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The Strategic CFO Ulrich Hommel • Michael Fabich Ervin Schellenberg • Lutz Firnkorn Editors The Strategic CFO Creating Value in a Dynamic Market Environment Editors Prof Dr Ulrich Hommel EBS Universitaăt fuăr Wirtschaft und Recht i Gr EBS Business School Gustav-Stresemann-Ring 65189 Wiesbaden Germany ulrich.hommel@ebs.edu Ervin Schellenberg EquityGate Advisors GmbH Mainzer Str 19 65185 Wiesbaden Germany schellenberg@equitygate.de Michael Fabich EquityGate Advisors GmbH Mainzer Str 19 65185 Wiesbaden Germany fabich@equitygate.de Lutz Firnkorn Ackeranlagen 74523 Schwaăbisch Hall Germany firnkorn@gmx.de ISBN 978-3-642-04348-2 e-ISBN 978-3-642-04349-9 DOI 10.1007/978-3-642-04349-9 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011939762 # Springer-Verlag Berlin Heidelberg 2012 This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer Violations are liable to prosecution under the German Copyright Law The use of general descriptive names, registered names, trademarks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Contents The Strategic CFO: New Responsibilities and Increasing Job Complexity Michael Fabich, Lutz Firnkorn, Ulrich Hommel, and Ervin Schellenberg Part I Strategy-Linked Approaches to Risk Management and Corporate Financing Linking Strategy to Finance and Risk-Based Capital Budgeting Ulrich Hommel and Mathias Gerner Linking Strategy, Operations and Finance with Simulation-Based Planning Processes 31 Michael Rees Risk-Return Management of the Corporate Portfolio 49 Ulrich Pidun and Matthias Kruăhler Capturing the Strategic Flexibility of Investment Decisions Through Real Options Analysis 69 Johnathan Mun Exposure-Based Cash-Flow-at-Risk for Value-Creating Risk Management Under Macroeconomic Uncertainty 85 Niclas Andre´n, Ha˚kan Jankensga˚rd, and Lars Oxelheim Part II Coping and Benefiting from the Dynamics of Financial Markets Capital Markets 2.0 – New Requirements for the Financial Manager? 109 Holger Wohlenberg and Jan-Carl Plagge v vi Contents Evolving Capital Markets and the Changing Role of the CFO 127 Hady Farag, Frank Plaschke, and Marc Rodt Integrated Capital Structure Management – Value Improvement by Overcoming the Silo Approach of Financial Institutions 143 Michael Fabich, Ervin Schellenberg, and Katinka Woălfer Managing Cash Flow and Control Risks of Financial Contracting 171 Petri Maăntysaari The CFOs Information Challenge in Managing Macroeconomic Risk 189 Lars Oxelheim, Clas Wihlborg, and Marcus Thorsheim Part III Linking the Dynamics of Financial Markets and Product Markets Capacity-Adjustment Decisions and Hysteresis 211 Benoıˆt Chevalier-Roignant and Arnd Huchzermeier Linking Strategy to the Real World: Working Toward Risk Based Supply Chain Optimization 227 Wilhelm K Kross Dealing with Recent Challenges in Cash Flow Management: Commodity Volatility and Competitive Pressure 249 Lutz Firnkorn, Arno Gerken, Sven Heiligtag, Konrad Richter, and Uwe Stegemann How Climate Change Impacts the Role of the CFO 265 Thomas Ruăschen and Markus Eckey Capturing the Impact of Market Dynamics on Firm Value for Service-Driven Enterprises 285 Diem Ho Creating Corporate Value with the Exposure to Financial Innovations: The Case of Interest Rates 295 Marcus Schulmerich Authors Biography Niclas Andre´n is an associate professor of the Department of Business Administration, Lund University School of Economics and Management, Lund, Sweden He holds a PhD in business administration Niclas Andre´n is the Director of the master program in Corporate and Financial Management and former Director of the master program in Finance, both at Lund University He has extensive teaching experience within corporate finance, esp in corporate risk management, valuation, and financial restructurings He has specialized in interactive and applied teaching pedagogics, not least case-based teaching His research interests are corporate risk management, behavioral corporate finance, and asset pricing Per-Olof Bjuggren has a Master of Political Science from Lund University and took his PhD in Economics at Lund University in 1986 The PhD thesis is about vertical integration in the Swedish pulp and paper industry A new theoretical paradigm, the transaction cost approach, is used It is one of first studies that use this approach empirically In 1994 he was appointed associate professor of Economics at Linkoăping University Since July 1995 he is Associate Professor of Economics at Joănkoăping International Business School His own research includes studies in the fields of industrial organization, law and economics and corporate governance He has published articles in journals such as the International Review of Law and Economics, Small Business Economics, Geneva Papers of Risk and Insurance and Family Business Review Several articles have also been published in refereed international books He has together with Arne M Andersson and Olle Ohlsson published industrial organization textbooks (in Swedish) Dr Benoıˆt Chevalier-Roignant graduated in business administration from EMLYON Business School and WHU – Otto Beisheim School of Management in September 2007 and subsequently joined the Munich office of L.E.K Consulting, a global consulting firm with focus on private equity advisory services From 2009 to 2011, he completed a doctorate at the Department of Production Management at vii viii Authors Biography WHU under the supervision of Arnd Huchzermeier, PhD and Lenos