Cost of capital applications and examples, 5th edition

CHAPTER 15APPENDIX 15A Other Data Issues Regarding the Size Effect 363 CHAPTER 16 CHAPTER 17 APPENDIX 17A Cost of Capital and the Valuation of Worthless Stock 428 CHAPTER 18 Other Method

Cost of Capital

Applications and Examples

Fifth Edition

SHANNON P PRATT ROGER J GRABOWSKI Cost of Capital

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ISBN 978-1-118-55580-4 (Hardcover) ISBN 978-1-118-85280-4 (ePDF) ISBN 978-1-118-85282-8 (ePub)

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

To our families for their support and encouragement, without which our careers and this book would not have been possible

Millie

Daughter-in-law Barbara Brooks Son-in-law Tim Wilder Randall and Kenny John, Calvin, and Meg

Daughter-in-law Jenny Pratt Son-in-law Tom Senor

Mary Ann Son Roger Grabowski Jr., MA

Daughter-in-law Misako Takahashi

Rob, Sayaka, and Asami Tokyo, Japan

Daughter Sarah Harte, MA Son-in-law Michael Harte, MS, JD Kevin and Rosemary

Arlington Heights, IL

Daughter Julia Grabowski, MD Son Paul Grabowski, MS PhD

Casey and Louis Chicago, IL

CHAPTER 3 Net Cash Flow: The Preferred Measure of Economic Income 17 APPENDIX 3A

Alternative Measures of Economic Income 30 CHAPTER 4

APPENDIX 4A Equivalency of Capitalizing Residual Income 56 CHAPTER 5

CHAPTER 6 Relationship between Risk and the Cost of Capital 70

vii

APPENDIX 11A Examples of Computing OLS Beta, Sum Beta, and Full-information Beta Estimates 225

APPENDIX 11B Estimating Beta: Interpreting Regression Statistics 234 CHAPTER 12

Unlevering and Levering Equity Betas 243 CHAPTER 13

Criticism of CAPM and Beta versus Other Risk Measures 269

APPENDIX 13A Example of Computing Downside Beta Estimates 298 CHAPTER 14

CHAPTER 15

APPENDIX 15A Other Data Issues Regarding the Size Effect 363 CHAPTER 16

CHAPTER 17

APPENDIX 17A Cost of Capital and the Valuation of Worthless Stock 428 CHAPTER 18

Other Methods of Estimating the Cost of Equity Capital 444 CHAPTER 19

Using the Duff & Phelps Risk Premium Report Data 471

APPENDIX 19A Examples Using the Duff & Phelps Risk Premium Report Data 499

PART THREE

CHAPTER 20 Other Components of a Business's Capital Structure 521 CHAPTER 21

APPENDIX 21A Iterative Process Using CAPM to Calculate the Cost of Equity Component of the Weighted Average Cost of Capital 576

PART FOUR

Estimating the Cost of Capital—Non-Freely Traded Interests 609

CHAPTER 22 Handling Discounts for Lack of Marketability and Liquidity for Minority

CHAPTER 23 Cost of Capital of Family Holding Company Interests 630 CHAPTER 24

The Private Company Discount for Operating Businesses 650 CHAPTER 25

Cost of Capital of Interests in Pass-through Entities 663 CHAPTER 26

Relationship between Risk and Returns in Venture Capital and Private

CHAPTER 27 Cost of Capital for Closely Held Businesses 693

PART FIVE

Corporate Finance Officers: Using Cost of Capital Data 711

CHAPTER 28 Capital Budgeting and Feasibility Studies 713 CHAPTER 29

Cost of Capital for Divisions and Reporting Units 722 CHAPTER 30

Cost of Capital for Fair Value Reporting of Intangible Assets 757 CHAPTER 31

Cost of Capital in Evaluating Mergers and Acquisitions 779 CHAPTER 32

Cost of Capital in Transfer Pricing 793 APPENDIX 32A

Cost of Capital in Transfer Pricing Example 822 CHAPTER 33

The Role of the Cost of Capital in EVA and in Corporate Value-Based Management 825

CHAPTER 35 Minority versus Control Implications of Cost of Capital Data 861 CHAPTER 36

How Cost of Capital Relates to the Excess Earnings Method of Valuation 873 CHAPTER 37

Adjusting the Discount Rate to Alternative Economic Income Measures 881

CHAPTER 41 Cost of Capital of Real Estate Entities 1084

APPENDIX 42A Report for Cost of Capital for a Mid-Sized Company 1138 CHAPTER 43

Cost of Capital for a Smaller-Sized Company 1162

APPENDIX 43A Report for Cost of Capital for a Smaller-Sized Company 1168

PART NINE

CHAPTER 44 Common Errors in Estimation and Use of Cost of Capital 1181 CHAPTER 45

Advice on Dealing with Cost of Capital Issues 1199

About the Authors

Dr Shannon P Pratt, CFA, FASA, ARM, MCBA, ABAR, CM&AA, is the chairman

and CEO of Shannon Pratt Valuations, Inc., a nationally recognized business tion firm headquartered in Portland, Oregon He is also the founder and editoremeritus of Business Valuation Resources, LLC

valua-Dr Pratt has performed valuation assignments for the following purposes:transaction (acquisition, divestiture, reorganization, public offerings, public compa-nies going private); taxation (federal income, gift, and estate and local ad valorem);financing (securitization, recapitalization, restructuring), litigation support and dis-pute resolution (including dissenting stockholder suits, damage cases, and corporateand marital dissolution cases); and management information and planning He hasalso managed a variety of fairness opinion and solvency opinion engagements Heregularly reviews business valuation reports for attorneys in litigation matters

Dr Pratt has testified on hundreds of occasions in such litigated matters asdissenting stockholder suits, various types of damages cases (including breach ofcontract, antitrust, and breach of fiduciary duty), divorces, and estate and gift taxcases Among the cases in which he has testified are Estate of Mark S Gallo v Commissioner, Charles S Foltz, et al v U.S News & World Report et al., Estate of Martha Watts v Commissioner, and Okerlund v United States He has also served as

appointed arbitrator in numerous cases

Previous Experience

Dr Pratt was a professor of business administration at Portland State Universityfrom 1963 to 1969 During this time, he directed a research center known as theInvestment Analysis Center, which worked closely with the University of Chicago’sCenter for Research in Security Prices He entered the business valuation profession

in 1969

Education

Doctor of business administration,finance, Indiana University

Bachelor of arts, business administration, University of Washington

Professional Affiliations

Dr Pratt is an Accredited Senior Appraiser and Fellow (FASA), Certified in BusinessValuation, of the American Society of Appraisers (ASA) (their highest designation)and is also accredited in Appraisal Review and Management (ARM) He is aChartered Financial Analyst (CFA) He is a Master Certified Business Appraiser(MCBA) with the Institute of Business Appraisers and also thefirst life member with

xiii

the organization He is Accredited in Business Appraisal Review (ABAR) with theNational Association of Certified Valuators and Analysts (NACVA) and recipient ofNACVA’s Magna Cum Laude Award He is a Master Certified Business Counselor(MCBC), and is Certified in Mergers and Acquisitions (CM&AA) with the Alliance ofMerger and Acquisition Advisors.

