Financial Modeling, 3rd Edition

FINANCIAL MODELING

The materials in this book are intended for instructional and educational purposes, to illustrate situations similar to those encountered 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.

FINANCIAL MODELING

Simon Benninga

with a section on Visual Basic for Applications by Benjamin Czaczkes

THIRD EDITION

The MIT Press Cambridge, Massachusetts London, England

© 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. Finance—Mathematical models. I. Title. HG173.B46 2008 332.01′5118—dc22 2007038629 10 9 8 7 6

To our parents: Helen and Noach Benninga; Esther and Alfred Czaczkes

Contents

Preface Preface to the Second Edition Preface to the First Edition

xxiii xxix xxxi

I

Corporate Finance Models

1

Basic Financial Calculations 1.1 Overview 1.2 Present Value and Net Present Value 1.3 Internal Rate of Return and Loan Tables 1.4 Multiple Internal Rates of Return 1.5 Flat Payment Schedules 1.6 Future Values and Applications 1.7 A Pension Problem—Complicating the Future-Value Problem 1.8 Continuous Compounding 1.9 Discounting Using Dated Cash Flows Exercises

3 3 4 9 15 17 19

Calculating the Cost of Capital 2.1 Overview 2.2 The Gordon Dividend Model 2.3 Adjusting the Gordon Model to Account for All Cash Flows to Equity 2.4 “Supernormal Growth” and the Gordon Model 2.5 Using the Capital Asset Pricing Model to Determine the Cost of Equity rE 2.6 Using the Security Market Line to Calculate Intel’s Cost of Equity 2.7 Three Approaches to Computing the Expected Return on the Market E(rM) 2.8 Calculating the Cost of Debt 2.9 Computing the WACC: Three Cases 2.10 Computing the WACC for Kraft Corporation 2.11 Computing the WACC for Tyson Foods 2.12 Computing the WACC for Cascade Corporation 2.13 When the Models Don’t Work

39 39 40

2

1

21 25 30 31

44 48 52 59 62 66 70 70 73 77 81

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3

4

Contents

2.14 Conclusion Exercises Appendix 1: Why Is β a Good Measurement of Risk? Portfolio β versus Individual Stock B Appendix 2: Getting Data from the Internet

86 87

Financial Statement Modeling 3.1 Overview 3.2 How Financial Models Work: Theory and an Initial Example 3.3 Free Cash Flow: Measuring the Cash Produced by the Business 3.4 Using the Free Cash Flow to Value the Firm and Its Equity 3.5 Some Notes on the Valuation Procedure 3.6 Sensitivity Analysis 3.7 Debt as a Plug 3.8 Incorporating a Target Debt/Equity Ration into a Pro Forma 3.9 Project Finance: Debt Repayment Schedules 3.10 Calculating the Return on Equity 3.11 Conclusion Exercises Appendix 1: Calculating the Free Cash Flows When There Are Negative Profits Appendix 2: Accelerated Depreciation in Pro Forma Models

103 103

130 131

Building a Financial Model: The Case of PPG Corporation 4.1 Overview 4.2 PPG Financial Statements, 1991–2000 4.3 Analyzing the Financial Statements 4.4 A Model for PPG 4.5 Back to Treasury Stock and the Dividend 4.6 The Whole Model 4.7 Free Cash Flows and Valuation 4.8 What Is PPG’s Dividend Policy?

135 135 136 138 142 146 147 148 151

92 95

103 111 113 115 117 118 121 122 125 127 127

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Contents

4.9 Modeling PPG’s Dividend Policy 4.10 Computing PPG’s Cost of Equity rE and Its Cost of Debt rD 4.11 What Is PPG’s Weighted Average Cost of Capital? 4.12 Back to the Valuation—Sensitivity Analyses Exercises Appendix: Some Accounting Issues 5

6

7

Bank Valuation 5.1 Overview 5.2 Analyzing Bank Balance Sheets 5.3 The Bank’s Free Cash Flow 5.4 Large Bank Corporation Buys Small Bank: A Valuation Example 5.5 Calculating the Exchange Ratio 5.6 Alternatives to FCF Valuation of Financial Institutions 5.7 Valuing a Bank by Using Capital Adequacy Ratios 5.8 Using P/Es to Value a Bank Acquisition: First Federal Savings Bank The 6.1 6.2 6.3

