The Value of Private Businesses in the United States (original) (raw)

Abstract

The vast majority of businesses in the United States are privately held, and approximately 99 percent meet a common government definition of “small.” However, we know surprisingly little about the market values of these organizations. In this paper, we estimate the market value of privately held firms in the United States from sources on earnings, assets, and reported market value of multiple forms of business entities, including corporations, partnerships, LLCs, and sole proprietorships. We discuss various theoretical and practical methods of valuing assets, including those arising from economics, neoclassical finance, portfolio theory, and tradition. Concluding that most of them are not appropriate for valuing private firms, we use insights from dynamic programming and ratio analyses from traditional technique to produce a new estimate based on reported taxable earnings, net worth, and tax filing status. Using this approach, we estimate that privately held U.S. firms had earnings that exceeded those of publicly held firms in two recent years by a significant margin. Moreover, the market value of these firms exceeded that of publicly traded firms. We also conclude that policymakers, perhaps grossly, underestimate the true scale of “small” and privately held firms in the economy.

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Notes

  1. S corporations are limited to 100 shareholders, which must be natural persons, estates, certain trusts, and certain exempt organizations. Shareholders must also be citizens or residents of the United States. There may only be one class of stock. This places both a practical and a legal obstacle to public ownership. See, for example, Commerce Clearing House [1996, Sec. 305].
  2. REITs file 1120-REIT; regulated investment companies file 1120-RIC income tax forms. Both of these entities must meet requirements to distribute the majority of their income, or an income tax is imposed on them similar to that of other corporations.
  3. The IRS describes a PTP as follows: “A publicly traded partnership is any partnership an interest in which is regularly traded on an established securities market regardless of the number of its partners. This does not include a publicly traded partnership treated as a corporation under Section 7704 of the Internal Revenue Code.” See IRS website at: http://www.irs.gov. See also the National Association of Publicly Traded Partnerships website, which lists entities in most states, at: http://www.naptp.org.
  4. Citing the SBA Office of Advocacy, it states, “Even obtaining the number of firms can be daunting” [Small Business Administration 2006, p. 8]. Given this caution, the SBA's estimates, based on Census Bureau and other data, should be assumed to involve a significant margin of error.
  5. The Forbes research staff estimated the revenue for some firms, and used company-provided estimates for others. The minimum worldwide revenue figure for the “list” was $1 billion. Nonprofits, foreign firms, mutual companies, auto dealership management, and real estate investment firms were excluded.
  6. The Dow Jones Wilshire 5000 index attempts to include all publicly traded companies in the United States. Although the number of included firms varies, it has included in recent years approximately 6,000 to 7,000 U.S. firms for which an identifiable equity security is traded. This may be an overestimate of the number of individual, nonfarm, nonfinancial firms with primary operations in the United States. The implied ratio of approximately one publicly traded firm per every 1,000 active businesses is corroborated by IRS and SBA data.
  7. The term “pink sheets” comes from the historical oddity of the pink-colored paper used to record trades decades ago. A company named Pink OTC Markets now serves as a market maker for some OTC traded securities. The National Association of Securities Dealers also offers an electronic trading service called the Over-the-Counter Bulletin Board, or OTCBB.
  8. Technically, many of these are not partners, but members in an LLC, shareholders in an S corp or C corp, or some combination (such as an LLC that is a partner in another firm).
  9. We note that the same legal compulsions to file tax returns also create incentives to report in the manner that minimizes tax liability. We also note that, as several recent scandals have confirmed, publicly traded firms feel pressured to announce good results, even when actual financial results are different. We should be mindful of both these incentives when using these data.
  10. There are, of course, statistics on farm workers, farms, various types of financial organizations, and nonprofits. However, the use of “nonfarm” employment in the standard labor market statistics, “nonfinancial corporate profits” in the National Income and Product Accounts, and “nonfarm nonfinancial” companies in the Flow of Funds statistics, all date back at least a half century. The common exclusion of nonprofits and GSEs from business statistics is easily explainable by the fact that these entities were relatively small shares of the economy until recently. However, the proliferation on tax-exempt entities under Section 501c of the Internal Revenue Code and the increasing importance of GSEs such as Fannie Mae and Freddy Mac may lead to reconsideration of whether they are businesses.
