793:intangible assets
1789:fair market value
1785:
1784:
1777:
1647:unsystematic risk
1625:Duff & Phelps
1334:
1333:
1326:
1188:
1187:
1180:
1111:capital structure
1107:capital structure
1096:overall cashflows
1069:
1068:
1061:
960:net present value
923:
922:
915:
840:fair market value
821:fair market value
774:financial options
755:net present value
728:fair market value
707:
706:
699:
617:
616:
609:
535:net present value
527:published surveys
514:
513:
506:
488:, as appropriate.
404:
403:
396:
336:Premises of value
322:
321:
314:
192:corporate finance
119:
118:
111:
93:
3581:
3539:
3538:
3532:
3524:
3506:
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3481:
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3321:
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3290:
3289:
3279:
3271:
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3249:
3248:
3211:
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3165:
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3134:
3125:
3114:
3108:
3102:
3096:
3087:
3081:
3070:
3064:
3063:
3055:
3049:
3048:
3028:
3022:
3007:Aswath Damodaran
3004:
2995:
2990:
2984:
2982:
2962:
2956:
2946:
2940:
2937:
2931:
2921:
2915:
2914:
2908:
2900:
2898:
2897:
2882:
2876:
2875:
2855:
2804:Patent valuation
2789:Intangible asset
2779:Fairness opinion
2719:
2712:
2708:
2705:
2699:
2668:
2660:
2637:
2630:
2626:
2623:
2617:
2586:
2578:
2555:restricted stock
2534:
2527:
2523:
2520:
2514:
2483:
2475:
2459:
2452:
2448:
2445:
2439:
2408:
2400:
2351:
2344:
2340:
2337:
2331:
2300:
2292:
2235:options on films
2182:natural resource
2077:
2070:
2066:
2063:
2057:
2026:
2018:
1969:
1962:
1958:
1955:
1949:
1918:
1910:
1894:
1887:
1883:
1880:
1874:
1843:
1835:
1801:enterprise value
1780:
1773:
1769:
1766:
1760:
1729:
1721:
1701:Aswath Damodaran
1635:systematic risks
1609:blue-chip stocks
1605:small cap stocks
1594:government bonds
1557:
1555:
1554:
1549:
1547:
1546:
1528:
1526:
1525:
1520:
1518:
1517:
1499:
1497:
1496:
1491:
1473:
1471:
1470:
1465:
1463:
1462:
1442:
1440:
1439:
1434:
1399:
1398:
1386:
1385:
1367:
1366:
1354:
1353:
1329:
1322:
1318:
1315:
1309:
1278:
1270:
1260:market anomalies
1183:
1176:
1172:
1169:
1163:
1132:
1124:
1064:
1057:
1053:
1050:
1044:
1013:
1005:
939:expected returns
918:
911:
907:
904:
898:
867:
859:
702:
695:
691:
688:
682:
651:
643:
612:
605:
601:
598:
592:
561:
553:
531:industry reports
509:
502:
498:
495:
489:
461:
460:
453:
399:
392:
388:
385:
379:
348:
340:
317:
310:
306:
303:
297:
266:
258:
221:over the counter
114:
107:
103:
100:
94:
92:
51:
27:
19:
3589:
3588:
3584:
3583:
3582:
3580:
3579:
3578:
3544:
3543:
3542:
3525:
3521:
3508:
3507:
3503:
3496:
3483:
3482:
3478:
3362:
3360:Further reading
3357:
3345:
3341:
3329:
3325:
3316:
3314:
3308:, Vol 61, No 1"
3301:
3300:
3296:
3287:
3285:
3277:
3273:
3272:
3268:
3256:
3252:
3213:
3212:
3208:
3203:Wayback Machine
3185:
3181:
3172:
3168:
3136:
3135:
3128:
3115:
3111:
3103:
3099:
3088:
3084:
3071:
3067:
3060:Journal of Risk
3057:
3056:
3052:
3030:
3029:
3025:
3005:
2998:
2991:
2987:
2979:
2964:
2963:
2959:
2947:
2943:
2938:
2934:
2922:
2918:
2901:
2895:
2893:
2884:
2883:
2879:
2872:
2857:
2856:
2852:
2848:
2843:
2738:
2720:
2709:
2703:
2700:
2685:
2669:
2658:
2638:
2627:
2621:
2618:
2603:
2587:
2576:
2574:Pre-IPO studies
2535:
2524:
2518:
2515:
2500:
2484:
2473:
2460:
2449:
2443:
2440:
2425:
2409:
2398:
2389:
2369:
2352:
2341:
2335:
2332:
2317:
2301:
2290:
2274:control premium
2262:levels of value
2251:
2116:
2088:
2078:
2067:
2061:
2058:
2043:
2027:
2016:
1996:private company
1980:
1970:
1959:
1953:
1950:
1935:
1919:
1908:
1895:
1884:
1878:
1875:
1860:
1844:
1833:
1781:
1770:
1764:
1761:
1746:
1730:
1719:
1699:, developed by
1574:build-up method
1570:
1568:Build-up method
1538:
1533:
1532:
1509:
1504:
1503:
1482:
1481:
1476:government bond
1454:
1449:
1448:
1390:
1377:
1358:
1345:
1340:
1339:
1330:
1319:
1313:
1310:
1295:
1279:
1268:
1220:
1196:Harry Markowitz
1184:
1173:
1167:
1164:
1149:
1133:
1122:
1077:cost of capital
1065:
1054:
1048:
1045:
1030:
1014:
1003:
956:cost of capital
919:
908:
902:
899:
884:
868:
857:
816:
810:
808:Income approach
798:
786:may also differ
746:
703:
692:
686:
683:
668:
652:
641:
613:
602:
596:
593:
578:
562:
551:
510:
499:
493:
490:
475:
462:
458:
451:
446:
400:
389:
383:
380:
365:
349:
338:
318:
307:
301:
298:
283:
267:
256:
243:
237:
212:
206:respectively.
