Roger J. Grabowski is a managing director with Duff & Phelps. He is coauthor of Cost of Capital – Applications and Examples, Fifth Edition, The Lawyer's Guide to Cost of Capital, and Cost of Capital in Litigation.James P. Harrington is a director at Duff & Phelps. He is a leading contributor to Duff & Phelps' efforts in the development of studies, surveys, online content and tools, firm-wide valuation models, data distribution platforms, and published thought leadership. He is a coauthor of the Duff & Phelps "Valuation Handbook" series, a contributing author to Cost of Capital – Applications and Examples, Fifth Edition, and a Duff & Phelps contributor to the Stocks, Bonds, Bills, and Inflation (SBBI) Yearbook. Carla S. Nunes is a managing director in the Office of Professional Practice at Duff & Phelps, where she provides firm-wide technical guidance on a variety of valuation, financial reporting, and tax issues, with a particular focus on cost of capital. She is a coauthor of the Duff & Phelps "Valuation Handbook" series and a contributing author to Cost of Capital – Applications and Examples, Fifth Edition.

• Acknowledgements xivIntroduction xvChapter 1 Cost of Capital Defined 1-1Introduction 1-1Income Approach Overview 1-2Discounting versus Capitalizing Concepts 1-2Valuation Date 1-5Basic Cost of Capital Concepts 1-5Sources of Capital 1-9Cost of Capital Input Assumptions 1-10Capital Structure Considerations 1-16Calculating WACC 1-18Estimates of Cost of Capital are Imprecise 1-19Key Things to Remember about Cost of Capital 1-21Chapter 2 Methods for Estimating the Cost of Equity Capital 2-1Basic Framework 2-1Types of Risk 2-6Cost of Equity Capital Estimation Methods 2-8Build-up 2-10CAPM 2-11Other Cost of Equity Capital Estimation Methods 2-15Key Things to Remember about the Methods for Estimating the Cost of Equity Capital 2-17Chapter 3 Basic Building Blocks of the Cost of Equity Capital– Risk-free Rate and Equity Risk Premium 3-1The Risk-free Rate and Equity Risk Premium: Interrelated Concepts 3-1Spot Risk-free Rates versus Normalized Risk-free Rates 3-2Global Turbulence and Impact on Interest Rates 3-14Methods of Risk-free Rate Normalization 3-19Spot Yield or Normalized Yield? 3-23Concluded Normalized Risk-free Rate 3-25Equity Risk Premium 3-26Estimating the Equity Risk Premium 3-27Duff & Phelps Recommended U.S. ERP 3-38Economic and Financial Market Indicators 3-39Quantitative Models 3-44Concluding on an ERP 3-48Chapter 4 Basic Building Blocks of the Cost of Equity Capital – Size Premium 4-1Size as a Predictor of Equity Returns 4-1Possible Explanations for the Greater Returns of Smaller Companies 4-2The Size Effect: Empirical Evidence 4-2The Size Effect Over Longer Periods 4-3The Size Effect Tends to Stabilize Over Time 4-6The Size Effect Changes Over Time 4-7Criticisms of the Size Effect 4-8Data Issues 4-12Has the Size Effect Disappeared in More Recent Periods? 4-17Relationship of Size and Liquidity 4-21Key Things to Remember about the Size Premium 4-26Chapter 5 Basic Building Blocks of the Cost of Equity Capital – Betas and Industry Risk Premia 5-1Beta 5-1Differences in Estimation of Equity Betas 5-7Full-Information Beta 5-11Industry Risk Premia 5-12Full-Information Beta Methodology 5-16Debt Betas 5-17Unlevering and Levering Equity Betas 5-18Key Things to Remember about Betas and the Industry Risk Premia 5-19Chapter 6 Basic Building Blocks of the Cost of Equity Capital – Company-specific Risk Premia 6-1Introduction 6-1Adjustments for Differences in Risk 6-2Adjustments for Risk in Net Cash Flows and Biased Projections 6-5Adjustments for Other Risk Factors 6-7Matching Fundamental Risk and Return 6-8Key Things to Remember about Company-specific Risk Premia 6-10Chapter 7 The CRSP Deciles Size Premia Studies and the Risk Premium Report Studies– A Comparison 7-1History of the CRSP Deciles Size Premia Studies 7-1History of the Risk Premium Report Studies 7-2Data Sources 7-2Definitions of “Size” 7-6Time Period Examined 7-7Number of Portfolios 7-7Portfolio Overlap 7-7Guideline Portfolio Method and Regression Equation Method 7-8Risk Premia Over CAPM (Size Premia) 7-8“Smoothed” Premia versus “Average” Premia 7-12OLS Beta versus Sum Beta 7-12Risk Premia Over the Risk Free Rate 7-12Unlevered Premia 7-13Risk Study 7-13Characteristics of