RealAnalysis Options Tools and Techniques for Valuing Strategic Investments and Decisions John Wiley & Sons Founded in 1807, John Wiley & Sons is the oldest independent publishing company in the United States With offices in North America, Europe, Australia, and Asia, Wiley is globally committed to developing and marketing print and electronic products and services for our customers’ professional and personal knowledge and understanding The Wiley Finance series contains books written specifically for finance and investment professionals as well as sophisticated individual investors and their financial advisors Book topics range from portfolio management to e-commerce, risk management, financial engineering, valuation and financial instrument analysis, as well as much more For a list of available titles, please visit our Web site at www.WileyFinance.com Additional Praise for Real Options Analysis “Real Options Analysis is the clearest book on real options that we have read to date It does an excellent job of demystifying a difficult and complex subject It provides a solid basis for conceiving, assessing, and evaluating real option investments, which will make it useful to practitioners and students alike.” — Ian C MacMillan, Ph.D., The Fred Sullivan Professor of Entrepreneurship and Department Chair, Wharton School, University of Pennsylvania (USA) “Mun demystifies real options analysis and delivers a powerful, pragmatic guide for decision-makers and practitioners alike Finally, there is a book that equips professionals to easily recognize, value, and seize real options in the world around them.” — Jim Schreckengast, Sr Vice President, R&D Strategy – Gemplus International SA (France) “Written from the viewpoint of an educator and a practitioner, Mun’s book offers a readable reference full of insightful decision-making tools to satisfy both the novice and the experienced veteran.” — Richard Kish, Ph.D., Associate Professor of Finance, Lehigh University (USA) “Mun has converted his tacit financial knowledge into a digestible user-friendly book He effectively leads the reader on a solid path starting from discounted cash flow, progressing through Monte Carlo analysis and evolving to real options to get even closer to the target of achieving confident corporate decisions His ability to clearly explain the relationships of popular competing analysis methods will make this a must-have reference book for today’s decision-makers.” — Kenneth English, Director of R&D, The Timken Company (USA) “The book leads the field in real options analytics and is a must-read for anyone interested in performing such analyses Mun has made a formidable subject crystal clear and exponentially easy for senior management to understand Monte Carlo simulation and real options software alone is worth the book price many times over.” — Morton Glantz, Renowned educator in finance, author of several books, financial advisor to government (USA) “The book is far and away the clearest, most comprehensive guide to real options analysis to date, and is destined to be a classic — it is a complete guide to the practical application of real options analysis It strikes a superb balance between solid intuition, rigorous analysis, and numerous practical examples.” — John Hogan, Ph.D., Boston College (USA) CHAPTER RealAnalysis Options Tools and Techniques for Valuing Strategic Investments and Decisions JOHNATHAN MUN John Wiley & Sons, Inc Microsoft is a registered trademark of Microsoft Corporation eBay is a registered trademark of eBay Inc Yahoo! is a registered trademark of Yahoo! Inc Copyright © 2002 by Johnathan Mun All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470 Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, 201-748-6011, fax 201-748-6008, e-mail: permcoordinator@wiley.com Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose No warranty may be created or extended by sales representatives or written sales materials The advice and strategies contained herein may not be suitable for your situation You should consult with a professional where appropriate Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages For general information on our other products and services, or technical support, please contact our Customer Care Department within the United States at 800-762-2974, outside the United States at 317-572-3993 or fax 317-572-4002 Designations used by companies to distinguish their products are often claimed as trademarks In all instances where John Wiley & Sons, Inc is aware of a claim, the product names appear in initial capital or all capital letters Readers, however, should contact the appropriate companies for more complete information regarding trademarks and