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This document is an abbreviated “Preview Version” of the key year-end (December 31, 2013) valuation data available in the new 2014 Valuation Handbook – Guide to Cost of Capital This document is made available to purchasers who have pre-ordered the 2014 Valuation Handbook, to provide key year-end 2013 data in their hands while the 2014 Valuation Handbook is being printed. The 2014 Valuation Handbook will ship in the third week of March 2014, and will include two sets of valuation data:

• The data previously available in the Morningstar/Ibbotson SBBI Valuation Yearbook; and • The data available in Risk Premium Report.

2014

Valuation Handbook

Market Results Through 2013

Preview Version

Guide to Cost of Capital (Preview Version)

Disclaimer/Publication and Purchasing Information

The information and data presented in the 2014 Valuation Handbook – Guide to Cost of Capital and the online Risk Premium Calculator has been obtained with the greatest of care from sources believed to be reliable, but is not guaranteed to be complete, accurate or timely. Duff & Phelps, LLC expressly disclaims any liability, including incidental or consequential damages, arising from the use of the 2014 Valuation Handbook – Guide to Cost of Capital and/or the online Risk Premium Calculator or any errors or omissions that may be contained in either the 2014 Valuation Handbook – Guide to Cost of Capital or the online Risk Premium Calculator.

Copyright © 2014 Duff & Phelps, LLC. All Rights Reserved. No part of this publication may be reproduced or used in any other form or by any other means – graphic, electronic, or mechanical, including photocopying, recording, taping, or information storage and retrieval systems – without Duff & Phelps’ prior, written permission. To obtain permission, please write to: Valuation Handbook, Duff & Phelps, 311 S. Wacker Dr., Suite 4200, Chicago, IL 60606. Your request should specify the data or other information you wish to use and the manner in which you wish to use it. In addition, you will need to include copies of any charts, tables, and/or figures that you have created based on that information. There is a $1,500 processing fee per request. There may be additional fees depending on your proposed usage.

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To download a free copy of “Developing the Cost of Equity Capital: Risk-Free Rate and ERP During Periods of ‘Flight to Quality’” by Roger J. Grabowski, visit: www.duffandphelps.com/costofcapital

To learn more about the latest theory and practice in cost of capital estimation, see Cost of Capital: Applications and Examples 5th edition, by Shannon P. Pratt and Roger J. Grabowski (John Wiley & Sons, Inc., 2014).

“Shannon Pratt and Roger Grabowski have produced a remarkably comprehensive review of the subject… it is a work that valuation practitioners, CFOs, and others will find an invaluable reference.”

– Professor Richard Brealey, London Business School (from the Foreword)

“Estimating the cost of capital is critical in determining the valuation of assets, in evaluating the capital structure of corporations, and in estimating the long run expected return of investments. Shannon Pratt and Roger Grabowski have the most thorough text on the subject, not only providing various estimation methods, but also numerous ways to use the cost of capital.”

Professor Roger G. Ibbotson, Yale School of Management, former chairman and founder of Ibbotson Associates, chairman, founder, and CIO of Zebra Capital.

Additional copies of the 2014 Valuation Handbook – Guide to Cost of Capital may be obtained from:

Business Valuation Resources (BVR) www.bvresources.com/costofcapital 1 (503) 291-7963 ext. 2

The 2014 Valuation Handbook is intended to be used as a companion publication to the online Risk Premium Calculator. The online Risk Premium Calculator is also available through Business Valuation Resources (BVR).

Introduction The Valuation Handbook – Guide to Cost of Capital (“Valuation Handbook”) is not designed to duplicate the contents of comprehensive, learned treatises on estimating the cost of equity capital such as, Shannon P. Pratt and Roger J. Grabowski, Cost of Capital: Applications and Examples 5th edition (John Wiley & Sons, Inc., 2014). That book, for example, covers the latest theory and practice in cost of capital estimation, including cost of capital for uses in business valuation, project assessment and capital budgeting, divisional cost of capital, reporting unit valuation and goodwill impairment testing, valuing intangible assets for financial reporting, and transfer pricing.

Rather, the Valuation Handbook is designed to complement such works, providing a brief refresher for valuation analyst on the approaches to valuation and estimating the cost of equity capital, but primarily focusing on the data sources commonly available for estimating the cost of equity capital.

Who Should Use the Valuation Handbook – Guide to Cost of Capital

The Valuation Handbook is designed to assist financial professionals in estimating the cost of equity capital (ke) for a subject company. Cost of equity capital is the return necessary to attract funds to an equity investment. The valuation data and methodology in the Valuation Handbook can be used to develop cost of equity capital estimates using both the build-up method and the capital asset pricing model (CAPM). In addition to the traditional professional valuation analyst, the Valuation Handbook, and the accompanying online Risk Premium Calculator (“Calculator”), are designed to serve the needs of:

• Corporate finance officers for pricing or evaluating mergers and acquisitions, raising private or public equity, property taxation, and stakeholder disputes.

• Corporate officers for the evaluation of investments for capital budgeting decisions.

• Investment bankers for pricing public offerings, mergers and acquisitions, and private equity financing.

• CPAs who deal with either valuation for financial reporting or client valuations issues.

• Judges and attorneys who deal with valuation issues in mergers and acquisitions (M&A), shareholder and partner disputes, damage cases, solvency cases, bankruptcy reorganizations, property taxes, rate setting, transfer pricing, and financial reporting.

Why did the authors write the Valuation Handbook – Guide to Cost of Capital

Morningstar, Inc. announced in September 2013 that it will no longer publish the SBBI® Valuation Yearbook and other valuation publications and products. The SBBI® Valuation Yearbook and other “Ibbotson” valuation products have been widely used and cited in valuation reports for nearly 15 years and are generally considered one of the essential tools needed in every valuation analyst’s toolbox.

Last year’s 2013 SBBI® Valuation Yearbook (with data through December 31, 2012) is Morningstar’s last SBBI® Valuation Yearbook – Morningstar will not be publishing a 2014 version (with data through December 31, 2013).

The new 2014 Valuation Handbook includes all of the critical year-end data (i.e., historical long-term ERP, supply-side long-term ERP, size premia, and industry risk premia, etc.) that was previously available in the SBBI® Valuation Yearbook and provides users of SBBI® valuation data with the same sources of data and methodology to complete year-end valuations, without interruption.

The 2014 Valuation Handbook includes two sets of valuation data:

• Data previously available in the SBBI® Valuation Yearbook; and

• Data available in the Duff & Phelps Risk Premium Report.

We have had to introduce some new terminology. Specifically, the size premia data previously published in the SBBI® Valuation Yearbook is referred to as the “CRSP Deciles Size Premia” exhibits in the Valuation Handbook, while the size and risk premia data published in the Duff & Phelps Risk Premium Report continues to be titled “Risk Premium Report” exhibits.

The Risk Premium Report has been published annually since 1996 and, like the former SBBI® Yearbook, provides data and methodology to assist financial professionals in estimating the cost of equity capital for a subject company using various build-up models and the CAPM. While the Risk Premium Report will no longer be published as a stand-alone publication, all of its data will be included in the Valuation Handbook.

In 2011, Duff & Phelps introduced the online Risk Premium Calculator. The 2014 version of the web-based Calculator will also include all of the key data available in both the former SBBI® Valuation Yearbook and the Risk Premium Report.

