Financial modeling bennina 3rd

• 1. FINANCIAL MODELING

2. The materials in this book are intended for instructional and edu- cational purposes, to illustrate situations similar to those encoun- tered in the real world. The reader will understand that MIT Press and its authors do not guarantee the accuracy or completeness of any information published in this book. Neither MIT Press nor its authors is responsible for the consequences of the implementation of models or information presented in this book. 3. FINANCIAL MODELING Simon Benninga with a section on Visual Basic for Applications by Benjamin Czaczkes THIRD EDITION The MIT Press Cambridge, Massachusetts London, England 4. 2008 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. This book was set in Times Roman by SNP Best-set Typesetter Ltd., Hong Kong, and was printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Benninga, Simon. Financial modeling / Simon Benninga.3rd ed. p. cm. Includes bibliographical references and index. ISBN 978-0-262-02628-4 1. FinanceMathematical models. I. Title. HG173.B46 2008 332.015118dc22 2007038629 10 9 8 7 6 5. To our parents: Helen and Noach Benninga; Esther and Alfred Czaczkes 6. Contents Preface xxiii Preface to the Second Edition xxix Preface to the First Edition xxxi I Corporate Finance Models 1 1 Basic Financial Calculations 3 1.1 Overview 3 1.2 Present Value and Net Present Value 4 1.3 Internal Rate of Return and Loan Tables 9 1.4 Multiple Internal Rates of Return 15 1.5 Flat Payment Schedules 17 1.6 Future Values and Applications 19 1.7 A Pension ProblemComplicating the Future-Value Problem 21 1.8 Continuous Compounding 25 1.9 Discounting Using Dated Cash Flows 30 Exercises 31 2 Calculating the Cost of Capital 39 2.1 Overview 39 2.2 The Gordon Dividend Model 40 2.3 Adjusting the Gordon Model to Account for All Cash Flows to Equity 44 2.4 Supernormal Growth and the Gordon Model 48 2.5 Using the Capital Asset Pricing Model to Determine the Cost of Equity rE 52 2.6 Using the Security Market Line to Calculate Intels Cost of Equity 59 2.7 Three Approaches to Computing the Expected Return on the Market E(rM) 62 2.8 Calculating the Cost of Debt 66 2.9 Computing the WACC: Three Cases 70 2.10 Computing the WACC for Kraft Corporation 70 2.11 Computing the WACC for Tyson Foods 73 2.12 Computing the WACC for Cascade Corporation 77 2.13 When the Models Dont Work 81 7. viii Contents 2.14 Conclusion 86 Exercises 87 Appendix 1: Why Is a Good Measurement of Risk? Portfolio versus Individual Stock B 92 Appendix 2: Getting Data from the Internet 95 3 Financial Statement Modeling 103 3.1 Overview 103 3.2 How Financial Models Work: Theory and an Initial Example 103 3.3 Free Cash Flow: Measuring the Cash Produced by the Business 111 3.4 Using the Free Cash Flow to Value the Firm and Its Equity 113 3.5 Some Notes on the Valuation Procedure 115 3.6 Sensitivity Analysis 117 3.7 Debt as a Plug 118 3.8 Incorporating a Target Debt/Equity Ration into a Pro Forma 121 3.9 Project Finance: Debt Repayment Schedules 122 3.10 Calculating the Return on Equity 125 3.11 Conclusion 127 Exercises 127 Appendix 1: Calculating the Free Cash Flows When There Are Negative Prots 130 Appendix 2: Accelerated Depreciation in Pro Forma Models 131 4 Building a Financial Model: The Case of PPG Corporation 135 4.1 Overview 135 4.2 PPG Financial Statements, 19912000 136 4.3 Analyzing the Financial Statements 138 4.4 A Model for PPG 142 4.5 Back to Treasury Stock and the Dividend 146 4.6 The Whole Model 147 4.7 Free Cash Flows and Valuation 148 4.8 What Is PPGs Dividend Policy? 151 8. ix Contents 4.9 Modeling PPGs Dividend Policy 155 4.10 Computing PPGs Cost of Equity rE and Its Cost of Debt rD 156 4.11 What Is PPGs Weighted Average Cost of Capital? 