Dr Pratt is a life member of the ASA, and a life member of the Business ValuationCommittee of that organization He frequently teaches courses for the ASA He is also

a lifetime member emeritus of the Advisory Committee on Valuations of the ESOPAssociation He is a member and a past president of the Portland Society of FinancialAnalysts, the recipient of the 2002 Distinguished Achievement Award, and a member

of the Association for Corporate Growth Dr Pratt is a past trustee of the AppraisalFoundation and is currently an outside director and chair of the audit committee ofPaulson Capital Corp., a NASDAQ-listed investment banking firm specializing insmall initial public offerings (usually under $50 million)

Publications

Dr Pratt is the author of more than 10 standard reference works for the valuation

profession, including Valuing a Business: The Analysis and Appraisal of Closely Held Companies, 5th ed (New York: McGraw-Hill, 2007); co-author, The Lawyer’s Guide to Cost of Capital, with Roger J Grabowski (Chicago: American Bar Associa- tion, 2014, forthcoming); co-author, Guide to Business Valuations, 23rd ed., with Jay

Fishman, Cliff Griffith, and Jim Hitchner (Fort Worth, TX: Practitioners Publishing

Company, 2013); co-author, Standards of Value, 2nd ed., with William Morrison and Jay Fishman (Hoboken, NJ: John Wiley & Sons, 2013); co-author, Business Valua- tion and Taxes: Procedure, Law, and Perspective, 2nd ed., with Judge David Laro (Hoboken, NJ: John Wiley & Sons, 2010); co-author, The Lawyer ’s Business Valuation Handbook, 2nd ed., with Alina V Niculita (Chicago: American Bar Association, 2010); co-author with Roger J Grabowski, Cost of Capital: Applications and Examples, 4th ed., (Hoboken, NJ: John Wiley & Sons, 2010); and co-author, Cost of Capital in Litigation: Applications and Examples, with Roger J Grabowski

(Hoboken, NJ: John Wiley & Sons, 2010) He has published nearly 200 articles onbusiness valuation topics

Roger J Grabowski, FASA, is a managing director of Duff & Phelps, LLC.

Mr Grabowski has directed valuations of businesses, partial interests in nesses, intellectual property, intangible assets, real property, and machinery andequipment for various purposes, including tax (income and ad valorem) andfinancialreporting, mergers and acquisitions, formation of joint ventures, divestitures, andfinancing He developed methodologies and statistical programs for analyzing usefullives of tangible and intangible assets, such as customers and subscribers Hisexperience includes work in a wide range of industries, including sports, movies,recording, broadcast, and other entertainment businesses; newspapers, magazines,music, and other publishing businesses; retail; banking, insurance, consumer credit,and otherfinancial services businesses; railroads and other transportation companies;mining ventures; software and electronic component businesses; and a variety ofmanufacturing businesses

busi-Mr Grabowski has testified in court as an expert witness on the value of closelyheld businesses and business interests; matters of solvency, valuation, and

amortization of intangible assets; and other valuation issues His testimony in U.S.District Court was referenced in the U.S Supreme Court opinion decided in his client’s

favor in the landmark Newark Morning Ledger income tax case Among other cases

in which he has testified were Herbert V Kohler Jr., et al., v Comm (value of stock of

the Kohler Company); The Northern Trust Company, et al., v Comm (thefirst U.S.Tax Court case that recognized the use of the discounted cashflow method for valuing

a closely held business); Oakland Raiders v Oakland —Alameda County Coliseum Inc et al (valuation of the Oakland Raiders); In re: Louisiana Riverboat Gaming Partnership, et al Debtors; and TMR Energy Limited v The State Property Fund of Ukraine (arbitration on behalf of the world’s largest private company on cost ofcapital in Ukraine in a contract dispute)

Previous Experience

Mr Grabowski was formerly managing director of the Standard & Poor’s CorporateValue Consulting practice, a partner of PricewaterhouseCoopers, LLP, and one of itspredecessor firms, Price Waterhouse (where he founded its U.S Valuation Servicespractice and managed the Real Estate Appraisal practice) Prior to Price Waterhouse,

he was afinance instructor at Loyola University of Chicago, a co-founder of ValtecAssociates, and a vice president of American Valuation Consultants

Education

Mr Grabowski received his BBA—Finance from Loyola University of Chicago andcompleted all coursework in the doctoral program in finance at NorthwesternUniversity, Chicago

Professional Affiliations

Mr Grabowski is an Accredited Senior Appraiser and Fellow (FASA), Certified inBusiness Valuation, of the American Society of Appraisers (ASA) (their highest

designation) He formerly served as editor of the Business Valuation Review, the

quarterly journal of the Business Valuation Committee of the ASA

John Wiley & Sons, 2010)

Recent articles include“Analysis of Long-Term Yields Since the Financial Crisis,”the Institute of Chartered Accountants of England and Wales Valuations Groupnewsletter, co-authored with James Harrington and Richard Clohessy (May 2012);

“Risk Free Rate Update,” Business Valuation Update (September 2011); “Developing

the Cost of Equity Capital: Risk-Free Rate and ERP during Periods of ‘Flight to

Quality,’” Business Valuation Review (Winter 2010); “Estimating Discounts forLack-of-Marketability for Restricted Stock,” with Daniel McConaughy, Valuation

Strategies (July/August 2010); and “Cost of Capital Estimation in the CurrentDistressed Environment,” Journal of Applied Research in Accounting and

Finance Vol 4, No 1 (July 2009).

Mr Grabowski teaches courses for the ASA, including Cost of Capital, a course

he developed

Mark Bronson is a managing director in the transfer pricing practice of Duff &

Phelps He has significant experience addressing transfer pricing issues for national companies and government agencies He has helped numerous clients resolvedisputes through audit, appeals, competent authority, and Advance Pricing Agree-ment (APA) venues Mr Bronson has a wide variety of industry experience, with aparticular focus on pharmaceutical, biomedical device, and other technology-drivenindustries His transfer pricing experience includes more than 15 years in a consultingenvironment, as well as two years as an economist with the APA program at theInternal Revenue Service

multi-Mr Bronson holds an MBA with accounting andfinance concentrations from theUniversity of Chicago Graduate School of Business He also has a BA from theUniversity of Rochester in economics and statistics

Joanne Fong, CFA, CPA, is a senior manager in the Transaction Advisory Services—

Valuation and Business Modeling practice in the Chicago office of Ernst & YoungLLP Ms Fong holds a master of business administration degree and a bachelor ofbusiness administration degree, both from the University of Michigan, Ross School ofBusiness

Ms Fong specializes in advising corporate clients on matters regarding value andvalue drivers (including risk-adjusted cost of capital) in connection with portfoliooptimization, mergers and acquisitions, divestitures, and restructurings

William H Frazier, ASA, is a managing director in the Valuation and Financial

Opinions Group of Stout Risius Ross, Inc He has over 35 years of experience

in business valuation and corporate finance He has participated as an appraiser

and/or expert witness in numerous U.S Tax Court cases, including Hendrix, Jelke, McCord, Dunn, and Gladys Cook Mr Frazier has written numerous articles on

the subject of business valuation for tax purposes, appearing in such publications

as the Business Valuation Review, Valuation Strategies, BV E-Letter, and Estate Planning.

Prior to joining Stout Risius Ross, Mr Frazier was a founding partner of HowardFrazier Barker Elliott, Inc (HFBE), where he providedfinancial advisory and valua-tion opinions for purposes of corporate mergers, acquisitions and spin-offs, reorgan-izations and recapitalizations; estate, gift, and income tax requirements; estateplanning, employee stock ownership plans; and other requirements Prior toHFBE, Mr Frazier was an officer of a major regional investment banking firm,where he was involved in public offerings of equity and debt securities, privateplacements, mergers and acquisitions, venture capital, and valuation and fairnessopinions Mr Frazier is the developer of the Non-Marketable Investment CompanyEvaluation (NICE) Method

Mr Frazier holds professional licenses as FINRA Series 7 General SecuritiesRepresentative, the FINRA Series 63 Uniform Securities Agent State Law Exam, andthe FINRA Series 24 General Securities Principal He previously was a member of theBusiness Valuation Committee of the American Society of Appraisers (ASA), serving

as treasurer and secretary He is currently the chairman of the Government RelationsCommittee of the ASA and serves on the board of the ASA’s Education Foundation

He served on the IRS Advisory Council (IRSAC) from 2008 to 2011 and was a

member of the Valuation Advisory Board of Trusts & Estates.