Same Data Sources

The same data sources used to produce the data in the former SBBI® Valuation Yearbook are used to produce the new Valuation Handbook:

• The Center for Research in Security Prices (CRSP) market-cap-based NYSE/AMEX/NASDAQ indices. To learn more about the Center for Research in Security Prices at the University of Chicago Booth School of Business, visit www.crsp.com

• Standard & Poor’s Research Insight database. To learn more about Standard and Poor’s, visit www.standardandpoors.com/home/en/us

• SBBI® Series from Morningstar’s EnCorr database. To learn more about Morningstar’s EnCorr database, visit www.corporate.morningstar.com

The following I the complete table of contents of the 2014 Valuation Handbook,"

Table of Contents Acknowledgements vii Introduction viii 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 1-8 Cost of Capital Input Assumptions 1-10 Capital Structure Considerations 1-12 Calculating WACC 1-13 Key Things to Remember about Cost of Capital 1-15

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

Basic Framework 2-1 Types of Risk 2-4

Cost of Equity Capital Estimation Methods 2-7 Build-up 2-8 CAPM 2-10 Key Things to Remember about the Methods for Estimating the Cost of Equity Capital 2-14

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 3-4 Spot Yield or Normalized Yield? 3-7 Equity Risk Premium 3-8 Estimating the Equity Risk Premium 3-9 Duff & Phelps Recommended ERP 3-21

Concluding on an ERP 3-23

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 4-11 Has the Size Effect Disappeared in More Recent Periods? 4-17 Is the Size Effect a Proxy for "Liquidity"? 4-21 Key Things to Remember about the Size Premium 4-22

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 Key Things to Remember about Beta and the Industry Risk Premium 5-23

Chapter 6 Basic Building Blocks of the Cost of Equity Capital – Company-specific Risk Premium 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 Premiums 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 7-6 Portfolio Overlap 7-7 Guideline Portfolio Method and Regression Equation Method 7-7 Risk Premia Over CAPM (Size Premia) 7-8 “Smoothed” Premia versus “Average” Premia 7-11 OLS Beta versus Sum Beta 7-11 Risk Premia Over the Risk Free Rate 7-12 Unlevered Premia 7-12 Risk Study 7-12 Characteristics of Companies in Portfolios 7-13 Online Calculator Application 7-13

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 8-6

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 9-3 “Smoothed” Premia versus “Average” Premia 9-7 The “Guideline Portfolio Method” versus the “Regression Equation Method” 9-7 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? 9-10 Key Things to Remember About the Risk Premium Report Exhibits 9-11

Chapter 10 Risk Premium Report Exhibits Examples 10-1 Size Study 10-1 Reason 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 10-31 Risk Study 10-36 Overview of Methods Used to Estimate Cost of Equity Capital Using the Risk Study 10-43 Risk Study Examples 10-46 Build-up 3-Unlevered 10-50 High-Financial-Risk Study 10-52 Overview of Methods Used to Estimate Cost of Equity Capital Using the High-Financial-Risk Study 10-58 Estimating Cost of Equity Capital Using the “Build-up 1-High-Financial-Risk” Method 10-59 Estimating Cost of Equity Capital Using the “CAPM Method-High-Financial-Risk” Method 10-62 Comparative Risk Study 10-64 Using the Comparative Risk Study to Refine Build-up Method Estimates 10-68 Using the Comparative Risk Study to Refine CAPM Estimates 10-70 Glossary Index Appendix 1 – Definitions of Standard and 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 4 – Risk Premium Report Study Exhibits

Key Year End Data

2014 Valuation Handbook (Preview Version)

The 2014 Valuation Handbook – Guide to Cost of Capital (with data through December 31, 2013) is intended to be used for calendar year 2014 valuation dates. The 2014 Valuation Handbook includes two sets of valuation data:

• The data previously published in the Morningstar/Ibbotson SBBI Valuation Yearbook. This is in the section entitled “CRSP Deciles Size Premia Study: Key Variables”.

• The data available in Risk Premium Report. This is in the section entitled “Risk Premium Report Study Exhibits”.

The data presented in the 2014 Valuation Handbook (Preview Version) includes abbreviated key year-end data (as of December 31, 2013) from both studies.

The hardcover 2014 Valuation Yearbook with all data tables will ship in the third week of March 2014.

CRSP Deciles Size Premia Study: Key Variables This section includes the “key variables in estimating the cost of capital” that were previously published in the Ibbotson Stocks, Bonds, Bills and Inflation (SBBI) Valuation Yearbook.1

The equity risk premium, size premium, and other valuation data reported in Appendix 3 of the 2014 Valuation Handbook were:

• Calculated using the same data sources that were used to calculate the equity risk premium, size premium, and other valuation data previously published in the former SBBI Valuation Yearbook, and

• Calculated using the same methodology that was used to calculate the equity risk premium, size premium, and other valuation data previously published in the former SBBI Valuation Yearbook.

The equity risk premium (ERP), size premium, and other valuation data reported here can be used to estimate cost of equity capital using the capital asset pricing model (CAPM) and the build-up method.

1 The Ibbotson SBBI Valuation Yearbook was previously published by Morningstar, Inc. (Chicago). The SBBI Valuation Yearbook was discontinued in 2013.

2014 Valuation Handbook – Guide to Cost of Capital

CRSP Deciles Size Premia Study: Key Variables

Yield (Risk-free Rate)1

Long-term (20-year) U.S. Treasury Coupon Bond Yield 3.67%

Equity Risk Premium

6.96

6.18

5.00

CRSP Deciles Size Premium

Decile

Market Capitalization of Smallest Company

(in millions)

Market Capitalization of Largest Company

(in millions)

Size Premium (Return in

Excess of CAPM)Mid-Cap 3-5 $2,432.888 $9,196.480 1.11%Low-Cap 6-8 636.747 2,431.229 1.98 Micro-Cap 9-10 2.395 632.770 3.87

Breakdown of CRSP Deciles 1-101-Largest $21,753.411 $428,699.798 -0.37%2 9,196.656 21,739.006 0.75 3 5,572.648 9,196.480 0.86 4 3,581.547 5,569.840 1.16 5 2,432.888 3,573.079 1.75 6 1,626.386 2,431.229 1.86 7 1,056.204 1,621.792 1.94 8 636.747 1,055.320 2.36 9 339.987 632.770 2.81 10-Smallest 2.395 338.829 5.99

Breakdown of CRSP 10th Decile 10a $184.928 $338.829 4.40%

10w 250.656 338.829 3.52 10x 184.928 250.532 5.67

10b $2.395 $184.865 8.99%10y 100.933 184.865 7.55 10z 2.395 100.821 12.12

1 As of December 31, 2013.

Sources of underlying data: 1.) CRSP U.S. Stock Database and CRSP U.S. Indices Database © 2014 Center for Research in Security Prices (CRSP®), University of Chicago Booth School of Business. 2.) Morningstar EnCorr database. Used with permission. All rights reserved. Calculations performed by Duff & Phelps LLC.

Long-horizon expected equity risk premium (supply-side) : historical equity risk premium minus price-to-earnings ratio calculated using three-year average earnings

Long-horizon expected equity risk premium (historical) : large company stock total returns minus long-term government bond income returns

Duff & Phelps recommended equity risk premium (conditional) : The Duff & Phelps recommended ERP was developed in relation to (and should be used in conjunction with) a 4.0% “normalized” risk-free rate

Risk Premium Report Study Exhibits The Risk Premium Report exhibits include the Size Study, the Risk Study, the High-Financial-Risk Study, and the Comparative Risk Study.

• Size Study: Comprised of Exhibits A-1 through A-8 (used in the build-up method) and Exhibits B-1 through B-8 (used in CAPM). Analyzes the relationship between equity returns and company size, using eight measures of company size.

• Risk Study: Comprised of Exhibits D-1, D-2, and D-3 (fundamental measures of risk based on accounting data). Analyzes the relationship between equity returns and three accounting-based fundamental risk measures.

• High-Financial-Risk Study: Comprised of Exhibits H-A, H-B, and H-C. Exhibit H-A is the high-financial-risk equivalent to the A exhibits, Exhibit H-B is the high-financial-risk equivalent to the B exhibits, and Exhibit H-C is the high-financial-risk equivalent to the C exhibits. Analyzes the relationship between equity returns and high-financial-risk, as measured by the Altman z-Score.

• Comparative Risk Study: Comprised of the C exhibits, when used in conjunction with the D exhibits. The C Exhibits can help valuation analysts further refine their cost of equity capital estimates by comparing their subject company’s fundamental risk factors to the fundamental risk factors of the companies that comprise the 25 Size Study portfolios.

For detailed examples of using the valuation data reported in Appendix 4 to estimate cost of equity capital using the capital asset pricing model (CAPM) and various build-up methods, see Chapter 9, “Risk Premium Report Exhibits – General Information” and Chapter10, “Risk Premium Report Exhibits – Examples”.