registration Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic books Library of Congress Cataloging-in-Publication Data: Mun, Johnathan Real options analysis : tools and techniques for valuing strategic investments and decisions / Johnathan Mun p cm (Wiley finance series) ISBN 0-471-25696-X (CLOTH/CD-ROM : alk paper) Real options (Finance) I Title II Series HG6042 M86 2002 332.63— dc21 Printed in the United States of America 10 2002008978 Specially dedicated to my wife Penny, the love and sunshine of my life, without whose encouragement, advice, support, and phenomenal editorial talents, this book would never have been completed I would also like to dedicate this book to my parents, for all their love and support for these many years “If you will walk in my ways and keep my requirements, then you will govern my house and have charge of my courts, and I will give you a place among these standing here.” Zechariah 3:7 (NIV) 189 Real Options Models %LQRPLDO $SSURDFK ± 6WHS ,, 2SWLRQ 9DOXDWLRQ /DWWLFH (;(&87( 23(1 23(1 ([HFXWLQJ ± ([HUFLVH 3ULFH 0D[ > @ (;(&87( 0D[LPXP EHWZHHQ ([HFXWLQJ WKH SXUFKDVH RSWLRQ RU 0D[ > @ (;(&87( TheELQRPLDO binomialRSWLRQ optionYDOXDWLRQ valuation FRPHV comes RXW out 7KH $37.53.&RPSDUH CompareWKLV this WR to Da QDwYH na¨ıve WRtoEHbe Black-Scholes result of $36.90 or a static %ODFN6FKROHV UHVXOW RI RU D VWDWLF NPV of $20 for a 1-year exercise and 139 RI IRU \HDU H[HUFLVH DQG $10 for a 2-year exercise IRU D \HDU H[HUFLVH &217,18( 0D[LPXP EHWZHHQ ([HFXWLQJ WKH SXUFKDVH RSWLRQ RU HHSLQJ WKH 2SWLRQ 2SHQ ([HFXWLQJ ± ([HUFLVH 3ULFH HHSLQJ WKH 2SWLRQ 2SHQ >3 3 @H[S ULVNIUHH GW Changing Strike Option (Valuation Lattice) FIGURE 7.13 CHANGING VOLATILITY Instead of changing strike costs over time, in certain cases, volatility on cash flow returns may differ over time This can be seen in Figures 7.14 and 7.15 In Figure 7.14, we see the example for a two-year option where volatility is 20 percent in the first year and 30 percent in the second year In this %LQRPLDO $SSURDFK ± 6WHS , /DWWLFH (YROXWLRQ WKHUnderlying 8QGHUO\LQJ n ofRIthe 100.0 S6 0 122.14 6 X S0u1 81.87 G S0d 1 Given: *LYHQ S6 == 100, X; ==110, T7 ==2,rfUI ==0.10, σ1 ==20% and DQGσ2 ==30% X = Hσ X = H δW σ δW = DQG G = H −σ = DQG G = H δW −σ δW 164.87 6SXuXu 6110.52 GX S 0d 1u 90.48 6SX0uG1d 660.65 GG S 0d1d = = H UI δW − G H UI δW − G = = DQG S = S = X−G X−G FIGURE 7.14 Changing Volatility Option (Underlying Lattice) APPLICATION 190 Binomial Approach Step II: Option Valuation Lattice 54.87 EXERCISE Maximum between Executing the purchase option or T Executing = 164.87 Exercise Price = $54.87 29.70 OPEN 0.52 19.19 END OPEN 0.28 OPEN U 0.00 END The binomial option valuation comes out to be $19.19 in expanded NPV, in comparison with a static NPV of -$10, providing a $29.19 option value Notice that this analysis type assumes a non-recombining tree analysis 0.00 END Maximum between Executing the purchase option or Keeping the Option Open Executing = 81.87 Exercise Price = -$28.13 Keeping the Option Open = [P(0.52) + (1 -P)(0.00)]exp( -riskfree*dt) = $0.28 FIGURE 7.15 Changing Volatility Option (Valuation Lattice) circumstance, the up and down factors are different over the two time periods Thus, the binomial lattice will no longer be recombining As a matter of fact, the underlying asset lattice branches cross over each other as shown in Figure 7.14 The upper bifurcation of the first lower branch (from $81.87 to $110.52) crosses the lower bifurcation of the upper first branch (from $122.14 to $90.48) This complex crossover will be compounded for multiple time-steps Figure 7.15 shows the option valuation lattice Similar calculations are performed for an option with changing volatilities as for other option types For instance, node T has a value of $54.87, which is the maximum of zero and $164.87 Ϫ $110 ϭ $54.87 For node U, the value of $0.28 million comes from the maximization of executing the option $81.87 Ϫ $110 ϭ Ϫ$28.13 million and keeping the option open with [(P)($0.52) ϩ (1 Ϫ P)($0)]exp [(Ϫrf )(␦t)] ϭ $0.28 million, which is the maximum value This calculation assumes a 10 percent risk-free rate rf, a time-step ␦t of 1, and a risk-neutral probability P of 0.5983 Using this backward induction technique, this valuation lattice is back-calculated to the starting point to obtain the value of $19.19 million, as compared to the static net present value of Ϫ$10 million (benefits of $100 million with a cost of $110 million) More complicated analyses can be obtained through this changing volatility condition For example, where there are multiple stochastic underlying variables driving the value of the option, each variable may have its own unique volatility, but the variables are correlated with each other Examples include the price