THE ECONOMICS OF BUSINESS VALUATION

Towards a Value Functional Approach

By PATRICK L. ANDERSON

Stanford University Press

Copyright © 2012 Board of Trustees of the Leland Stanford Junior University
All rights reserved.
ISBN: 978-0-8047-5830-7

Contents

Preface…………………………………………………………..ixPART I THEORIES OF VALUE……………………………………………1Chapter 1 Modern Value Quandaries……………………………………3Chapter 2 Theories of Value…………………………………………14Chapter 3 The Failure of the Neoclassical Investment Rule………………23PART II THE NATURE OF THE FIRM………………………………………43Chapter 4 The Nature of the Firm…………………………………….45Chapter 5 The Organization and Scale of Private Business……………….58Chapter 6 Accounting for the Firm……………………………………79PART III ECONOMIC THEORIES OF VALUE………………………………….89Chapter 7 Value in Classical Economics……………………………….91Chapter 8 Value in Neoclassical Economics…………………………….96Chapter 9 Modern Recursive Equilibrium and the Basic Pricing Equation……113PART IV FINANCE THEORIES OF VALUE……………………………………125Chapter 10 Arbitrage-Free Pricing in Complete Markets………………….127Chapter 11 Portfolio Pricing Methods…………………………………153Chapter 12 Real Options and Expanded Net Present Value…………………166PART V TRADITIONAL AND VALUE FUNCTIONAL THEORIES OF VALUE………………199Chapter 13 Traditional Valuation Methods……………………………..201Chapter 14 Practical Application of the Income Method………………….217Chapter 15 The Value Functional: Theory………………………………235PART VI APPLICATIONS……………………………………………….261Chapter 16 The Value Functional: Applications…………………………263Chapter 17 Applications: Finance and Valuation………………………..295Chapter 18 Applications: Law and Economics……………………………306PART VII APPENDICES………………………………………………..323Appendix A Key Formula and Notation Summary…………………………..325Appendix B Guide to the Solutions Manual……………………………..337Appendix C Description of Subject Companies…………………………..340Notes…………………………………………………………….347References………………………………………………………..391Index…………………………………………………………….409

CHAPTER 1

MODERN VALUE QUANDARIES

THE FIRM IN ECONOMICS AND FINANCE

For at least two millennia, private businesses have been undertaken by farmers, traders,and artisans across the globe. Such businesses—including small farms, fishing and herdingenterprises, textile and clothing producers, and larger ventures—have been the world’s primaryemployers and wealth producers for centuries. Furthermore, for at least the past twocenturies society has benefited from the formal study of economics, accounting, and theprecursors of finance. What we call a business, enterprise, undertaking, or “firm” figuresprominently in all of these fields. Yet with all of this scholarship, we really know very littleabout the definition and value of the firm. Addressing this poverty is the prime motivationof this book.

For graduates and holders of professional credentials in the fields of accounting, finance,economics, and business, this bold assertion of our lack of knowledge may seem overwrought.However, in this chapter, we pose several quandaries that illustrate this poverty. Ifwe really had a complete, coherent, and valid theory of the firm and its value, these quandarieswould not exist. The fact that they do exist, and that similar serious self-contradictionsexist in related fields of study, motivates this book.

TWO MILLENNIA OF BUSINESS: A BRIEF RECAP

Business from 500 BC to AD 1500

Two millennia ago, accounts of business activity and rules for business behavior appearedin ancient texts such as the books of the Old Testament of the Bible (including the booksof the Torah), the books of the New Testament, the Vedas of Hindu literature, and ancientlegal codes such as those of the Roman Empire and the Babylonian empire of Hammurabi.

During these twenty centuries, agriculture, hunting, fishing, and herding of game animalswere the primary occupations. These farmers, hunters, fishermen, and herders wereall engaged in business, and the prospect of hunger and famine made their business veryimportant indeed.

For roughly the last thousand years, the emerging civilizations of the world benefitedfrom mathematics, customs of trade, and other knowledge recorded in Greek and Romanliterature, as well as lesser-known literature from other lands. Critical scientific advancesthat occurred in Egypt, China, India, and the Near East—including the creation ofthe number system we use today, as well as basic algebra—were transmitted to the West,sometimes with the actual origins forgotten. Much of this knowledge was directly used inbusiness and trade, including weights and measures, arithmetic and numbering, geometry,timekeeping, navigation, water distribution, and cultivation.

Of course, such knowledge was not nicely recorded and widely distributed. Human andcivil rights, such as the right to property and the fruits of one’s own labor, were denied tomany. Life expectancy, literacy, and the need for subsistence were such that relatively fewpeople received a formal education as we now understand it. However, businesses wereorganized, grew, and failed; trade flourished, was interrupted, and then resumed; peoplereceived wages for their work and paid for their purchases; wars and pestilence came andwent; and somehow civilization survived—and with it, the institution of business survivedand grew.