Risk Premium Report – Exhibits A-1 through A-8 Premia Over the Risk-Free Rate (RPm+s) Risk premia over the risk-free rate reflect risk in terms of the combined effect of market risk and size risk in excess of the risk-free rate. These premia are added to the risk-free rate, within the context of the build-up method. An ERP Adjustment is required when using the A exhibits. The A Exhibits are used in the following method to estimate a cost of equity capital:

• Build-up 1

Size Measures:

• A-1: Market value of equity

• A-2: Book value of equity

• A-3: 5-year average net income

• A-4: Market value of invested capital (MVIC)

• A-5: Total assets

• A-6: 5-year average EBITDA

• A-7: Sales

• A-8: Number of employees

Note: When using the Risk Premium Report’s A exhibits, the equity risk premium (ERP) Adjustment is a necessary step. The ERP Adjustment is needed to account for the difference between the forward-looking ERP as of the valuation date that the valuation analyst has selected to use in his or her cost of equity capital calculations, and the historical (1963–present) ERP that was used as a convention in the calculations performed to create the Risk Premium Report exhibits.

In the 2014 Valuation Handbook, the historical ERP used as a convention in the calculations of the Risk Premium Report exhibits was (4.9%).2 The ERP adjustment for Risk Premium Report data published in the 2014 Valuation Handbook is therefore calculated as follows:


Companies Ranked by Market Value of Equity Premia Over the Risk-Free Rate (RP m+s ) Exhibit A-1

Historical Equity Risk Premium: Average Since 1963 Equity Risk Premium Study: Data through December 31, 2013

Data for Year Ending December 31, 2013 Data Smoothing with Regression Analysis

Dependent Variable: Arithmetic Average Risk Premium

Independent Variable: Log of Average Market Value of Equity

Portfolio Average Log of Number Beta Standard Geometric Arithmetic Arithmetic Smoothed Average

Rank Mkt. Value Average as of (Sum Beta) Deviation Average Average Average Risk Average Risk Debt/

by Size (in $millions) Mkt. Value 2013 Since '63 of Returns Return Return Premium Premium MVIC Regression Output:

1 143,782 5.16 42 0.83 16.17% 10.89% 12.14% 5.47% 3.06% 14.11% Constant 21.384%

2 41,383 4.62 35 0.95 16.98% 9.67% 11.07% 4.39% 4.98% 19.19% Standard Error of Y Estimate 1.069%

3 26,386 4.42 32 0.93 15.84% 10.22% 11.49% 4.81% 5.67% 20.73% R Squared 85%

4 18,966 4.28 29 0.94 16.77% 11.75% 13.09% 6.42% 6.18% 22.79% No. of Observations 25

5 14,414 4.16 38 0.99 17.11% 11.05% 12.47% 5.79% 6.61% 23.26% Degrees of Freedom 23

6 11,096 4.05 36 1.02 17.42% 11.31% 12.81% 6.14% 7.01% 22.85%

7 9,354 3.97 39 1.01 18.47% 11.97% 13.55% 6.87% 7.27% 23.41% X Coefficient(s) -3.553%

8 7,811 3.89 37 1.06 19.33% 13.36% 15.08% 8.41% 7.55% 22.58% Standard Error of Coefficient 0.312%

9 6,448 3.81 39 1.08 17.97% 13.72% 15.25% 8.57% 7.85% 22.79% t-Statistic -11.40

10 5,073 3.71 37 1.12 20.31% 13.49% 15.41% 8.74% 8.22% 23.06%

11 4,259 3.63 32 1.10 19.73% 13.05% 14.87% 8.19% 8.49% 22.91% Smoothed Premium = 21.384% - 3.553% * Log(Market Value)

12 3,752 3.57 31 1.11 19.53% 12.36% 14.18% 7.51% 8.68% 22.75%

13 3,351 3.53 34 1.11 19.30% 12.87% 14.59% 7.92% 8.86% 23.37%

14 3,018 3.48 34 1.15 20.51% 13.93% 15.91% 9.23% 9.02% 23.30%

15 2,637 3.42 46 1.14 20.39% 15.67% 17.62% 10.94% 9.23% 23.41%

16 2,186 3.34 39 1.17 20.55% 14.85% 16.79% 10.11% 9.52% 23.63%

17 1,852 3.27 50 1.19 21.82% 14.24% 16.40% 9.73% 9.77% 22.59%

18 1,583 3.20 41 1.22 20.70% 13.00% 15.08% 8.40% 10.02% 23.36%

19 1,359 3.13 55 1.21 22.48% 14.75% 17.09% 10.41% 10.25% 23.44%

20 1,083 3.03 84 1.21 22.60% 14.21% 16.54% 9.86% 10.60% 24.20%

21 826 2.92 62 1.26 22.81% 14.90% 17.27% 10.59% 11.02% 24.18%

22 646 2.81 78 1.23 23.99% 14.97% 17.60% 10.92% 11.40% 24.79%

23 497 2.70 66 1.26 23.37% 15.09% 17.51% 10.83% 11.80% 24.23%

24 339 2.53 100 1.24 25.02% 16.73% 19.49% 12.81% 12.40% 25.03%

25 107 2.03 285 1.28 30.01% 19.40% 23.25% 16.58% 14.17% 27.75%

Large Stocks (Ibbotson SBBI data) 10.20% 11.63% 4.95%

Small Stocks (Ibbotson SBBI data) 13.99% 16.74% 10.06%

Long-Term Treasury Income (Ibbotson SBBI data) 6.65% 6.68%

Sources of underlying data: 1.) © 201402 CRSP®, Center for Research in Security Prices. University of Chicago Booth School of Business used with permission. All rights reserved. 2.) Morningstar EnCorr database. Used with permission. All rights reserved. Calculations performed by Duff & Phelps LLC.

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Smoothed Premium vs. Arithmetic Premium


Companies Ranked by Book Value of Equity Premia Over the Risk-Free Rate (RP m+s ) Exhibit A-2




Independent Variable: Log of Average Book Value of Equity


Rank Book Val. Average as of (Sum Beta) Deviation Average Average Average Risk Average Risk Debt/

by Size (in $millions) Book Val. 2013 Since '63 of Returns Return Return Premium Premium MVIC Regression Output:

1 51,173 4.71 39 0.81 15.69% 10.88% 12.30% 5.62% 4.84% 23.47% Constant 17.737%


3 10,965 4.04 33 0.91 16.32% 12.01% 13.55% 6.87% 6.67% 28.75% R Squared 85%



6 4,073 3.61 34 1.02 18.08% 12.26% 14.07% 7.39% 7.85% 26.10%

7 3,479 3.54 30 1.05 20.02% 12.29% 14.41% 7.73% 8.04% 24.96% X Coefficient(s) -2.738%


9 2,447 3.39 38 1.12 20.55% 12.81% 15.08% 8.41% 8.46% 24.84% t-Statistic -11.23

10 2,062 3.31 40 1.07 18.99% 13.09% 15.01% 8.33% 8.66% 25.36%

11 1,794 3.25 35 1.09 19.96% 13.22% 15.37% 8.69% 8.83% 26.37% Smoothed Premium = 17.737% - 2.738% * Log(Book Value)

12 1,532 3.19 37 1.09 20.07% 14.54% 16.68% 10.00% 9.01% 25.29%

13 1,360 3.13 36 1.11 21.29% 14.00% 16.40% 9.72% 9.16% 25.04%

14 1,228 3.09 31 1.13 20.50% 12.92% 15.10% 8.43% 9.28% 23.64%

15 1,116 3.05 40 1.11 20.71% 14.98% 17.23% 10.56% 9.39% 23.57%

16 990 3.00 47 1.22 24.04% 15.49% 18.38% 11.70% 9.53% 23.75%

17 864 2.94 38 1.20 23.31% 13.78% 16.52% 9.85% 9.70% 22.98%

18 780 2.89 38 1.19 21.86% 14.55% 17.03% 10.35% 9.82% 23.52%

19 660 2.82 62 1.24 21.17% 13.14% 15.55% 8.87% 10.02% 23.23%

20 532 2.73 77 1.21 21.85% 13.79% 16.26% 9.58% 10.27% 23.03%

21 425 2.63 67 1.21 20.76% 15.53% 17.84% 11.16% 10.54% 23.01%

22 318 2.50 91 1.24 22.96% 14.24% 17.04% 10.36% 10.88% 23.33%

23 250 2.40 71 1.25 23.20% 14.80% 17.55% 10.88% 11.17% 23.47%

24 188 2.27 102 1.27 24.93% 15.18% 18.39% 11.72% 11.51% 22.92%

25 68 1.83 282 1.26 25.81% 15.74% 19.13% 12.45% 12.71% 23.46%





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Companies Ranked by 5-Year Average Net Income Premia Over the Risk-Free Rate (RP m+s ) Exhibit A-3