155 156 160 161 163 163 177 177 177 185 188 193 194 194 196

Financial Analysis of Leasing Overview A Simple Example Leasing and Firm Financing: The Equivalent-Loan Method 6.4 The Lessor’s Problem: Calculating the Highest Acceptable Lease Rental 6.5 Asset Residual Value and Other Considerations 6.6 Summary Exercises Appendix: The Tax and Accounting Treatment of Leases

208 212 214 214 215

The 7.1 7.2 7.3 7.4

219 219 220 224 226

Financial Analysis of Leveraged Leases Overview An Example Analyzing the Cash Flows by NPV or IRR What Does the IRR Mean?

203 203 203 205

x

Contents

7.5

Accounting for Leveraged Leases: The “Multiple Phases Method” 7.6 Comparing the MPM Rate of Return with the IRR 7.7 Summary Exercises

230 234 234 235

II

Portfolio Models

237

8

Portfolio Models—Introduction 8.1 Overview 8.2 Computing Returns for Walmart and Target 8.3 Calculating Portfolio Means and Variances 8.4 Portfolio Means and Variances—The General Case 8.5 Efficient Portfolios 8.6 Conclusion Exercises Appendix 1: Adjusting for Dividends Appendix 2: Continuously Compounded versus Geometric Returns

239 239 239 245 246 250 252 252 255

9

10

257

Calculating Efficient Portfolios When There Are No Short-Sale Restrictions 9.1 Overview 9.2 Some Preliminary Definitions and Notation 9.3 Some Theorems on Efficient Portfolios and CAPM 9.4 Calculating the Efficient Frontier: An Example 9.5 Three Notes on the Optimization Procedure 9.6 Finding Efficient Portfolios in One Step 9.7 Finding the Market Portfolio: The Capital Market Line 9.8 Testing the SML: Implementing Propositions 3–5 9.9 Summary Exercises Appendix

261 261 261 263 268 272 276 278 280 283 283 285

Calculating the Variance-Covariance Matrix 10.1 Overview 10.2 Computing the Sample Variance-Covariance Matrix

291 291 291

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Contents

10.3

Should We Divide by M or by M – 1? Excel versus Statistics 10.4 Alternate Methods for Computing the Sample VarianceCovariance Matrix 10.5 Computing the Global Minimum Variance Portfolio 10.6 Computing an Efficient Portfolio 10.7 Alternatives to the Sample Variance-Covariance: The Single-Index Model 10.8 Alternatives to the Sample Variance-Covariance: Constant Correlation 10.9 Shrinkage Methods 10.10 Alternatives to the Variance-Covariance Matrix: Impact on the Minimum-Variance Portfolio and the Optimal Portfolio 10.11 Summary Exercises 11

12

295 297 299 301 304 306 308

310 315 315

Estimating Betas and the Security Market Line 11.1 Overview 11.2 Testing the Security Market Line 11.3 Did We Learn Something? 11.4 The Inefficiency of the “Market Portfolio” 11.5 So What’s the Real Market Portfolio? How Can We Test the CAPM? 11.6 Using Excess Returns 11.7 Does the CAPM Have Any Uses? Exercises

317 317 320 324 326

Efficient Portfolios without Short Sales 12.1 Overview 12.2 A Numerical Example 12.3 The Efficient Frontier with Short-Sale Restrictions 12.4 A VBA Program to Create the Efficient Frontier 12.5 Other Position Restrictions 12.6 Conclusion Exercises

335 335 336 341 343 345 347 347

329 330 332 333

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Contents

13

The Black-Litterman Approach to Portfolio Optimization 13.1 Overview 13.2 A Naive Problem 13.3 Black and Litterman’s Solution to the Optimization Problem 13.4 Black-Litterman Step 1: What Does the Market Think? 13.5 Black-Litterman Step 2: Introducing Opinions—What Does Joanna Think? 13.6 Implementing Black-Litterman on an International Portfolio 13.7 Summary Exercises

