Über die Autorin bzw. den Autor

Avinash K. Dixit is John J. F. Sherrerd '52 University Professor of Economics at Princeton University. His most recent book is Thinking Strategically, with Barry Nalebuff (Norton). Robert S. Pindyck is Mitsubishi Bank Professor of Economics at the Sloan School of Management, MIT. His books include Econometric Models and Economic Forecasts, with Daniel L. Rubinfeld (McGraw-Hill).

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"[The authors'] approach has powerful implications for investors in marketable assets as well. No investment professional or CFO can afford to ignore this brilliant new book."--Peter L. Bernstein, author ofCapital Ideas: The Improbable Origins of Modern Wall Street

"Avinash Dixit and Robert Pindyck have successfully applied to capital budgeting the ideas and techniques of option pricing that have so enriched our understanding of financial markets."--Merton H. Miller, Nobel Laureate in Economics

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"[The authors'] approach has powerful implications for investors in marketable assets as well. No investment professional or CFO can afford to ignore this brilliant new book."--Peter L. Bernstein, author ofCapital Ideas: The Improbable Origins of Modern Wall Street

"Avinash Dixit and Robert Pindyck have successfully applied to capital budgeting the ideas and techniques of option pricing that have so enriched our understanding of financial markets."--Merton H. Miller, Nobel Laureate in Economics

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Investment under Uncertainty

Princeton University Press

Contents

Preface.................................................................xi1 A New View of Investment..............................................32 Developing the Concepts Through Simple Examples.......................263 Stochastic Processes and Ito's Lemma..................................594 Dynamic Optimization under Uncertainty................................935 Investment Opportunities and Investment Timing........................1356 The Value of a Project and the Decision to Invest.....................1757 Entry, Exit, Lay-Up, and Scrapping....................................2138 Dynamic Equilibrium in a Competitive Industry.........................2479 Policy Intervention and Imperfect Competition.........................28210 Sequential Investment................................................31911 Incremental Investment and Capacity Choice...........................35712 Applications and Empirical Research..................................394References..............................................................429Symbol Glossary.........................................................445

Chapter One

Economics defines investment as the act of incurring an immediate cost in the expectation of future rewards. Firms that construct plants and install equipment, merchants who lay in a stock of goods for sale, and persons who spend time on vocational education are all investors in this sense. Somewhat less obviously, a firm that shuts down a loss-making plant is also "investing": the payments it must make to extract itself from contractual commitments, including severance payments to labor, are the initial expenditure, and the prospective reward is the reduction in future losses.

Viewed from this perspective, investment decisions are ubiquitous. Your purchase of this book was an investment. The reward, we hope, will be an improved understanding of investment decisions if you are an economist, and an improved ability to make such decisions in the course of your future career if you are a business school student.

Most investment decisions share three important characteristics in varying degrees. First, the investment is partially or completely irreversible. In other words, the initial cost of investment is at least partially sunk; you cannot recover it all should you change your mind. Second, there is uncertainty over the future rewards from the investment. The best you can do is to assess the probabilities of the alternative outcomes that can mean greater or smaller profit (or loss) for your venture. Third, you have some leeway about the timing of your investment. You can postpone action to get more information (but never, of course, complete certainty) about the future.

These three characteristics interact to determine the optimal decisions of investors. This interaction is the focus of this book. We develop the theory of irreversible investment under uncertainty, and illustrate it with some practical applications.

The orthodox theory of investment has not recognized the important qualitative and quantitative implications of the interaction between irreversibility, uncertainty, and the choice of timing. We will argue that this neglect explains some of the failures of that theory. For example, compared to the predictions of most earlier models, real world investment seems much less sensitive to interest rate changes and tax policy changes, and much more sensitive to volatility and uncertainty over the economic environment. We will show how the new view resolves these anomalies, and in the process offers some guidance for designing more effective public policies concerning investment.

Some seemingly noneconomic personal decisions also have the characteristics of an investment. To give just one example, marriage involves an up-front cost of courtship, with uncertain future happiness or misery. It may be reversed by divorce, but only at a substantial cost. Many public policy decisions also have similar features. For instance, public opinion about the relative importance of civil rights of the accused and of social order fluctuates through time, and it is costly to make or change laws that embody a particular relative weight for the two. Of course the costs and benefits of such noneconomic decisions are difficult or even impossible to quantify, but our general theory will offer some qualitative insights for them, too.

1 The Orthodox Theory

How should a firm, facing uncertainty over future market conditions, decide whether to invest in a new factory? Most economics and business school students are taught a simple rule to apply to problems of this sort. First, calculate the present value of the expected stream of profits that this factory will generate. Second, calculate the present value of the stream of expenditures required to build the factory. Finally, determine whether the difference between the two—the net present value (NPV) of the investment—is greater than zero. If it is, go ahead and invest.