Thomas W Hamilton, PhD, CRE, FRICS, CVS, is a commercial real estate professor

at the University of St Thomas Opus College of Business and founder and president ofKarvel-Hamilton Real Estate Analytics/PROTEC He holds an MS and a PhD in realestate and urban land economics from the University of Wisconsin–Madison, an MS

infinance from the University of Wyoming, and a BS in natural resources from theUniversity of Wisconsin–Madison He has been a consultant to the telecommunica-tions industry and the public utility industry in the United States for over 20 years,verifying and evaluating valuation and ad valorem tax strategies and problems, andhas been a consultant to numerous local and state agencies in the analysis of propertytax equity and incidence He is a Counselor of Real Estate (CRE), a Fellow of theRoyal Institution of Chartered Surveyors (FRICS), a Distinguished Fellow of theNational Association of Industrial and Office Properties (NAIOP), and a licensed realestate broker and a licensed appraiser He is a former Fellow and adjunct facultymember of the Lincoln Land Institute in Cambridge, Massachusetts, and formerresearch associate with the International Association of Assessing Officers in Chicago,Illinois

Dr Hamilton has researched and published numerous articles on complexappraisal techniques and ad valorem issues and concerns in national and internationaljournals and has been a nationally syndicated real estate columnist His researchcurrently focuses on income-based valuation methodologies for complex real estateassets, and he has successfully developed methods to identify and correct systematic,inequitable mass appraisal valuation processes Dr Hamilton has spoken to numer-ous organizations across the United States on topics ranging from general urban landeconomics, to financial risk management and to econometric analyses of the builtenvironment

James Harrington is a director at Duff & Phelps, where he provides technical

support on client engagements involving cost of capital and business valuationmatters, and is a major contributor in the development of Duff & Phelps’s studies,surveys, online content and tools, and internal models for use by thefirm’s analysts

worldwide Mr Harrington is the editor of the Duff & Phelps Risk Premium Report and developer of the Report ’s online companion application, the Risk Premium Calculator.

Previously, Mr Harrington was director of valuation research in Morningstar’s

Financial Communications Business, and led the group that produced the Ibbotson SBBI Valuation Yearbook, SBBI Classic Yearbook, and Ibbotson Cost of Capital Yearbook Mr Harrington holds a bachelor’s degree in marketing from Ohio StateUniversity and an MBA in bothfinance and economics from the University of Illinois

at Chicago

Michelle Johnson is a managing director in the Transfer Pricing practice of Duff &

Phelps Ms Johnson has significant experience advising clients on transfer pricing andvaluation matters, including transfer pricing documentation preparation, ASC 740(FIN 48) recognition and measurement analyses, advanced pricing agreements, andtransfer pricing policy development She led the development of the practice’s ASC

740 service line and has taken leadership roles, including management of the group’snational operations She is an award-winning speaker and has presented at numerousconferences and seminars regarding transfer pricing issues

Ms Johnson’s recent publications include Wolter Kluwer’s Guide to tional Transfer Pricing: Law, Compliance and Tax Planning Strategies, and the BNA Tax Management Portfolio on ASC 740-10 (FIN 48) (published in 2012) She

Interna-obtained her master’s degree in economics from New York University and a BS ineconomics and French from the University of Illinois

Glen N Kernick is a managing director in the Silicon Valley office of Duff & Phelps,

LLC and the Technology Industry practice leader He has performed numerousvaluations and financial analyses for more than 16 years for a variety of purposesincludingfinancial reporting, tax, fairness opinions, litigation, and strategic planning

He was formerly a managing director of the Standard & Poor’s Corporate ValueConsulting practice and a director at PricewaterhouseCoopers, LLP Mr Kernickreceived an MBA from the University of Washington and a bachelor of arts ineconomics from the University of California, San Diego

Kimberly Linebarger, ASA, CVA, is a senior financial analyst with Shannon Pratt

Valuations Mrs Linebarger has managed business valuation projects for a variety ofpurposes, including shareholder disputes, marital dissolutions, mergers and acquis-itions, damages actions, and estate matters Mrs Linebarger received a bachelor ofscience degree with an emphasis in finance from Portland State University Shecurrently serves on the National Association of Certified Valuators and Analysts’Valuation Credentialing Board As an analyst with Shannon Pratt Valuations she hascontributed to multiple publications on business valuation

James Morris, PhD, AM, received his PhD in finance from the University of

Califor-nia, Berkeley He is a retired professor emeritus of finance at the University ofColorado at Denver, where he taught courses in business valuation,financial model-ing, and financial management; he has also served on the finance faculties at theWharton School of the University of Pennsylvania and at the University of Houston,and also has taught finance courses at business schools in England, France, andGermany In addition, he has taught short programs onfinancial modeling to industryaudiences in Australia, New Zealand, and Singapore

Dr Morris’s recent publications include: Introduction to Financial Models for

Management and Planning, with J Daley (CRC Press, 2009); “Life and Death ofBusinesses: A Review of Research on Firm Mortality,” Journal of Business Valuation

and Economic Analysis (2009); “Firm Mortality and Business Valuation,” Valuation Strategies (September/October 2009);“The Iterative Process Using CAPM to Calcu-late the Cost of Equity Component of the Weighted Average Cost of Capital WhenCapital Structure Is Changing,” Appendix 7.2 in Pratt and Grabowski, Cost of

Capital: Applications and Examples, 3rd ed (Hoboken, NJ: John Wiley & Sons,

2008);“Growth in the Constant Growth Model,” Business Valuation Review (Winter

2006);“Understanding the Minefield of Weighted Average Cost of Capital,” Business Valuation Review (Fall 2005); and “Reconciling the Equity and Invested CapitalMethods of Valuation When the Capital Structure Is Changing,” Business Valuation

Review (March 2004) In addition, his research articles have been published in the Journal of Finance, Journal of Financial & Quantitative Analysis, Journal of Applied Psychology, Academy of Management Journal, and Management Science, among

others In addition to teaching, he provides valuation services to the businesscommunity

Alina V Niculita, ASA, CFA, is president and COO of Shannon Pratt Valuations,

where she works on all aspects of case management, including the fundamentalaspects of business valuation,financial analysis, and report writing Ms Niculita hasbeen involved in business valuation engagements for various purposes such asbusiness transactions, gift and estate taxes, employee stock ownership plans (ESOPs),marital dissolution, bankruptcy, and litigation support She also worked on valua-tions of intangible assets, goodwill, solvency, and fairness opinions, and she isfrequently involved in report review work

Ms Niculita is a co-author of The Lawyer ’s Business Valuation Handbook, 2nd ed., with Shannon Pratt (Chicago: American Bar Association, 2010) and Closely Held Business Valuation with Nicholas J Mastracchio (Bloomberg BNA Portfolio); she is a contributing author to several books including Cost of Capital Applications and Examples, 4th ed.; Valuing a Business: The Analysis and Appraisal of Closely Held Companies, 5th ed.; The Market Approach to Valuing Businesses Workbook, 2nd ed.; Business Valuation Body of Knowledge Workbook, 2nd ed.; and Cost of Capital Workbook, 2nd ed Ms Niculita received a dual MBA infinance from the Joseph M.Katz Graduate School of Business, University of Pittsburgh, and from the CzechManagement Center, Czech Republic She also received a bachelor of sciences degree

in economics with a concentration in banking and finance from the Academy ofEconomic Studies, Bucharest, Romania

