Real Options in Capital Investment: Models, Strategies, and Applications

By Lenos Trigeorgis | Go to book overview

these expected rates. If the firm could invest only at a fixed time point, T, then the value of the option to invest would be given by Equation (6.2) for a European exchange option. Using an equilibrium argument, McDonald and Siegel valued this option when its life is either infinite or random.

The general valuation formula, Equation (6.12), can also be derived in an equilibrium model. The formula may then be used to value a timing option that expires within a fixed period of time. Concrete examples of this situation may occur when a firm has an option to buy land or to drill for oil within, say, six months. Alternatively, a patent, injunction, or a temporary competitive advantage may allow a firm to exploit a production opportunity for a limited period of time.

The option to abandon a project, having current value Dt, in exchange for its salvage (or best alternative use) value, Vt, has been studied in Myers and Majd ( 1990) and McDonald and Siegel ( 1986). This abandonment option is a mirror problem to that of the timing option and can be similarly valued with our general formula with a suitable reinterpretation of variables. Other real options, such as to switch inputs or outputs in production, can be valued similarly.

The major impediment to such real option applications appears to be the potential unobservability of the asset values, Vt and Dt. In certain situations, these values can be backed out of a valuation model that employs observable prices as inputs. For example, Brennan and Schwartz ( 1985a) valued a mine when the ore is traded in the futures markets. Assuming that a geometric Brownian motion is a reasonable approximation for the dynamics of the mine's value, the American option to buy or sell the mine can be valued using the results of this chapter.

Alternatively, the effect of the unobservability of the asset values, Vt and Dt, can be included in the valuation model. For example, one could assume that these quantities are observed with noise, the principal effect of which would be to induce suboptimal exercise. In particular, real options might be exercised when they are out-of-the-money, and deep in-the-money options may sometimes fail to be optimally exercised. These effects work to reduce option value relative to the case with perfect observability. The magnitude of mispricing would depend positively on the amount of noise (or the variance of the error term).


6.6 CONCLUSION

This chapter has developed a model for valuing American exchange options on dividend-paying assets. After a brief review of the literature, a general formula was developed which was shown to encompass many earlier results under suitable parameter restrictions. In particular, this general formula

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Real Options in Capital Investment: Models, Strategies, and Applications
Table of contents

Table of contents

  • Title Page iii
  • Contents v
  • Tables and Figures ix
  • Preface xiii
  • Chapter 1 Real Options: An Overview 1
  • Introduction 1
  • Acknowledgments 28
  • Notes 28
  • Part I Real Options and Alternative Valuation Paradigms 29
  • Chapter 2 Methods for Evaluating Capital Investment Decisions Under Uncertainty 31
  • Introduction 31
  • Conclusion 44
  • Notes 45
  • Chapter 3 Merging Finance Theory and Decision Analysis 47
  • Introduction 47
  • Summary and Conclusion 65
  • Acknowledgments 66
  • Notes 66
  • Chapter 4 The Strategic Capital Budgeting Process: A Review of Theories and Practice 69
  • Introduction 69
  • Conclusions 84
  • Acknowledgments 86
  • Notes 86
  • Part II General Exchange or Switching Options and Options Interdependencies 87
  • Chapter 5 The Value of Flexibility: A General Model of Real Options 89
  • Introduction 89
  • Concluding Remarks 105
  • Acknowledgments 105
  • Notes 106
  • Chapter 6 The Valuation of American Exchange Options with Application to Real Options 109
  • Introduction 109
  • Conclusion 119
  • Acknowledgments 120
  • Notes 120
  • Chapter 7 Operating Flexibilities in Capital Budgeting: Substitutability and Complementarity in Real Options 121
  • Introduction 121
  • Conclusion 130
  • Acknowledgments 131
  • Notes 131
  • Part III Strategy, Infrastructure, and Foreign Investment Options 133
  • Chapter 8 The Value of Options in Strategic Acquisitions 135
  • Introduction 135
  • Implications and Conclusions 147
  • Acknowledgments 148
  • Notes 148
  • Chapter 9 Corporate Governance, Long-term Investment Orientation, and Real Options in Japan 151
  • Introduction 151
  • Implications and Conclusions 158
  • Notes 160
  • Chapter 10 Volatile Exchange Rates and the Multinational Firm: Entry, Exit, and Capacity Options 163
  • Introduction 163
  • Conclusions 178
  • Acknowledgments 180
  • Notes 180
  • Part IV Mean Reversion/ Alternative Formulations in Natural Resources, Shipping, and Start - Up Ventures 183
  • Chapter 11 The Effects of Reversion on Commodity Projects of Different Length 185
  • Introduction 185
  • Conclusions and Extensions 199
  • Appendix 201
  • Acknowledgments 204
  • Notes 204
  • Chapter 12 Contingent Claims Evaluation of Mean-Reverting Cash Flows in Shipping 207
  • Introduction 207
  • Conclusions 216
  • Appendix 217
  • Acknowledgments 218
  • Notes 218
  • Chapter 13 Valuing Start-Up Venture Growth Options 221
  • Introduction 221
  • Conclusion 236
  • Appendix 237
  • Acknowledgments 238
  • Notes 238
  • Part V Other Applications: Pollution Compliance, Land Development, Flexible Manufacturing, and Financial Default 241
  • Chapter 14 Investment in Pollution Compliance Options: The Case of Georgia Power 243
  • Introduction 243
  • Notes 262
  • Chapter 15 Optimal Land Development 265
  • Introduction 265
  • Conclusions and Extensions 277
  • Appendix 278
  • Acknowledgments 279
  • Notes 279
  • Chapter 16 Multiproduct Manufacturing with Stochastic Input Prices and Output Yield Uncertainty 281
  • Introduction 281
  • Conclusion 298
  • Appendix 300
  • Notes 301
  • Chapter 17 Default Risk in the Contingent Claims Model of Debt 303
  • Introduction 303
  • Conclusions and Extensions 317
  • Acknowledgments 318
  • Notes 319
  • Bibliography 323
  • Author Index 347
  • Subject Index 351
  • About the Editor and Contributors 357
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