160 4.12 Back to the ValuationSensitivity Analyses 161 Exercises 163 Appendix: Some Accounting Issues 163 5 Bank Valuation 177 5.1 Overview 177 5.2 Analyzing Bank Balance Sheets 177 5.3 The Banks Free Cash Flow 185 5.4 Large Bank Corporation Buys Small Bank: A Valuation Example 188 5.5 Calculating the Exchange Ratio 193 5.6 Alternatives to FCF Valuation of Financial Institutions 194 5.7 Valuing a Bank by Using Capital Adequacy Ratios 194 5.8 Using P/Es to Value a Bank Acquisition: First Federal Savings Bank 196 6 The Financial Analysis of Leasing 203 6.1 Overview 203 6.2 A Simple Example 203 6.3 Leasing and Firm Financing: The Equivalent-Loan Method 205 6.4 The Lessors Problem: Calculating the Highest Acceptable Lease Rental 208 6.5 Asset Residual Value and Other Considerations 212 6.6 Summary 214 Exercises 214 Appendix: The Tax and Accounting Treatment of Leases 215 7 The Financial Analysis of Leveraged Leases 219 7.1 Overview 219 7.2 An Example 220 7.3 Analyzing the Cash Flows by NPV or IRR 224 7.4 What Does the IRR Mean? 226 9. x Contents 7.5 Accounting for Leveraged Leases: The Multiple Phases Method 230 7.6 Comparing the MPM Rate of Return with the IRR 234 7.7 Summary 234 Exercises 235 II Portfolio Models 237 8 Portfolio ModelsIntroduction 239 8.1 Overview 239 8.2 Computing Returns for Walmart and Target 239 8.3 Calculating Portfolio Means and Variances 245 8.4 Portfolio Means and VariancesThe General Case 246 8.5 Efcient Portfolios 250 8.6 Conclusion 252 Exercises 252 Appendix 1: Adjusting for Dividends 255 Appendix 2: Continuously Compounded versus Geometric Returns 257 9 Calculating Efcient Portfolios When There Are No Short-Sale Restrictions 261 9.1 Overview 261 9.2 Some Preliminary Denitions and Notation 261 9.3 Some Theorems on Efcient Portfolios and CAPM 263 9.4 Calculating the Efcient Frontier: An Example 268 9.5 Three Notes on the Optimization Procedure 272 9.6 Finding Efcient Portfolios in One Step 276 9.7 Finding the Market Portfolio: The Capital Market Line 278 9.8 Testing the SML: Implementing Propositions 35 280 9.9 Summary 283 Exercises 283 Appendix 285 10 Calculating the Variance-Covariance Matrix 291 10.1 Overview 291 10.2 Computing the Sample Variance-Covariance Matrix 291 10. xi Contents 10.3 Should We Divide by M or by M 1? Excel versus Statistics 295 10.4 Alternate Methods for Computing the Sample Variance- Covariance Matrix 297 10.5 Computing the Global Minimum Variance Portfolio 299 10.6 Computing an Efcient Portfolio 301 10.7 Alternatives to the Sample Variance-Covariance: The Single-Index Model 304 10.8 Alternatives to the Sample Variance-Covariance: Constant Correlation 306 10.9 Shrinkage Methods 308 10.10 Alternatives to the Variance-Covariance Matrix: Impact on the Minimum-Variance Portfolio and the Optimal Portfolio 310 10.11 Summary 315 Exercises 315 11 Estimating Betas and the Security Market Line 317 11.1 Overview 317 11.2 Testing the Security Market Line 320 11.3 Did We Learn Something? 324 11.4 The Inefciency of the Market Portfolio 326 11.5 So Whats the Real Market Portfolio? How Can We Test the CAPM? 329 11.6 Using Excess Returns 330 11.7 Does the CAPM Have Any Uses? 332 Exercises 333 12 Efcient Portfolios without Short Sales 335 12.1 Overview 335 12.2 A Numerical Example 336 12.3 The Efcient Frontier with Short-Sale Restrictions 341 12.4 A VBA Program to Create the Efcient Frontier 343 12.5 Other Position Restrictions 345 12.6 Conclusion 347 Exercises 347 11. xii Contents 13 The Black-Litterman Approach to Portfolio Optimization 349 13.1 Overview 349 13.2 A Naive Problem 351 13.3 Black and Littermans Solution to the Optimization Problem 357 13.4 Black-Litterman Step 1: What Does the Market Think? 357 13.5 Black-Litterman Step 2: Introducing OpinionsWhat Does Joanna Think? 360 13.6 Implementing Black-Litterman on an International Portfolio 365 13.7 Summary 368 Exercises 369 14 Event Studies 371 14.1 Overview 371 14.2 Outline of an Event Study 371 14.3 An Initial Event Study: Procter & Gamble Buys Gillette 375 14.4 A Fuller Event Study: Impact of Earnings Announcements on Stock Prices 382 14.5 Using a Two-Factor Model of Returns for an Event Study 390 14.6 Using Excels Offset Function to Locate a Regression in a Data Set 394 14.7 Conclusion 396 15 Value at Risk 397 15.1 Overview 397 15.2 A Really Simple Example 397 15.3 Dening Quantiles in Excel 399 15.4 A Three-Asset Problem: The Importance of the Variance-Covariance Matrix 402 15.5 Simulating DataBootstrapping 404 Appendix: How to Bootstrap: Making a Bingo Card in Excel 409 12. xiii Contents III Option-Pricing Models 419 16 An Introduction to Options 421 16.1 Overview 421 16.2 Basic Option Denitions and Terminology 421 16.3 Some Examples 424 16.4 Option Payoff and Prot Patterns 426 16.5 Option Strategies: Payoffs from Portfolios of Options and Stocks 430 16.6 Option Arbitrage Propositions 432 16.7 Summary 439 Exercises 439 17 The Binomial Option-Pricing Model 443 17.1 Overview 443 17.2 Two-Date Binomial Pricing 443 17.3 State Prices 445 17.4 The Multiperiod