Carla Nunes, CFA, is a director in the Office of Professional Practice of Duff & Phelps

LLC, where she provides firmwide technical guidance on a variety of valuation,financial, and tax reporting issues She recently spent a year in Duff & Phelps’sLondon office, promoting the firm’s International Financial Reporting Standards(IFRS) education efforts and marketing initiatives, as well as dealing with IFRSimplementation issues

Prior to this role, Ms Nunes was part of Duff & Phelps’s Valuation AdvisoryServices business unit, focusing on the valuation needs of consumer and industrialproducts firms, primarily for financial reporting or tax purposes Before Duff &Phelps, she was a manager in the Standard & Poor’s Corporate Value Consultingpractice and a senior associate at PricewaterhouseCoopers, LLP She has 17 years ofexperience in providing valuation,financial analysis, and tax services

Ms Nunes has conducted numerous business and asset valuations for a variety ofpurposes, including purchase price allocations, goodwill impairment testing, mergersand acquisitions, corporate tax restructuring, and debt analyses She has substantialexperience working with multinational companies, having addressed complextax, international cost of capital, and foreign exchange issues She is also one of

Duff & Phelps’s experts in addressing valuation issues related to cost of capital andforeign exchange Ms Nunes is a regular instructor at Duff & Phelps’s annual new-hire training event.

Ms Nunes received her MBA in finance from the University of Rochester,completed coursework for a masters of taxation from Villanova University School

of Law, and received an honors degree in business administration from the TechnicalUniversity of Lisbon She also holds the Chartered Financial Analyst (CFA) designa-tion and is a member of the CFA Institute, the CFA Society of Philadelphia, and theAmerican Institute of Certified Public Accountants

Niel Patel is an analyst in the Valuation Advisory Services and Office of Professional

Practice of Duff & Phelps, where he providesfirmwide technical guidance on clientengagements involving cost of capital, business valuation matters, and designing andimplementing various valuation models

Mr Patel is a contributor to the Duff & Phelps 2012 and 2013 Risk Premium Reports and online Calculator, 2012 U.S and Canadian Goodwill Impairment Studies, and the quarterly publication of Duff & Phelps, Valuation Insight He

received his bachelor’s degree in accounting and finance from Loyola University ofChicago

David M Ptashne, CFA, is a director with the Chicago office of Duff & Phelps LLC.

His more than 10 years of valuation and economic consulting experience includesignificant experience performing valuation studies of businesses, interests in busi-nesses, and intangible property His services have been rendered for a variety ofpurposes, including tax planning and compliance (frequently in connection withtransfer pricing), litigation and international arbitration,financial reporting, mergersand acquisitions, management planning, and estate and gift tax matters Mr Ptashne

is an active participant with industry groups such as the National Association forBusiness Economics and Bloomberg BNA, where he has been an award-winningspeaker He has also contributed to various publications concerning cost of capitaland transfer pricing, including prior editions of this book He received a bachelor ofscience degree infinance with high honors from the University of Illinois at Urbana–Champaign

Gary Roland, CFA, CPA, is a managing director in the Office of Professional Practice

residing in the Philadelphia office of Duff & Phelps The Office of Professional Practiceprovides technical interpretation and guidance on financial reporting valuationmatters such as business combinations, intangible assets, goodwill and asset impair-ments Mr Roland has 28 years of valuation experience He was formerly a director inStandard & Poor’s Corporate Value Consulting practice and at Pricewaterhou-seCoopers, LLP He received an MBA and a bachelor of sciences degree in engineeringfrom the State University of New York at Buffalo

Mark W Shirley, CPA/ABV/CFF, CVA, CFFA, CFE, is the managing partner of

V & L Consultants, LLC, in Baton Rouge, Louisiana Prior to entering theprivate sector, Mr Shirley received extensive training and experience during hisemployment with the Internal Revenue Service Since 1984, his consulting practice has

conce ntrated on the discipline s of busines s valuation , forensi c/investi gative accoun ing, and fina ncial analys is/modeli ng.

t-Techni cal and acad emic mater ials by Mr Shirley ha ve been publ ished by WileyLaw Publica tions, Aspen Leg al Pr ess, and Bus iness Val uation Resou rces includi ng

contri butions to: Tax and Finan cial Planning Strategies in Divor ce ; Cost of Capital , 3rd and 4th ed s and 4th ed Workbo ok; Valu ing Professi onal Pr actices and Licenses ; and BVR ’ s Guide to Perso nal v Enterp rise Goo dwill Technica l articles have been publis hed in The Valuati on Examiner , Bewert ungsP raktik er Nr., The Pr actical Account ant , CPA Litigation S ervices Counse lor , the Gatekee per Quarterly , and the Journal of Forensi c Account ing

Mr Shirley has developed training and con tinuing ed ucation courses fo r the legal ,accou nting, and valuation/app raisal profess ions Addi tional ly, he has developedadvan ced trai ning co urses in ap plied statisti cs and finan cial modeling for valua-tion/ apprais al accredi ting organiz ations Curren t acad emic project s include the de vel-opmen t of forensi c accoun ting course mater ials for uni versity MB A an d mast er ’s inaccou nting curri culum an d refer ence material s for the Loui siana fami ly law cou rts

Mr Shirley is an adjunct faculty member at the National Judici al Col lege,

Unive rsity of Nevada , Reno, an d serves on the Advisory Panel for Md ex Online and The Daub ert Tracker , an online Daubert research database

Benne tt Stew art is the chairm an and chief executiv e of fi cer of EVA Dimensi ons

LLC, and an ex pert in sharehol der value, perform ance managem ent, and incen tivecompen sation

Mr Stewart is best known for developing and promoting the pr actical cations of economic profi t under the trademark name of EVA (economic value

appli-added), s tarting w ith publication of his 1991 bo ok, The Q uest for Value (H ar

per-Business), which f ormally l aunched EVA as a corporate management technique and

precipitated its appearance on the cover of Fortune magazine in September 1993

with the tagline, “ EV A— It ’ s the Real Key t o Creating Wealth.” His new book,

Best-Practice EVA (John Wiley & Sons, 2013), presents a signi fi cantly improv ed version

of EVA t hat m akes it a f ar more practical tool for corporate m anagement and inboardrooms

Mr Stewart fo rmed EVA Dime nsions in 2006 (as a spin-of f from Stern Stew art,the global EVA consultin g firm) with the go al to turn EVA into an acknowl edgedstandard of excellence in corporate financial management and equity research Inrecent years he was instrumental in developing a predictive stock-rating model calledPRVit (pronounced “prove-it” and standing for the “performance-risk-valuationinvestment technology”), which scores stocks as attractive to own or sell based ontheir fundamental EVA values The buy-sell ratings are updated daily on Bloomberg,and PRV it repo rts are availab le throu gh Fidelity com EVA Dimen sions ’ equ ityresearch team uses PRVit to help fund managers at investment houses make betterbuy-sell decisions

Mr Stewart holds a cum laude degree in electrical engineering from PrincetonUniversity (1974) and an MBA from the University of Chicago (1976) He chairs theaudit and finance committee of ITC Holdings (NYSE:ITC), is a member of the

Advisory Board for the Morgan Stanley Journal of Applied Corporate Finance,

and formerly chaired the Alumni Advisory Council for Princeton’s Department ofOperations Research and Financial Engineering