Companies in Portfolios 7-13Online Applications 7-14Chapter 8 CRSP Deciles Size Premia Examples 8-1Build-up Example 8-1CAPM Example 8-4Key Things to Remember about the CRSP Deciles Size Premia 8-7Chapter 9 Risk Premium Report Exhibits – General Information 9-1Appropriate Use of the Risk Premium Report Exhibits 9-1How the Risk Premium Report Exhibits are Organized 9-2Cost of Equity Capital Estimation Methods Available 9-3Proper Application of the Equity Risk Premium (ERP) Adjustment 9-4“Smoothed” Premia versus “Average” Premia 9-7The “Guideline Portfolio Method” versus the “Regression Equation Method” 9-8Example: Calculating an Interpolated Premium Using the Regression Equation Method 9-9Tips Regarding the Regression Equation Method 9-10Can the Regression Equation Method be Used If the Subject Company Is Small? 9-10Size Study or Risk Study? 9-11Key Things to Remember About the Risk Premium Report Exhibits 9-12Chapter 10 Risk Premium Report Exhibits – Examples 10-1Size Study 10-1Reasons for Using Additional Measures of Size 10-1The Difference Between the Size Study’s A Exhibits and the B Exhibits 10-2The Difference Between “Risk Premia Over the Risk-free Rate” and “Risk Premia Over CAPM” 10-2Calculating Custom Interpolated Premia for Smaller Companies 10-6Overview of Methods Used to Estimate Cost of Equity Capital Using the Size Study 10-9Size Study Examples: Assumptions Used 10-10Size Study Examples 10-12Unlevered Cost of Equity Capital 10-17Overview of the Methodology and Assumptions Used to Unlever Risk Premia 10-18Estimating Cost of Equity Capital Using the “Build-up 1-Unlevered” Method 10-22Estimating Cost of Equity Capital Using the Capital Asset Pricing Model (CAPM) 10-26Estimating Cost of Equity Capital Using the “Build-up 2” Method 10-30Risk Study 10-35Overview of Methods Used to Estimate Cost of Equity Capital Using the Risk Study 10-42Risk Study Examples 10-45Build-up 3-Unlevered 10-49High-Financial-Risk Study 10-51Overview of Methods Used to Estimate Cost of Equity Capital Using the High-Financial-Risk Study 10-57Estimating Cost of Equity Capital Using the “Build-up 1-High-Financial-Risk” Method 10-58Estimating Cost of Equity Capital Using the “CAPM-High-Financial-Risk” Method 10-61Comparative Risk Study 10-63Using the Comparative Risk Study to Refine Build-up Method Estimates 10-67Using the Comparative Risk Study to Refine CAPM Estimates 10-69Chapter 11 Real Estate 11-1Individual Real Estate Assets 11-1Real Estate Investment Trusts (REITs) 11-2Structure of Real Estate Entities 11-3Correlation of U.S. REITs Compared to Other U.S. Asset Classes 11-4Summary Statistics of U.S. REITs Compared to Other U.S. Asset Classes 11-6Real Estate Property Valuation Inputs 11-8Key Things to Remember about Real Property Valuation 11-17Chapter 12 Answers to Commonly Asked Questions 12-1GlossaryIndexAppendix 1 – Definitions of Standard & Poor’s Compustat Data Items Used to Calculate the Risk Premium Report ExhibitsAppendix 2 – Changes to the Risk Premium Report Over TimeAppendix 3 – CRSP Deciles Size Premia Study: Key VariablesAppendix 3a – Industry Risk Premium (RPi)Appendix 3b – Debt BetasAppendix 4 – Risk Premium Report Study Exhibits

Roger J. Grabowski is a managing director with Duff & Phelps. He is coauthor of Cost of Capital – Applications and Examples, Fifth Edition, The Lawyer's Guide to Cost of Capital, and Cost of Capital in Litigation.James P. Harrington is a director at Duff & Phelps. He is a leading contributor to Duff & Phelps' efforts in the development of studies, surveys, online content and tools, firm-wide valuation models, data distribution platforms, and published thought leadership. He is a coauthor of the Duff & Phelps "Valuation Handbook" series, a contributing author to Cost of Capital – Applications and Examples, Fifth Edition, and a Duff & Phelps contributor to the Stocks, Bonds, Bills, and Inflation (SBBI) Yearbook. Carla S. Nunes is a managing director in the Office of Professional Practice at Duff & Phelps, where she provides firm-wide technical guidance on a variety of valuation, financial reporting, and tax issues, with a particular focus on cost of capital. She is a coauthor of the Duff & Phelps "Valuation Handbook" series and a contributing author to Cost of Capital – Applications and Examples, Fifth Edition.