Independent Variable: Log of Average Net Income


Rank Net Inc. Average as of (Sum Beta) Deviation Average Average Average Risk Average Risk Debt/

by Size (in $millions) Net Inc. 2013 Since '63 of Returns Return Return Premium Premium MVIC Regression Output:

1 8,122 3.91 39 0.77 16.05% 12.04% 13.27% 6.60% 4.33% 20.11% Constant 15.414%


3 1,418 3.15 30 0.86 16.19% 12.58% 13.80% 7.12% 6.48% 26.68% R Squared 86%


5 735 2.87 35 0.95 17.07% 11.85% 13.23% 6.56% 7.29% 26.26% Degrees of Freedom 23

6 521 2.72 38 0.98 18.04% 11.82% 13.29% 6.61% 7.71% 24.64%

7 397 2.60 33 1.05 18.35% 12.28% 13.90% 7.22% 8.05% 24.76% X Coefficient(s) -2.836%

8 330 2.52 38 1.10 18.75% 12.97% 14.61% 7.94% 8.27% 24.00% Standard Error of Coefficient 0.236%

9 270 2.43 37 1.04 18.14% 13.02% 14.60% 7.93% 8.52% 23.66% t-Statistic -12.02

10 233 2.37 35 1.07 18.17% 13.06% 14.58% 7.90% 8.70% 23.93%

11 198 2.30 36 1.08 19.78% 14.22% 16.01% 9.33% 8.90% 23.52% Smoothed Premium = 15.414% - 2.836% * Log(Net Income)

12 171 2.23 32 1.08 20.20% 14.19% 16.10% 9.42% 9.08% 24.55%

13 147 2.17 34 1.06 18.80% 14.70% 16.34% 9.66% 9.26% 23.74%

14 129 2.11 40 1.15 20.25% 13.21% 15.18% 8.50% 9.43% 24.06%

15 113 2.05 38 1.12 21.96% 13.38% 15.55% 8.88% 9.60% 23.56%

16 98 1.99 41 1.13 20.26% 15.25% 17.16% 10.48% 9.77% 23.11%

17 83 1.92 45 1.18 21.12% 13.87% 15.97% 9.29% 9.97% 22.63%

18 72 1.86 40 1.21 21.03% 15.33% 17.39% 10.71% 10.14% 22.92%

19 62 1.79 44 1.25 22.06% 14.21% 16.51% 9.83% 10.33% 23.49%

20 49 1.69 81 1.23 22.28% 16.51% 18.76% 12.08% 10.62% 24.03%

21 35 1.54 82 1.22 22.09% 15.49% 17.70% 11.02% 11.04% 24.61%

22 25 1.40 86 1.23 23.64% 14.77% 17.39% 10.71% 11.44% 23.95%

23 17 1.24 112 1.26 24.56% 16.66% 19.26% 12.58% 11.91% 23.07%

24 11 1.03 97 1.25 24.83% 16.15% 18.88% 12.20% 12.50% 24.07%

25 4 0.58 245 1.32 29.20% 17.90% 21.70% 15.02% 13.77% 25.21%





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Companies Ranked by Market Value of Invested Capital Premia Over the Risk-Free Rate (RP m+s ) Exhibit A-4




Independent Variable: Log of Average MVIC


Rank MVIC Average as of (Sum Beta) Deviation Average Average Average Risk Average Risk Debt/

by Size (in $millions) MVIC 2013 Since '63 of Returns Return Return Premium Premium MVIC Regression Output:

1 171,547 5.23 43 0.80 16.04% 10.87% 12.11% 5.43% 3.38% 18.89% Constant 21.464%


3 34,181 4.53 33 0.90 16.01% 10.47% 11.73% 5.05% 5.80% 27.14% R Squared 87%



6 14,547 4.16 38 1.00 16.53% 11.20% 12.56% 5.89% 7.08% 26.05%

7 12,000 4.08 36 0.99 17.87% 12.89% 14.35% 7.67% 7.37% 24.23% X Coefficient(s) -3.455%


9 8,707 3.94 37 1.09 19.10% 12.39% 14.14% 7.46% 7.85% 24.38% t-Statistic -12.50

10 7,268 3.86 37 1.10 19.90% 13.82% 15.65% 8.98% 8.12% 24.16%

11 6,170 3.79 36 1.11 19.19% 13.41% 15.17% 8.49% 8.37% 25.33% Smoothed Premium = 21.464% - 3.455% * Log(MVIC)

12 5,189 3.72 37 1.05 19.02% 13.54% 15.21% 8.53% 8.63% 25.03%

13 4,399 3.64 30 1.15 20.07% 13.23% 15.10% 8.42% 8.88% 25.13%

14 3,883 3.59 33 1.17 20.98% 13.47% 15.57% 8.89% 9.06% 23.81%

15 3,424 3.53 33 1.17 21.63% 13.86% 16.03% 9.36% 9.25% 24.54%

16 3,009 3.48 45 1.20 21.45% 14.75% 16.88% 10.20% 9.45% 23.49%

17 2,470 3.39 48 1.23 22.26% 15.33% 17.65% 10.98% 9.74% 23.98%

18 2,048 3.31 43 1.17 20.64% 15.21% 17.18% 10.51% 10.02% 23.33%

19 1,712 3.23 54 1.21 22.22% 12.95% 15.23% 8.55% 10.29% 24.05%

20 1,422 3.15 61 1.25 22.13% 13.82% 16.10% 9.43% 10.57% 25.37%

21 1,121 3.05 88 1.27 23.17% 14.15% 16.62% 9.95% 10.93% 24.40%

22 824 2.92 72 1.24 22.50% 15.22% 17.49% 10.81% 11.39% 24.57%

23 645 2.81 71 1.26 25.05% 16.24% 19.03% 12.35% 11.76% 23.97%

24 459 2.66 81 1.25 25.11% 15.87% 18.63% 11.95% 12.27% 24.55%

25 147 2.17 316 1.27 28.97% 18.94% 22.58% 15.90% 13.97% 22.80%





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Log of Average Market Value of Invested Capital



Companies Ranked by Total Assets Premia Over the Risk-Free Rate (RP m+s ) Exhibit A-5




Independent Variable: Log of Total Assets


Rank Total Assets Average as of (Sum Beta) Deviation Average Average Average Risk Average Risk Debt/

by Size (in $millions) Assets 2013 Since '63 of Returns Return Return Premium Premium MVIC Regression Output:

1 137,196 5.14 36 0.80 16.19% 10.87% 12.54% 5.86% 4.59% 28.26% Constant 19.495%


3 30,116 4.48 31 0.91 16.86% 10.47% 13.14% 6.46% 6.50% 31.28% R Squared 91%



6 11,841 4.07 30 0.95 16.40% 11.20% 14.25% 7.57% 7.67% 28.31%

7 9,414 3.97 34 1.06 19.12% 12.89% 14.98% 8.31% 7.96% 26.98% X Coefficient(s) -2.902%


9 6,818 3.83 32 1.09 19.88% 12.39% 14.11% 7.44% 8.37% 27.99% t-Statistic -14.84

10 5,851 3.77 34 1.10 19.25% 13.82% 14.49% 7.82% 8.56% 27.44%

11 5,045 3.70 36 1.11 20.40% 13.41% 14.86% 8.19% 8.75% 27.60% Smoothed Premium = 19.495% - 2.902% * Log(Assets)