349 349 351

Event Studies 14.1 Overview 14.2 Outline of an Event Study 14.3 An Initial Event Study: Procter & Gamble Buys Gillette 14.4 A Fuller Event Study: Impact of Earnings Announcements on Stock Prices 14.5 Using a Two-Factor Model of Returns for an Event Study 14.6 Using Excel’s Offset Function to Locate a Regression in a Data Set 14.7 Conclusion

371 371 371

Value at Risk 15.1 Overview 15.2 A Really Simple Example 15.3 Defining Quantiles in Excel 15.4 A Three-Asset Problem: The Importance of the Variance-Covariance Matrix 15.5 Simulating Data—Bootstrapping Appendix: How to Bootstrap: Making a Bingo Card in Excel

397 397 397 399

14

15

357 357 360 365 368 369

375 382 390 394 396

402 404 409

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Contents

III

Option-Pricing Models

419

16

An Introduction to Options 16.1 Overview 16.2 Basic Option Definitions and Terminology 16.3 Some Examples 16.4 Option Payoff and Profit Patterns 16.5 Option Strategies: Payoffs from Portfolios of Options and Stocks 16.6 Option Arbitrage Propositions 16.7 Summary Exercises

421 421 421 424 426

The Binomial Option-Pricing Model 17.1 Overview 17.2 Two-Date Binomial Pricing 17.3 State Prices 17.4 The Multiperiod Binomial Model 17.5 Pricing American Options Using the Binomial Pricing Model 17.6 Programming the Binomial Option-Pricing Model in VBA 17.7 Convergence of Binomial Pricing in the Black-Scholes Price 17.8 Using the Binomial Model to Price Employee Stock Options 17.9 Using the Binomial Model to Price Nonstandard Options: An Example 17.10 Summary Exercises

443 443 443 445 449

The Lognormal Distribution 18.1 Overview 18.2 What Do Stock Prices Look Like? 18.3 Lognormal Price Distributions and Geometric Diffusions 18.4 What Does the Lognormal Distribution Look Like? 18.5 Simulating Lognormal Price Paths

483 483 484

17

18

430 432 439 439

455 458 463 466 476 478 478

492 495 498

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Contents

18.6 18.7

Technical Analysis Calculating the Parameters of the Lognormal Distribution from Stock Prices 18.8 Summary Exercises

502

The Black-Scholes Model 19.1 Overview 19.2 The Black-Scholes Model 19.3 Using VBA to Define a Black-Scholes Pricing Function 19.4 Calculating the Implied Volatility 19.5 A VBA Function to Find the Implied Variance 19.6 Dividend Adjustments to the Black-Scholes 19.7 Using the Black-Scholes Formula to Price Structured Securities 19.8 Bang for the Buck with Options 19.9 The Black (1976) Model for Bond Option Valuation 19.10 Summary Exercises

509 509 509 511 513 517 520 525 539 541 544 544

20

Option Greeks 20.1 Overview 20.2 Defining and Computing the Greeks 20.3 Delta Hedging a Call 20.4 Hedging a Collar 20.5 Summary Exercises

549 549 550 555 564 574 575

21

Portfolio Insurance 21.1 Overview 21.2 Portfolio Insurance on More Complicated Assets 21.3 An Example 21.4 Some Properties of Portfolio Insurance 21.5 What Do Portfolio Insurance Strategies Look Like? A Simulation 21.6 Insuring Total Portfolio Returns 21.7 Implicit Puts and Asset Values

577 577 578 580 584

19

503 505 505

585 588 592

xv

22

23

24

Contents

21.8 Summary Exercises

593 594

An Introduction of Monte Carlo Methods 22.1 Overview 22.2 Computing π Using Monte Carlo 22.3 Writing a VBA Program 22.4 Another Monte Carlo Problem: Investment and Retirement 22.5 A Monte Carlo Simulation of the Investment Problem 22.6 Summary Exercises

597 597 597 602 604 607 610 610

Using Monte Carlo Methods for Option Pricing 23.1 Overview 23.2 State Prices, Probabilities, and Risk Neutrality 23.3 Pricing a Plain-Vanilla Call Using Monte Carlo Methods 23.4 Monte Carlo Plain-Vanilla Call Pricing Converges to Black-Scholes 23.5 Pricing Asian Options 23.6 Pricing Asian Options with a VBA Program 23.7 Pricing Barrier Options with Monte Carlo 23.8 Using VBA and Monte Carlo to Price a Barrier Option 23.9 Summary Exercises