Binomial Model 449 17.5 Pricing American Options Using the Binomial Pricing Model 455 17.6 Programming the Binomial Option-Pricing Model in VBA 458 17.7 Convergence of Binomial Pricing in the Black-Scholes Price 463 17.8 Using the Binomial Model to Price Employee Stock Options 466 17.9 Using the Binomial Model to Price Nonstandard Options: An Example 476 17.10 Summary 478 Exercises 478 18 The Lognormal Distribution 483 18.1 Overview 483 18.2 What Do Stock Prices Look Like? 484 18.3 Lognormal Price Distributions and Geometric Diffusions 492 18.4 What Does the Lognormal Distribution Look Like? 495 18.5 Simulating Lognormal Price Paths 498 13. xiv Contents 18.6 Technical Analysis 502 18.7 Calculating the Parameters of the Lognormal Distribution from Stock Prices 503 18.8 Summary 505 Exercises 505 19 The Black-Scholes Model 509 19.1 Overview 509 19.2 The Black-Scholes Model 509 19.3 Using VBA to Dene a Black-Scholes Pricing Function 511 19.4 Calculating the Implied Volatility 513 19.5 A VBA Function to Find the Implied Variance 517 19.6 Dividend Adjustments to the Black-Scholes 520 19.7 Using the Black-Scholes Formula to Price Structured Securities 525 19.8 Bang for the Buck with Options 539 19.9 The Black (1976) Model for Bond Option Valuation 541 19.10 Summary 544 Exercises 544 20 Option Greeks 549 20.1 Overview 549 20.2 Dening and Computing the Greeks 550 20.3 Delta Hedging a Call 555 20.4 Hedging a Collar 564 20.5 Summary 574 Exercises 575 21 Portfolio Insurance 577 21.1 Overview 577 21.2 Portfolio Insurance on More Complicated Assets 578 21.3 An Example 580 21.4 Some Properties of Portfolio Insurance 584 21.5 What Do Portfolio Insurance Strategies Look Like? A Simulation 585 21.6 Insuring Total Portfolio Returns 588 21.7 Implicit Puts and Asset Values 592 14. xv Contents 21.8 Summary 593 Exercises 594 22 An Introduction of Monte Carlo Methods 597 22.1 Overview 597 22.2 Computing Using Monte Carlo 597 22.3 Writing a VBA Program 602 22.4 Another Monte Carlo Problem: Investment and Retirement 604 22.5 A Monte Carlo Simulation of the Investment Problem 607 22.6 Summary 610 Exercises 610 23 Using Monte Carlo Methods for Option Pricing 613 23.1 Overview 613 23.2 State Prices, Probabilities, and Risk Neutrality 613 23.3 Pricing a Plain-Vanilla Call Using Monte Carlo Methods 615 23.4 Monte Carlo Plain-Vanilla Call Pricing Converges to Black-Scholes 618 23.5 Pricing Asian Options 625 23.6 Pricing Asian Options with a VBA Program 633 23.7 Pricing Barrier Options with Monte Carlo 638 23.8 Using VBA and Monte Carlo to Price a Barrier Option 642 23.9 Summary 646 Exercises 646 24 Real Options 649 24.1 Overview 649 24.2 A Simple Example of the Option to Expand 650 24.3 The Abandonment Option 653 24.4 Valuing the Abandonment Option as a Series of Puts 659 24.5 Valuing a Biotechnology Project 662 24.6 Conclusion 667 Exercises 667 15. xvi Contents IV Bonds 669 25 Duration 671 25.1 Overview 671 25.2 Two Examples 671 25.3 What Does Duration Mean? 674 25.4 Duration Patterns 678 25.5 The Duration of a Bond with Uneven Payments 679 25.6 Nonat Term Structures and Duration 687 25.7 Summary 689 Exercises 689 26 Immunization Strategies 693 26.1 Overview 693 26.2 A Basic Simple Immunization Model 693 26.3 A Numerical Example 695 26.4 Convexity: A Continuation of Our Immunization Experiment 698 26.5 Building a Better Mousetrap 700 26.6 Summary 704 Exercises 704 27 Modeling the Term Structure 705 27.1 Overview 705 27.2 An Initial Example 705 27.3 Description of the Data 710 27.4 The Treasury Yield Curve 713 27.5 Computing Par Yields from a Zero-Coupon Yield Curve 715 27.6 Summary 716 Exercises 717 28 Calculating Default-Adjusted Expected Bond Returns 719 28.1 Overview 719 28.2 Calculating the Expected Bond Return in a One-Period Framework 721 28.3 Calculating the Expected Bond Return in a Multiperiod Framework 722 28.4 A Numerical Example 726 16. xvii Contents 28.5 Experimenting with the Example 728 28.6 Computing the Bond Expected Return for an Actual Bond 730 28.7 Semiannual Transition Matrices 734 28.8 Computing Bond Beta 737 28.9 Summary 739 Exercises 740 V Technical Considerations 743 29 Generating Random Numbers 745 29.1 Overview 745 29.2 Rand( ) and Rnd: The Excel and VBA Random-Number Generators 746 29.3 Testing Random-Number Generators 749 29.4 Generating Normally Distributed Random Numbers 754 29.5 Summary 762 Exercises 762 30 Data Tables 765 30.1 