12 4,207 3.62 37 1.10 20.67% 13.54% 15.90% 9.22% 8.98% 25.62%

13 3,562 3.55 36 1.15 20.03% 13.23% 16.03% 9.35% 9.19% 25.92%

14 3,090 3.49 36 1.12 21.18% 13.47% 15.84% 9.16% 9.37% 25.62%

15 2,732 3.44 39 1.16 19.52% 13.86% 16.33% 9.65% 9.52% 25.42%

16 2,344 3.37 33 1.18 21.04% 14.75% 17.00% 10.33% 9.71% 24.22%

17 2,029 3.31 41 1.18 20.00% 15.33% 17.39% 10.72% 9.90% 24.39%

18 1,721 3.24 55 1.22 22.93% 15.21% 17.48% 10.80% 10.10% 25.05%

19 1,390 3.14 60 1.23 22.05% 12.95% 16.77% 10.10% 10.37% 25.27%

20 1,115 3.05 64 1.24 23.66% 13.82% 16.57% 9.90% 10.65% 24.16%

21 883 2.95 59 1.24 21.79% 14.15% 16.43% 9.76% 10.95% 23.97%

22 721 2.86 78 1.24 23.23% 15.22% 17.51% 10.83% 11.20% 23.17%

23 554 2.74 69 1.25 23.24% 16.24% 18.47% 11.79% 11.53% 22.81%

24 381 2.58 119 1.25 24.43% 15.87% 18.45% 11.78% 12.00% 21.79%

25 135 2.13 316 1.27 28.01% 18.94% 21.45% 14.78% 13.31% 19.24%





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Log of Average Total Assets



Companies Ranked by 5-Year Average EBITDA Premia Over the Risk-Free Rate (RP m+s ) Exhibit A-6




Independent Variable: Log of Average EBITDA


Rank EBITDA Average as of (Sum Beta) Deviation Average Average Average Risk Average Risk Debt/

by Size (in $millions) EBITDA 2013 Since '63 of Returns Return Return Premium Premium MVIC Regression Output:

1 20,266 4.31 35 0.79 15.93% 11.72% 12.92% 6.24% 4.50% 22.97% Constant 16.969%


3 3,675 3.57 31 0.88 16.02% 11.90% 13.12% 6.45% 6.65% 29.18% R Squared 88%



6 1,412 3.15 27 0.93 16.51% 12.89% 14.19% 7.52% 7.85% 28.09%

7 1,164 3.07 35 1.02 18.71% 12.69% 14.27% 7.59% 8.09% 25.83% X Coefficient(s) -2.895%

8 931 2.97 34 1.05 17.55% 13.28% 14.75% 8.07% 8.37% 25.11% Standard Error of Coefficient 0.222%

9 773 2.89 34 1.11 19.70% 11.94% 13.76% 7.08% 8.61% 24.69% t-Statistic -13.04

10 676 2.83 37 1.09 19.33% 12.50% 14.23% 7.55% 8.78% 25.81%

11 604 2.78 33 1.01 18.42% 13.89% 15.49% 8.81% 8.92% 24.70% Smoothed Premium = 16.969% - 2.895% * Log(EBITDA)

12 510 2.71 36 1.09 21.41% 14.33% 16.51% 9.84% 9.13% 25.90%

13 433 2.64 37 1.07 20.06% 14.68% 16.57% 9.89% 9.34% 25.83%

14 372 2.57 33 1.15 20.24% 15.02% 16.90% 10.22% 9.53% 24.28%

15 327 2.52 35 1.15 20.95% 13.51% 15.66% 8.99% 9.69% 24.53%

16 281 2.45 41 1.18 20.91% 14.36% 16.43% 9.75% 9.88% 23.84%

17 243 2.39 41 1.19 21.77% 15.71% 17.86% 11.19% 10.06% 24.42%

18 213 2.33 46 1.20 22.53% 14.92% 17.20% 10.52% 10.23% 24.86%

19 179 2.25 50 1.24 20.97% 15.04% 17.12% 10.44% 10.45% 24.66%

20 148 2.17 66 1.25 22.22% 13.76% 16.09% 9.42% 10.69% 24.85%

21 117 2.07 59 1.23 23.65% 15.36% 17.80% 11.12% 10.98% 24.35%

22 89 1.95 84 1.22 22.02% 16.42% 18.63% 11.95% 11.33% 23.83%

23 65 1.81 70 1.24 24.09% 15.99% 18.59% 11.91% 11.72% 23.35%

24 47 1.67 109 1.26 24.48% 16.05% 18.74% 12.07% 12.14% 23.40%

25 15 1.19 327 1.30 28.33% 17.38% 20.92% 14.25% 13.53% 22.12%





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Log of Average 5-Year Average EBITDA



Companies Ranked by Sales Premia Over the Risk-Free Rate (RP m+s ) Exhibit A-7




Independent Variable: Log of Average Sales


Rank Sales Average as of (Sum Beta) Deviation Average Average Average Risk Average Risk Debt/

by Size (in $millions) Sales 2013 Since '63 of Returns Return Return Premium Premium MVIC Regression Output:

1 116,719 5.07 35 0.89 17.39% 11.74% 13.22% 6.54% 5.92% 23.38% Constant 17.369%


3 20,701 4.32 29 0.99 16.91% 12.06% 13.40% 6.72% 7.62% 26.77% R Squared 76%



6 9,300 3.97 31 1.02 18.26% 13.62% 15.17% 8.49% 8.40% 27.80%

7 7,739 3.89 30 1.08 19.74% 13.91% 15.67% 9.00% 8.58% 25.64% X Coefficient(s) -2.259%


9 5,658 3.75 30 1.09 20.41% 12.96% 14.85% 8.18% 8.89% 26.32% t-Statistic -8.60

10 4,861 3.69 42 1.11 20.07% 13.67% 15.56% 8.88% 9.04% 26.14%

11 4,155 3.62 38 1.11 18.98% 13.78% 15.50% 8.82% 9.19% 26.31% Smoothed Premium = 17.369% - 2.259% * Log(Sales)

12 3,397 3.53 40 1.10 21.11% 14.81% 16.85% 10.18% 9.39% 26.40%

13 2,833 3.45 40 1.20 21.07% 15.66% 17.78% 11.10% 9.57% 26.40%

14 2,471 3.39 38 1.12 21.09% 15.08% 17.10% 10.42% 9.70% 26.57%

15 2,203 3.34 40 1.12 19.16% 15.29% 16.95% 10.27% 9.82% 25.35%

16 1,956 3.29 37 1.14 20.38% 13.37% 15.36% 8.68% 9.93% 25.59%

17 1,700 3.23 49 1.15 21.89% 15.20% 17.41% 10.74% 10.07% 26.12%

18 1,462 3.17 45 1.21 21.51% 15.06% 17.24% 10.56% 10.22% 26.27%

19 1,236 3.09 47 1.24 21.34% 12.53% 14.71% 8.03% 10.38% 25.85%

20 1,003 3.00 58 1.17 22.13% 15.49% 17.73% 11.05% 10.59% 25.94%

21 817 2.91 66 1.18 23.27% 14.88% 17.29% 10.61% 10.79% 24.85%

22 665 2.82 70 1.25 22.38% 14.98% 17.26% 10.58% 10.99% 24.80%

23 519 2.72 78 1.24 24.78% 15.48% 18.20% 11.52% 11.23% 24.00%

24 363 2.56 118 1.24 23.86% 15.26% 17.89% 11.22% 11.59% 22.65%

25 123 2.09 304 1.25 25.71% 17.17% 20.14% 13.46% 12.65% 20.01%





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Companies Ranked by Number of Employees Premia Over the Risk-Free Rate (RP m+s ) Exhibit A-8




Independent Variable: Log of Average Employees


Rank Number of Number of as of (Sum Beta) Deviation Average Average Average Risk Average Risk Debt/

by Size Employees Employees 2013 Since '63 of Returns Return Return Premium Premium MVIC Regression Output:

1 311,358 5.49 30 0.99 18.92% 11.55% 13.23% 6.56% 6.18% 24.08% Constant 17.830%


3 59,734 4.78 35 1.06 19.16% 12.68% 14.42% 7.75% 7.70% 24.59% R Squared 77%



6 27,320 4.44 32 1.12 20.84% 14.28% 16.22% 9.54% 8.42% 23.17%

7 22,035 4.34 35 1.06 20.06% 12.51% 14.37% 7.69% 8.62% 24.18% X Coefficient(s) -2.120%


9 15,640 4.19 40 1.16 21.17% 13.91% 15.99% 9.31% 8.94% 26.58% t-Statistic -8.81

10 13,188 4.12 44 1.12 21.71% 14.62% 16.70% 10.03% 9.10% 25.36%

11 11,012 4.04 37 1.17 21.07% 14.64% 16.67% 10.00% 9.26% 25.61% Smoothed Premium = 17.830% - 2.120% * Log(Employees)