613 613 613

Real Options 24.1 Overview 24.2 A Simple Example of the Option to Expand 24.3 The Abandonment Option 24.4 Valuing the Abandonment Option as a Series of Puts 24.5 Valuing a Biotechnology Project 24.6 Conclusion Exercises

649 649 650 653 659 662 667 667

615 618 625 633 638 642 646 646

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Contents

IV

Bonds

669

25

Duration 25.1 Overview 25.2 Two Examples 25.3 What Does Duration Mean? 25.4 Duration Patterns 25.5 The Duration of a Bond with Uneven Payments 25.6 Nonflat Term Structures and Duration 25.7 Summary Exercises

671 671 671 674 678 679 687 689 689

26

Immunization Strategies 26.1 Overview 26.2 A Basic Simple Immunization Model 26.3 A Numerical Example 26.4 Convexity: A Continuation of Our Immunization Experiment 26.5 Building a Better Mousetrap 26.6 Summary Exercises

693 693 693 695

27

Modeling the Term Structure 27.1 Overview 27.2 An Initial Example 27.3 Description of the Data 27.4 The Treasury Yield Curve 27.5 Computing Par Yields from a Zero-Coupon Yield Curve 27.6 Summary Exercises

705 705 705 710 713 715 716 717

28

Calculating Default-Adjusted Expected Bond Returns 28.1 Overview 28.2 Calculating the Expected Bond Return in a One-Period Framework 28.3 Calculating the Expected Bond Return in a Multiperiod Framework 28.4 A Numerical Example

719 719

698 700 704 704

721 722 726

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Contents

28.5 28.6

Experimenting with the Example Computing the Bond Expected Return for an Actual Bond 28.7 Semiannual Transition Matrices 28.8 Computing Bond Beta 28.9 Summary Exercises

728

V

Technical Considerations

743

29

Generating Random Numbers 29.1 Overview 29.2 Rand( ) and Rnd: The Excel and VBA Random-Number Generators 29.3 Testing Random-Number Generators 29.4 Generating Normally Distributed Random Numbers 29.5 Summary Exercises

745 745 746 749 754 762 762

30

Data Tables 30.1 Overview 30.2 An Example 30.3 Setting Up a Data Table 30.4 Building a Two-Dimensional Data Table 30.5 An Aesthetic Note: Hiding the Formula Cells 30.6 Excel Data Tables Are Arrays Exercises

765 765 765 766 768 769 770 771

31

Matrices 31.1 Overview 31.2 Matrix Operations 31.3 Matrix Inverses 31.4 Solving Systems of Simultaneous Linear Equations Exercises

775 775 776 779 781 782

32

The Gauss-Seidel Method 32.1 Overview 32.2 A Simple Example 32.3 A More Concise Solution

785 785 785 786

730 734 737 739 740

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Contents

32.4 Conclusion Exercises

787 787

33

Excel 33.1 33.2 33.3 33.4 33.5 33.6 33.7 33.8 33.9 33.10 33.11

789 789 789 796 802 805 808 815 816 817 819 821

34

Using Array Functions and Formulas 34.1 Overview 34.2 Some Built-in Array Functions 34.3 Homemade Array Functions 34.4 Array Formulas with Matrices Exercises

825 825 825 830 833 838

35

Some 35.1 35.2 35.3 35.4 35.5 35.6 35.7 35.8 35.9 35.10 35.11 35.12 35.13

841 841 841 843 845 847 847 850 853 854 856 857 859 861

Functions Overview Financial Functions Dates and Date Functions The Functions XIRR and XNPV Statistical Functions Doing Regressions with Excel Conditional Functions Large and Rank, Percentile, and Percentrank Count, CountA, CountIF Boolean Functions Offset

Excel Hints Overview Fast Copy: Filling in Data Next to a Filled-in Column Multiline Cells Writing on Multiple Spreadsheets Text Functions in Excel Chart Titles That Update Getformula: A Useful Way of Annotating Spreadsheets Putting Greek Symbols in Cells Superscripts and Subscripts Named Cells Hiding Cells Formula Auditing Formulating Millions as Thousands