Overview 765 30.2 An Example 765 30.3 Setting Up a Data Table 766 30.4 Building a Two-Dimensional Data Table 768 30.5 An Aesthetic Note: Hiding the Formula Cells 769 30.6 Excel Data Tables Are Arrays 770 Exercises 771 31 Matrices 775 31.1 Overview 775 31.2 Matrix Operations 776 31.3 Matrix Inverses 779 31.4 Solving Systems of Simultaneous Linear Equations 781 Exercises 782 32 The Gauss-Seidel Method 785 32.1 Overview 785 32.2 A Simple Example 785 32.3 A More Concise Solution 786 17. xviii Contents 32.4 Conclusion 787 Exercises 787 33 Excel Functions 789 33.1 Overview 789 33.2 Financial Functions 789 33.3 Dates and Date Functions 796 33.4 The Functions XIRR and XNPV 802 33.5 Statistical Functions 805 33.6 Doing Regressions with Excel 808 33.7 Conditional Functions 815 33.8 Large and Rank, Percentile, and Percentrank 816 33.9 Count, CountA, CountIF 817 33.10 Boolean Functions 819 33.11 Offset 821 34 Using Array Functions and Formulas 825 34.1 Overview 825 34.2 Some Built-in Array Functions 825 34.3 Homemade Array Functions 830 34.4 Array Formulas with Matrices 833 Exercises 838 35 Some Excel Hints 841 35.1 Overview 841 35.2 Fast Copy: Filling in Data Next to a Filled-in Column 841 35.3 Multiline Cells 843 35.4 Writing on Multiple Spreadsheets 845 35.5 Text Functions in Excel 847 35.6 Chart Titles That Update 847 35.7 Getformula: A Useful Way of Annotating Spreadsheets 850 35.8 Putting Greek Symbols in Cells 853 35.9 Superscripts and Subscripts 854 35.10 Named Cells 856 35.11 Hiding Cells 857 35.12 Formula Auditing 859 35.13 Formulating Millions as Thousands 861 18. xix Contents VI Introduction to Visual Basic for Applications 865 36 User-Dened Functions with VBA 867 36.1 Overview 867 36.2 Using the VBA Editor to Build a User-Dened Function 867 36.3 Providing Help for the User-Dened Functions in the Function Wizard 872 36.4 Fixing Mistakes in VBA 875 36.5 Conditional Execution: Using If Statements in VBA Functions 877 36.6 The Select Case Statement 882 36.7 Using Excel Functions in VBA 884 36.8 Using User-Dened Functions in User-Dened Functions 885 Exercises 888 Appendix: Cell Errors in Excel and VBA 892 37 Types and Loops 895 37.1 Overview 895 37.2 Using Types 895 37.3 Variables and Variable Types 897 37.4 Boolean and Comparison Operators 901 37.5 Loops 904 37.6 Summary 913 Exercises 913 38 Macros and User Interaction 919 38.1 Overview 919 38.2 Macro Subroutines 919 38.3 User Output and the MsgBox Function 926 38.4 User Input and the InputBox Function 930 38.5 Modules 932 38.6 Summary 935 Exercises 935 39 Arrays 941 39.1 Overview 941 39.2 Simple Arrays 941 19. xx Contents 39.3 Multidimensional Arrays 946 39.4 Dynamic Arrays and the ReDim Statement 948 39.5 Array Assignment 959 39.6 Variants Containing an Array 960 39.7 Arrays as Parameters to Functions 963 39.8 Summary 971 Exercises 971 40 Objects and Add-Ins 975 40.1 Overview 975 40.2 An Introduction to Worksheet Objects 975 40.3 The Range Object 979 40.4 The With Statement 984 40.5 Collections 985 40.6 Names 991 40.7 Using the Object Browser 995 40.8 References to External Functions in Excel 997 40.9 References to External Functions in VBA 999 40.10 Add-Ins and Integration 1008 40.11 Summary 1014 Exercises 1014 Appendix 1: The Excel Object Model 1018 Appendix 2: Extracts from the Help File for Some Methods 1020 41 Information from the Web 1029 41.1 Overview 1029 41.2 Copy and Paste as a Simple Data-Acquisition Technique 1029 41.3 Dynamic Web Queries 1035 41.4 Web Queries: The iqy File 1041 41.5 Parametric Web Pages 1047 41.6 Web Queries: Parameters 1049 41.7 Web Queries: CSV Files and Postprocessing 1056 41.8 A VBA Application: Importing Price Data from Yahoo 1059 41.9 Summary 1089 Exercises 1089 20. xxi Contents Appendix 1: Excerpts from the Help File 1090 Appendix 2: The R1C1 Reference Style 1093 References 1095 Index 1107 21. Preface The two previous editions of Financial Modeling have received a gratify- ingly positive response from readers. The cookbook combination that mixes explanation and implementation using Excel fullls a need in both the academic and practitioner markets for readers who realize that the implementation of the nance basics typically studied in an introductory nance course requires another, more heavily computational and imple- mentational, approach. Excel, the most widely used computational tool in nance, is a natural vehicle for deepening our