Trigeorgis, DBA In September 2011, he joined the University of Texas at Dallas as postdoctoral fellow under the supervision of Dr Alain Bensoussan His research deals with application of stochastic control theory and differential games to the analysis of real options in competitive settings Benoıˆt co-authored Competitive Strategy with Lenos Trigeorgis (forthcoming at the MIT Press) and has published in leading academic journals such as the European Journal of Operational Research Dr Diem Ho is manager of University Relations for IBM Europe Middle East and Africa He is in charge of research collaborations, skill development, and technology access with/for the academic community and driving higher education reforms to meet industry needs and societal challenges in a service dominant economy Diem has held many different positions in IBM, from research, consulting to management He has successfully led management consulting engagements at more than 16 leading European banks and financial services companies throughout Europe He was elected to the IBM Academy of Technology in 1995 He is an associate editor of the Journal of Computational Economics and has been guest editor for a number of journal special issues Dr Ho is also a member of the peer review teams for the EFMD-EQUIS and EPAS accreditation programmes (European Foundation for Management Development – European Quality Improvement System and Programme Accreditation System) and a member of the EPAS committee and has involved in a number industry group initiatives such as the Career Space Consortium (ICT skills and new University curricula for the 21st Century Economy) and the European Learning Industry Group (ELIG) He’s supervised PhD candidates and published widely in Engineering, Physics, Mathematics, Remote Sensing, Image Processing, Optimization, Finance and Business Intelligence He is also a frequent invited contributor to the OECD and UNESCO conferences and publications Diem obtained M.S degrees and a Ph.D degree from Stanford University, California Dr Markus Eckey is a Vice President in Deutsche Bank´s Global Credit Trading division where he originates and executes structured asset finance transactions Before, he worked in Deutsche Bank´s Corporate Development department focussing on principal M&A transactions and strategy-related projects Prior to joining Deutsche Bank, Markus worked in the Investment Banking Division of Goldman, Sachs & Co., specialising in M&A and IPO transactions across a variety of industries Markus holds a diploma in Business Administration from the University of Mannheim and a Ph.D from the European Business School (ebs) Michael Fabich is co-Founder and Managing Partner of EquityGate Advisors GmbH in Wiesbaden (Germany) With over 25 years of professional experience, Michael coheads EquityGate’s corporate finance team He has previously been Head of the German investmentbanking division of Salomon Smith Barney (Citigroup), Member of the Board at Salomon Brothers AG in Frankfurt, and Member of the Global and European Investmentbanking Committees Previously he was Co-Head of M&A Authors Biography ix Germany at Dresdner Kleinwort Benson Michael founded and headed Schroăder Muănchmeyer Hengst Corporate Finance GmbH Before setting up EquityGate, he was Chairman of the German Advisory Board of Duke Street Capital in London Michael graduated from the University of Applied Sciences in Mainz, and is a Member of the Advisory Board of the Strategic Finance Institute (SFI) at European Business School (EBS) International University Dr Hady Farag is a Principal in the Frankfurt office of The Boston Consulting Group (BCG) He is a core member of the Corporate Development practice area and the Corporate Finance Task Force He has supported clients across a wide variety of industries and geographies, including Europe, Southeast Asia, and South America, focussing on capital market and M&A-related projects Prior to joining BCG, Dr Farag served as researcher and later Head of University Development at the European Business School (EBS), where he earned a doctorate degree in business administration He also holds master-level degrees from both EBS and the Joseph M Katz Graduate School of Business (University of Pittsburgh) Lutz Firnkorn is a Project Manager in McKinsey & Company’s Frankfurt office, where he focuses predominantly on risk management for European financial institution Furthermore, he is a PhD candidate at the endowned chair for corporate finance and capital markets at the European Business School (EBS), with research focus on corporate finance and corporate risk management Lutz Firnkorn holds a Masters degree (Diplom Grande Ecole) from the ESCP-EAP in Paris Mathias Gerner is a Research Assistant and Doctoral Candidate at European Business School (EBS) International University in Germany In addition, he was a Visiting Scholar at The University of Texas at Austin (UT) during the summer 2009 He completed his studies in Industrial Engineering at The University of Karlsruhe (TH) including a semester abroad at the Mathematics and Statistics Department at the Herriot-Watt University of Edinburgh Between 2006 and 2008 he successfully finished the Management Trainee Program (SGP) of the Siemens AG, Sector Energy His main research areas are commodity risk management, energy prices and derivatives Dr Arno Gerken is a Director in McKinsey & Company’s Frankfurt Office, and is leading McKinsey’s Global Risk Management Practice out of Europe