David Turf, CFA, is a managing director in the Investment Banking Group of Duff &

Phelps LLC He is a member of the Transaction Opinions practice and serves on theSenior Review Committee He has extensive experience executing engagements forfairness opinions, solvency opinions, and valuation opinions

Mr Turf has advised boards of directors, management, trustees and shareholders

on a variety of corporate finance and valuation issues for mergers, acquisitions,divestitures, ESOPs,financings, and other general corporate purposes He has providedfairness opinions in a variety of transactions, including going-private, reverse-merger,restructuring, and related-party transactions He has provided solvency opinions inspin-offs, leveraged buyouts and recapitalizations, and other transactions In addition,

he has structured debt securities and issued commercially reasonable opinions for debtissuances in related-party transactions

Prior to joining Duff & Phelps in 1997, Mr Turf was an assistant vice president

in the commercial loan department of Corus Bank He received an MBA with a focus

on finance and organizational behavior from the J L Kellogg Graduate School ofManagement at Northwestern University He also received a BS infinance from theUniversity of Illinois at Urbana–Champaign

The opportunity cost of capital is one of the most important concepts infinance

For example, if you are a chieffinancial officer contemplating a possible capitalexpenditure, you need to know what return you should look to earn from theinvestment If you are an investor who needs to plan for future expenditures, youneed to ask what return you can expect to earn on your portfolio

Shannon Pratt and Roger Grabowski have produced a remarkably sive review of the subject With over 1,000 pages of close-packed material, the book isnot for bedtime reading, but it is a work that valuation practitioners, CFOs, and otherswillfind an invaluable reference

comprehen-The book is somewhat wider ranging than its title suggests, for its focus is onvaluation It does not simply discuss how to estimate the cost of capital, but also showshow this estimate can be used to solve a variety of valuation problems Indeed, it ishere that the book makes some of its most useful contributions Most finance textsprovide an overview of how the cost of capital can be used to discount the expectedcashflows from a proposed capital project What I find most interesting about thisbook is that it also tackles much less well covered topics For example, boards ofsecuritiesfirms that need to value level 3 securities will find useful advice on illiquiditydiscounts Practitioners who need to estimate the value of control willfind a chapter

on this issue And so on It is this all-embracing nature of the analysis that makes thisbook such a valuable addition to thefinancial manager’s bookshelf

Richard BrealeyLondon Business School

xxiii

Cost of capital is an essential, albeit complex element of virtually every application

offinance Literally billions and billions of dollars turn on decisions regarding thecost of capital in each of the following contexts:

■ Mergers and acquisitions

■ Shareholder disputes

■ Capital budgeting

■ Bankruptcies and reorganizations

■ Business damages cases

■ Gift, estate, and income tax matters

■ Marital property settlements

■ Ratemaking in regulated industries

■ Property taxationThis book addresses developments related to estimating the cost of capital in all of

these contexts We use the term estimates rather than determinations because the cost

of capital is forward-looking It is the expected rate of return required to attract capital

to a particular investment or project as of a given date, reflecting economic and otherfactors surrounding the expected returns and the risk of the investment or project atthat particular point in time

Cost of capital is the pricing of risk Since risk is in the mind of the beholder, itcannot be measured directly This book addresses ways to measure risk to lead to anestimate of the appropriate cost of capital

EFFECT OF FEDERAL RESERVE ACTIONS ON LONG-TERM INTEREST RATES

Federal Reserve actions kept long-term interest rates low from 1942 through 1951and again from the fall of 2011 through at least the writing of this book We analyzethe effect of these actions on the traditional data and procedures used to estimate thecost of capital, and suggest ways to control for it

WHY DID WE UNDERTAKE UPDATING THE BOOK?

Our experience tells us that practitioners need assistance to better understandand estimate the cost of capital and in communicating their results, not from theviewpoint of portfolio management but from the viewpoint of business ownersand managers

xxv

We decided to do this update to the book because of the changes in cost of capitalresulting from thefinancial crisis that began in 2008, the subsequent recession, andtoday’s uncertain environment.

The purpose of this book is to present both the theoretical development of cost ofcapital estimation and its practical application to valuation and capital budgeting incurrent practice It is intended both as a learning text for those who want to study thesubject and as a handy reference for those who are interested in background or seekdirection in some specific aspect of cost of capital

The objective is to serve two primary categories of users:

1 The practitioner who seeks a greater understanding of the latest theory and

practice in cost of capital estimation

2 The reviewer who needs to make an informed evaluation of another party’s

methodology and data used to produce a cost of capital estimate

No other valuation text designed for the practitioner treats the cost of capital withthe breadth and depth that this one does In terms of breadth, this book treats cost ofcapital for uses in business valuation, project assessment and capital budgeting,divisional cost of capital, reporting unit valuation, goodwill impairment testing,valuing intangible assets for financial reporting, and transfer pricing

The reader can expect to learn about:

■ The theory of what drives the cost of capital

■ Procedures currently in use to estimate cost of capital

■ Data available as inputs to the models to estimate cost of capital

Our emphasis is on the cost of equity capital We present in-depth analysis of thecomponents, including the equity risk premium, beta, and the size effect We alsoanalyze criticism of many procedures used for developing estimates of the cost ofcapital and present a number of alternative procedures

WHAT’S NEW IN THIS EDITION

There has been a surge of new research since the previous edition We have attempted

to reflect these developments through the time we are writing this book, found innew and updated books, in newly published articles, and, particularly, in manyunpublished working papers Readers can access most of the working papers throughour footnote references

New chapters:

■ “How Courts View Cost of Capital” (Chapter 38), dealing with oppression andfairness matters; estate and gift matters; corporate restructuring and other federaltax matters, including transfer pricing; cost of capital issues in intellectualproperty and other damages disputes; bankruptcy cases; family law matters;

ad valorem taxation matters; and regulated industry matters

■ Cost of capital for closely held businesses (Chapter 27)

■ Two new case studies detailing the procedures for estimating cost of capital

Updat ed and expan ded discus sion of many impor tant topics , includi ng:

■ Equity risk premi um an d the risk- free rate, includi ng the impac t of FederalReserve actions

■ Devel opment of cost of cap ital in merge rs and acquisi tions;

■ How to use Ibbotson ’ s and Duff & Phe lps cost of capita l data

■ Com pany-speci fic risk— factor s to con sider and how to measur e

■ Criti cisms of CA PM and reasons why mult iple proced ures sho uld be used indevelopi ng discount and capita lization rates

■ Added evidence of the exist ence an d magn itude of the size effect

■ Updat ed chapter on co st of capital in transf er prici ng

■ Cost of capita l for fami ly holding companie s

■ Cost of Capital of REITs

■ Globa l cost of capita l estimatio n, includi ng a new size study of Euro peancompan ies

■ Adju sting discount an d cap italization rates for diffe rent measur es of econo micincome, includi ng pretax discount rates

■ Changi ng discount rates refl ecting chan ges in risk

■ Additional residual (terminal) value m ode ls to prov ide more flexibility to the a nalyst

■ “Glos sary of Cost of Capi tal Terms ” (Appe ndix III) — added term s as defined bythe Internat ional Valuati on Standards Commit tee

We again expanded t he chapters on com m on errors made in valuation andadvice from the authors about dealing w ith specifi c, of ten controversial, cost ofcapital i ssues

Supplemental information is available to readers on the John Wiley & Sons website,including hundreds of PowerPoints to use in the classroom and for presentations.Finally, the index is newly improved to make it easier for readers to locatematerial on a particular topic

