risk premium data: ibbotson vs. duff

NYSSCPA Business Valuation Conference 2009 New York May 18, 2009

Jim Hitchner, CPA/ABV/CFF, ASAManaging Director, Financial Valuation Advisors

CEO, Valuation Products and ServicesPresident, Financial Consulting Group

Risk Premium Data: Ibbotson vs. Duff & Phelps

And the Winner is?

© 2009 Valuation Products and Services, LLC © 2009 Valuation Products and Services, LLC 22

Jim Hitchner, CPA/ABV/CFF, ASAManaging Director, Financial Valuation Advisors, a Managing Director, Financial Valuation Advisors, a national financial advisory services firm specializing national financial advisory services firm specializing in valuation and litigation servicesin valuation and litigation servicesCEO, Valuation Products and Services CEO, Valuation Products and Services President, Financial Consulting GroupPresident, Financial Consulting Group• Nation's largest organization of independently Nation's largest organization of independently

owned accounting, business valuation, and owned accounting, business valuation, and financial services firmsfinancial services firms

Editor in Chief, Editor in Chief, Financial Valuation and Litigation Financial Valuation and Litigation ExpertExpert29 years in valuation services29 years in valuation services Over seven years with Phillips Hitchner Group Over seven years with Phillips Hitchner Group Partner-in-charge of valuation services for the Partner-in-charge of valuation services for the

Southern Region of Coopers & Lybrand (now PWC) Southern Region of Coopers & Lybrand (now PWC)

© 2009 Valuation Products and Services, LLC© 2009 Valuation Products and Services, LLC 33

Jim Hitchner Qualified expert witness; has provided testimony on Qualified expert witness; has provided testimony on valuations in numerous state and federal courtsvaluations in numerous state and federal courts

Inductee in the AICPA BV Hall of FameInductee in the AICPA BV Hall of Fame

Two time recipient of the AICPA Volunteer of the Year Two time recipient of the AICPA Volunteer of the Year awardaward

Co-authored over 20 courses; taught over 60 coursesCo-authored over 20 courses; taught over 60 courses

Published over 60 articles; made over 100 Published over 60 articles; made over 100 presentationspresentations

Former member of the AICPA task force on BV Former member of the AICPA task force on BV StandardsStandards

Editor and/or co-author of the books: Editor and/or co-author of the books: Financial Valuation: Applications and Models, Financial Valuation: Applications and Models, 22ndnd

edition edition Financial Valuation Workbook, Financial Valuation Workbook, 22ndnd edition edition Valuation for Financial Reporting: Fair Value Valuation for Financial Reporting: Fair Value

Measurements and Reporting, Intangible Assets, Measurements and Reporting, Intangible Assets, Goodwill, and Impairment, 2Goodwill, and Impairment, 2ndnd edition edition

PPC Guide to Business Valuations, 19PPC Guide to Business Valuations, 19thth edition edition


Learning Objectives

The participant will learn: The participant will learn: – What’s new in the 2009 editions of Ibbotson What’s new in the 2009 editions of Ibbotson

and Duff & Phelps (D&P)and Duff & Phelps (D&P)– The differences between Ibbotson and D&P The differences between Ibbotson and D&P

datadata– What’s better, Ibbotson or D&PWhat’s better, Ibbotson or D&P– Equity risk and size premiums and Equity risk and size premiums and

measurement periodsmeasurement periods– How size is definedHow size is defined– About size category pollutionAbout size category pollution– About risk measures other than sizeAbout risk measures other than size– How to mix Ibbotson industry risk premiums How to mix Ibbotson industry risk premiums