Dr Arno Gerken has vaste experience in risk management for financial institutions as well as for corporates Dr Arno Gerken holds a diploma in national economics, with majors in game theory, micro theory, and statistics and received his PhD from the University of Bonn, Germany, on credit portfolio modeling Dr Sven Heiligtag is a Principal in McKinsey & Company´s Hamburg Office and a member of both the Transportation & Logistics as well as the Risk Management Practice He has significant experience in advising clients on corporate finance, strategy, organizational and marketing/sales topics Dr Sven Heiligtag has a x Authors Biography Masters degree in Chemistry from the University of Hamburg, a Ph.D in Biochemistry from the University of Hamburg and the Cancer Research Center of Hawaii Prof Ulrich Hommel PhD is a Full Professor of Finance and heads the Endowed Chair of Corporate Finance & Capital Markets at European Business School (EBS) Ulrich Hommel holds a Ph.D in Economics from the University of Michigan, Ann Arbor, and has completed his habilitation in Business Administration at the WHU, Germany He was an Assistant Professor of Finance at the WHU from 1994 to 1999 and has subsequently joined the faculty of the EBS He is the Director of the Strategic Finance Institute at the EBS In the past, Ulrich Hommel has held visiting appointments at the Stephen M Ross School of Business (University of Michigan), the Krannert School of Management (Purdue University) and the Bordeaux Business School His main research interests are corporate risk management, venture capital & private equity, family business finance and corporate restructuring Ulrich Hommel has been Academic Dean of the Faculty at the EBS from 2000 to 2002 and has subsequently held the position of Rector and Managing Director from 2003 to 2006 Since 2007, he is also an Associate Director of Quality Services at the European Foundation for Management Development (EFMD) in Brussels and, as one of the Directors, is responsible for the EFMD Programme Accreditation System (EPAS) Prof Dr Arnd Huchzermeier chairs the Production Management Department and the Center for Collaborative Commerce (CCC) of WHU – Otto Beisheim School of Management in Vallendar In 1986, he received a masters degree in business administration as well as computer science and operations research from the Karlsruhe Institute of Technology (KIT) In 1991, he received a Ph.D degree in Operations Management from the Wharton School of the University of Pennsylvania, USA He published, among others, in Interfaces, Management Science, Manufacturing & Service Operations Management, Marketing Science and Operations Research Since 2007, he is Member of the Board of ECR Europe’s International Commerce Institute; Belgium, and Executive Editor of the International Commerce Review: ECR Journal In 2000, he was awarded the Mercurius Award by Fedis, the European Federation of Distribution Societies, Belgium In 2002, he received the Franz Edelman Finalist Award from the Institute for Operations Research and Management Science/INFORMS, U.S.A In 2003, he won both the ISMS Practice Prize from the Marketing Science Institute, U.S.A and the Management Science Strategic Innovation Prize from the European Associations of Operational Research Societies / EURO, Belgium In 2009, he was awarded the ECCH Case Award from the European Case Clearing House, U.K., in the category ‘Production and Operations Management’ Since 1995, he acts as Academic Director of the German industry competition ‘Best Factory/Industrial Excellence Award’ (jointly with the business journal Wirtschaftswoche and INSEAD, France) In 2009, he co-founded the car sharing company Mobility Now Creating Corporate Value with the Exposure to Financial Innovations 301 Yield in % 10 5 Maturity in yrs 10 Months after April1, 1997 20 30 Fig Term structure of U.S Zero yields, April 1997–March 2000, monthly data (Source: Thomson Reuters Datastream) 10 Yield in % 10 Maturity in yrs 20 Months after April1, 2007 30 Fig Term structure of U.S Zero yields, April 2000–March 2003, monthly data (Source: Thomson Reuters Datastream) for over years in concert with high growth in the U.S (and also in other parts of the world) By the end of 2006, the market situation started to change A new word was created and hit the headlines: The “subprime crisis” unfolded But what started as a problem limited to the Finance industry, turned into a devastating global tsunami that wiped out some of the biggest players in Finance like Lehman Brothers or Bear 302 M Schulmerich Yield in % 10 Maturity in yrs 10 Months after April1, 2003 20 30 Fig Term structure of U.S Zero yields, April 2003–March 2006, monthly data (Source: Thomson Reuters Datastream) Stearns In the last quarter of 2008, the impact on the real economy became evident An economic downturn unfolded and turned into the biggest global financial and economic crisis since the great depression of the 1930s All over the world, the central banks reacted That this crisis was different from previous ones is shown by the fact that interest rates in the U.S have been pushed down to as low as zero percent and have remained at this level since the end of 2008 Accordingly, the shape of the yield curve changed dramatically from the end of 2007 onwards The term structure movements of the 1-month to 10-years U.S Zero yield curve between April 2003 and March 2009 can be seen in Fig (for April 2003–March 2006) and Fig (for April 2006–March 