  11. This is, given the integration of the world economy and the tax incentives that affect both investors and companies, a difficult task. The Flow of Funds data are adjusted to separate out net foreign investment. In the private firm value estimate we derive from tax data below, we implicitly adopt the assumption that the foreign ownership of U.S. firms is roughly canceled out by U.S. investor's ownership of foreign operations. The error introduced by this assumption is probably of small magnitude when compared to the overall level of precision possible, given the aggregate data we are using.
  12. As of the revision date of this paper, the 2007 SCF raw data were still being tabulated.
  13. Note that the data in Table 3 are disaggregated between direct and indirect stock ownership.
  14. This tendency has been demonstrated for over two decades [Avery, Elliehausen, and Kennickell 1988]. In addition, consumers may easily underreport the value of their business investments for at least two reasons: first, they may recall the original investment amounts (especially in retirement and long-term savings accounts) and neglect recent increases in value; this was probably the case for many consumers during the time when the stock market was trending upwards. Second, they, like professionals, have difficulty estimating the value of private-firm investment, and therefore are probably inclined to use a lower estimate, possibly based on their initial investment or some other past event.
  15. Avery, Elliehausen, and Kennickell [1988] compared the implied estimates of household ownership of business equity between the Flow of Funds and the Survey of Consumer Finance, noting the following:“In principle, the FOF measure of corporate equities includes all corporate equities. However, in practice, only publicly traded equities are captured in the data used to construct this figure. Almost all holdings of small, closely-held corporations, except those allocated to other categories such as real estate, are missed” [p. 351]
  16. The seminal reference for this definition is the IRS Revenue Ruling 59–60 [U.S. Internal Revenue Service 1959], which is excerpted in most of the business valuation texts cited in this paper.
  17. Of course, the bid-ask spread, the transaction costs (such as commissions), and other factors create a small zone of uncertainty for even very large publicly traded stocks.
  18. As discussed above, the lack of an active market does not mean there are no transactions, or that no market exists.
  19. Two obvious examples follow: First, a partner in professional service firm may need to sell his or her interest in order to retire. Second, a prospective partner may be compelled by the membership agreement to buy an interest, in order to secure employment.
  20. Often, a small number of prospective buyers (often one) is granted the right to perform “due diligence” once a confidentiality agreement is signed with the seller. This is an explicit cost to potential purchasers. Such expense is implicitly borne by stockholders of publicly traded companies through the costs of producing annual reports, filing disclosures with the Securities and Exchange Commission, and having outside auditors.
  21. One complication that affects the price is the “control premium” embedded in prices of equity interests large enough to carry management control as well as title to earnings. In addition, large-share transactions often involve other considerations (such as real-estate encumbrances, implied pension benefits, implied salaries and benefits, or personal guarantees), thus rendering the actual equity interest price less apparent.
  22. The measures of income, the method of projecting them into the future, and the origin and application of the discount rate all vary under this approach.
  23. We distinguish this approach by the primary reliance on asset records, which in accounting are based on historical costs. Normally, substantial adjustments are necessary to make these consistent with market value. This necessity is a frequent and valid criticism of this approach.
  24. Or course, if we were considering the value of specific private firms, we may have powerful market evidence—or none at all.
  25. Indeed, even the IRS has abandoned the “excess earnings” method, which is a common variant of this approach, when any other method is available [Anderson 2005].
  26. The empirical evidence for a discount for lack of marketability is largely based on studies of restricted stock, which isolates that factor. Such studies are summarized in references such as Gaughan [2002, p. 573]. However, private firm equity often brings with it benefits that similar dollar investments in publicly traded firms do not. Among these: enhanced ability to control management; ability to use the good offices or other assets of the firm for convenience, status, or other benefits; flexibility; avoidance of the burdens of publicly traded company; avoidance of public scrutiny; and ability to largely ignore analyst opinions, market sentiment, and other annoyances that are part of the environment for the management of publicly traded firms.