• Acknowledgements xivIntroduction xvChapter 1 Cost of Capital Defined 1-1Introduction 1-1Income Approach Overview 1-2Discounting versus Capitalizing Concepts 1-2Valuation Date 1-5Basic Cost of Capital Concepts 1-5Sources of Capital 1-9Cost of Capital Input Assumptions 1-10Capital Structure Considerations 1-16Calculating WACC 1-18Estimates of Cost of Capital are Imprecise 1-19Key Things to Remember about Cost of Capital 1-21Chapter 2 Methods for Estimating the Cost of Equity Capital 2-1Basic Framework 2-1Types of Risk 2-6Cost of Equity Capital Estimation Methods 2-8Build-up 2-10CAPM 2-11Other Cost of Equity Capital Estimation Methods 2-15Key Things to Remember about the Methods for Estimating the Cost of Equity Capital 2-17Chapter 3 Basic Building Blocks of the Cost of Equity Capital– Risk-free Rate and Equity Risk Premium 3-1The Risk-free Rate and Equity Risk Premium: Interrelated Concepts 3-1Spot Risk-free Rates versus Normalized Risk-free Rates 3-2Global Turbulence and Impact on Interest Rates 3-14Methods of Risk-free Rate Normalization 3-19Spot Yield or Normalized Yield? 3-23Concluded Normalized Risk-free Rate 3-25Equity Risk Premium 3-26Estimating the Equity Risk Premium 3-27Duff & Phelps Recommended U.S. ERP 3-38Economic and Financial Market Indicators 3-39Quantitative Models 3-44Concluding on an ERP 3-48Chapter 4 Basic Building Blocks of the Cost of Equity Capital – Size Premium 4-1Size as a Predictor of Equity Returns 4-1Possible Explanations for the Greater Returns of Smaller Companies 4-2The Size Effect: Empirical Evidence 4-2The Size Effect Over Longer Periods 4-3The Size Effect Tends to Stabilize Over Time 4-6The Size Effect Changes Over Time 4-7Criticisms of the Size Effect 4-8Data Issues 4-12Has the Size Effect Disappeared in More Recent Periods? 4-17Relationship of Size and Liquidity 4-21Key Things to Remember about the Size Premium 4-26Chapter 5 Basic Building Blocks of the Cost of Equity Capital – Betas and Industry Risk Premia 5-1Beta 5-1Differences in Estimation of Equity Betas 5-7Full-Information Beta 5-11Industry Risk Premia 5-12Full-Information Beta Methodology 5-16Debt Betas 5-17Unlevering and Levering Equity Betas 5-18Key Things to Remember about Betas and the Industry Risk Premia 5-19Chapter 6 Basic Building Blocks of the Cost of Equity Capital – Company-specific Risk Premia 6-1Introduction 6-1Adjustments for Differences in Risk 6-2Adjustments for Risk in Net Cash Flows and Biased Projections 6-5Adjustments for Other Risk Factors 6-7Matching Fundamental Risk and Return 6-8Key Things to Remember about Company-specific Risk Premia 6-10Chapter 7 The CRSP Deciles Size Premia Studies and the Risk Premium Report Studies– A Comparison 7-1History of the CRSP Deciles Size Premia Studies 7-1History of the Risk Premium Report Studies 7-2Data Sources 7-2Definitions of “Size” 7-6Time Period Examined 7-7Number of Portfolios 7-7Portfolio Overlap 7-7Guideline Portfolio Method and Regression Equation Method 7-8Risk Premia Over CAPM (Size Premia) 7-8“Smoothed” Premia versus “Average” Premia 7-12OLS Beta versus Sum Beta 7-12Risk Premia Over the Risk Free Rate 7-12Unlevered Premia 7-13Risk Study 7-13Characteristics of