204:business broker
200:investment bank
173:stock valuation
171:as compared to
115:
104:
98:
95:
52:
50:
40:
28:
17:
12:
11:
5:
3587:
3585:
3577:
3576:
3571:
3566:
3561:
3556:
3546:
3545:
3541:
3540:
3520:978-1119776796
3519:
3501:
3495:978-1118558768
3494:
3475:
3474:
3473:
3466:
3459:
3456:
3453:
3450:
3447:
3444:
3441:
3438:
3435:
3432:
3429:
3418:
3407:
3396:
3385:
3374:
3361:
3358:
3356:
3355:
3339:
3323:
3312:willamette.com
3294:
3266:
3250:
3237:10.1086/296288
3231:(2): 135–157.
3206:
3179:
3166:
3151:10.1086/260062
3145:(3): 637–654.
3126:
3109:
3097:
3082:
3065:
3050:
3039:(2): 306–317.
3023:
2996:
2985:
2977:
2957:
2941:
2932:
2916:
2877:
2870:
2849:
2847:
2844:
2842:
2841:
2836:
2831:
2826:
2821:
2816:
2811:
2806:
2801:
2796:
2791:
2786:
2781:
2776:
2771:
2766:
2761:
2760:
2759:
2753:
2745:
2739:
2737:
2734:
2729:rate of return
2722:
2721:
2672:
2670:
2663:
2657:
2654:
2640:
2639:
2590:
2588:
2581:
2575:
2572:
2537:
2536:
2487:
2485:
2478:
2472:
2471:Option pricing
2469:
2462:
2461:
2412:
2410:
2403:
2397:
2394:
2388:
2385:
2368:
2365:
2354:
2353:
2304:
2302:
2295:
2289:
2286:
2250:
2247:
2226:pharmaceutical
2150:bond valuation
2115:
2112:
2080:
2079:
2030:
2028:
2021:
2015:
2012:
2000:public company
1976:Main article:
1972:
1971:
1922:
1920:
1913:
1907:
1904:
1897:
1896:
1847:
1845:
1838:
1832:
1829:
1824:net book value
1783:
1782:
1733:
1731:
1724:
1718:
1715:
1689:
1688:
1687:
1686:
1671:
1670:
1664:
1629:
1628:
1601:
1586:
1583:risk-free rate
1569:
1566:
1545:
1541:
1516:
1512:
1489:
1461:
1457:
1432:
1429:
1426:
1423:
1420:
1417:
1414:
1411:
1408:
1405:
1402:
1397:
1393:
1389:
1384:
1380:
1376:
1373:
1370:
1365:
1361:
1357:
1352:
1348:
1332:
1331:
1282:
1280:
1273:
1267:
1264:
1256:
1255:
1252:
1247:
1242:
1238:Models of the
1219:
1216:
1204:William Sharpe
1186:
1185:
1136:
1134:
1127:
1121:
1118:
1085:cost of equity
1067:
1066:
1017:
1015:
1008:
1002:
999:
972:risk-free rate
968:
967:
963:
921:
920:
871:
869:
862:
856:
853:
809:
806:
797:
794:
765:
764:
761:
758:
745:
742:
741:
740:
736:
732:
724:
705:
704:
655:
653:
646:
640:
637:
625:ratio analysis
615:
614:
565:
563:
556:
550:
547:
512:
511:
472:of the subject
470:worldwide view
465:
463:
456:
450:
447:
445:
442:
429:
428:
425:
418:
417:
414:
411:
408:
402:
401:
352:
350:
343:
337:
334:
333:
332:
329:
326:
320:
319:
270:
268:
261:
255:
252:
236:
233:
211:
208:
126:economic value
117:
116:
31:
29:
22:
15:
13:
10:
9:
6:
4:
3:
2:
3586:
3575:
3572:
3570:
3567:
3565:
3562:
3560:
3557:
3555:
3552:
3551:
3549:
3536:
3530:
3522:
3516:
3512:
3505:
3502:
3497:
3491:
3487:
3480:
3477:
3471:
3467:
3464:
3460:
3457:
3454:
3451:
3448:
3445:
3442:
3439:
3436:
3433:
3430:
3427:
3426:0-471-11213-5
3423:
3419:
3416:
3415:0-88800-614-4
3412:
3408:
3405:
3401:
3397:
3394:
3393:0-585-13223-2
3390:
3386:
3383:
3382:0-7623-1270-X
3379:
3375:
3372:
3371:1-58488-348-0
3368:
3364:
3363:
3359:
3353:
3349:
3343:
3340:
3337:
3333:
3327:
3324:
3313:
3309:
3307:
3298:
3295:
3283:
3276:
3270:
3267:
3264:
3260:
3254:
3251:
3246:
3242:
3238:
3234:
3230:
3226:
3225:
3220:
3216:
3210:
3207:
3204:
3200:
3197:
3193:
3189:
3183:
3180:
3176:
3170:
3167:
3164:
3160:
3156:
3152:
3148:
3144:
3140:
3133:
3131:
3127:
3123:
3119:
3113:
3110:
3107:
3101:
3098:
3095:
3091:
3086:
3083:
3079:
3075:
3069:
3066:
3061:
3054:
3051:
3046:
3042:
3038:
3034:
3027:
3024:
3020:
3016:
3012:
3008:
3003:
3001:
2997:
2994:
2989:
2986:
2980:
2978:0-07-135615-0
2974:
2970:
2969:
2961:
2958:
2955:
2951:
2945:
2942:
2936:
2933:
2930:
2926:
2920:
2917:
2912:
2906:
2892:
2888:
2881:
2878:
2873:
2867:
2863:
2862:
2854:
2851:
2845:
2840:
2837:
2835:
2832:
2830:
2827:
2825:
2822:
2820:
2817:
2815:
2812:
2810:
2807:
2805:
2802:
2800:
2797:
2795:
2792:
2790:
2787:
2785:
2782:
2780:
2777:
2775:
2772:
2770:
2767:
2765:
2762:
2757:
2754:
2752:
2749:
2748:
2746:
2744:
2741:
2740:
2735:
2733:
2730:
2718:
2715:
2707:
2697:
2693:
2689:
2683:
2682:
2678:
2673:This section
2671:
2667:
2662:
2661:
2655:
2653:
2649:
2647:
2636:
2633:
2625:
2615:
2611:
2607:
2601:
2600:
2596:
2591:This section
2589:
2585:
2580:
2579:
2573:
2571:
2569:
2564:
2560:
2556:
2552:
2548:
2544:
2533:
2530:
2522:
2512:
2508:
2504:
2498:
2497:
2493:
2488:This section
2486:
2482:
2477:
2476:
2470:
2468:
2458:
2455:
2447:
2437:
2433:
2429:
2423:
2422:
2418:
2413:This section
2411:
2407:
2402:
2401:
2395:
2393:
2386:
2384:
2380:
2376:
2372:
2366:
2364:
2362:
2350:
2347:
2339:
2329:
2325:
2321:
2315:
2314:
2310:
2305:This section
2303:
2299:
2294:
2293:
2287:
2285:
2281:
2277:
2275:
2269:
2265:
2263:
2258:
2256:
2248:
2246:
2244:
2240:
2236:
2232:
2231:present value
2227:
2223:
2219:
2215:
2210:
2208:
2204:
2200:
2199:resource firm
2196:
2192:
2188:
2183:
2178:
2176:
2170:
2168:
2163:
2162:out the money
2159:
2156:) and not to
2155:
2151:
2147:
2143:
2142:Black–Scholes
2139:
2135:
2130:
2128:
2124:
2120:
2113:
2111:
2107:
2105:
2101:
2097:
2093:
2087:
2076:
2073:
2065:
2055:
2051:
2047:
2041:
2040:
2036:
2031:This section
2029:
2025:
2020:
2019:
2013:
2011:
2007:
2005:
2001:
1997:
1992:
1990:
1986:
1979:
1968:
1965:
1957:
1947:
1943:
1939:
1933:
1932:
1928:
1923:This section
1921:
1917:
1912:
1911:
1905:
1903:
1893:
1890:
1882:
1872:
1868:
1864:
1858:
1857:
1853:
1848:This section
1846:
1842:
1837:
1836:
1830:
1828:
1825:
1820:
1816:
1814:
1810:
1806:
1802:
1798:
1794:
1790:
1779:
1776:
1768:
1758:
1754:
1750:
1744:
1743:
1739:
1734:This section
1732:
1728:
1723:
1722:
1716:
1714:
1712:
1708:
1704:
1702:
1698:
1693:
1684:
1683:
1681:
1680:
1679:
1677:
1668:
1665:
1661:
1657:
1653:
1652:
1651:
1648:
1643:
1641:
1637:
1636:
1626:
1622:
1619:'s (formerly
1618:
1614:
1610:
1606:
1602:
1599:
1595:
1591:
1587:
1584:
1580:
1579:
1578:
1575:
1567:
1565:
1562:
1559:
1543:
1539:
1530:
1514:
1510:
1501:
1487:
1479:
1477:
1459:
1455:
1446:
1443:
1430:
1427:
1424:
1421:
1418:
1415:
1412:
1409:
1406:
1403:
1395:
1391:
1387:
1382:
1378:
1371:
1368:
1363:
1359:
1355:
1350:
1346:
1337:
1328:
1325:
1317:
1307:
1303:
1299:
1293:
1292:
1288:
1283:This section
1281:
1277:
1272:
1271:
1265:
1263:
1261:
1253:
1251:
1248:
1246:
1243:
1241:
1237:
1236:
1235:
1233:
1229:
1225:
1217:
1215:
1211:
1209:
1205:
1201:
1197:
1193:
1182:
1179:
1171:
1161:
1157:
1153:
1147:
1146:
1142:
1137:This section
1135:
1131:
1126:
1125:
1119:
1117:
1114:
1112:
1108:
1103:
1101:
1097:
1092:
1090:
1089:interest rate
1086:
1082:
1078:
1074:
1063:
1060:
1052:
1042:
1038:
1034:
1028:
1027:
1023:
1018:This section
1016:
1012:
1007:
1006:
1000:
998:
996:
990:
988:
983:
980:
977:
973:
964:
961:
957:
953:
949:
948:
947:
944:
940:
936:
935:present value
932:
928:
927:discount rate
917:
914:
906:
896:
892:
888:
882:
881:
877:
872:This section
870:
866:
861:
860:
854:
852:
848:
846:
841:
837:
833:
828:
826:
825:present value
822:
815:
807:
805:
803:
795:
793:
789:
787:
783:
779:
775:
771:
762:
759:
756:
752:
751:
750:
743:
737:
733:
729:
725:
722:
717:
713:
712:
711:
701:
698:
690:
680:
676:
672:
666:
665:
661:
656:This section
654:
650:
645:
644:
638:
636:
633:
630:
626:
622:
611:
608:
600:
590:
586:
582:
576:
575:
571:
566:This section
564:
560:
555:
554:
548:
546:
544:
540:
536:
532:
528:
524:
520:
508:
505:
497:
487:
483:
479:
473:
471:
464:
455:
454:
448:
443:
441:
437:
433:
426:
423:
422:
421:
415:
412:
409:
406:
405:
398:
395:
387:
377:
373:
369:
363:
362:
358:
353:This section
351:
347:
342:
341:
335:
330:
327:
324:
323:
316:
313:
305:
295:
291:
287:
281:
280:
276:
271:This section
269:
265:
260:
259:
253:
251:
247:
242:
234:
232:
228:
226:
222:
218:
209:
207:
205:
201:
197:
193:
188:
186:
185:going concern
182:
178:
177:share trading
174:
170:
165:
163:
159:
155:
151:
147:
143:
142:CBV Institute
138:
135:
131:
127:
123:
113:
110:
102:
91:
88:
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36:verification
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3215:Brennan, J.
2361:U.S. entity
2218:bio-science
2195:call option
2134:call option
1617:Morningstar
1200:James Tobin
225:pink sheets
169:perspective
3548:Categories
3317:2019-10-18
3306:Tax Lawyer
3288:2019-10-18
2896:2020-07-13
2846:References
2764:Divestment
2222:technology
2096:comparison
2094:entails a
1815:industry.
1795:, such as
1697:total beta
1676:total beta
987:net income
832:cash flows
519:Beige Book
494:March 2011
239:See also:
69:newspapers
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3159:154552078
2809:P/E ratio
2774:EV/EBITDA
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482:talk page
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3199:Archived
3092:(2009).
2905:cite web
2736:See also
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2104:multiple
1797:goodwill
1621:Ibbotson
1240:Q theory
1232:multiple
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476:You may
444:Elements
130:business
3472:, 2021
3465:, 2013
3282:irs.gov
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