  27. Given the data published by the IRS, we could not precisely decompose the data into C corps, S corps, and other corporate filers (such as REITs) by size. Nonetheless, the clear implication is that a very large share of C corps was reporting negative taxable earnings in that year.
  28. The method is described in the Appendix, along with the notion of “real options.”
  29. This occurs because of scale; access to capital markets; value of assets like brands, distribution networks, and supplier networks; and the breadth of investors. Such benefits motivate firms to become “listed” companies on a major exchange.
  30. This occurs for at least two reasons: one is the existence of “real options” that cannot be valued using traditional discounted cash flow analysis; the second is the valuation decision of the investor, which is encapsulated in a value functional equation described below.
  31. In terms of the dynamic programming method, the “value functional equation” sets the current market value to the maximization, across the set of actions available to the investor and management, of the expected discounted sum of future earnings and capital gains. This is not a simple linear transformation of current earnings. For a distressed firm, this must include some expected gain in the future or else the investor would liquidate his or her holdings.
  32. Jacques Drèze, one of the most influential microeconomists of the 20th century, put this memorably: “The firm fits into general equilibrium theory as a balloon fits into an envelope: flattened out! Try with a blown-up balloon: the envelope may tear, or fly away: at best, it will be hard to seal and impossible to mail. Instead, burst the balloon flat, and everything becomes easy. Similarly with the firm and general equilibrium—though the analogy requires a word of explanation” [Drèze 1985, p. 1].
  33. Of the many authors that have written (with widely varying skill) on these topics, we would single out Michael E. Porter for strategy [Porter 1980]; John Kay with comparative advantage in relevant markets [Kay 1993]; John W. Deming with quality; and Tom Peters and Robert Waterman [1982] on entrepreneurship, culture, and management motivation.
  34. There is a formal folk theorem in game theory, which involves the potential for players to punish a player that deviates from a certain equilibrium in a multi-player game. As these parties have the ability to punish a business (for example, by refusing to lend to it, or by patronizing a competitor) when that business fails to comport with accepted practices, there is something of a business value folk theorem at work.
  35. “Prices” in this school are often described in terms of risk premium and “risks” in terms of volatility and covariance. Ross [2005, Ch. 1] lists specifically the Arbitrage Pricing Theory (APT), the Capital Asset Pricing Model (CAPM), and the Consumption Beta Model (CBM).
  36. It is interesting to note that most contemporary summaries of the “Roll critique” include as other assets human capital, real estate, artwork, commodities—and often neglect to mention private firm equity.
  37. Anderson [2005] offers a critique of naïve use of the CAPM in setting discount rates for investors in private firms. This ubiquity of the CAPM in contemporary valuation texts (including those identified earlier in this article) testify to its continuing use (or misuse) in applied work involving private firms.
  38. The key mathematical innovations included an application of the Reisz representation theorem from functional analysis, which tied together the NA assumption with the existence of a positive linear pricing operator [Ross 1973] and its later development by Harrison and Kreps [1979]. The seminal paper on option pricing, which relies on the no-arbitrage assumption, as well as other strong assumptions, was Black and Scholes [1973]. Dybig and Ross [1987] are responsible for much of the nomenclature, including the “Fundamental Theorem of Finance.” A contemporary explication of this school of thought, and defense against the critique of “behavioral finance,” is Ross [2005]. Standard references to mathematical finance include Duffie [2001] and Shreve [2004].
  39. One formulation of the Fundamental Theorem of Asset Pricing is: a market is arbitrage-free if and only if there exists an equivalent martingale measure; and a market is complete if and only if there exists a unique equivalent martingale measure.
  40. Real option valuation (or “contingent claims”) is based on the insight of Black and Scholes [1973] in their original work on the value of a financial option, where they recognize that corporate equity can be viewed as an option. However, unlike financial options, the underlying asset is “real,” and therefore the owner of the claim has a “real option.” See Schwartz and Trigeorgis [2001] for a survey of the literature; Damodoran [2002] for application to valuation of private firms; and Dixit and Pindyck [1994] for the seminal work establishing that the existence of real options means the value of a firm is not simply the expected net present value of its future earnings.