12 9,587 3.98 41 1.10 20.68% 14.95% 16.89% 10.21% 9.39% 25.58%

13 8,474 3.93 40 1.15 19.79% 13.61% 15.52% 8.85% 9.50% 25.80%

14 7,248 3.86 48 1.15 19.93% 13.17% 15.12% 8.44% 9.65% 26.76%

15 6,165 3.79 51 1.17 21.87% 14.62% 16.86% 10.18% 9.80% 26.96%

16 5,427 3.73 41 1.13 20.60% 13.89% 15.85% 9.17% 9.91% 26.89%

17 4,694 3.67 48 1.20 21.21% 13.30% 15.43% 8.76% 10.05% 26.25%

18 3,881 3.59 47 1.20 20.51% 15.38% 17.41% 10.74% 10.22% 26.72%

19 3,182 3.50 68 1.14 21.54% 13.92% 16.01% 9.34% 10.40% 25.50%

20 2,576 3.41 58 1.17 21.71% 13.73% 15.94% 9.26% 10.60% 24.67%

21 2,095 3.32 59 1.18 23.20% 15.64% 18.10% 11.42% 10.79% 25.10%

22 1,679 3.23 67 1.18 21.83% 15.62% 17.78% 11.10% 10.99% 24.96%

23 1,221 3.09 88 1.21 23.35% 15.38% 17.92% 11.24% 11.29% 24.33%

24 791 2.90 105 1.20 23.39% 16.58% 19.11% 12.43% 11.69% 23.95%

25 265 2.42 244 1.23 25.01% 17.52% 20.29% 13.61% 12.69% 20.65%





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Risk Premium Report – Exhibits B-1 through B-8 Premia Over CAPM (RPs) Premia over CAPM (commonly referred to as “size premia”) represent the difference between historical (observed) excess return and the excess return predicted by the capital asset pricing model (CAPM). Size premia can be added to cost of capital estimation models as an adjustment for the additional risk of small companies relative to large companies.

The B Exhibits are used in the following method to estimate a cost of equity capital:

CAPM

• Build-up 2

Size Measures:

• B-1: Market value of equity

• B-2: Book value of equity

• B-3: 5-year average net income

• B-4: Market value of invested capital (MVIC)

• B-5: Total assets

• B-6: 5-year average EBITDA

• B-7: Sales

• B-8: Number of employees


Companies Ranked by Market Value of Equity Premia over CAPM (Size Premia, RP s ) Exhibit B-1



Dependent Variable: Premium over CAPM

Independent Variable: Log of Average Market Value of Equity

SmoothedPortfolio Average Log of Beta Arithmetic Arithmetic Indicated Premium PremiumRank Mkt. Value Average (Sum Beta) Average Average Risk CAPM over overby Size (in $millions) Mkt. Value Since '63 Return Premium Premium CAPM CAPM Regression Output:

1 143,782 5.16 0.83 12.14% 5.47% 4.12% 1.34% -1.12% Constant 12.971%

2 41,383 4.62 0.95 11.07% 4.39% 4.72% -0.32% 0.35% Standard Error of Y Estimate 1.128%

3 26,386 4.42 0.93 11.49% 4.81% 4.61% 0.20% 0.89% R Squared 75%

4 18,966 4.28 0.94 13.09% 6.42% 4.64% 1.78% 1.28% No. of Observations 25

5 14,414 4.16 0.99 12.47% 5.79% 4.91% 0.88% 1.61% Degrees of Freedom 23

6 11,096 4.05 1.02 12.81% 6.14% 5.06% 1.08% 1.92%

7 9,354 3.97 1.01 13.55% 6.87% 5.01% 1.86% 2.12% X Coefficient(s) -2.733%

8 7,811 3.89 1.06 15.08% 8.41% 5.23% 3.17% 2.33% Standard Error of Coefficient 0.329%

9 6,448 3.81 1.08 15.25% 8.57% 5.35% 3.22% 2.56% t-Statistic -8.30

10 5,073 3.71 1.12 15.41% 8.74% 5.53% 3.20% 2.85%

11 4,259 3.63 1.10 14.87% 8.19% 5.44% 2.75% 3.05% Smoothed Premium = 12.971% - 2.733% * Log(Market Value)

12 3,752 3.57 1.11 14.18% 7.51% 5.48% 2.03% 3.20%

13 3,351 3.53 1.11 14.59% 7.92% 5.50% 2.42% 3.34%

14 3,018 3.48 1.15 15.91% 9.23% 5.68% 3.55% 3.46%

15 2,637 3.42 1.14 17.62% 10.94% 5.65% 5.29% 3.62%

16 2,186 3.34 1.17 16.79% 10.11% 5.78% 4.33% 3.84%

17 1,852 3.27 1.19 16.40% 9.73% 5.90% 3.83% 4.04%

18 1,583 3.20 1.22 15.08% 8.40% 6.03% 2.37% 4.23%

19 1,359 3.13 1.21 17.09% 10.41% 5.98% 4.43% 4.41%

20 1,083 3.03 1.21 16.54% 9.86% 5.99% 3.87% 4.68%

21 826 2.92 1.26 17.27% 10.59% 6.22% 4.37% 5.00%

22 646 2.81 1.23 17.60% 10.92% 6.09% 4.83% 5.29%

23 497 2.70 1.26 17.51% 10.83% 6.22% 4.61% 5.60%

24 339 2.53 1.24 19.49% 12.81% 6.15% 6.66% 6.06%

25 107 2.03 1.28 23.25% 16.58% 6.33% 10.25% 7.42%

Large Stocks (Ibbotson SBBI data) 11.63% 4.95%

Small Stocks (Ibbotson SBBI data) 16.74% 10.06%

Long-Term Treasury Income (Ibbotson SBBI data) 6.68%


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Smoothed Premium vs. Unadjusted Premium


Companies Ranked by Book Value of Equity Premia over CAPM (Size Premia, RP s ) Exhibit B-2




Independent Variable: Log of Average Book Value of Equity

SmoothedPortfolio Average Log of Beta Arithmetic Arithmetic Indicated Premium PremiumRank Book Val. Average (Sum Beta) Average Average Risk CAPM over overby Size (in $millions) Book Val. Since '63 Return Premium Premium CAPM CAPM Regression Output:

1 51,173 4.71 0.81 12.30% 5.62% 4.01% 1.61% 0.81% Constant 9.244%

2 16,346 4.21 0.86 12.45% 5.77% 4.25% 1.53% 1.70% Standard Error of Y Estimate 0.762%

3 10,965 4.04 0.91 13.55% 6.87% 4.51% 2.36% 2.01% R Squared 70%



6 4,073 3.61 1.02 14.07% 7.39% 5.05% 2.34% 2.78%

7 3,479 3.54 1.05 14.41% 7.73% 5.18% 2.56% 2.90% X Coefficient(s) -1.791%


9 2,447 3.39 1.12 15.08% 8.41% 5.55% 2.85% 3.17% t-Statistic -7.40

10 2,062 3.31 1.07 15.01% 8.33% 5.31% 3.02% 3.31%

11 1,794 3.25 1.09 15.37% 8.69% 5.38% 3.31% 3.42% Smoothed Premium = 9.244% - 1.791% * Log(Book Value)

12 1,532 3.19 1.09 16.68% 10.00% 5.39% 4.62% 3.54%

13 1,360 3.13 1.11 16.40% 9.72% 5.49% 4.23% 3.63%

14 1,228 3.09 1.13 15.10% 8.43% 5.60% 2.82% 3.71%

15 1,116 3.05 1.11 17.23% 10.56% 5.50% 5.05% 3.79%

16 990 3.00 1.22 18.38% 11.70% 6.04% 5.67% 3.88%

17 864 2.94 1.20 16.52% 9.85% 5.96% 3.89% 3.98%

18 780 2.89 1.19 17.03% 10.35% 5.87% 4.49% 4.06%

19 660 2.82 1.24 15.55% 8.87% 6.13% 2.74% 4.19%

20 532 2.73 1.21 16.26% 9.58% 5.97% 3.61% 4.36%

21 425 2.63 1.21 17.84% 11.16% 6.01% 5.15% 4.54%

22 318 2.50 1.24 17.04% 10.36% 6.13% 4.22% 4.76%

23 250 2.40 1.25 17.55% 10.88% 6.18% 4.70% 4.95%

24 188 2.27 1.27 18.39% 11.72% 6.29% 5.43% 5.17%

25 68 1.83 1.26 19.13% 12.45% 6.22% 6.23% 5.96%





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Log of Average Book Value of Equity