understanding of the materials. Financial Modeling is organized along six different subject areas. Each of the rst four sections of the book relates to a specic area of nance. These sections are independent of each other, though the reader should realize that they all assume some familiarity with the nance area Financial Modeling is not an introductory text. Section I (Chapters 17) deals with corporate nance topics; Section II (Chapters 815) with portfolio models; Section III (Chapters 1624) with option models; and Section IV (Chapters 2528) with bond-related topics. The last two sections of Financial Modeling are technical in nature. Section V (Chapters 2935) relates to various Excel topics that are used throughout the book. Chapters in this section can be read and accessed as necessary. Section VI (Chapters 3641) deals with Excels program- ming language, Visual Basic for Applications (VBA). VBA is used throughout Financial Modeling to create functions and routines that make life easier, but it is never intrusivein principle the reader can understand the materials in all of the other chapters of Financial Model- ing without needing the VBA chapters. New Chapters Finance is a very dynamic area. The new edition of Financial Modeling contains many updates and changes that track new developments in the area of computational nance. In addition, almost all the chapters have been revised to make explanations more up-to-date. The third edition of Financial Modeling contains eight completely new chapters: Chapter 5 discusses bank valuation. The basic valuation framework of Chapter 3 is applied to the valuation of nancial institutions. 22. Chapter 13 adds an exposition of the Black-Litterman model of port- folio choice to the section on portfolio models. This model, widely used in asset allocation, is not discussed in any major textbook. Chapter 14 discusses event studies, the most prominent tool for judging the effect of market events on the returns of individual stocks. Chapter 20, on Greeks, has been added to Section III, on options. Chapters 22 and 23 discuss the implementation of Monte Carlo methods to option valuation. Chapter 34 discusses array functions, both those included with Excel and the construction of homemade array functions. Chapter 41 shows how to use VBA to extract Web information to Excel. In addition to the new chapters, many of the Financial Modeling chap- ters have been substantially rewritten. Following are a few examples: Chapter 2 includes a number of new cases used to illustrate the estima- tion of the cost of capital. Chapter 4 has a new example (PPG Corporation) for the implementa- tion of pro forma models and valuation. Chapter 10 now includes a discussion of shrinkage methods and their use in the estimation of the variance-covariance methods. Chapter 17 shows how to use the binomial option pricing model to price employee stock options. Chapter 19 adds discussions of structured securities and the Merton model within the framework of Black-Scholes. Chapter 27, on polynomial term structure models, is based on new mate- rials and a new data set of zero-coupon bonds from the Federal Reserve. Getformula The Excel les with this edition include a function called Getformula that enables the user to track cell contents. The disk that comes with Financial Modeling has a document on how users can add Getformula to their les. In order to allow Getformula to work, you must set your xxiv Preface 23. Excel security settings (Tools|Macro|Security) to Medium. If you have done this, then when opening an Excel notebook, you will be confronted by the following screen: You can safely click Enable Macros, which enables the formulas on the notebook. A separate le on the CD-ROM tells you how to implant this useful program on your own Excel notebooks. Excel 2007 As this book went to press in late 2007, Excel 2007 was starting to be used on many computer systems. The differences between Excel 2007 and previous versions of Excel are largely esthetic and not substantive. Since most readers of this book are likely to have older versions of Excel on their computers, I have chosen to continue using Excel 2003 in this edition. A document relating to Excel 2007 is on the disk with Financial Modeling. The Disk The CD-ROM included with Financial Modeling provides les that give all the Excel contents of each chapter as well as les that give the