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Acknowledgements

I wish to thank Keith Pinkerton, Ilhan Geckil, and two anonymous referees for their comments on an earlier manuscript; and Justin Eli and Darci Keyes for their research into tax filing data on U.S. firms.

Authors

  1. Patrick L Anderson
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Additional information

*Patrick Anderson founded Anderson Economic Group in 1996, and serves as a Principal and Chief Executive Officer of the economic consulting firm. In this role he has successfully directed projects for state governments, cities, counties, nonprofit organizations, and corporations throughout the United States. Anderson is a recognized authority on business valuation and commercial damages and has provided expert testimony and consulting advice to major private and public sector organizations. Before founding Anderson Economic Group, he served as the Chief of Staff of the Michigan Department of State and as Deputy Budget Director for the State of Michigan under Governor John Engler. He was awarded NABE's Edmund Mennis Award for the best contributed paper in 2004. Anderson holds a Master's degree in Public Policy and a Bachelor's degree in Political Science from the University of Michigan. He is a member of NABE and the National Association of Forensic Economists.

Appendix

Appendix

Theories of Value and Methods of Valuation

Value in classical economics

The economic study of value can be traced at least as far back as the “labor theory of value” that originated with Adam Smith, and was developed by David Ricardo, Karl Marx, and many others. In Smith's famous example of the beaver and the deer, the relative labor inputs required for a commodity largely determine its relative worth:

If among a nation of hunters, for example, it usually costs twice the labour to kill a beaver which it does to kill a deer, one beaver should naturally exchange for or be worth two deer. It is natural that what is usually the produce of two days or two hours labour, should be worth double of what is usually the produce of one day's or one hour's labour. [Smith 1776, Book I]

Value of a firm in neoclassical economics

The neoclassical economics that emerged a century after Adam Smith brought with it a primitive understanding of the firm. Indeed, one might argue that in the neoclassical world of perfect competition the firm is almost completely abstracted away.Footnote 34

The very rationale of a firm has received only recent attention in economics. It was Ronald Coase [1937] that introduced the “transactions cost” theory: that companies were organized because it was too costly for individuals to contract for others to perform all the tasks that could be done by a company. This argument explains why firms are organized, but the value implication is unclear. In particular, inefficient companies can be worth more than efficient companies, particularly if they have a license, monopoly, or intellectual property right that enables them to capture above-average earnings.

Business value and success strategies: A folk theorem

One might assemble a popular theory of business value from the wide collection of attributes to which business success has been attributed. Although economists since Adam Smith have pointed to comparative advantage or entrepreneurial spirits, contemporary authors have been far less timid. The list of “success” attributes in the business literature includes strategy, innovation, “culture,” marketing, branding, “leadership,” and quality systems.Footnote 35 Without delving too far into this fulsome debate, it is clear that the organization of the firm, its management, and its existing tangible and intangible assets are critical underpinnings of the ability of the firm to earn profits in the future. We might also observe that—at least as indicated by sales of business books—a large number of bankers, employees, managers, and customers of businesses think that these success attributes are important to business success. Given the likelihood that some of these influential people act in a manner consistent with these thoughts, we conjecture that business value is partially dependent on congruence with accepted business success strategies. We call this a “business value folk theorem.”Footnote 36