Companies in Portfolios 7-13Online Applications 7-14Chapter 8 CRSP Deciles Size Premia Examples 8-1Build-up Example 8-1CAPM Example 8-4Key Things to Remember about the CRSP Deciles Size Premia 8-7Chapter 9 Risk Premium Report Exhibits – General Information 9-1Appropriate Use of the Risk Premium Report Exhibits 9-1How the Risk Premium Report Exhibits are Organized 9-2Cost of Equity Capital Estimation Methods Available 9-3Proper Application of the Equity Risk Premium (ERP) Adjustment 9-4“Smoothed” Premia versus “Average” Premia 9-7The “Guideline Portfolio Method” versus the “Regression Equation Method” 9-8Example: Calculating an Interpolated Premium Using the Regression Equation Method 9-9Tips Regarding the Regression Equation Method 9-10Can the Regression Equation Method be Used If the Subject Company Is Small? 9-10Size Study or Risk Study? 9-11Key Things to Remember About the Risk Premium Report Exhibits 9-12Chapter 10 Risk Premium Report Exhibits – Examples 10-1Size Study 10-1Reasons for Using Additional Measures of Size 10-1The Difference Between the Size Study’s A Exhibits and the B Exhibits 10-2The Difference Between “Risk Premia Over the Risk-free Rate” and “Risk Premia Over CAPM” 10-2Calculating Custom Interpolated Premia for Smaller Companies 10-6Overview of Methods Used to Estimate Cost of Equity Capital Using the Size Study 10-9Size Study Examples: Assumptions Used 10-10Size Study Examples 10-12Unlevered Cost of Equity Capital 10-17Overview of the Methodology and Assumptions Used to Unlever Risk Premia 10-18Estimating Cost of Equity Capital Using the “Build-up 1-Unlevered” Method 10-22Estimating Cost of Equity Capital Using the Capital Asset Pricing Model (CAPM) 10-26Estimating Cost of Equity Capital Using the “Build-up 2” Method 10-30Risk Study 10-35Overview of Methods Used to Estimate Cost of Equity Capital Using the Risk Study 10-42Risk Study Examples 10-45Build-up 3-Unlevered 10-49High-Financial-Risk Study 10-51Overview of Methods Used to Estimate Cost of Equity Capital Using the High-Financial-Risk Study 10-57Estimating Cost of Equity Capital Using the “Build-up 1-High-Financial-Risk” Method 10-58Estimating Cost of Equity Capital Using the “CAPM-High-Financial-Risk” Method 10-61Comparative Risk Study 10-63Using the Comparative Risk Study to Refine Build-up Method Estimates 10-67Using the Comparative Risk Study to Refine CAPM Estimates 10-69Chapter 11 Real Estate 11-1Individual Real Estate Assets 11-1Real Estate Investment Trusts (REITs) 11-2Structure of Real Estate Entities 11-3Correlation of U.S. REITs Compared to Other U.S. Asset Classes 11-4Summary Statistics of U.S. REITs Compared to Other U.S. Asset Classes 11-6Real Estate Property Valuation Inputs 11-8Key Things to Remember about Real Property Valuation 11-17Chapter 12 Answers to Commonly Asked Questions 12-1GlossaryIndexAppendix 1 – Definitions of Standard & Poor’s Compustat Data Items Used to Calculate the Risk Premium Report ExhibitsAppendix 2 – Changes to the Risk Premium Report Over TimeAppendix 3 – CRSP Deciles Size Premia Study: Key VariablesAppendix 3a – Industry Risk Premium (RPi)Appendix 3b – Debt BetasAppendix 4 – Risk Premium Report Study Exhibits