answers to each of the end-of-chapter questions. All the books les have been checked and work with Excel 2007. The disk also includes documents on the differences between Excel 2003 and Excel 2007, on adding Getfor- xxv Preface 24. mula to spreadsheets, and on some problems encountered with Excels XNPV and XIRR functions. Using Financial Modeling in a University Course Financial Modeling has become the book of choice in many intermediate and advanced nance classes that stress the combination of modeling/ Excel skills and a deeper understanding of the underlying nancial models. The Financial Modelingbased courses are often a third- or fourth-year undergraduate or second-year MBA course. These courses are often very different from each other and include much instructor- specic input, but they seem to have a few general features: A typical course starts with two or three classes that stress the Excel skills needed for nancial modeling. Often these classes are held in a computer lab. Though almost all business school students know Excel, they may not know how to nesse data tables (Chapter 30) or some of the basic nancial functions (Chapters 1 and 33) and array functions (Chapter 34). The initial classes give the instructor a chance to level the playing eld. Most one-semester courses then cover, at most, one of the Financial Modeling sections. If we assume that in a typical university course, cover- ing one chapter per week is an upper limit (and many chapters will require two weeks), then a typical course might concentrate on either corporate nance (Chapters 17), portfolio models (Chapters 815), or options (Chapters 1624). At a stretch, the instructor could perhaps throw in the shorter bond section (Chapters 2528). I suggest that after the initial classes in a computer lab, the instructor move to a regular classroom. This enables the classroom emphasis to be on discussions of theory and implementation, with student homework concentrating on actual spreadsheets. An alternative to the preceding structure is to build an even more advanced course around VBA. I teach a nancial engineering course that starts with binomial option pricing, proceeds to cover some of the VBA chapters (3638), and then covers Black-Scholes and Monte Carlo methods (Chapters 1823). xxvi Preface 25. A major problem with a computer-based course is how to structure the nal examination. Two solutions seem to work well. One alternative is to have students (whether alone or in teams) submit a nal project. Examples might be a corporate valuation if the course is based on Section I of the book, an event study for Section II, an option-based project for Section III, or the computation of a bond expected return if the emphasis is on Section IV. A second alternative is to have students submit, by e-mail, a spreadsheet-based examination with severe time limits. One instructor using this book sends his class the nal exam (a compendium of spreadsheet problems) at nine oclock in the morning and requires an e-mail with a spreadsheet answer by noon. Acknowledgments I want to start by thanking a group of wonderful editors: John Covell, Nancy Lombardi, Elizabeth Murry, Ellen Pope, and Peter Reinhart. My next thanks go to a dedicated group of colleagues who read the typescripts for Financial Modeling: Arindam Bandopadhyaya, Michael Chau, Jaksa Cvitanic, Richard Harris, Aurele Houngbedji, Iordanis Karagiannidis, Yvan Lengwiler, Nejat Seyhun, Gke Soydemir, and David Y. Suk. Many of the changes in this edition of Financial Modeling are due to the comments of readers, who have been assiduous in offering sugges- tions and improvements for the book. I follow a tradition started with the rst two editions of Financial Modeling by acknowledging those readers whose comments have been incorporated into this edition: Meni Abudy, Zvika Ak, Gordon Alexander, Naomi Belfer, David Biere, Vitaliy Bilyk, Oded Braverman, Roeland Brinkers, Salvio Cardozo, Israel Dac,JeremyDarhansoff,ToondeBakker,GovindvyasDharwada,Davey Disatnik, Kevin Dowd, Brice Dupoyet, Orit Eshel, Yaara Geyra, Rana P. Ghosh, Bjarne Jensen, Marek Jochec, Milton Joseph, Erez Kamer, Saggi Katz, Emir Kiamilev, Paul Legerer, David Martin, Tom McCurdy, Tsahi Melamed, Tal Mofkadi, Geoffrey Morrisett, Sandip Mukherji, David Pedersen, Georgio Questo, Alex Riahi, Arad Rostampour, Joseph Rubin, Or Shatz, Mel Tukman, Guy Vishnia, Torben