Business Since AD 1500

In the last five hundred years, business practices were further developed, as were a numberof related fields of study, particularly the following:

1500s

• Traders and other businesspeople developed a formal system of accounting to recordtransactions within a firm. Such practices allowed commerce to grow and are still thebases for trade, contracts, and business investment.

1700s & 1800s

• Economists began writing about the economies of modern societies. Classical economistssuch as Adam Smith and David Ricardo proposed an explicit labor theory ofvalue.

1900s

• Neoclassical economics emerged as a dominant influence in the whole of socialscience. It introduced the concepts of marginal cost, consumer utility, and profitmaximization, which are now used in economics, law, government, sociology, andcommerce. The pervasive idea that prices are set when supply meets demand in anopen market took hold.

1940s

• A school of modern finance emerged as a separate discipline. Building on both neoclassicalmicroeconomics and mathematics, modern finance developed notions ofarbitrage, martingale pricing, portfolio choice, and mean-variance analysis.

1950s

• Formal credentials were developed for professionals engaged in selling securities offirms, providing advice for individuals investing in firms, accounting or auditing theaccounts of firms, and appraising business property. The Modigliani-Miller propositionemerged as a pillar of modern finance. The basis for modern portfolio theorywas established.

1970s–2010

• A specialized professional literature in the valuation of business developed. Alongsideit grew a smaller literature for forensic economists, who estimate the change in valueof firms for the purpose of estimating damages to businesses caused by breachesof contract and natural disasters. A formula for the valuation of certain financialoptions became widely available. Financial engineering and discounted cash flowanalysis became ubiquitous.

We must acknowledge this tremendous progress in the fields of economics, finance,and accounting, and the ongoing efforts of scholars and professional societies dealing withbusinesses and business value. Indeed, we will devote several chapters to doing exactly that!

THE QUANDARIES

With all this knowledge, we should have a very well-developed theory of the firm and avery well-developed theory of the value of a firm. These theories should be amply tested byreality, comprehensive, and internally consistent.

Unfortunately, few theories provide a sound basis for determining the market value of aprivately held firm. Moreover, we still have large gaps in our knowledge about the rationaleof firms in the modern economy, and no workable universal definition of the firm. Notionsof the firm used in microeconomics, accounting, corporate finance, and option pricing alldiffer. Finally, professionals who seek practical guidance on the definition and value of afirm routinely find it—at least in the United States—from an unlikely source for intellectualenlightenment: the federal taxation authorities.

This unsatisfactory state of affairs can be illustrated by the seven quandaries posed next.Each illustrates a significant gap in the orthodox theories of business drawn from economics,finance, and accounting.

Quandary 1: Mainstream Economics Ignores the Firm

The Neglect of the Firm in Economics

This quandary dates back to the creation of the mathematical models that form the basisof general equilibrium economics. Consider this statement by Léon Walras, the pioneer ofwelfare economics, writing in the nineteenth century:

Once the equilibrium has been established in principle, exchange can take placeimmediately. Production, however, requires a certain lapse of time. We shall resolve thesecond difficulty purely and simply by ignoring the time element at this point. (Walras,1874, p. 242)

Walras developed the early model of exchange equilibrium, meaning that the buyers andsellers in a market reach agreements at market-clearing prices. However, in order to dothis he had to ignore the fact that production took some time. It is the firm (or set of firms)that directly internalizes the time, cost, and uncertainty of production. Walras dealt withimportant issues in economics, and his thought is the basis for much of what we call microeconomicstoday. But he explicitly ignored the inner workings of the firm. In essence,the firm vanishes from the theoretical model of production, exchange, and consumption.

Next we quote an influential modern-era microeconomist:

The firm fits into general equilibrium theory as a balloon fits into an envelope: flattenedout! Try with a blown-up balloon: the envelope may tear, or fly away: at best, it will be hardto seal and impossible to mail…. Instead, burst the balloon flat, and everything becomeseasy. Similarly with the firm and general equilibrium—though the analogy requires a wordof explanation.

Jacques H. Drèze, “Uncertainty and the Firm in General Equilibrium Theory,” EconomicJournal, 1985, p. 1.

These observations about the state of economic science are telling. In more than a hundredyears, economics had moved quite far—but still typically viewed the firm as a “flattenedballoon” abstraction. A few decades later, the standard presentation of the firm in bothmicroeconomics and macroeconomics remains quite primitive.

In the standard microeconomics model, firms are typically assumed to sell homogenousgoods using a simple production function. Workers adjust their consumption according totheir wages and interest rates. To the extent that firms’ production plans are even considered,they are often presented as solutions to single-period profit maximization problems,or as the intersections of average cost curves, assuming static production technology andmarket structure. Entrepreneurial interests, uncertainty, institutional factors, and numerousfinancial, managerial, and practical considerations in the organization and operation ofthe firm are largely assumed away.