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VI

Introduction to Visual Basic for Applications

865

36

User-Defined Functions with VBA 36.1 Overview 36.2 Using the VBA Editor to Build a User-Defined Function 36.3 Providing Help for the User-Defined Functions in the Function Wizard 36.4 Fixing Mistakes in VBA 36.5 Conditional Execution: Using If Statements in VBA Functions 36.6 The Select Case Statement 36.7 Using Excel Functions in VBA 36.8 Using User-Defined Functions in User-Defined Functions Exercises Appendix: Cell Errors in Excel and VBA

867 867 867

37

Types and Loops 37.1 Overview 37.2 Using Types 37.3 Variables and Variable Types 37.4 Boolean and Comparison Operators 37.5 Loops 37.6 Summary Exercises

895 895 895 897 901 904 913 913

38

Macros and User Interaction 38.1 Overview 38.2 Macro Subroutines 38.3 User Output and the MsgBox Function 38.4 User Input and the InputBox Function 38.5 Modules 38.6 Summary Exercises

919 919 919 926 930 932 935 935

39

Arrays 39.1 Overview 39.2 Simple Arrays

941 941 941

872 875 877 882 884 885 888 892

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Contents

39.3 Multidimensional Arrays 39.4 Dynamic Arrays and the ReDim Statement 39.5 Array Assignment 39.6 Variants Containing an Array 39.7 Arrays as Parameters to Functions 39.8 Summary Exercises

946 948 959 960 963 971 971

40

Objects and Add-Ins 40.1 Overview 40.2 An Introduction to Worksheet Objects 40.3 The Range Object 40.4 The With Statement 40.5 Collections 40.6 Names 40.7 Using the Object Browser 40.8 References to External Functions in Excel 40.9 References to External Functions in VBA 40.10 Add-Ins and Integration 40.11 Summary Exercises Appendix 1: The Excel Object Model Appendix 2: Extracts from the Help File for Some Methods

975 975 975 979 984 985 991 995 997 999 1008 1014 1014 1018 1020

41

Information from the Web 41.1 Overview 41.2 Copy and Paste as a Simple Data-Acquisition Technique 41.3 Dynamic Web Queries 41.4 Web Queries: The iqy File 41.5 Parametric Web Pages 41.6 Web Queries: Parameters 41.7 Web Queries: CSV Files and Postprocessing 41.8 A VBA Application: Importing Price Data from Yahoo 41.9 Summary Exercises

1029 1029 1029 1035 1041 1047 1049 1056 1059 1089 1089

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Contents

Appendix 1: Excerpts from the Help File Appendix 2: The R1C1 Reference Style

1090 1093

References Index

1095 1107

Preface

The two previous editions of Financial Modeling have received a gratifyingly positive response from readers. The “cookbook combination” that mixes explanation and implementation using Excel fulfills a need in both the academic and practitioner markets for readers who realize that the implementation of the finance basics typically studied in an introductory finance course requires another, more heavily computational and implementational, approach. Excel, the most widely used computational tool in finance, is a natural vehicle for deepening our understanding of the materials. Financial Modeling is organized along six different subject areas. Each of the first four sections of the book relates to a specific area of finance. These sections are independent of each other, though the reader should realize that they all assume some familiarity with the finance area— Financial Modeling is not an introductory text. Section I (Chapters 1–7) deals with corporate finance topics; Section II (Chapters 8–15) with portfolio models; Section III (Chapters 16–24) with option models; and Section IV (Chapters 25–28) with bond-related topics. The last two sections of Financial Modeling are technical in nature. Section V (Chapters 29–35) 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 36–41) deals with Excel’s programming 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 intrusive—in principle the reader can understand the materials in all of the other chapters of Financial Modeling 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 finance. 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 financial institutions. •

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Chapter 13 adds an exposition of the Black-Litterman model of portfolio 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 chapters have been substantially rewritten. Following are a few examples: Chapter 2 includes a number of new cases used to illustrate the estimation of the cost of capital. Chapter 4 has a new example (PPG Corporation) for the implementation 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 materials and a new data set of zero-coupon bonds from the Federal Reserve. Getformula The Excel files 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 files. In order to allow Getformula to work, you must set your