ABOUT THE WEBSITE

We have added the following materials to the companion website

URL : www wiley com/g o/costofc apital

Password: coc5e

Appendices

IV Sample Report Submitted to U.S Tax CourtExample of a report submitted to the U.S Tax Court to assist in communicatingapplication of cost of capital estimation procedures in a straightforward manner

to the nontechnical reader

V Review of Statistical AnalysisComprehensive review of the statistics discussed and used in developing cost ofcapital estimates

VI Notat ion System and Abbrev iations Used in Thi s BookVII PowerPoi nts That Accomp any the Chapt ers

To assi st those that may want to use the book in seminars and in the classroom.VIII Exam ples (Mic rosoft Excel models ) of changing capita l structu res discus sed inAppendi x 21A

AUDIENCES F OR THE BOOK

In additio n to the tradi tional pro fessional valuat ion practi tioner , we designe d thisbook to serve the needs of:

■ Corporate fi nance offi cers for pricing or evaluating mergers and acquisitions,

raising private or public equity, prope rty taxation, and s takeholder disputes

■ Invest ment ban kers for pr icing, publ ic offerin gs, merge rs and acquisi tions, and

private equity financing

■ CPAs who de al wit h either valuation fo r fi nancial reporting or client valuat ionsissues

■ Judges a nd attorney s who deal wit h valuat ion issues

■ Acade micians and students who wish to learn anything from the ba sic theory to

the lates t resear chOur goal is to enh ance the insights of users of cost of cap ital applic ations as wel l asoriginators of such applica tions Several chapter appen dixes present detailed expo-sitions of the more c omplex pro cedures

FINAL T HOUGHTS

We hav e enjoyed the cha llenge of assem bling the mater ials for this editi on We doanticipate updating the book again, so please contact the autho rs with any que stions,comments, or suggestions for the next edition

Shannon P Pratt, CFA, FASA, ARM, MCBA, ABAR, CM&AAShannon Pratt Valuations, Inc

9725 S.W Beaverton-Hillsdale Highway, Suite 360Beaverton, OR 97005

(503) 716-8532

www shanno npratt.co m

E-mai l: shanno n@shann onpratt com

Roger J Grabowski, FASADuff & Phelps, LLC

311 S Wacker Drive, Suite 4200Chicago, IL 60606

(312) 697-4720

www duffandp helps.co m

E-mai l: roger.g rabowsk i@duffandph elps.com

This book has benefited immensely from review by many people with a high level

of knowledge and experience in cost of capital and valuation These peoplereviewed the manuscript (or parts of it), and the book reflects their invaluable effortsand legions of constructive suggestions

Jay AbramsAbrams Valuation GroupNorth Hollywood, CA

Diane Coogan PushnerDepartment of EconomicsQueens College,

City University of New YorkBruce Bingham

Capstone Advisory Group LLCNew York, NY

Raymond RathGlobalview AdvisorsLos Angeles, CAStephen J Bravo

Apogee Business ValuationFramingham, MA

William RedpathBAI/KelseyWashington, DCJames Budyak

Valuation Research Corp

Milwaukee, WI

Matthew SteeleMesirow Financial ConsultingChicago, IL

David ClarkeThe Griffing Group

Houlihan LokeySan Francisco, CAJaime d’Almeida

Duff & Phelps LLC

Houlihan LokeyLos Angeles, CAJames Hitchner

Financial Valuation Advisors

International Valuation StandardsCommittee

London, UKDavid King CFA

Mesirow Financial Consulting

MNP LLPMontreal (Quebec), CanadaJames Krillenberger

Value Knowledge LLCChicago, IL

xxix

In addition, we thank:

■ Yang Luo and Pradnya Patil for assistance with editing and research, includingupdating of the bibliography; updating and shepherding the manuscript amongreviewers, contributors, authors, and publisher; typing; obtaining permissions;and other invaluable help

■ Niel Patel, Carla Nunes, James Harrington, Kang Sheng He, Jonathan Ho,Alessandra Malik, and Dan Cecchin of Duff & Phelps, LLC for preparingnumerous tables and calculations that appear throughout the book

■ Noah Gordon of Shannon Pratt Valuations, Inc., for general editorialassistance

For the granting of permissions, we would like to thank:

■ Gilbert Matthews, Alina Niculita, Robert Lloyd, Chris Bakewell, Raji Seshan,Michael Vitti, Terry Evans, Myron Marcinkowski, Carl R E Hoemke, TobyReese, Alan E Finder, Paul T Hunt, and Enrique Bacalao for allowing us to

condense their chapters from The Lawyer ’s Guide to Cost of Capital.

■ Professor Ashok Bhardwaj Abbott

■ Professor Edwin Burmeister, Duke University

■ Business Valuation Resources, LLC

■ Center for Research in Security Prices, University of Chicago

■ Professors Elroy Dimson, Paul Marsh, and Mike Staunton, London School ofEconomics

■ Duff & Phelps, LLC

■ FactSet Mergerstat, LLC

■ FMV Opinions, Inc

■ Professor Terry V Grissom, University of Washington

■ Institutional Investor

■ Professor Arthur Korteweg, Stanford Graduate School of Business

■ Jim MacCrate, MAI, MacCrate Associates, LLC

■ Morningstar, Inc

■ Glen Mueller, Dividend Capital Group

■ National Association of Real Estate Investment Trusts

■ Pluris Valuation Advisors, LLC

■ Standard & Poor’s (a division of McGraw-Hill Financial)

■ Thomson Corporation

■ Valuation Advisors, LLC

Thank you to those whose ideas contributed to several of the analyses rated herein:

incorpo-■ David King, Mesirow Financial Consulting, LLC

■ Professor Timothy Luehrman, Harvard University

We thank all of the people singled out for their assistance Of course, any errorsherein are our responsibility.1

Shannon PrattRoger Grabowski

1 Any opinions presented in this book are those of the authors and contributing authors The opinions of Mr Grabowski and other contributing authors from Duff & Phelps do not represent the of ficial position of Duff

& Phelps, LLC This material is offered for educational purposes with the understanding that neither the authors nor Duff & Phelps, LLC are engaged in rendering legal, accounting, or any other professional service through presentation of this material The information presented in this book has been obtained with the greatest of care from sources believed to be reliable, but is not guaranteed to be complete, accurate, or timely The authors and Duff & Phelps, LLC expressly disclaim any liability, including incidental or consequential damages, arising from the use of this material or any errors or omissions that may be contained in it.

PART One Cost of Capital Basics

Cost of Capital: Applications and Examples, Fifth Edition Shannon P Pratt and Roger J Grabowski.

 2014 John Wiley & Sons, Inc Published 2014 by John Wiley & Sons, Inc.

CHAPTER 1

Defining Cost of Capital

IntroductionComponents of a Capital StructureCost of Capital Is a Function of the InvestmentCost of Capital Is Forward-looking

Cost of Capital Is Based on Market ValueCost of Capital Is Usually Stated in Nominal TermsCost of Capital Equals the Discount Rate

Discount Rate Is Not the Same as Capitalization RateStandard (Basis) of Value

The term market refers to the universe of investors who are reasonable candidates

to fund a particular investment Capital or funds are usually provided in the form ofcash, although in some instances capital may be provided in the form of other assets.The cost of capital is usually expressed in percentage terms, that is, the annual amount

of dollars that the investor requires or expects to realize from the investment,expressed as a percentage of the dollar amount invested

As Ibbotson puts it:

The opportunity cost of capital is equal to the return that could have beenearned on alternative investments at a similar level of risk and liquidity.1

1Roger Ibbotson, Yale University, 2013

3

Cost of Capital: Applications and Examples, Fifth Edition Shannon P Pratt and Roger J Grabowski.

