The Economics of Business Valuation
Towards a Value Functional Approach
Patrick L. Anderson

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The Economics of Business Valuation: Towards a Value Functional Approach

Author(s): Patrick L. Anderson

book abstract

For decades, the traditional approaches to business valuation (market, asset, and income) have taken center stage in the assessment of the firm. This book presents an expanded valuation toolkit, consisting of nine well-defined valuation principles hailing from the fields of economics, finance, accounting, taxation, and management. It ultimately argues that the "value functional" approach to business valuation avoids most of the shortcomings of its competitors, and more correctly matches the actual motivations and information held by stakeholders. To remedy the shortcomings of existing theory, the author proposes a new definition of the firm that is consistent with the principle that entrepreneurs maximize value, not profit.

1 Modern Value Quandaries
chapter abstract

The author traces the importance of the business, company, or firm in Economics, society, and world history over two millennia. The author notes that, given its importance and centrality in modern economies, there should be a well-developed theory of the firm that pervades both Economics and Finance. However, a series of "quandaries" are posed that illustrate that this is not the case. These include the fact that neoclassical economics essentially ignores the firm, that mainstream Economics largely ignores the entrepreneur, and that real entrepreneurs do not maximize profits. Furthermore, much of Finance focuses on publicly-traded firms, while 99% of firms are privately held, and mathematical finance often assumes complete markets, which are a rarity in the actual world. These provocative statements motivate much of the theory and applications developed in the rest of the book.

2 Methods and Theories of Value
chapter abstract

This chapter reviews the common definition of "market value" in Economics, and the practical use of the term in tax, accounting, and other fields. It then introduces ten different valuation theories. Among these are three different valuation principles derived from the Economics literature, three traditional methods of valuation, three from Mathematical Finance, and one novel principle that emerges from both Economics and Control Theory. Each of these is based on principles distinct from each other, in the sense that each fundamentally derives "value" from a different source.

3 The Failure of the Neoclassical Investment Rule
chapter abstract

This chapter presents telling evidence that the value of a firm is not the net present value of its expected profits. This is a provocative statement, and deserves careful support: the notion that the value of investments in firms is the expected net present value of their earnings is a pillar of Finance. The author summarizes the intellectual history of this notion, and then presents six major failings of the "NPV rule," in particular, that decision-makers often don't follow this rule.

4 The Nature of the Firm
chapter abstract

This chapter presents three competing definitions of the firm, including a common definition of any organization that has a profit motive, a modern neoclassical definition of a transaction institution whose incentives differ from those of its owners, and a new three-part definition. The elements of the new definition of the firm include an organization with a profit motive for its investors, a separate identity, and replicable business practices.

5 The Organization and Scale of Private Business
chapter abstract

This chapter presents the available information on the number of businesses in the United States, and the number by size class, the share that fulfill a common definition of "small" business, and the data on survivorship rates for newly-established businesses in multiple countries. It critically examines the stylized facts about such businesses in the United States. Finally, it provides updated data on the value of privately-held businesses in the U.S., following the methodology of Anderson (2009). Those data suggest that equity in privately held firms form a larger share of household assets than stocks in publicly-traded firms among U.S. households.

6 Accounting for the Firm
chapter abstract

This chapter focuses on the history, proper role, and limitations of accounting. It covers the vital role of accounting in business, why accounting is not the same as valuation, management, or finance, the history of accounting, and principles of accounting, starting with the most important one: ethics, as well as the historical cost principle.

7 Value in Classical Economics
chapter abstract

The author begins a review of 10 different theories of value with this chapter on classical economic thought. The labor theory of value dates as least as far back as Adam Smith and the 18th century, and may have independently been articulated by the Indian sage Kautilya in the 3rd century BC. The author observes that the labor theory fails to explain the actual determination of prices in a market economy, but still provides valuable insight into human behavior in the modern economy.

8 Value in Neoclassical Economics
chapter abstract

The neoclassical model is familiar to generations of college students. This chapter reviews the emergence of the neoclassical or "marginalist" school of economics in the late 19th century, and its formal elements and basic mathematics. It notes elements of the theory that are not settled: utility, risk aversion, and time preference, and discusses the critique of the "behaviorist." The author then tests the neoclassical model as a practical valuation tool for a business, applying it to three actual businesses. This analysis shows the neoclassical model is not a practical valuation tool.

9 Modern Recursive Equilibrium and the Basic Pricing Equation
chapter abstract

The author introduces the "recursive" model that has emerged within micro-economics over the past few decades. This modern recursive equilibrium model is contrasted with the neoclassical model, in terms of the optimization and time periods involved. The modern, multi-period consumer savings problem is introduced, as well as the "cake eating" problem and basic pricing equation. The author argues these form the basis of a modern microeconomic theory, and that the stochastic discount factor that emerges from the basic pricing equation provides a valuable insight that is lacking in the neoclassical and classical worlds. As with other valuation principles, the author tests the principle as a practical valuation tool for three actual businesses, demonstrating that is provides an incomplete basis for valuation of private firms.