Voetmann, James Ward, Roberto Wessels, Geva Yaniv, and Werner Zitzman. xxvii Preface 26. Finally, I want to thank my very patient wife Terry, who has maintained her own and my equilibrium through two books and a business school deanship in the past ve years. As always, I welcome comments and corrections! Simon Benninga [email protected] xxviii Preface 27. Preface to the Second Edition The purpose of this book remains to provide a cookbook for imple- menting common nancial models in Excel. This edition has been expanded by six additional chapters, covering nancial calculations, cost of capital, value at risk (VaR), real options, early exercise boundaries, and term-structure modeling. There is also an additional technical chapter containing a potpourri of Excel hints. I am indebted to a number of people (in addition to those mentioned in the previous preface) for help and suggestions: Andrew A. Adamovich, Alejandro Sanchez Arevalo, Yoni Aziz, Thierry Berger-Helmchen, Roman Weissman Bermann, Michael Giacomo Bertolino, John Bol- linger, Enrico Camerini, Manuel Carrera, John Carson, Roy Carson, Lydia Cassorla, Philippe Charlier, Michael J. Clarke, Alvaro Cobo, Beni Daniel, Ismail Dawood, Ian Dickson, Moacyr Dutra, Hector Tassinari Eldridge, Shlomy Elias, Peng Eng, Jon Fantell, Erik Ferning, Raz Gilad, Nir Gluzman, Michael Gofman, Doron Greenberg, Phil Hamilton, Morten Helbak, Hitoshi Hibino, Foo Siat Hong, Marek Jochec, Russell W. Judson, Tiffani Kaliko, Boris Karasik, Rick Labs, Allen Lee, Paul Legerer, Guoli Li, Richard Liu, Moti Marcus, Gershon Mensher, Tal Mofkadi,GlennMorley,StephenONeil,StevenOng,OrenOssad,Jackie Rosner, Steve Rubin, Dvir Sabah, Ori Salinger, Meir Shahar, Roger Shelor, David Siu, Maja Sliwinski, Bob Taggart, Maurry Tamarkin, Mun Hon Tham, Efrat Tolkowsky, Mel Tukman, Sandra van Balen, Michael Verhofen, Lia Wang, Roberto Wessels, Ethan Weyand, Ubbo Wiersema, Weiqin Xie, Ke Yang, Ken Yook, George Yuan, Khurshid Zaynutdinov, Ehud Ziegelman, and Eric Zivot. I also want to thank my editors, who again have been a great help: Nancy Lombardi, Peter Reinhart, Victoria Richardson, and Terry Vaughn. As always I welcome suggestions and comments. Simon Benninga http://nance.wharton.upenn.edu/~benninga [email protected] 28. Preface to the First Edition Like its predecessor Numerical Techniques in Finance, this book presents some important nancial models and shows how they can be solved numerically and/or simulated using Excel. In this sense this is a nance cookbook; like any cookbook, it gives recipes with a list of ingredients and instructions for making and baking. As any cook knows, a recipe is just a starting point; having followed the recipe a number of times, you can think of your own variations and make the results suit your tastes and needs. Financial Modeling covers standard nancial models in the areas of corporate nance, nancial statement simulation, portfolio problems, options, portfolio insurance, duration, and immunization. Clear and concise explanations are provided in each case for the implementation of the models using Excel. Very little theory is offered except where necessary to understand the numerical implementations. While Excel is often inappropriate for high-level, industrial-strength calculations (portfolios are an example), it is an excellent tool for under- standing the computational intricacies involved in nancial modeling. It is often the case that the fullest understanding of the models comes by calculating them, and Excel is one of the most accessible and powerful tools available for this purpose. Along the way a lot of students, colleagues, and friends (these are nonexclusive categories) have helped me with advice and comments. In particular I would like to thank Olivier Blechner, Miryam Brand, Elizabeth Caulk, John Caulk, Benjamin Czaczkes, John Ferrari, John P. Flagler, Kunihiko Higashi, Julia Hynes, Don Keim, Anthony Kim, Ken Kunimoto, Philippe Nore, Nir Sharabi, Mark Thaler, Terry Vaughn, and Xiaoge Zhou. Finally, my thanks go to a wonderful set of editors: Nancy Lombardi, Peter Reinhart, Victoria Richardson, and Terry Vaughn. 