Title Details

Roger J. Grabowski, Managing Director of Duff & Phelps LLC, is a major speaker at conferences and has testified in court as an expert witness on the value of closely held businesses and business interests, matters of solvency, valuation and amortization of intangible assets and other valuation issues. He testified in the Northern Trust case, the first U.S. Tax Court decision that adopted the discounted cash flow method to value the stock of a closely-held business with the discount rate based on the capital asset pricing model.

James P. Harrington, Director in the Office of Professional Practice at Duff & Phelps, is an accomplished financial writer and analyst. He provides technical support on client engagements involving cost of capital and business valuation matters, and leads efforts for development of Duff & Phelps’ studies, surveys, online content and tools, and internal models. He is also the co-developer of the online Duff & Phelps Risk Premium Calculator, which is based on the data and methodology of the Duff & Phelps Risk Premium Report.

Carla Nunes, Director in the Office of Professional Practice of Duff & Phelps LLC, provides firmwide technical guidance on a variety of valuation, financial and tax reporting issues. She has directed multiple valuation assignments for a wide range of industries, including pharmaceutical, biotechnology, healthcare and specialty chemicals.

Introduction xii

Chapter 1 Cost of Capital Defined 1-1

Introduction 1-1

Income Approach Overview 1-2

Discounting versus Capitalizing Concepts 1-2

Valuation Date 1-5

Basic Cost of Capital Concepts 1-5

Sources of Capital 1-9

Cost of Capital Input Assumptions 1-10

Capital Structure Considerations 1-16

Calculating WACC 1-17

Estimates of Cost of Capital are Imprecise 1-19

Key Things to Remember about Cost of Capital 1-20

Chapter 2 Methods for Estimating the Cost of Equity Capital 2-1

Basic Framework 2-1

Types of Risk 2-6

Cost of Equity Capital Estimation Methods 2-8

Build-up 2-10

CAPM 2-11

Other Cost of Equity Capital Estimation Methods 2-15

Key Things to Remember about the Methods for Estimating the Cost of Equity Capital 2-16

Chapter 3 Basic Building Blocks of the Cost of Equity Capital – Risk-free Rate and Equity Risk Premium 3-1

The Risk-free Rate and Equity Risk Premium: Interrelated Concepts 3-1

Spot Risk-free Rates versus Normalized Risk-free Rates 3-2

Methods of Risk-free Rate Normalization 3-15

Spot Yield or Normalized Yield? 3-18

Equity Risk Premium 3-20

Estimating the Equity Risk Premium 3-21

Duff & Phelps Recommended ERP 3-33

Concluding on an ERP 3-39

Chapter 4 Basic Building Blocks of the Cost of Equity Capital – Size Premium 4-1

Size as a Predictor of Equity Returns 4-1

Possible Explanations for the Greater Returns of Smaller Companies 4-2

The Size Effect: Empirical Evidence 4-2

The Size Effect Over Longer Periods 4-3

The Size Effect Tends to Stabilize Over Time 4-6

The Size Effect Changes Over Time 4-7

Criticisms of the Size Effect 4-8

Data Issues 4-12

Has the Size Effect Disappeared in More Recent Periods? 4-17

Relationship of Size and Liquidity 4-21

Key Things to Remember about the Size Premium 4-26

Chapter 5 Basic Building Blocks of the Cost of Equity Capital – Betas and Industry Risk Premia 5-1

Beta 5-1

Differences in Estimation of Equity Betas 5-7

Full-Information Beta 5-11

Industry Risk Premia 5-12

Full-Information Beta Methodology 5-16

Debt Betas 5-17

Unlevering and Levering Equity Betas 5-18

Key Things to Remember about Betas and the Industry Risk Premia 5-19

Chapter 6 Basic Building Blocks of the Cost of Equity Capital – Company-specific Risk Premia 6-1

Introduction 6-1

Adjustments for Differences in Risk 6-2

Adjustments for Risk in Net Cash Flows and Biased Projections 6-5

Adjustments for Other Risk Factors 6-7

Matching Fundamental Risk and Return 6-8

Key Things to Remember about Company-specific Risk Premia 6-10

Chapter 7 The CRSP Deciles Size Premia Studies and the Risk Premium Report Studies – A Comparison 7-1