2009) 3.1 Valuation Models that Apply a Constant Risk-Free Interest Rate This section very briefly reviews important numerical real options valuation methods Although analytical methods for pricing real options are plentiful, their application to real options practice is rather limited To quote Trigeorgis (see Trigeorgis 1991, p 310): Real-life investments are often more complex in that they may involve more than one option simultaneously In such cases, analytic solutions may not exist and it might not even be possible to write down the set of partial differential equations describing the underlying stochastic processes Valuing each option separately and adding up the individual results is often inappropriate since multiple options may in fact interact Creating Corporate Value with the Exposure to Financial Innovations 303 Yield in % 10 Maturity in yrs 10 Months after April 1, 2006 20 30 Fig Term structure of U.S Zero yields, April 2006–March 2009, monthly data (Source: Thomson Reuters Datastream) Table Categorization of numerical methods to price real options Approximation of partial Approximation of the underlying stochastic process differential equations Implicit finite differences methods Monte Carlo simulation Use Gauss algorithm to solve the Simulates the underlying stochastic process several times in linear equation system order to obtain a distribution of the real options price Explicit finite differences method Tree methods (e.g., Cox-Ross-Rubinstein binomial tree) Simple solving of various equations Create replicating portfolios to calculate the real options price in a backward solving tree algorithm In contrast, numerical methods can easily be applied to various complex situations, which occur in Corporate Finance practices Moreover, they can easily be modified to include a non-constant interest rate, which is often not feasible for analytical models due to mathematical complexities Table provides an overview of the most important numerical real options valuation methods as shown in Schulmerich (2003), p 67: 3.2 Valuation Models that Allow for a Non-constant Risk-Free Interest Rate Common real options pricing tools use a constant risk-free interest rate To be more specific, they assume the risk-free interest rate to be the same for all time periods 304 M Schulmerich and constant over time, which corresponds to a flat and constant term structure of interest rates over time For the remainder of this chapter we also assume that T > is the length of the investment project that we later want to evaluate by using a real options approach We divide the time between now (t ¼ 0) and the end of the investment project (t ¼ T) in N > time points ¼ t0 < t1 < tN ¼ T which are assumed to be equidistant, i.e., tj À tjÀ1 ¼ Dt :¼ T N for j ¼ 1; :::; N: This gives N subintervals of equal length The time interval (tjÀ1, tj) is named subinterval j or subperiod j, j N In his book Options, Futures, and Other Derivatives, Hull describes a specific approach to use a non-constant risk-free rate in the subintervals of the Cox-RossRubinstein binomial tree method and details circumstances when such an approach is recommended (Hull 1997, pp 356–357): The usual assumption when American options are being valued is that interest rates are constant When the term structure is steeply upward or downward sloping, this may not be a satisfactory assumption It is more appropriate to assume that the interest rate for a period of length Dt in the future equals the current forward interest rate for that period [ .] This does not change the geometry of the tree [ .] It is important to notice that, compared to the traditional Cox-Ross-Rubinstein binomial tree, the risk-free interest rate rf is now a function of time t ! and is no longer a constant.1 We will look at the maths behind this “modified” Cox-RossRubinstein binomial tree method in Sect 3.2.1 3.2.1 The Cox-Ross-Rubinstein Method A good start for developing real options valuation methods that allow for a nonconstant risk-free rate is to use existing methods for a constant risk-free rate and to modify them for using a non-constant risk-free rate In this section we look at a modification of the standard Cox-Ross-Rubinstein binomial tree model Modeling the non-constant risk-free rate will be discussed in the section thereafter The following definitions will be used2: V ¼ total value of the project S ¼ price of the twin security that is almost perfectly correlated with V E ¼ equity value of the project for the shareholder This function is not the short-rate process (rt)t!0, which will be introduced later, but just a timedependent function Schulmerich (2005), Sect 4.4.2 for more details The basic Cox-Ross-Rubinstein binomial tree model is described in Schulmerich (2005) Sect 4.2.1 or in Schulmerich (2003), Sect 4.3 Creating Corporate Value with the Exposure to Financial Innovations 305 u ¼ multiplicative factor for up-movements of V and S per period d ¼ multiplicative factor for down-movements of V and S per period jị rf ẳ risk-free interest rate in time period j pjị ẳ risk-neutral probability for up-movements of V and S in time period j Notice that the only difference between this model and the original Cox-RossRubinstein binomial tree model is that rf and p are now dependent on the time period j in the tree The price S of the underlying and the project value V develop as in the traditional Cox-Ross-Rubinstein model, i.e., if at the beginning of a time interval with length Dt