 2014 John Wiley & Sons, Inc Published 2014 by John Wiley & Sons, Inc.

Cost of Capital: Applications and Examples, Fifth Edition Shannon P Pratt and Roger J Grabowski.

 2014 John Wiley & Sons, Inc Published 2014 by John Wiley & Sons, Inc.

In other words, it is the competitive return available in the market on acomparable investment, with risk being the most important component of compara-bility The degree of liquidity is one element of risk.

Put another way:

Since the cost of anything can be defined as the price one must pay to acquire

it, the cost of capital is the return a company must promise in order to raisecapital from the market, either debt or equity A company does not set its owncost of capital; it must go to the market to discover it Yet meeting this cost isthefinancial market’s one basic yardstick for determining whether a com-pany’s performance is adequate.2

As the quote suggests, most of the information for estimating the cost of capitalfor a business, security, or project comes from the investment market The cost of

capital is always an expected (or forward-looking) return While would-be investors

can observe analysts’ views as to expected returns at the time of their investment, there

is no quotation available to investors for cost of capital comparable to stock quotes.Thus, we often form our views of the future by analyzing historical market data.Past returns at best provide some guidance as to what might be expected for a givenlevel of risk

The key component of the valuation process is pricing risk—that is the expectedreturn for the given amount of risk The cost of capital is the expected returnappropriate for the expected level of risk But often, observed returns do not matchexpected returns That is the essence of risk (See Chapter 6 for a more completediscussion of risk.)

COMPONENTS OF A CAPITAL STRUCTURE

The term capital in this context means the components of an entity’s capital structure.

The primary components of a capital structure include:

■ Debt capital (liabilities on or off the balance sheet that lead some analysts to viewlease obligations as debt capital)

■ Preferred equity capital (i.e., stock, partnership, limited liability company, orother type of entity interests with preference features, such as seniority in receipt

of dividends, distributions, or liquidation proceeds)

■ Common equity capital (i.e., stock, partnership, limited liability company, orother type of entity interests at the lowest or residual level of the capital structure)There may be more than one subcategory in any or all of the listed categories ofcapital Also, there may be related forms of capital, such as warrants or options Eachcomponent of an entity’s capital structure has its own unique cost, dependingprimarily on its respective risk

2Mike Kaufman,“Profitability and the Cost of Capital,” Chapter 14 of William R Lalli, ed.,

Handbook of Budgeting, 6th ed (Hoboken, NJ: John Wiley & Sons, 2012): 265.

When we talk about the cost of common equity capital (e.g., the expected return

to common equity investors), we usually use the phrase cost of equity capital.

Simply and cogently stated, “The cost of equity is the rate of return investorsrequire on an equity investment in afirm.”3

When we talk about the cost of capital to the business overall (e.g., the average cost

of capital for both equity ownership interests and debt interests), we commonly use the

phrases weighted average cost of capital (WACC), blended cost of capital, or overall cost

of capital In rate-making cases, this array is sometimes called the band of investment.

The next quote explains how the cost of capital can be viewed from three differentperspectives:

On the asset side of afirm’s balance sheet, it is the rate that should be used todiscount to a present value the future expected cash flows On the liabilityside, it is the economic cost to the business of attracting and retaining capital

in a competitive environment, in which investors (capital providers) carefullyanalyze and compare all return-generating opportunities On the investor’sside, it is the return one expects and requires from an investment in abusiness’s debt or equity While each of these perspectives might view thecost of capital differently, they are all dealing with the same number.4Recognizing that the cost of capital applies to both debt and equity investments, awell-known text states:

Since free cashflow is the cash flow available to all financial investors, thecompany’s WACC must also include the required return for each investor.5

COST OF CAPITAL IS A FUNCTION OF THE INVESTMENT

As Ibbotson puts it, “The cost of capital is a function of the investment, not theinvestor.”6The cost of capital comes from the marketplace, and the marketplace is thepool of investors“pricing” the risk of a particular asset Thus it represents the consensusassessment of the pool of investors that are participants in a particular market.Brealey, Myers, and Allen state the same concept:“The opportunity cost of capitaldepends on the use to which that capital is put.”7They make the point that it would be anerror to evaluate a potential investment on the basis of a business’s overall cost of capital

3Aswath Damodaran, Investment Valuation: Tools and Techniques for Determining the Value

of Any Asset, 3rd ed (Hoboken, NJ: John Wiley & Sons, 2012): 183.

42012 IbbotsonStocks, Bonds, Bills, and Inflation

Valuation Yearbook (Chicago:

Morning-star, 2012): 21 Note that thefirm’s after-tax cost of debt differs from investors’ returns on debt

by the income tax savings to thefirm due to the tax deductibility of interest expense (the affect)

tax-5Tim Koller, Marc Goedhart, and David Wessels, Valuation: Measuring and Managing the Value of Companies, 5th ed (Hoboken, NJ: John Wiley & Sons, 2010): 231.

6Ibbotson Associates, “What Is the Cost of Capital?” 1999 Cost of Capital Workshop

(Chicago: Ibbotson Associates, 1999)

7Richard A Brealey, Stewart C Myers, and Franklin Allen, Principles of Corporate Finance,

11th ed (New York: McGraw-Hill/Irwin, 2014): 219

if that investment were more or less risky than the business’s existing business “Each

project should in principle be evaluated at its own opportunity cost of capital.”8When a business uses a given cost of capital to evaluate a commitment of capital to

an investment or project, it often refers to that cost of capital as the hurdle rate The

hurdle rate is the minimum expected rate of return that the business would be willing

to accept to justify making the investment Depending on the degree of risk of theprospective investment compared with the business’s overall risk, the hurdle rate forany given prospective investment may be at, above, or below the business’s existingoverall cost of capital

Generally contemporary corporatefinance holds that companies should be makinginvestments, either capital investments or acquisitions, such that the returns will exceedthe cost of capital for that investment Doing so creates value and is sometimes referred

to as economic value added, economic pro fit, or shareholder value added.9

COST OF CAPITAL IS FORWARD-LOOKING

The cost of capital represents investors’ expectations There are two basic elements tothese expectations:

1 Risk-free rate, which includes:

■ Rental rate Real return for lending the funds free of default risk, thus foregoing

consumption for which the funds otherwise could be used

■ Inflation (and inflation risk premium) Expected rate of inflation over the term

of the risk-free investment (and the risk that expected inflation will increase)

■ Maturity risk (also called investment rate risk or term risk) Risk that the

investment’s principal market value will rise or fall during the period tomaturity as a function of changes in the general level of interest rates

2 Risk premium—the added return expected by market participants to compensate

them for uncertainty as to when and how much cash flow or other economicincome will be received

Risk is discussed more fully in Chapter 6

The combination of the three items comprising the risk-free rate is sometimes

referred to as the time value of money While these expectations, including assessment

of risk, may be different for different investors, the market tends to form a consensuswith respect to a particular investment or category of investments That consensusdetermines the cost of capital for investments of varying levels of risk

The cost of capital, derived from investors’ expectations and the market’s

consensus of those expectations, is applied to expected economic income, usually measured in terms of net cash flows We convert the stream of expected economic

benefits to its present value equivalent to compare investment alternatives of similar or

8Ibid

9See, for example, Tim Koller, Marc Goedhart, and David Wessels, Valuation: Measuring and Managing the Value of Companies, 5th ed (Hoboken, NJ: John Wiley & Sons, 2010); also see Alfred Rappaport, Creating Shareholder Value: A Guide for Managers and Investors, revised

ed (New York: Free Press, 1997)

differing levels of risk Present value, in this context, refers to the dollar amount that a

rational and well-informed investor would be willing to pay today for the stream ofexpected economic income In mathematical terms, the cost of capital is the percentagerate of return that equates the stream of expected economic income with its presentcash value (see Chapter 4)