Of course, there are issues that arise in calculating this net present value. Just how should the expected stream of profits from a new factory be estimated? How should inflation be treated? And what discount rate (or rates) should be used in calculating the present values? Resolving issues like these are important topics in courses in corporate finance, and especially capital budgeting, but the basic principle is fairly simple—calculate the NPV of an investment project and see whether it is positive.

The net present value rule is also the basis for the neoclassical theory of investment as taught to undergraduate and graduate students of economics. Here we find the rule expressed using the standard incremental or marginal approach of the economist: invest until the value of an incremental unit of capital is just equal to its cost. Again, issues arise in determining the value of an incremental unit of capital, and in determining its cost. For example, what production structure should be posited? How should taxes and depreciation be treated?

Much of the theoretical and empirical literature on the economics of investment deals with issues of this sort. We find two essentially equivalent approaches. One, following Jorgenson (1963), compares the per-period value of an incremental unit of capital (its marginal product) and an "equivalent per-period rental cost" or "user cost" that can be computed from the purchase price, the interest and depreciation rates, and applicable taxes. The firm's desired stock of capital is found by equating the marginal product and the user cost. The actual stock is assumed to adjust to the ideal, either as an ad hoc lag process, or as the optimal response to an explicit cost of adjustment. The book by Nickell (1978) provides a particularly good exposition of developments of this approach.

The other formulation, due to Tobin (1969), compares the capitalized value of the marginal investment to its purchase cost. The value can be observed directly if the ownership of the investment can be traded in a secondary market; otherwise it is an imputed value computed as the expected present value of the stream of profits it would yield. The ratio of this to the purchase price (replacement cost) of the unit, called Tobin's q, governs the investment decision. Investment should be undertaken or expanded if q exceeds 1; it should not be undertaken, and existing capital should be reduced, if q < 1. The optimal rate of expansion or contraction is found by equating the marginal cost of adjustment to its benefit, which depends on the difference between q and 1. Tax rules can alter this somewhat, but the basic principle is similar. Abel (1990) offers an excellent survey of this q-theory of investment. In all of this, the underlying principle is the basic net present value rule.

2 The Option Approach

The net present value rule, however, is based on some implicit assumptions that are often overlooked. Most important, it assumes that either the investment is reversible, that is, it can somehow be undone and the expenditures recovered should market conditions turn out to be worse than anticipated, or, if the investment is irreversible, it is a now or never proposition, that is, if the firm does not undertake the investment now, it will not be able to in the future.

Although some investments meet these conditions, most do not. Irreversibility and the possibility of delay are very important characteristics of most investments in reality. As a rapidly growing literature has shown, the ability to delay an irreversible investment expenditure can profoundly affect the decision to invest. It also undermines the simple net present value rule, and hence the theoretical foundation of standard neoclassical investment models. The reason is that a firm with an opportunity to invest is holding an "option" analogous to a financial call option—it has the right but not the obligation to buy an asset at some future time of its choosing. When a firm makes an irreversible investment expenditure, it exercises, or "kills," its option to invest. It gives up the possibility of waiting for new information to arrive that might affect the desirability or timing of the expenditure; it cannot disinvest should market conditions change adversely. This lost option value is an opportunity cost that must be included as part of the cost of the investment. As a result, the NPV rule "invest when the value of a unit of capital is at least as large as its purchase and installation cost" must be modified. The value of the unit must exceed the purchase and installation cost, by an amount equal to the value of keeping the investment option alive.

Recent studies have shown that this opportunity cost of investing can be large, and investment rules that ignore it can be grossly in error. Also, this opportunity cost is highly sensitive to uncertainty over the future value of the project, so that changing economic conditions that affect the perceived riskiness of future cash flows can have a large impact on investment spending, larger than, say, a change in interest rates. This may help to explain why neoclassical investment theory has so far failed to provide good empirical models of investment behavior, and has led to overly optimistic forecasts of effectiveness of interest rate and tax policies in stimulating investment.

The option insight also helps explain why the actual investment behavior of firms differs from the received wisdom taught in business schools. Firms invest in projects that are expected to yield a return in excess of a required, or "hurdle," rate. Observers of business practice find that such hurdle rates are typically three or four times the cost of capital. In other words, firms do not invest until price rises substantially above long-run average cost. On the downside, firms stay in business for lengthy periods while absorbing operating losses, and price can fall substantially below average variable cost without inducing disinvestment or exit. This also seems to conflict with standard theory, but as we will see, it can be explained once irreversibility and option value are accounted for.