10 Arbitrage-Free Pricing in Complete Markets
chapter abstract

The author describes one of the breakthrough concepts of modern finance: the use of the no arbitrage principle in complete markets as the basis for the powerful mathematics of "risk neutral" or "equivalent martingale" pricing. This neoclassical finance model relies on two intertwined assumptions: the existence of complete markets, and the assumption that market participants will act to ensure that no arbitrage profits are possible. The author then presents strong evidence that both of these assumptions are lacking for private businesses and their investors, because markets for the equity in these firms are incomplete. The author argues that this severely undermines this model as a practical valuation tool. As with other principles, this assertion is tested by applying it to three actual companies.

11 Portfolio Pricing Methods
chapter abstract

The idea of business investments assembled as part of an investment portfolio is a powerful one with ramifications that extend to the pricing of individual investments. The author describes the mean-variance framework, as outlined by Harvey Markowitz in the 1950s, as establishing the basis for an entire class of Modern Portfolio Theory models. The author then outlines the relationship between portfolio models and the Basic Pricing Equation, the most familiar of the portfolio models, the Capital Asset Pricing Model, including a recursive derivation of the CAPM that is somewhat closer to actual household behavior than the typical presentation, and the Roll critique of CAPM and similar models, and extends that critique noting that equity in 99% of firms do not fit into portfolio models. Portfolio models are then tested to see if they provide a practical basis for valuing three actual firms.

12 Real Options and Expanded Net Present Value
chapter abstract

This chapter demonstrates the importance of management flexibility regarding the timing, scale, and type of investments, which is the basis for the study of "real options." The chapter describes an opportunity and its contractual equivalent, an option, the history of option contracts, the classic Black-Scholes-Merton option model of the firm, and the formula for pricing, under ideal conditions, a pure financial call option. From this basis, the author draws the conclusion that the existence of an option premium alone renders invalid the Net Present Value rule for the value of the firm. The author then describes techniques for valuing "real options," including extensions of financial options methods, Decision Tree Analysis, Monte Carlo, stochastic control, and value functional models, and "good deal" bounds. Finally it describes a recently-proposed synthesis of traditional income methods and real options analysis, which the author calls "expanded net present value" or XNPV.

13 Traditional Valuation Methods
chapter abstract

This chapter describes the three traditional methods of valuing a business: the market approach, asset approach and income approach. For each, he describes a valuation principle and an underlying mathematical equation. The author describes the income or "discounted cash flow" approach is a workhorse of practical valuation. He observes the heavy reliance on subjective adjustments in actual use of this approach, which he argues supports the critique of the net present value rule and the weakness of this and other approaches in which subjective judgment, rather than actual use of a method, is the dominant factor. Finally, two of these traditional approaches are used to value three example firms, with the weaknesses in certain methods and the dominance of subjective adjustments made apparent.

14 Practical Application of the Income Method
chapter abstract

The author focuses in this chapter on the workhorse income approach to valuation. Based on his extensive practical experience, he discusses the essential steps of forecasting future business revenue, identifying income arising from that revenue, and discounting that future income for time and risk. The author argues that, while each of these tasks are important, forecasting business revenue is often the most important.

15 The Value Functional: Theory
chapter abstract

This chapter presents the theory behind the novel value functional method. This includes the importance of the definition of the firm introduced in this book, which includes separation, replicable business practices, and an objective of the firm that is not restricted to profit maximization, the maximization of value, rather than profit, a whirlwind introduction to control theory, and the distinction between the familiar concept of a function and the obscure notion of a functional. The author then presents a functional equation (or Bellman equation) that relates the value of a firm to specific optimization by the manager or entrepreneur. This theory is the basis for the tenth approach to valuation described in this book: the "recursive" or "value functional" approach. The author concludes by proposing conditions for the existence of a solution to the value functional equation for actual firms, basing these in human transversality conditions that he outlines.

16 The Value Functional: Applications
chapter abstract

This chapter demonstrates practical uses of the value functional approach in the estimation of the value of operating businesses. It includes a detailed discussion of state and control variables, a presentation of four different ways to formulate and solve a value functional problem, including dynamic programming (also called "stochastic control"), Markov Decision Problem ("MDP"), Hamilton-Jacobi-Bellman ("HJB") method, and "by hand." The author also presents computational designs for these methods, and observations on the practical difficulties of using them. Finally, the author demonstrates the use of this approach on three actual companies. This allows the reader to see the difference in results (and of the necessity for subjective adjustments) among the value functional and other valuation methods described in this book.

17 Applications: Finance &Valuation
chapter abstract

The author argues that start-up firms, distressed firms, and near-bankrupt firms are the exception, not the rule, in the modern economy. This raises the question of whether such firms, which are commonly small and financed largely by the entrepreneurs involved, have value. The chapter also discusses the applicability of traditional valuation methods for such firms, compared with the novel value functional or recursive method. The author concludes that, when properly evaluated, start-ups and distressed firms do have value.

18 Applications: Law & Economics
chapter abstract

This chapter demonstrates applications of the value functional or recursive approach to topics in law and economics, including the effects of government policy on business decisions, and the estimation of economic damages incurred due to breaches of contracts. The effect of uncertainty in future government policies on private sector hiring decisions is one topic for which the value functional method provides an insight that is lacking in the standard neoclassical model. The author presents a model in which managers maximize value, rather than maximize profit. In such a model, businesses may rationally reduce current hiring due to the risk of policies that would impose higher costs in the future. The value functional approach also provides powerful methods to estimate commercial damages in breaches of contract involving intellectual property, new businesses, the ability to open or expand operations, and other situations commonly arising in business.