COST OF CAPITAL IS BASED ON MARKET VALUE

The cost of capital is the expected rate of return on some base value The base value ismeasured as the market value of an asset (or liability), not its book value, par value, orcarrying value

For example, the yield to maturity shown in the bond quotations in thefinancialpress is based on the closing market price of a bond, not on its face value Similarly, theimplied cost of equity for a company’s stock is based on the market price per share atwhich it trades, not on the company’s book value per share of stock

The cost of capital is estimated from market data These data refer to expectedreturns relative to market prices By applying the cost of capital derived from marketexpectations to the expected net cashflows (or other measure of economic income) fromthe investment or project under consideration, the market value can be estimated

COST OF CAPITAL IS USUALLY STATED IN NOMINAL TERMS

Keep in mind that we have talked about expectations including inflation Assuminginflationary expectations, the return an investor requires includes compensation forreduced purchasing power of the currency over the life of the investment Therefore, whenthe analyst or investor applies the cost of capital to expected returns in order to estimatevalue, he or she must also include an expected inflation rate in those expected returns.This obviously assumes that investors have reasonable consensus expectationsregarding inflation For countries subject to unpredictable hyperinflation, it is some-times more practical to estimate the cost of capital in“real” terms (a rate of return thatdoes not include an inflation expectation) rather than in nominal terms and apply it toexpected net cashflows expressed in real terms We discuss the problems in estimatingcashflows and cost of capital in real terms in Chapter 34

COST OF CAPITAL EQUALS THE DISCOUNT RATE

The essence of the cost of capital is that it is the percentage return that equatesexpected economic income with present value The expected rate of return in this

context is called a discount rate By discount rate, thefinancial community means a

compounded rate (typically expressed as an annual rate) at which each increment of

expected economic income is discounted back to its present value A discount ratereflects both the time value of money and risk-profile of the expected income stream.Therefore, in its totality it represents the cost of capital The sum of the discountedpresent values of each future period’s expected net cash flow or other measure ofreturn equals the present value of the investment, reflecting the expected amounts of

return ov er the life of the invest ment The term s discount rate, co st of capita l, and requir ed rate of return are often used inter changeably

The eco nomic income refer enced here repres ents total expected ben e fits in terms

of money or money ’ s worth In other words , this economic income includes ments of cash flow reali zed by the investor whil e holding the invest ment, as well asproceeds to the investo r upon liquid ation of the invest ment The rate at whic h theseexpected future total returns are reduced to present value is the discount rate, which is

incre-the co st of capital (required rate of return) for a particu lar investment.

DISCOUNT RATE IS NOT THE SAME AS CAPITALIZATION RATE

Because some pr actitioners and the ir clie nts confuse the term s, we poin t out here that

discount rate and capita lization rate are two disti nctly diffe rent conce pts Disc ount rate equates to cost of capital It is a rate applied to all expected eco nomic income to

convert the exp ected eco nomic income stream to a present value

A cap italizat ion rate, however , is merely a divisor app lied to one singl e elem ent or

period of th e economic income stream to estimate a pre sent value The only insta nce inwhich the discou nt rate is eq ual to the cap italization rate is when each fu ture pe riod ’seconomic income is eq ual (i.e., absent any growth or decli ne), and the economicincome is ex pected to con tinue into perpetui ty One of the few exampl es would be aprefer red stock paying a fi xed dividen d amo unt pe r share in perpetui ty

The relationship between discount and capitalization rates is discussed in Chapter 4

STANDARD (BASIS) OF VALUE

Throug hout this book, we discus s e xpected eco nomic income an d cost of capita l in thecontext of various defi nitions of the generic term v alue The term has many mean ings

In th is book, a standar d of value (titled ba sis of value by the Internat ional

Valuati on Standard Counci l [IVSC ] Glossary of Val uation Ter ms) is a de finitio n of thetype of value be ing sought The standar d of value ad dresse s th e questi ons: “value towhom? ” and “value unde r what circum stances ? ” We wil l identi fy the app licablestandar d of v alue and its mean ing when we are speak ing abo ut a parti cular ap plica-tion For backgrou nd, a quick summ ary here would be useful 10

10Definitions of fair market value, investment value, and intrinsic value are included in theInternational Glossary of Business Valuation Terms, jointly developed by the American Institute

of Certi fied Public Accountants, American Society of Appraisers, Canadian Institute ofChartered Business Valuators, National Association of Certi fied Valuation Analysts, andthe Institute of Business Appraisers For a more complete discussion, see Chapter 2 in Shannon

P Pratt, with Alina Niculita, Valuing a Business: The Analysis and Appraisal of Closely Held Companies, 5th ed (New York: McGraw-Hill, 2008); and Jay Fishman, Shannon Pratt, and William Morrison, Standards of Value: Theory and Applications, 2nd ed (Hoboken, NJ: John

Wiley & Sons, 2013) Definition of basis of value, market value, fair value, and investment valueare included in the International Valuation Standards Council’s International Glossary ofValuation Terms, available at: www.ivsc.org/glossary

Fair market value is the value standard used in most federal income tax matters,

including gift and estate and income taxes In general, it is the price at which theproperty would change hands between a hypothetical willing buyer and a hypotheticalwilling seller The pool of willing buyers and willing sellers for a property defines the

“market” for that property.11 It is an objective standard

Arm’s length value is the value (in terms of price and terms) at which a transaction

would take place between unrelated buyers and sellers.12

Fair value has several separate and unrelated meanings depending on the context

in which it is used

Fair value under state statutes, in most states, is the statutory standard of value in

cases of dissenting stockholder appraisal rights and shareholder (or partner) sion cases Definitions vary from state to state

oppres-Fair value under IVSC is “the estimated price for the transfer of an asset orliability between identified knowledgeable and willing parties that reflects the respec-tive interests of those parties.”

Fair value for financial reporting is defined by ASC 820, Fair Value Measurements (formerly FASB Statement No 157, Fair Value Measurements), which codified

Generally Accepted Accounting Principles (GAAP) and is required for financialreporting by the Securities and Exchange Commission (SEC) The definition of fairvalue for financial reporting is now aligned between ASC 820 and InternationalFinancial Reporting Standards (IFRS) 13 It is the standard of value for reporting ofmarket-based financial statements

While there is no definition of fair value under the bankruptcy code the federal

definition of insolvency is defined as a “financial condition such that the sum of [the]

entity’s debts is greater than all of [the] entity’s property, at a fair valuation” (U.S.C

§101(32)/1/201)

In the United States, the most widely recognized and accepted standard of value

related to real estate appraisals is market value, which is essentially equivalent to fair

of investment value is very similar: the value of an asset to the owner or a prospective

owner for individual investment or operational objectives There can be different costs

of capital to different investors, depending on different circumstances and perceptions

Intrinsic value (sometimes called fundamental value) is the specific value of aninvestment based on its perceived characteristics inherent in the investment but not

11See, for example, explanation by Mark Lee in Shannon P Pratt, Business Valuation Discounts and Premiums, 2nd ed (Hoboken, NJ: John Wiley & Sons, 2009): 34–37 Lee makes adistinction between the stock market (diversified buyers and sellers) and the mergers andacquisitions market

12David Laro and Shannon Pratt, Business Valuation and Federal Taxes: Procedure, Law, and Perspective, 2nd Edition (Hoboken, NJ: John Wiley & Sons, 2011): 115 David Laro is a senior

judge on the U.S Tax Court