and quantity sold where there is a negative correlation between these two variables (the downward-sloping demand curve) The Real 191 Real Options Models Options Analysis Toolkit software CD-ROM handles some of these more difficult calculations SEQUENTIAL COMPOUND OPTION A sequential compound option exists when a project has multiple phases and latter phases depend on the success of previous phases Figures 7.16 to 7.19 show the calculation of a sequential compound option Suppose a project has two phases, where the first phase has a one-year expiration that costs $500 million The second phase’s expiration is three years and costs $700 million Using Monte Carlo simulation, the implied volatility of the logarithmic returns on the projected expected future cash flows is calculated to be 20 percent The risk-free rate on a riskless asset for the next three years is found to be yielding 7.7 percent The static valuation of future profitability using a discounted cash flow model (that is, the present value of the future cash flows discounted at an appropriate market risk-adjusted discount rate) is found to be $1,000 million The underlying asset lattice is seen in Figure 7.16 The calculation of this initial underlying asset lattice is similar to previous option types by first calculating the up and down factors and evolving the present value of the future cash flow for the next three years Figure 7.17 shows the second step in calculating the equity lattice of the second option The analysis requires the calculation of the longer-term option first and then the shorter-term option because the value of a compound option is based on another option At node V, the value is $1,122.1 %LQRPLDO $SSURDFK ± 6WHS , /DWWLFH (YROXWLRQ onRIofWKH the8QGHUO\LQJ Underlying 1000.0 S0 1221.4 6 XS0u 818.7 6 GS0d *LYHQ S6 == 1,000, σ X;1==500, X;2 ==700 Given: == 0.20, X=H S= = DQG G = H 1000.0 6 XG S0ud 670.3 6 G S 0d 1221.4 XGS0u d 818.7 6 XGS0ud 7 = 7 = UI = σ δW 1491.8 X S0u 1822.1 S u3 6 X −σ δW = 6 G 548.8 S0d H UI δW − G = X−G FIGURE 7.16 Sequential Compound Option (Underlying Lattice) APPLICATION 192 %LQRPLDO $SSURDFK ± 6WHS ,, 0D[LPXP EHWZHHQ ([HFXWLQJ RU (TXLW\ /DWWLFH ([HFXWH ± ,QYHVWPHQW &RVW 0D[ > @ 0D[ > @ 7KLV LV WKH LQWHUPHGLDWH (TXLW\ 9DOXDWLRQ /DWWLFH UHTXLUHG WR VROYH WKH &RPSRXQG 2SWLRQ : 0D[LPXP ([HFXWLQJ RU HHSLQJ WKH 2SWLRQ 2SHQ ([HFXWLQJ ± ,QYHVWPHQW &RVW HHSLQJ 2SWLRQ 2SHQ FIGURE 7.17 >3 3 @ H[S UI GW Sequential Compound Option (Equity Lattice) million because it is the maximum between zero and executing the option through $1,822.1 Ϫ $700 ϭ $1,122.1 million The intermediate node W is $71.3 million, its being the maximum between executing the option $670.3 Ϫ $700 ϭ Ϫ$29.7 million and keeping the option open with [(P)($118.7) ϩ (1 Ϫ P)($0.0)]exp[(Ϫrf )(␦t)] ϭ $71.3 million, which is the maximum value This calculation assumes a 7.7 percent risk-free rate rf, a time-step ␦t of 1, and a risk-neutral probability P of 0.6488 Using this backward induction technique, this first equity lattice is back-calculated to the starting point to obtain the value of $449.5 million Figure 7.18 shows the equity valuation of the first, shorter-term option The analysis on this lattice depends on the lattice of the second, longer-term option as shown in Figure 7.17 For instance, node X has a value of $121.3 million, which is the maximum between zero and executing the option $621.27 Ϫ $500 ϭ $121.27 million Notice that $621.27 is the value of the second, longer-term equity lattice as shown in Figure 7.17 and $500 is the implementation cost on the first option Node Y on the other hand uses a backward induction calculation, where the value $72.86 million is obtained through the maximization between executing the option $449.5 Ϫ $500 ϭ Ϫ$50.5 million and keeping the option open with [(P)($121.3) ϩ (1 Ϫ P)($0.0)]exp[(Ϫrf )(␦t)] ϭ $72.86 million, which is the maximum value The maximum value comes from keeping the option open This calculation assumes a 7.7 percent risk-free rate rf, a time-step ␦t of 1, and a risk-neutral probability P of 0.6488 Again notice that $500 million is the implementation cost of the first option ... Success Factors Project-Based Risk Analysis Simulated Discounted Payback Analysis Discount Rate Analysis Real Options Assumptions Real Options Analysis Real Options Risk Analysis 10.1 10.2 10.3 10.4... Statement Analysis Discount Rate versus Risk-Free Rate Real Options Analysis Introduction The Fundamental Essence of Real Options The Basics of Real Options A Simplified Example of Real Options. .. of Contents CHAPTER The Real Options Process Introduction Critical Steps in Performing Real Options Analysis Summary Chapter Questions CHAPTER Real Options, Financial Options, Monte Carlo Simulation,