the underlying value is S, it is assumed that at the end of this time interval the underlying can take two values, uS and dS, whereby u > and d < In the case of a non-constant risk-free rate, the risk-neutral p for the up-case and 1-p for the down-case depend on the prevailing risk-free rate rf(j) in the corresponding time interval j Therefore, the superscript p(j) is necessary Figure provides a graphical overview of the modified Cox-Ross-Rubinstein binomial tree, if a non-constant risk-free rate is applied The continuous-time counterpart is S being a Geometric Brownian Motion with volatility s In a risk-neutral world, the return of the underlying is the risk-free interest rate With the continuously compounded, annualized risk-free rate rf(j) for subinterval j this means ðjÞ Dt ẳ pjị uS ỵ pjị dS; jị Dt ẳ pjị u ỵ pjị d: S Á er f which is equivalent to er f (1) According to Hull (1997), Eq 11.4 on page 344 as well as pages 356–357, the variance of the change in the underlying within subinterval j is ðjÞ e2rf Dtỵs2 Dt ẳ pjị u2 ỵ pðjÞ d2 : (2) Equations and impose two conditions on p(j), u, and d A third condition is given (on each of the N subintervals separately) by Cox, Ross and Rubinstein via u ¼ 1/d, see Cox et al (1979) According to Hull (1997), page 345 and pages 356–357, these three conditions imply rﬃﬃﬃﬃ! T u ¼ exp s ẳ N d jị and p jị erf Dt À d : ¼ uÀd 306 M Schulmerich Fig Modified Cox-Ross-Rubinstein binomial tree method with update of the risk-free rate for each subinterval The goal is now to replicate the pay-off structure of the project in each subinterval j through the purchase of n shares of the twin security and through issuing of a Dt – year Zero bond with nominal value B and risk-free return rf(j) for this subinterval This means that the replicating portfolio has to incorporate the nonconstant risk-free interest rate rf(j) This is shown in Fig By choosing the replicating portfolio approach E ¼ nS – B, the two Eqs a and b in Fig have to be solved simultaneously to get n and B The solutions to this problem are given in Fig 10 Creating Corporate Value with the Exposure to Financial Innovations Fig The concept of a replicating portfolio in the Cox-Ross-Rubinstein binomial tree with nonconstant risk-free interest rate for time period j, j N Fig 10 Solutions for a replicating portfolio in the modified Cox-RossRubinstein binomial tree model for time period j, j N 3.2.2 307 p ( j) (a) Eu = nSu – e ( j) r f Dt B -p ( j) (b) Ed = nSd – e ( j) r f Dt B E = nS – B n= p( j) Eu - Ed S u - Sd = e ( j) r f Dt -d u-d E= p( j)Eu + (1 - p( j) )Ed e B= ( j) r f Dt Eu Sd - Ed Su ( j) Dt (Su - Sd) e r f Modelling of a Non-constant Interest Rate The simplest way of modelling a non-constant interest rate is using the forward rate implied in the prevailing term structure of interest rates A more difficult approach is to derive the non-constant interest rate from stochastic term structure models The first stochastic term structure model was developed in Vasicek (1977) The key of each stochastic term structure model is the short-rate model Common to all of these approaches is the same basic terminology and notation In order to introduce this basic terminology, a Zero bond is considered that pays 1$ at maturity The time point of today is t ¼ and the Zero is assumed to mature at time point t ¼ T ! The unit for the time axis is always years This means that today the Zero is a T–year Zero The question is, how much would someone be willing to pay for this bond at time t, t T? Figure 11 gives a graphical explanation of this situation Summary of Notation as used by (Clewlow and Strickland 1998, p 184): P(t, T) ¼ price at time t of a Zero bond that matures at time T R(t, T) ¼ continuously compounded yield at time t on the Zero bond that matures at time T (also called spot rate) rt ¼ short-term interest rate at time t (also called short rate) f(t, T) ¼ instantaneous forward rate at time t for time T The function R describes the term structure of interest rates The difference between the term structure of interest rates and a yield curve is that a yield curve shows the yield of a particular bond, which does not need to be a Zero bond In the special case where this bond is a Zero bond, the yield of the bond is the spot rate and the term structure of interest rates is the yield curve for that bond 308 M Schulmerich cash inflow 1$ (= today) t maturity T cash outflow (< 0) time (in years) Fig 11 Cash flow of a Zero bond The pricing relationship for a Zero bond is: Pt; Tị ẳ eRt;TịTtị : (3) If the bond price is given, the spot rate R(t, T) can be calculated as Rt; T ị ẳ ln Pðt; T Þ: TÀt (4) The instantaneous forward rate f(t, T) is defined as f ðt; T Þ :ẳ @ ln Pt; T ị: @T (5) Using Eqs and for t ¼ and combining them yields: f t; T ị ẳ @ Rt; T Þ Á T Þ: @T (6) For example, Eq with t ¼ gives the currently prevailing instantaneous forward rate for time T In the following we will look at the specification of the risk-free rate, which is needed in the binomial tree More precisely, we need to calculate the risk-free rate rf(j) for each of the N subintervals in the binomial tree Hence the risk-free rate is a discrete function of the subinterval’s number j The first way to determine this function is based on the unbiased expectations theory for the term structure of interest rates The unbiased expectations theory assumes that the currently implied forward rates are an unbiased estimate of the future spot rates Under this theory, since the latter are the ones we need in the binomial tree, we can simply use the forward rate as the future spot rate rf(j) in the respective subinterval In the following, this approach to calculate the future risk-free interest rate will be called the implied forward rates approach Creating Corporate Value with the Exposure to Financial Innovations 309 The second way to determine the risk-free rate function is using a stochastic term structure model Such a stochastic model calculates the function R using a so-called short-rate process The short rate rt is the instantaneous interest rate, see e.g Schulmerich (2005), Sect 3.2.1 This means that rt, t ! 