Companies Ranked by 5-Year Average Net Income Premia over CAPM (Size Premia, RP s ) Exhibit B-3




Independent Variable: Log of Average Net Income

SmoothedPortfolio Average Log of Beta Arithmetic Arithmetic Indicated Premium PremiumRank Net Inc. Average (Sum Beta) Average Average Risk CAPM over overby Size (in $millions) Net Inc. Since '63 Return Premium Premium CAPM CAPM Regression Output:

1 8,122 3.91 0.77 13.27% 6.60% 3.83% 2.77% 0.46% Constant 8.018%


3 1,418 3.15 0.86 13.80% 7.12% 4.26% 2.87% 1.93% R Squared 72%


5 735 2.87 0.95 13.23% 6.56% 4.70% 1.86% 2.48% Degrees of Freedom 23

6 521 2.72 0.98 13.29% 6.61% 4.84% 1.77% 2.77%

7 397 2.60 1.05 13.90% 7.22% 5.19% 2.04% 3.00% X Coefficient(s) -1.933%

8 330 2.52 1.10 14.61% 7.94% 5.42% 2.51% 3.15% Standard Error of Coefficient 0.251%

9 270 2.43 1.04 14.60% 7.93% 5.17% 2.76% 3.32% t-Statistic -7.70

10 233 2.37 1.07 14.58% 7.90% 5.30% 2.60% 3.44%

11 198 2.30 1.08 16.01% 9.33% 5.34% 3.99% 3.58% Smoothed Premium = 8.018% - 1.933% * Log(Net Income)

12 171 2.23 1.08 16.10% 9.42% 5.34% 4.08% 3.70%

13 147 2.17 1.06 16.34% 9.66% 5.25% 4.41% 3.83%

14 129 2.11 1.15 15.18% 8.50% 5.69% 2.81% 3.94%

15 113 2.05 1.12 15.55% 8.88% 5.53% 3.35% 4.05%

16 98 1.99 1.13 17.16% 10.48% 5.60% 4.89% 4.17%

17 83 1.92 1.18 15.97% 9.29% 5.85% 3.44% 4.31%

18 72 1.86 1.21 17.39% 10.71% 5.99% 4.73% 4.43%

19 62 1.79 1.25 16.51% 9.83% 6.18% 3.65% 4.55%

20 49 1.69 1.23 18.76% 12.08% 6.07% 6.01% 4.75%

21 35 1.54 1.22 17.70% 11.02% 6.05% 4.97% 5.03%

22 25 1.40 1.23 17.39% 10.71% 6.07% 4.64% 5.31%

23 17 1.24 1.26 19.26% 12.58% 6.22% 6.36% 5.63%

24 11 1.03 1.25 18.88% 12.20% 6.19% 6.02% 6.03%

25 4 0.58 1.32 21.70% 15.02% 6.53% 8.50% 6.90%





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Log of Average 5-Year Average Net Income



Companies Ranked by Market Value of Invested Capital Premia over CAPM (Size Premia, RP s ) Exhibit B-4




Independent Variable: Log of Average MVIC

SmoothedPortfolio Average Log of Beta Arithmetic Arithmetic Indicated Premium PremiumRank MVIC Average (Sum Beta) Average Average Risk CAPM over overby Size (in $millions) MVIC Since '63 Return Premium Premium CAPM CAPM Regression Output:

1 171,547 5.23 0.80 12.11% 5.43% 3.95% 1.48% -0.66% Constant 12.570%


3 34,181 4.53 0.90 11.73% 5.05% 4.44% 0.61% 1.11% R Squared 76%



6 14,547 4.16 1.00 12.56% 5.89% 4.96% 0.93% 2.05%

7 12,000 4.08 0.99 14.35% 7.67% 4.90% 2.77% 2.26% X Coefficient(s) -2.527%


9 8,707 3.94 1.09 14.14% 7.46% 5.42% 2.05% 2.62% t-Statistic -8.53

10 7,268 3.86 1.10 15.65% 8.98% 5.43% 3.55% 2.81%

11 6,170 3.79 1.11 15.17% 8.49% 5.51% 2.98% 2.99% Smoothed Premium = 12.570% - 2.527% * Log(MVIC)

12 5,189 3.72 1.05 15.21% 8.53% 5.22% 3.32% 3.18%

13 4,399 3.64 1.15 15.10% 8.42% 5.70% 2.72% 3.36%

14 3,883 3.59 1.17 15.57% 8.89% 5.80% 3.10% 3.50%

15 3,424 3.53 1.17 16.03% 9.36% 5.77% 3.59% 3.64%

16 3,009 3.48 1.20 16.88% 10.20% 5.93% 4.27% 3.78%

17 2,470 3.39 1.23 17.65% 10.98% 6.08% 4.90% 4.00%

18 2,048 3.31 1.17 17.18% 10.51% 5.77% 4.74% 4.20%

19 1,712 3.23 1.21 15.23% 8.55% 6.01% 2.54% 4.40%

20 1,422 3.15 1.25 16.10% 9.43% 6.17% 3.25% 4.60%

21 1,121 3.05 1.27 16.62% 9.95% 6.29% 3.66% 4.86%

22 824 2.92 1.24 17.49% 10.81% 6.15% 4.66% 5.20%

23 645 2.81 1.26 19.03% 12.35% 6.24% 6.11% 5.47%

24 459 2.66 1.25 18.63% 11.95% 6.19% 5.76% 5.84%

25 147 2.17 1.27 22.58% 15.90% 6.28% 9.62% 7.09%





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Log of Average Market Value of Invested Capital



Companies Ranked by Total Assets Premia over CAPM (Size Premia, RP s ) Exhibit B-5




Independent Variable: Log of Average Total Assets

SmoothedPortfolio Average Log of Beta Arithmetic Arithmetic Indicated Premium PremiumRank Total Assets Average (Sum Beta) Average Average Risk CAPM over overby Size (in $millions) Assets Since '63 Return Premium Premium CAPM CAPM Regression Output:

1 137,196 5.14 0.80 12.54% 5.86% 3.95% 1.92% 0.63% Constant 10.572%


3 30,116 4.48 0.91 13.14% 6.46% 4.53% 1.93% 1.90% R Squared 77%



6 11,841 4.07 0.95 14.25% 7.57% 4.69% 2.88% 2.69%

7 9,414 3.97 1.06 14.98% 8.31% 5.23% 3.07% 2.88% X Coefficient(s) -1.936%


9 6,818 3.83 1.09 14.11% 7.44% 5.41% 2.03% 3.15% t-Statistic -8.77

10 5,851 3.77 1.10 14.49% 7.82% 5.44% 2.37% 3.28%

11 5,045 3.70 1.11 14.86% 8.19% 5.52% 2.67% 3.40% Smoothed Premium = 10.572% - 1.936% * Log(Total Assets)

12 4,207 3.62 1.10 15.90% 9.22% 5.46% 3.77% 3.56%

13 3,562 3.55 1.15 16.03% 9.35% 5.68% 3.67% 3.70%

14 3,090 3.49 1.12 15.84% 9.16% 5.53% 3.64% 3.82%

15 2,732 3.44 1.16 16.33% 9.65% 5.72% 3.93% 3.92%

16 2,344 3.37 1.18 17.00% 10.33% 5.86% 4.46% 4.05%

17 2,029 3.31 1.18 17.39% 10.72% 5.86% 4.86% 4.17%

18 1,721 3.24 1.22 17.48% 10.80% 6.04% 4.76% 4.31%

19 1,390 3.14 1.23 16.77% 10.10% 6.09% 4.01% 4.49%

20 1,115 3.05 1.24 16.57% 9.90% 6.14% 3.76% 4.67%

21 883 2.95 1.24 16.43% 9.76% 6.15% 3.61% 4.87%

22 721 2.86 1.24 17.51% 10.83% 6.16% 4.67% 5.04%

23 554 2.74 1.25 18.47% 11.79% 6.19% 5.60% 5.26%

24 381 2.58 1.25 18.45% 11.78% 6.20% 5.58% 5.58%

25 135 2.13 1.27 21.45% 14.78% 6.30% 8.47% 6.45%





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Log of Average Total Assets



Companies Ranked by 5-Year Average EBITDA Premia over CAPM (Size Premia, RP s ) Exhibit B-6