Of course, one can always redefine NPV by subtracting from the conventional calculation the opportunity cost of exercising the option to invest, and then say that the rule "invest if NPV is positive" holds once this correction has been made. However, to do so is to accept our criticism. To highlight the importance of option values, in this book we prefer to keep them separate from the conventional NPV. If others prefer to continue to use "positive NPV" terminology, that is fine as long as they are careful to include all relevant option values in their definition of NPV. Readers who prefer that usage can readily translate our statements into that language.

In this book we develop the basic theory of irreversible investment under uncertainty, emphasizing the option-like characteristics of investment opportunities. We show how optimal investment rules can be obtained from methods that have been developed for pricing options in financial markets. We also develop an equivalent approach based on the mathematical theory of optimal sequential decisions under uncertainty—dynamic programming. We illustrate the optimal investment decisions of firms in a variety of situations—new entry, determination of the initial scale of the firm and future costly changes of scale, choice between different forms of investment that offer different degrees of flexibility to meet future conditions, completion of successive stages of a complex multistage project, temporary shutdown and restart, permanent exit, and so forth. We also analyze how the actions of such firms are aggregated to determine the dynamic equilibrium of an industry.

To stress the analogy with options on financial assets, the opportunities to acquire real assets are sometimes called "real options." Therefore this book could be titled "The Real Options Approach to Investment."

3 Irreversibility and the Ability to Wait

Before proceeding, it is important to clarify the notions of irreversibility, the ability to delay an investment, and the option to invest. Most important, what makes an investment expenditure a sunk cost and thus irreversible?

Investment expenditures are sunk costs when they are firm or industry specific. For example, most investments in marketing and advertising are firm specific and cannot be recovered. Hence they are clearly sunk costs. A steel plant, on the other hand, is industry specific—it can only be used to produce steel. One might think that because in principle the plant could be sold to another steel company, the investment expenditure is recoverable and is not a sunk cost. This is incorrect. If the industry is reasonably competitive, the value of the plant will be about the same for all firms in the industry, so there would be little to gain from selling it. For example, if the price of steel falls so that a plant turns out, ex post, to have been a "bad" investment for the firm that built it, it will also be viewed as a bad investment by other steel companies, and the ability to sell the plant will not be worth much. As a result, an investment in a steel plant (or any other industry-specific capital) should be viewed as largely a sunk cost.

Even investments that are not firm or industry specific are often partly irreversible because buyers in markets for used machines, unable to evaluate the quality of an item, will offer a price that corresponds to the average quality in the market. Sellers, who know the quality of the item they are selling, will be reluctant to sell an above-average item. This will lower the market average quality, and therefore the market price. This "lemons" problem (see Akerlof, 1970) plagues many such markets. For example, office equipment, cars, trucks, and computers are not industry specific, and although they can be sold to companies in other industries, their resale value will be well below their purchase cost, even if they are almost new.

Irreversibility can also arise because of government regulations or institutional arrangements. For example, capital controls may make it impossible for foreign (or domestic) investors to sell assets and reallocate their funds, and investments in new workers may be partly irreversible because of high costs of hiring, training, and firing. Hence most major capital investments are in large part irreversible.

Let us turn next to the possibilities for delaying investments. Of course, firms do not always have the opportunity to delay their investments. For example, there can be occasions in which strategic considerations make it imperative for a firm to invest quickly and thereby preempt investment by existing or potential competitors. However, in most cases, delay is at least feasible. There may be a cost to delay—the risk of entry by other firms, or simply foregone cash flows—but this cost must be weighed against the benefits of waiting for new information. Those benefits are often large.

As we said earlier, an irreversible investment opportunity is much like a financial call option. A call option gives the holder the right, for some specified amount of time, to pay an exercise price and in return receive an asset (e.g., a share of stock) that has some value. Exercising the option is irreversible; although the asset can be sold to another investor, one cannot retrieve the option or the money that was paid to exercise it. A firm with an investment opportunity likewise has the option to spend money (the "exercise price"), now or in the future, in return for an asset (e.g., a project) of some value. Again, the asset can be sold to another firm, but the investment is irreversible. As with the financial call option, this option to invest is valuable in part because the future value of the asset obtained by investing is uncertain. If the asset rises in value, the net payoff from investing rises. If it falls in value, the firm need not invest, and will only lose what it spent to obtain the investment opportunity. The models of irreversible investment that will be developed in Chapter 2 and in later chapters will help to clarify the optionlike nature of an investment opportunity.

(Continues...)

Excerpted from Investment under Uncertaintyby Avinash K. Dixit Robert S. Pindyck Copyright © 1994 by Princeton University Press. Excerpted by permission of Princeton University Press. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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