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Preface

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 file 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 files that give all the Excel contents of each chapter as well as files that give the answers to each of the end-of-chapter questions. All the book’s files 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-

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mula to spreadsheets, and on some problems encountered with Excel’s XNPV and XIRR functions. Using Financial Modeling in a University Course Financial Modeling has become the book of choice in many intermediate and advanced finance classes that stress the combination of modeling/ Excel skills and a deeper understanding of the underlying financial models. The Financial Modeling–based 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 instructorspecific 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 financial modeling. Often these classes are held in a computer lab. Though almost all business school students know Excel, they may not know how to finesse data tables (Chapter 30) or some of the basic financial functions (Chapters 1 and 33) and array functions (Chapter 34). The initial classes give the instructor a chance to level the playing field. •

Most one-semester courses then cover, at most, one of the Financial Modeling sections. If we assume that in a typical university course, covering one chapter per week is an upper limit (and many chapters will require two weeks), then a typical course might concentrate on either corporate finance (Chapters 1–7), portfolio models (Chapters 8–15), or options (Chapters 16–24). At a stretch, the instructor could perhaps throw in the shorter bond section (Chapters 25–28). •

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 financial engineering course that starts with binomial option pricing, proceeds to cover some of the VBA chapters (36–38), and then covers Black-Scholes and Monte Carlo methods (Chapters 18–23).

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Preface

A major problem with a computer-based course is how to structure the final examination. Two solutions seem to work well. One alternative is to have students (whether alone or in teams) submit a final 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 final exam (a compendium of spreadsheet problems) at nine o’clock 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, Gökçe 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 suggestions and improvements for the book. I follow a tradition started with the first two editions of Financial Modeling by acknowledging those readers whose comments have been incorporated into this edition: Meni Abudy, Zvika Afik, Gordon Alexander, Naomi Belfer, David Biere, Vitaliy Bilyk, Oded Braverman, Roeland Brinkers, Salvio Cardozo, Israel Dac, Jeremy Darhansoff, Toon de Bakker, Govindvyas Dharwada, 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, Ofir Shatz, Mel Tukman, Guy Vishnia, Torben Voetmann, James Ward, Roberto Wessels, Geva Yaniv, and Werner Zitzman.

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Preface

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 five years. As always, I welcome comments and corrections! Simon Benninga [email protected]

Preface to the Second Edition

The purpose of this book remains to provide a “cookbook” for implementing common financial models in Excel. This edition has been expanded by six additional chapters, covering financial 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 Bollinger, 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, Glenn Morley, Stephen O’Neil, Steven Ong, Oren Ossad, 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://finance.wharton.upenn.edu/~benninga [email protected]

Preface to the First Edition

Like its predecessor Numerical Techniques in Finance, this book presents some important financial models and shows how they can be solved numerically and/or simulated using Excel. In this sense this is a finance “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 financial models in the areas of corporate finance, financial 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 understanding the computational intricacies involved in financial 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.

I

Corporate Finance Models

The seven chapters that open the third edition of Financial Modeling cover basic problems and techniques in corporate finance. Chapters 1 and 2 are both review chapters. Chapter 1 is an introduction to basic financial calculations using Excel. Almost all of the applications discussed center on variations of the discounted cash flow method. The cost of capital, discussed in Chapter 2, is the rate at which corporate cash flows 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 finance applications, including business plans, credit analyses, and valuations. The models require a mixture of finance, 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 financial analysis of leasing. In Chapter 6 we concentrate on the basic lease/purchase decision using the equivalent loan method. An appendix to Chapter 6 discusses some tax and accounting considerations relating to leases. Chapter 7 discusses the financial 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.

1 1.1

Basic Financial Calculations

Overview This chapter aims to give you some finance basics and their Excel implementation. If you have had a good introductory course in finance, 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 financial problems center on finding the value today of a series of cash receipts over time. The cash receipts (or cash flows, as we will call them) may be certain or uncertain. The present value of a cash CFt flow CFt anticipated to be received at time t is . The numerator (1 + r )t of this expression is usually understood to be the expected time-t cash flow, and the discount rate r in the denominator is adjusted for the riskiness of this expected cash flow—the higher the risk, the higher the discount 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, investments. In the financial literature there are many synonyms for opportunity cost, among them discount rate, cost of capital, and interest rate. When the opportunity cost is applied to risky cash flows, we will sometimes 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 finance literature discusses how to make this adjustment. As illustrated in this chapter, when we calculate the net present value, we use the investment’s opportunity 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/finance topics at greater length.