0, is the annualized interest rate prevailing at time t for the infinitesimal time period (t, t + dt) with dt as an infinitesimal short time period Using the short rate process, a bank deposit for 1$ earns 0T ð exp@ rt dtA À dollars as interest during the investment interval (0, T) The continuously compounded risk-free interest rate rf(j) :¼ rf ([jÀ1]Dt) for subinterval j in the binomial tree then is the interest rate R([jÀ1] Dt, j Dt) There exist many ways how to model the short rate as a stochastic process One of these models is the Ho-Lee model The Ho-Lee model, published in 1986 (Ho and Lee 1986), was the first no-arbitrage model presented in the literature as can be seen in Clewlow and Strickland (1998), p 208 Ho and Lee were the first authors to develop a model consistent with the initial term structure of interest rates This is particularly important since the acceptance of such a yield curve model is much higher in practice than for term structure models that not reproduce the current term structure The process of the Ho-Lee model is described via the SDE drt ẳ ytịdt ỵ sdBt ; t ! 0; ytị ẳ @f 0; tị ỵ s2 t @t where 8t ! 0; s IRỵ : y(ã) represents a time-dependent drift that can according to Hull and White (1994), p 8, be seen as an approximation of the slope of the initial instantaneous forward rate curve f The following formulas hold for the price of a Zero bond that matures at time T (Clewlow and Strickland 1998, p 209): Pt; T ị ẳ Aðt; T ÞeÀrt Bðt;T Þ ; t T; with : Pð0; T Þ @ ln Pð0; tÞ À Bðt; T Þ À s tBðt; T Þ2 ; Aðt; T Þ ¼ exp ln Pð0; tÞ @t Bt; T ị ẳ T t: (7) (8) (9) If the price of the Zero bond is given, the yield that determines the yield curve can be calculated using Eq When simulating a path of the short-rate process, the question that has to be answered is how to set the start value r0 of this process For the Ho-Lee model r0 310 M Schulmerich can be chosen such that the yield curve for t ¼ coincides exactly with the observed yield curve at t ¼ in the capital market: According to Eqs 7, and 9, it holds for the current (i.e., t ¼ 0) Zero price: P0; T ị ẳ A0; T ịert Bð0;T Þ ; T ! 0; (10) Að0; T Þ ẳ expfR0; T ịT ỵ B0; T ịf 0; 0ịg; (11) B0; T ị ẳ T: (12) with Putting Eqs 11 and 12 into Eq 10 and applying Eq yields: P0; T ị ẳ expfR0; T ịT ỵ T r0 f 0; 0ịịg ẳ expfR0; T ịT g This equation has to hold for all T ! which can only be achieved if r0 ¼ f(0,0) Therefore, when simulating a path of the short-rate process in the Ho-Lee model, f (0,0) has to be chosen as the start value r0 to get a term structure consistent model As an example, Fig 12 shows a realized path of the Ho-Lee model using the inverted yield curve as of December 1, 2000, as input parameter Figure 13 displays the development of this initial yield curve over time for this specific path of the short rate process, see, e.g., Schulmerich (2005), Sect 3.3.2: Fig 12 Example of a short-rate path in the Ho-Lee model Inverted U.S Zero yield curve from December 1, 2000, as input parameter Creating Corporate Value with the Exposure to Financial Innovations 311 Fig 13 Example of the development of the term structure of interest rates over years in the Ho-Lee model, corresponding to Fig 12 Two Real Options Case Studies 1997–2009 4.1 Description of the Case Studies In his book “Real Options Valuation” from 2005, Schulmerich undertook the first complex case study including various real options cases and historical backtesting, see Schulmerich (2005), Sect The goals of his analyses were to answer the following three questions: How the various real options influence the total value of the project, i.e., the project value including all real options? In the case of stochastically modelled risk-free interest rates, how does the choice of the term structure model and its parameters influence the real options value and, accordingly, the net present value of the project? Does a stochastically modeled risk-free rate better capture the interest rate volatility that could be observed in the capital markets, especially between 1999 and 2002, compared with models with a constant risk-free rate? To answer these questions, three cases were analyzed The real options included in these cases were chosen on the basis of empirical analyses done by Vollrath (2001), p 73, among a sample of firms with headquarters in Germany These real options were combined with the three cases with the idea of showing how the project value gradually changes by including more and more real options: 312 M Schulmerich • Case 1: Option to abandon the project at any time during the construction period for a salvage value X Since such a real option is an American put option, the salvage value is the strike price of this option • Case 2: Option to abandon the project at any time during the construction period for a salvage value X (case 