History of the CRSP Deciles Size Premia Studies 7-1

History of the Risk Premium Report Studies 7-2

Data Sources 7-2

Definitions of “Size” 7-6

Time Period Examined 7-6

Number of Portfolios 7-7

Portfolio Overlap 7-7

Guideline Portfolio Method and Regression Equation Method 7-8

Risk Premia Over CAPM (Size Premia) 7-8

“Smoothed” Premia versus “Average” Premia 7-12

OLS Beta versus Sum Beta 7-12

Risk Premia Over the Risk Free Rate 7-12

Unlevered Premia 7-13

Risk Study 7-13

Characteristics of Companies in Portfolios 7-13

Online Applications 7-14

Chapter 8 CRSP Deciles Size Premia Examples 8-1

Build-up Example 8-1

CAPM Example 8-4

Key Things to Remember about the CRSP Deciles Size Premia 8-7

Chapter 9 Risk Premium Report Exhibits – General Information 9-1

Appropriate Use of the Risk Premium Report Exhibits 9-1

How the Risk Premium Report Exhibits are Organized 9-1

Cost of Equity Capital Estimation Methods Available 9-3

Proper Application of the Equity Risk Premium (ERP) Adjustment 9-4

“Smoothed” Premia versus “Average” Premia 9-7

The “Guideline Portfolio Method” versus the “Regression Equation Method” 9-8

Example: Calculating an Interpolated Premium Using the Regression Equation Method 9-9

Tips Regarding the Regression Equation Method 9-10

Can the Regression Equation Method be Used if the Subject Company is Small? 9-10

Size Study or Risk Study? 9-11

Key Things to Remember About the Risk Premium Report Exhibits 9-12

Chapter 10 Risk Premium Report Exhibits – Examples 10-1

Size Study 10-1

Reasons for Using Additional Measures of Size 10-1

The Difference Between the Size Study’s A Exhibits and the B Exhibits 10-2

The Difference Between “Risk Premia Over the Risk-free Rate” and “Risk Premia Over CAPM” 10-2

Calculating Custom Interpolated Premia for Smaller Companies 10-6

Overview of Methods Used to Estimate Cost of Equity Capital Using the Size Study 10-9

Size Study Examples: Assumptions Used 10-10

Size Study Examples 10-12

Unlevered Cost of Equity Capital 10-17

Overview of the Methodology and Assumptions Used to Unlever Risk Premia 10-18

Estimating Cost of Equity Capital Using the “Build-up 1-Unlevered” Method 10-22

Estimating Cost of Equity Capital Using the Capital Asset Pricing Model (CAPM) 10-26

Estimating Cost of Equity Capital Using the “Build-up 2” Method 10-30

Risk Study 10-35

Overview of Methods Used to Estimate Cost of Equity Capital Using the Risk Study 10-42

Risk Study Examples 10-45

Build-up 3-Unlevered 10-49

High-Financial-Risk Study 10-51

Overview of Methods Used to Estimate Cost of Equity Capital Using the High-Financial-Risk Study 10-57

Estimating Cost of Equity Capital Using the “Build-up 1-High-Financial-Risk” Method 10-58

Estimating Cost of Equity Capital Using the “CAPM-High-Financial-Risk” Method 10-61

Comparative Risk Study 10-63

Using the Comparative Risk Study to Refine Build-up Method Estimates 10-67

Using the Comparative Risk Study to Refine CAPM Estimates 10-69

Chapter 11 Real Estate 11-1

Individual Real Estate Assets 11-1

Real Estate Investment Trusts (REITs) 11-2

Structure of Real Estate Entities 11-2

Correlation of U.S. REITs Compared to Other U.S. Asset Classes 11-3

Summary Statistics of U.S. REITs Compared to Other U.S. Asset Classes 11-5

Real Estate Property Valuation Inputs 11-8

Key Things to Remember about Real Property Valuation 11-16

Chapter 12 Answers to Commonly Asked Questions 12-1

Glossary

Index

Appendix 1 – Definitions of Standard & Poor’s Compustat Data Items Used to Calculated the Risk Premium Report Exhibits

Appendix 2 – Changes to the Risk Premium Report Over Time

Appendix 3 – CRSP Deciles Size Premia Study: Key Variables

Appendix 3a – Industry Risk Premium (RPi)

Appendix 3b – Debt Betas

Appendix 4 – Risk Premium Report Study Exhibits