To be sure, even this primitive specification of the firm leaves plenty of room for issuessuch as monetary policy, fiscal policy, trade policy, labor policy, regulation of markets witholigopoly structures, causes of business cycles, and so on. However, it also leaves a ratherlarge void.

The Fulsome Importance of the Firm in the Real Economy

Consider the dimensions in which the firm has an essential, if not dominant, role in society:

• Most firms in the United States are “small” and privately held. Furthermore, thesefirms appear to employ most of the private-sector workers in the country.

• Equity interests in firms appear to be a very large portion of household wealth.

• One cannot endure an election cycle—at least in the United States—without somebusinesses, or entire industries being pilloried in campaign rhetoric.

• Much of popular media, entertainment, and sporting events are financed by advertisingby firms.

• Successful entrepreneurs have often used their riches to create or endow importantcharitable, cultural, and educational institutions.

• Finally, a significant portion of the tax revenue of most state and national governmentsconsists of taxes imposed on, or collected by, firms.

The firm is relegated to such inferior status in economics, but not because it is an inferiorpart of the economy.

Quandary 2: Mainstream Economics Ignores the Entrepreneur

The Much-Loved, but Ignored, Entrepreneur

To understand business value, we must recognize the motivations of those who createbusinesses and run them. However, neoclassical economics—the dominant school withineconomics for the past century—largely ignores such people. We discussed earlier howneoclassical economics ignores the inner workings of firms; the entrepreneur can be seenas the inner-inner working of all firms. The relegation of entrepreneurs to an abstractionwithin neoclassical economics means that these inner workings—so critical to the understandingof business creation, destruction, and value—are also abstracted away. Outsidemicroeconomics, the entrepreneur enjoys a much better public reputation.

Although the notion of the “greedy business executive” is a staple of movies and televisionshows, the entrepreneur is usually shown in a more favorable light. A good part ofpopular culture appears to accept the notion that entrepreneurs typically focus on muchmore than money during their (often long and sometimes unsuccessful) efforts.

Perhaps the most influential modern philosopher of entrepreneurship is George Gilder,whose 1981 book Wealth and Poverty became a best-seller and something of a touchstoneof the presidency of Ronald Reagan. Gilder writes of the entrepreneur’s desire to create,to give, even to love.

This idea of the entrepreneur actually goes back centuries. The Irish economist RichardCantillon described the entrepreneur as a risk-bearer in the eighteenth century, beforeAdam Smith wrote his Wealth of Nations. Among classic economists, John Stuart Mill andothers recognized the vital role of the entrepreneur.

The great twentieth-century economist Joseph Schumpeter coined a phrase that shouldresonate with anyone who ever worked to build a business, or rebuild it, or expand it. Theterm is creative destruction:

The opening up of new markets, foreign or domestic, and the organizational developmentfrom the craft shop and factory to such concerns as U.S. Steel illustrate the same process ofindustrial mutation—if I may use that biological term—that incessantly revolutionizes theeconomic structure from within, incessantly destroying the old one, incessantly creating anew one. This process of Creative Destruction is the essential fact about capitalism.

Every piece of business strategy acquires its true significance only against the backgroundof that process and within the situation created by it. It must be seen in its role inthe perennial gale of creative destruction; it cannot be understood irrespective of it or, infact, on the hypothesis that there is a perennial lull. (Schumpeter, 1975, pp. 83–84; emphasisin original)

Modern Brush-Asides

However prescient Gilder, Cantillon, and Schumpeter’s ideas about entrepreneurshipmay have been, they were not adopted by the mainstream of the economics profession. Theimportance of entrepreneurship in the dominant economics paradigm diminished greatlyin the twentieth century and is still largely missing from general equilibrium economictheory. Some reasons for this disappearance are as follows:

• The neoclassical model relies on equilibrium in a nearly perfect market. This leaveslittle room for the risk-taking and judgment (not to mention animal spirits) that arethe lifeblood of the true entrepreneur.

• The reliance on (some would say infatuation with) mathematical models in moderneconomics requires much abstraction. Such abstraction cuts against the inclusion ofcomplicated—and mathematically messy—factors such as transaction costs, barriersto entry, uncertainty, and limited ability to finance, all of which are ubiquitousconcerns of the entrepreneur.

• A cultural bias exists against “boot strappers” among the well-credentialed academicswho write most economics and finance textbooks. This is probably due to a predictablesympathy toward the traditions, mores, and work habits common where one livesand works, and the large differences between the typical life experiences of professorsand entrepreneurs.

• There are readily available data on very large, publicly traded firms—providing aconvenient basis for academic research and publication opportunities—but relativelylittle data on privately held firms.
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