1) and option to expand the project once by an expand factor (e.g., expand project by 30%) for an expand investment at the end of the construction period The expand investment is assumed to be a fraction of the initial investment cost • Case 3: Complex real option in case combined with an option to delay the project start by exactly year The project can start today or in exactly year from today if the investment in year has a positive NPV If, in year from now, the NPV will be negative, the project will not be started at all In all of these analyses, historical data between April 1997 and March 2003 were used and conclusions drawn Especially, the months after April 1, 1998, show a rich pattern of term structure shapes: During the months period from July 1998 until March 1999 the term structure changed tremendously and took a normal, a flat, and an inverted shape on different days For the details of this analysis, please see Schulmerich (2005), Sect 5.8 In the second edition of his book, published in 2010, Schulmerich analyzed a much longer historical time period, i.e., April 1997–March 2009, in order to answer the following question (see Schulmerich 2010): How the findings of the historical backtesting for the second edition, which covers far more scenarios and a much longer time period, compare to the results of the first edition? The tested real options cases were identical to those in the first edition of his book Again, historical backtesting was key to assess how far the real options approach including a non-constant risk-free interest rate is consistent with reality when interest rates fluctuate in a wide range, like they did in the last 12 years Importantly, the time between 2004 and 2009 exhibits two extreme patterns for the short-term interest rate At first, it increased steadily, but then fell at a rapid speed with a peak in September 2008 when Lehman Brothers went bankrupt These movements were already displayed in Fig The historical backtests to price the above three real options cases were carried out using the modified Cox-Ross-Rubinstein binomial tree method as presented in Sect 3.2.1 Three different ways of calculating the risk-free interest rates were used: • Constant risk-free interest rate • Risk-free interest rate calculated using the implied forward rates method (see Sect 3.2.2) • Ho-Lee model for the stochastic simulation of the future interest rate movements (see Sect 3.2.2) The results were then compared to the real options pricing with the historical risk-free interest rates that prevailed during the historical backtesting period being Creating Corporate Value with the Exposure to Financial Innovations 313 used as a benchmark In the following we briefly present the main results of this research For the detailed results, please see Schulmerich (2010), Sect 5.8 4.2 Case Study Results In the case study of 2010, 24 scenarios were tested for the second edition versus nine for the first edition of 2005 Therefore, the derived implications have a more general meaning The goal of the second edition was to check the validity of the results from the first edition for more tested historical scenarios and for a longer time period While only data from April 1997 until March 2003 were available for the first edition, the second edition uses data from April 1997 until March 2009 Therefore, the second edition also contains scenarios covering the time period of the subprime crisis The implied forward rates approach by and large yields the best results in historical backtesting in eight test scenarios while the Ho-Lee approach yields the best results in nine In addition, the implied forward rate approach yields the second best results in 14 test scenarios while the Ho-Lee approach yields the second best results in eight test scenarios This means that in all 24 test scenarios analyzed, the implied forward rates approach used for real options valuation only yields the worst results in two scenarios whereas the currently prevailing practice to use a constant risk-free rate leads to the worst NPV results in 62.5% (15 out of 24) of the test scenarios It also means that the Ho-Lee approach yields the best or second best results in 17 out of all 24 test scenarios analyzed but with computational requirements far exceeding those of the implied forward rates approach Consequently, the approach of using the forward rates that are implied in the current yield curve has to be preferred in general over using a constant risk-free rate for real options valuation This is the central result of the 2010 case study and confirms the findings of the 2005 case study, i.e.: All major findings of the 2005 case study were proved to be valid in the 2010 case study which covers far more test scenarios over a far longer time period, including the subprime crisis Summary This chapter looks at the inclusion of non-constant risk-free interest rates in the pricing procedure of real options Literature and detailed case studies on this topic are scarce Until today, constant risk-free rates are primarily applied in pricing methods like the Cox-Ross-Rubinstein binomial tree method This is due to the fact that financial options are usually short lived which encourages the application of a constant interest rate However, real options long-lived options with a time to maturity of several years, depending on the investment project 314 M Schulmerich After elaborating on the problems of the risk-free rate in the context of the dot com