29. I Corporate Finance Models The seven chapters that open the third edition of Financial Modeling cover basic problems and techniques in corporate nance. Chapters 1 and 2 are both review chapters. Chapter 1 is an introduction to basic nancial calculations using Excel. Almost all of the applications dis- cussed center on variations of the discounted cash ow method. The cost of capital, discussed in Chapter 2, is the rate at which corporate cash ows are discounted to arrive at enterprise value. Calculating this rate is not trivial and involves a combination of theoretical models and numerical computation, both discussed in the chapter. Chapter 3 shows how to build pro forma models, which simulate the corporate income statement and balance sheets. Pro forma models are at the heart of many corporate nance applications, including business plans, credit analyses, and valuations. The models require a mixture of nance, accounting, and Excel. Chapter 4 develops a pro forma model to value PPG Corporation. The example we develop is typical of an exercise that accompanies many merger and acquisition valuations. Chapter 5 shows how to apply the valuation technology to banks; it also includes a short discussion of applying price-earnings techniques to bank valuation. Chapters 6 and 7 discuss the nancial analysis of leasing. In Chapter 6 we concentrate on the basic lease/purchase decision using the equiva- lent loan method. An appendix to Chapter 6 discusses some tax and accounting considerations relating to leases. Chapter 7 discusses the nancial analysis of leveraged lease arrangements, including a discussion of the multiple-phases method of FASB 13. The multiple-phases method rate of return is a hybrid IRR, and Excel can easily be used to calculate this return. 30. 1 Basic Financial Calculations 1.1 Overview This chapter aims to give you some nance basics and their Excel imple- mentation. If you have had a good introductory course in nance, this chapter is likely to be at best a refresher.1 This chapter covers Net present value (NPV) Internal rate of return (IRR) Payment schedules and loan tables Future value Pension and accumulation problems Continuously compounded interest Almost all nancial problems center on nding the value today of a series of cash receipts over time. The cash receipts (or cash ows, as we will call them) may be certain or uncertain. The present value of a cash ow CFt anticipated to be received at time t is CF r t t ( )1+ . The numerator of this expression is usually understood to be the expected time-t cash ow, and the discount rate r in the denominator is adjusted for the riski- ness of this expected cash owthe higher the risk, the higher the dis- count rate. The basic concept in present-value calculations is the concept of opportunity cost. Opportunity cost is the return that would be required of an investment to make it a viable alternative to other, similar, invest- ments. In the nancial literature there are many synonyms for opportu- nity cost, among them discount rate, cost of capital, and interest rate. When the opportunity cost is applied to risky cash ows, we will some- times call it the risk-adjusted discount rate (RADR) or the weighted average cost of capital (WACC). It goes without saying that this discount rate should be risk adjusted, and much of the standard nance literature discusses how to make this adjustment. As illustrated in this chapter, when we calculate the net present value, we use the investments oppor- tunity cost as a discount rate. When we calculate the internal rate of 1. In my book Principles of Finance with Excel (Oxford University Press, 2006), I have discussed many basic Excel/nance topics at greater length. 31. 4 Chapter 1 return, we compare the calculated return to the investments opportunity cost to judge its value. 1.2 Present Value and Net Present Value Both concepts, present value and net present value, are related to the value today of a set of future anticipated cash ows. As an example, suppose we are valuing an investment that promises $100 per year at the end of this and the next four years. We suppose that there is no doubt that this series of ve payments of $100 each will actually be paid. If a bank pays an annual interest rate of 10 percent on a ve-year deposit, then this 10 percent is the investments opportunity cost, the alternative benchmark return to which we want to compare the investment. We may calculate the value of the investment by discounting its cash ows using this opportunity cost as a discount rate: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 A B C D Discount rate 10% Year Cash flow Present value 1 100 90.9091