4

Chapter 1

return, we compare the calculated return to the investment’s 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 flows. 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 five payments of $100 each will actually be paid. If a bank pays an annual interest rate of 10 percent on a five-year deposit, then this 10 percent is the investment’s 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 flows using this opportunity cost as a discount rate: A 1 COMPUTING 2 Discount rate 3 Year 4 5 1 6 2 7 3 8 4 9 5 10 11 Net present value 12 Summing cells C5:C9 13 Using Excel's NPV function 14 Using Excel's PV function

B

C

D

THE PRESENT VALUE 10%

Cash flow 100 100 100 100 100

Present value 90.9091 82.6446 75.1315 68.3013 62.0921

22 Book value of equity 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

Purchase price Assets Cash Current assets

2,000

Plant property and equipment At cost Accumulated depreciation Net PP&E Goodwill

8,500

64.22 8.0% 8.5% 9.0% 9.5% 10.0% 10.5% 11.0% 11.5% 12.0%

0% 43.85 43.02 42.22 41.44 40.67 39.92 39.19 38.47 37.78

2% 51.36 50.39 49.43 48.50 47.59 46.70 45.83 44.99 44.16

3% 56.54 55.45 54.39 53.36 52.35 51.37 50.41 49.47 48.55

5% 72.08 70.68 69.31 67.97 66.66 65.39 64.15 62.93 61.75

The efficiency ratio is an important determinant of the valuation. If Small Bank’s noninterest expense ratio can be reduced by a further 5 percent, then the valuation rises significantly:

6% 84.54 82.88 81.26 79.68 78.14 76.63 75.16 73.73 72.33

193

Bank Valuation

A

B

C

D

E

F

G

Sensitivity analysis of Small Bank's value as function of its WACC and long-term growth 126 Noninterest expense as % of net interest income (cell B15): 65.00% 127 128 129 130 131 132 133 134 135 136 137

Data table header: =B112 -->

5.5

0% 47.36 46.48 45.62 44.78 43.95 43.15 42.37 41.60 40.85

69.18 8.0% 8.5% 9.0% 9.5% 10.0% 10.5% 11.0% 11.5% 12.0%

2% 55.41 54.36 53.34 52.34 51.37 50.41 49.48 48.58 47.69

3% 60.95 59.79 58.66 57.55 56.47 55.41 54.38 53.38 52.39

5% 77.60 76.10 74.63 73.20 71.80 70.43 69.10 67.80 66.53

6% 90.95 89.17 87.43 85.74 84.09 82.47 80.90 79.36 77.86

Calculating the Exchange Ratio At the time of the case, Large Bank had 294,330,960 shares worth $58 per share. Large Bank intended to do an exchange offer for Small Bank’s shares, and the question about the proper exchange ratio was discussed. Assuming that the pro forma valuation of Large Bank is correct, this yields an exchange ratio of x=

Calculated per-share valuation of Small Bank Current market pricee per share of Large Bank

Doing these calculations yields the following: 108 109 110 111 112 113 114 115 116

A Value of Small Bank Long-term debt Implied equity value Number of Small Bank shares Imputed per-share value of Small Bank

Number of Large Bank shares Value of Large Bank share Market value of Large Bank equity, before merger Exchange ratio (number of shares of Large Bank 117 offered per share of Small Bank), x 118 119 Check 120 Number of shares, new entity 121 Value of equity, new entity 122 Total value of Large Bank ex-shareholders 123 Total value of Small Bank ex-shareholders

B 2,210,090,780 128,952,000 2,081,138,780 32,406,000 64.22

C D E Standard Error --> 2 R --> F statistic --> SSxy -->

Industry 0.4157 0.0851 0.3140 56.9738 0.0122

Market 0.5095 0.1410 0.0103 249 0.0266

4.8818

3.6142

t-stat

Days in estimation 11 window 12 13 Date

Intercept 0.0012 0.0007 #N/A #N/A #N/A 1.8367