Independent Variable: Log of Average EBITDA

SmoothedPortfolio Average Log of Beta Arithmetic Arithmetic Indicated Premium PremiumRank EBITDA Average (Sum Beta) Average Average Risk CAPM over overby Size (in $millions) EBITDA Since '63 Return Premium Premium CAPM CAPM Regression Output:

1 20,266 4.31 0.79 12.92% 6.24% 3.89% 2.35% 0.68% Constant 8.948%


3 3,675 3.57 0.88 13.12% 6.45% 4.37% 2.08% 2.10% R Squared 73%



6 1,412 3.15 0.93 14.19% 7.52% 4.58% 2.93% 2.90%

7 1,164 3.07 1.02 14.27% 7.59% 5.05% 2.54% 3.06% X Coefficient(s) -1.920%

8 931 2.97 1.05 14.75% 8.07% 5.21% 2.86% 3.25% Standard Error of Coefficient 0.243%

9 773 2.89 1.11 13.76% 7.08% 5.50% 1.58% 3.40% t-Statistic -7.90

10 676 2.83 1.09 14.23% 7.55% 5.40% 2.15% 3.51%

11 604 2.78 1.01 15.49% 8.81% 5.01% 3.80% 3.61% Smoothed Premium = 8.948% - 1.920% * Log(EBITDA)

12 510 2.71 1.09 16.51% 9.84% 5.42% 4.42% 3.75%

13 433 2.64 1.07 16.57% 9.89% 5.31% 4.59% 3.89%

14 372 2.57 1.15 16.90% 10.22% 5.69% 4.53% 4.01%

15 327 2.52 1.15 15.66% 8.99% 5.67% 3.32% 4.12%

16 281 2.45 1.18 16.43% 9.75% 5.83% 3.92% 4.25%

17 243 2.39 1.19 17.86% 11.19% 5.88% 5.31% 4.37%

18 213 2.33 1.20 17.20% 10.52% 5.94% 4.58% 4.48%

19 179 2.25 1.24 17.12% 10.44% 6.12% 4.32% 4.62%

20 148 2.17 1.25 16.09% 9.42% 6.17% 3.24% 4.78%

21 117 2.07 1.23 17.80% 11.12% 6.07% 5.05% 4.98%

22 89 1.95 1.22 18.63% 11.95% 6.02% 5.93% 5.21%

23 65 1.81 1.24 18.59% 11.91% 6.11% 5.80% 5.47%

24 47 1.67 1.26 18.74% 12.07% 6.26% 5.81% 5.74%

25 15 1.19 1.30 20.92% 14.25% 6.43% 7.81% 6.66%





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Companies Ranked by Sales Premia over CAPM (Size Premia, RP s ) Exhibit B-7




Independent Variable: Log of Average Sales

SmoothedPortfolio Average Log of Beta Arithmetic Arithmetic Indicated Premium PremiumRank Sales Average (Sum Beta) Average Average Risk CAPM over overby Size (in $millions) Sales Since '63 Return Premium Premium CAPM CAPM Regression Output:

1 116,719 5.07 0.89 13.22% 6.54% 4.38% 2.16% 1.47% Constant 9.412%


3 20,701 4.32 0.99 13.40% 6.72% 4.92% 1.80% 2.65% R Squared 58%



6 9,300 3.97 1.02 15.17% 8.49% 5.02% 3.47% 3.19%

7 7,739 3.89 1.08 15.67% 9.00% 5.35% 3.65% 3.32% X Coefficient(s) -1.567%


9 5,658 3.75 1.09 14.85% 8.18% 5.41% 2.76% 3.53% t-Statistic -5.64

10 4,861 3.69 1.11 15.56% 8.88% 5.52% 3.36% 3.64%

11 4,155 3.62 1.11 15.50% 8.82% 5.50% 3.32% 3.74% Smoothed Premium = 9.412% - 1.567% * Log(Sales)

12 3,397 3.53 1.10 16.85% 10.18% 5.44% 4.73% 3.88%

13 2,833 3.45 1.20 17.78% 11.10% 5.96% 5.14% 4.00%

14 2,471 3.39 1.12 17.10% 10.42% 5.56% 4.86% 4.10%

15 2,203 3.34 1.12 16.95% 10.27% 5.56% 4.71% 4.17%

16 1,956 3.29 1.14 15.36% 8.68% 5.66% 3.02% 4.25%

17 1,700 3.23 1.15 17.41% 10.74% 5.68% 5.05% 4.35%

18 1,462 3.17 1.21 17.24% 10.56% 5.97% 4.59% 4.45%

19 1,236 3.09 1.24 14.71% 8.03% 6.15% 1.88% 4.57%

20 1,003 3.00 1.17 17.73% 11.05% 5.78% 5.27% 4.71%

21 817 2.91 1.18 17.29% 10.61% 5.84% 4.77% 4.85%

22 665 2.82 1.25 17.26% 10.58% 6.18% 4.40% 4.99%

23 519 2.72 1.24 18.20% 11.52% 6.12% 5.41% 5.16%

24 363 2.56 1.24 17.89% 11.22% 6.11% 5.11% 5.40%

25 123 2.09 1.25 20.14% 13.46% 6.17% 7.29% 6.14%





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Log of Average Sales



Companies Ranked by Number of Employees Premia over CAPM (Size Premia, RP s ) Exhibit B-8




Independent Variable: Log of Average Employees

SmoothedPortfolio Average Log of Beta Arithmetic Arithmetic Indicated Premium PremiumRank Number of Average (Sum Beta) Average Average Risk CAPM over overby Size Employees Employees Since '63 Return Premium Premium CAPM CAPM Regression Output:

1 311,358 5.49 0.99 13.23% 6.56% 4.91% 1.65% 1.16% Constant 10.688%


3 59,734 4.78 1.06 14.42% 7.75% 5.25% 2.50% 2.40% R Squared 70%



6 27,320 4.44 1.12 16.22% 9.54% 5.55% 3.99% 2.99%

7 22,035 4.34 1.06 14.37% 7.69% 5.25% 2.44% 3.16% X Coefficient(s) -1.734%


9 15,640 4.19 1.16 15.99% 9.31% 5.75% 3.56% 3.41% t-Statistic -7.38

10 13,188 4.12 1.12 16.70% 10.03% 5.56% 4.47% 3.54%

11 11,012 4.04 1.17 16.67% 10.00% 5.81% 4.18% 3.68% Smoothed Premium = 10.688% - 1.734% * Log(Employees)

12 9,587 3.98 1.10 16.89% 10.21% 5.44% 4.77% 3.78%

13 8,474 3.93 1.15 15.52% 8.85% 5.67% 3.17% 3.88%

14 7,248 3.86 1.15 15.12% 8.44% 5.70% 2.75% 3.99%

15 6,165 3.79 1.17 16.86% 10.18% 5.79% 4.39% 4.11%

16 5,427 3.73 1.13 15.85% 9.17% 5.59% 3.58% 4.21%

17 4,694 3.67 1.20 15.43% 8.76% 5.94% 2.81% 4.32%

18 3,881 3.59 1.20 17.41% 10.74% 5.93% 4.81% 4.46%

19 3,182 3.50 1.14 16.01% 9.34% 5.62% 3.72% 4.61%

20 2,576 3.41 1.17 15.94% 9.26% 5.81% 3.45% 4.77%

21 2,095 3.32 1.18 18.10% 11.42% 5.85% 5.57% 4.93%

22 1,679 3.23 1.18 17.78% 11.10% 5.86% 5.25% 5.09%

23 1,221 3.09 1.21 17.92% 11.24% 5.99% 5.25% 5.33%

24 791 2.90 1.20 19.11% 12.43% 5.94% 6.49% 5.66%

25 265 2.42 1.23 20.29% 13.61% 6.09% 7.52% 6.48%





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Log of Average Number of Employees


Valuation Handbook - edisciplinas.usp.br · Professor Roger G. Ibbotson, Yale School of Management,...

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Transcript of Valuation Handbook - edisciplinas.usp.br · Professor Roger G. Ibbotson, Yale School of Management,...