and subprime crises in the first section, a modification of the Cox-RossRubinstein binomial tree method is presented which allows for a non-constant risk-free rate Two methods of how to determine this risk-free rate are presented: the implied forward rates approach and the stochastic simulation of future interest rates using the Ho-Lee model Finally, the chapter looks at two case studies that analyzed various types of real options over a shorter and a longer historical time period, respectively The results of both case studies were alike The implications for Corporate Finance practice are clear The implementation of a non-constant risk-free interest rate in the Cox-Ross-Rubinstein binomial tree to value an investment project is relatively easy for the implied forward rates approach All information about the risk-free interest rates needed for the real options valuation tree can easily be derived from the current yield curve On the other hand, the implementation of a stochastic term structure model to derive the appropriate risk-free rate for the real options valuation tree is technically difficult and requires detailed knowledge about stochastic calculus and stochastic simulation in discrete time Accordingly, from the stand point of implementational convenience, the implied forward rates approach is better suited for Corporate Finance practice than a stochastic term structure model like the Ho-Lee model References Alvarez, L.H.R., & Koskela, E (2002) Irreversible investment and interest rate variability (Working Paper) Turku: Turku School of Economics and Business Administration May 2002 Clewlow, L., & Strickland, C (1998) Implementing derivatives models Chichester: Wiley Cox, J C., Ross, S A., & Rubinstein, M (1979) Option pricing: A simplified approach Journal of Financial Economics, 7, 229–263 Danis, M.A., & Pennington-Cross, A (2005) The delinquency of subprime mortgages (Working Paper 2005-022A) St Louis: The Federal Reserve Bank of St Louis Federal Reserve Bank of San Francisco (2006) The rise in homeownership FRBSF Economic Letter Number 2006-30 San Francisco, Nov 2006 Ho, T S Y., & Lee, S B (1986) Term structure movements and pricing interest rate contingent claims The Journal of Finance, 41, 1011–1029 Hommel, U., Scholich, M., & Baecker, P N (2003) Reale optionen Berlin: Springer Hull, J C (1997) Options, futures, and other derivatives (3rd ed.) New Jersey: Prentice Hall Hull, J C., & White, A (1994) Numerical procedures for implementing term structure models I: Single-factor models Journal of Derivatives, 2, 7–16 Ingersoll, J E., Jr., & Ross, S A (1992) Waiting to invest: Investment and uncertainty Journal of Business, 65(1), 1–29 Klyuev, V., & Mills, P (2007) Is housing wealth an ‘ATM’? International Monetary Fund (IMF) Staff Papers, 54(3), 539–561 Miltersen, K R (2000) Valuation of natural resource investments with stochastic convenience yields and interest rates In M J Brennan & L Trigeorgis (Eds.), Project flexibility, agency, and competition (pp 183–204) New York: Oxford University Press Creating Corporate Value with the Exposure to Financial Innovations 315 Miltersen, K.R., & Schwartz, S.E (1998) Pricing of options on commodity futures with stochastic term structures of convenience yields and interest rates (Finance Working Paper, 5–97) UCLA: The John E Anderson Graduate School of Management.Journal of Financial and Quantitative Analysis Schulmerich, M (2003) Einsatz und pricing von realoptionen In U Hommel, M Scholich, & P N Baecker (Eds.), Real options (pp 63–96) Heidelberg: Springer Schulmerich, M (2005) Real options valuation (1st ed.) Heidelberg: Springer Schulmerich, M (2010) Real options valuation (2nd ed.) Heidelberg: Springer Trigeorgis, L (1991) A log-transformed binomial analysis method for valuing complex multioption investments Journal of Financial and Quantitative Analysis, 26(3), 310 Vasicek, O (1977) An equilibrium characterization of the term structure Journal of Financial Economics, 5, 177–188 Vollrath, R (2001) Die Ber€ ucksichtigung von Handlungsflexibilit€at bei Investitionsentscheidungen – Eine empirische Untersuchung In U Hommel, M Scholich, & R Vollrath (Eds.), Published in realoptionen in der Unternehmenspraxis (pp 45–77) Heidelberg: Springer ... chairman of Stoxx Ltd., Market News International Inc., Infobolsa S .A and holds a board seat in Indexium AG Katinka Woălfer is a Doctoral Candidate at the Strategic Finance Institute (SFI) at... arising from financial market globalization, liberalization and innovation and describe the challenges associated with financial market fragmentation, lacking transparency as well as regulatory... 85 Niclas Andre´n, Ha˚kan Jankensga˚rd, and Lars Oxelheim Part II Coping and Benefiting from the Dynamics of Financial Markets Capital Markets 2.0 – New Requirements for the Financial Manager?
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Xem thêm: The strategic CFO creating value in a dynamic market , The strategic CFO creating value in a dynamic market , 2 Relevant Risks, Distributional Properties and Their Aggregation, 5 Risk-Based Planning with Response, and Real Options, 5 Step 5: Modeling the Impact of Risks, 4 Steps 4-6: Sampling, Generating Cash-Flow Distributions, and Calculating CFaR, Capital Markets 2.0 - New Requirements for the Financial Manager?, 4 Management´s View on Market Price Relationships, 5 Management of Commercial Operations; Flexibility and Real Options, 2 ``Dynamic´´ Frameworks of Risk Management