Modern portfolio theory

A revolution in finance began in the middle of the 20th century with the establishment by Harry Markowitz of the mean-variance framework for explaining investors’ asset purchase preferences. This, along with the insight about borrowing due to James Tobin, led to the CAPM of William Sharpe and John Lintner.Footnote 37 These innovations became the basis for modern portfolio theory (MPT), which was based on the insight that the relationship between risk and the prices investors would pay for an asset relied on observations about the portfolio, not just the particular asset itself.Footnote 38

Probably the most celebrated of the tools of MPT is the CAPM, which assumes a linear relationship between expected returns and the returns on the “wealth portfolio” of all available investments, sometimes called the market portfolio. The CAPM has been extensively tested with mixed results, almost always with the wealth portfolio proxied by the stock market [Cochrane 2001, Section 9.1]. However, Richard Roll [1977] noted that the actual wealth portfolio includes investments other than publicly traded stocks, and therefore empirical tests of the CAPM using the stock market as the “wealth portfolio” were actually joint tests of the definition of the market as a whole and the CAPM model.Footnote 39 This “Roll critique” had a strong effect on theoretical understanding of the limits of the CAPM, but an apparently limited effect on the practical use of the CAPM in valuation work.Footnote 40

Risk-neutral pricing and complete markets

The mathematics of what is now called “risk neutral pricing” are based on the powerful insight that participants in exchange markets will not allow others to make riskless profits (an “arbitrage”) through trades among different securities.Footnote 41 The “no arbitrage” assumption has become ubiquitous enough to earn its own acronym (“NA”) in finance texts, and a vast “neoclassical finance” literature has developed around it. However, the standard findings of neoclassical finance are often based on very specific assumptions about assets, including: little (or no) transaction costs, traded assets available to a wide class of investors, ability to borrow at the risk-free rate, and risks that were incorporated directly or “spanned” by available assets. In general, only under such restrictive assumptions do the intricate mathematics of risk-neutral pricing (such as the existence of an “equivalent martingale measure”) and the implications of the “First Fundamental Theorem of Finance” apply.Footnote 42

In particular, they do not apply in “incomplete markets.” High transaction costs, lack of instruments that price in all risks (“spanning” the market), and the lack of trading all make markets incomplete. Clearly, many owners of equity interests in privately held firms often face risks (such as the risks inherent in the entrepreneur's role in the firm) that are not spanned in the market.

Real options and dynamic programming

We should also consider two newer methods: real options and dynamic programming. Real options analysis is especially useful for assets that may have some value at some time in the future, and whose value is contingent on some type of event.Footnote 43 Examples include patents, some real estate, and intellectual property. However, real option valuation techniques are much less useful when dealing with an aggregate of operating firms.

Dynamic programming is based on the insight of the mathematician Richard Bellman in his brilliant original work on multi-period optimization problems [Bellman 1957; Stokey and Lucas 1989]. Bellman considered the task of an individual who seeks to maximize the benefits from some activity over time, when the policy choices made during one period affect the ability to enjoy benefits in the future. The classic economic explication of this is known as the “cake eating problem,” in which a person chooses to eat a certain amount from a fixed-size cake each day, knowing that it reduces the size of the cake for tomorrow. A cake-eater is tempted to adopt the policy of gobbling the entire dessert the first day, thus leaving no cake for tomorrow. However, the enjoyment of eating the third piece of cake is smaller than that for the first, so most eaters delay a portion of the gratification from eating cake until the next day. The “Bellman equation,” which is technically a value functional equation, encapsulates the desire to maximize benefits over time, and the tension between enjoying current benefits and postponing them to enjoy greater benefits tomorrow.

The application of the technique to private firm valuation was recently described by Anderson [2004].Footnote 44 If we consider the management decisions of an entrepreneur as the “policy,” and the distribution of earnings or capital from the firm as “eating the cake,” then the Bellman equation captures exactly the imperative that entrepreneurs are presumed to follow. There are serious difficulties in applying this technique in practical situations, though significant progress has been made in recent years.

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Anderson, P. The Value of Private Businesses in the United States.Bus Econ 44, 87–108 (2009). https://doi.org/10.1057/be.2009.4

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