into D&P datainto D&P data


Acknowledgements

We would like to thank Morningstar, Inc. for their We would like to thank Morningstar, Inc. for their permission to use most of the information on these permission to use most of the information on these slides. These slides are only a summary of the slides. These slides are only a summary of the material contained in Morningstar’s material contained in Morningstar’s Ibbotson SBBI Ibbotson SBBI Valuation Edition 2009 Yearbook.Valuation Edition 2009 Yearbook.Analysts should not use this information on a Analysts should not use this information on a standalone basis without first reading the Ibbotson standalone basis without first reading the Ibbotson book. book. It is highly recommended that analysts It is highly recommended that analysts purchase and read each yearly edition of this purchase and read each yearly edition of this book.book.Source: Stocks, Bonds and Bills and Inflation Valuation Edition 2009 Yearbook. Copyright 2009 Morningstar, Inc. All rights reserved. Used with permission. To purchase copies of the Valuation Edition, or for more information on other Morningstar publications, please visit global.morningstar.com/DataPublications.


Acknowledgements

We would like to thank Duff & Phelps, LLC for their We would like to thank Duff & Phelps, LLC for their permission to use most of the information on these permission to use most of the information on these slides. These slides are only a summary of the slides. These slides are only a summary of the material contained in material contained in Duff & Phelps, LLC Risk Duff & Phelps, LLC Risk Premium Report 2009.Premium Report 2009.Analysts should not use this information on a Analysts should not use this information on a standalone basis without first reading the Duff & standalone basis without first reading the Duff & Phelps Report. Phelps Report. It is highly recommended that It is highly recommended that analysts purchase and read each yearly analysts purchase and read each yearly Report.Report.Source: Duff & Phelps, LLC Risk Premium Report 2009, Copyright 2009 Duff & Phelps, LLC. All rights reserved. Used with permission. To purchase copies of the Report or for more information please visit www.bvresources.com


Build Up ModelThe basic formula for the build-up model is/can be:The basic formula for the build-up model is/can be:

E(RE(Rii) = R) = RFF + RP + RPmm + RP + RPss + RP + RPu u + (RP+ (RPi i ?)?)

Where:Where:

E(RE(R11) = Expected (market required) rate of return on a security) = Expected (market required) rate of return on a security

RRf f = Return for a risk-free security as of the valuation date = Return for a risk-free security as of the valuation date

RPRPmm = Equity risk premium (ERP) for the “market” = Equity risk premium (ERP) for the “market”

RPRPss = Risk premium for small size = Risk premium for small size

RPRPuu = Risk premium for specific company, where u stands for = Risk premium for specific company, where u stands for unsystematic riskunsystematic risk

RPRPii = Risk premium for the industry = Risk premium for the industry

RPRPmm + RP + RPss

D&P


MCAPMThe basic formula for the MCAPM model is:The basic formula for the MCAPM model is:

E(RE(Rii) = R) = RFF + B(RP + B(RPmm) + RP) + RPss + RP + RPuu

Where:Where:

E(RE(R11) = Expected (market required) rate of return on a security) = Expected (market required) rate of return on a security

RRf f = Return for a risk-free security as of the valuation date = Return for a risk-free security as of the valuation dateBB = Beta= Beta

RPRPmm = Equity risk premium (ERP) for the “market” = Equity risk premium (ERP) for the “market”

RPRPss = Risk premium for small size = Risk premium for small size

RPRPuu = Risk premium for specific company, where u stands for = Risk premium for specific company, where u stands for unsystematic riskunsystematic risk

Ibbotson D&P Case 5/1/09


Some Company, Inc. Cost of Equity (ke) Valuation date: May 1, 2009

Build-up Method, ke = Rf + RPm + RPs + RPi + RPu Ibbotson D&P D&P D&P Risk 4

Risk-Free Rate (Rf) 4.10% 4.10% 4.10% 4.10%Market Premium (RPm) 6.50% 3.84%Size Premium (RPs) 5.81% 11.00% 1 6.00% 10.00%Industry Risk Premium (RPi)? 1.45% 0.86% 2 0.86% 3 0.86% 5

Company Specific Risk Premium (RPu) 2.00% 2.00% 2.00% 2.00% 5ke = 19.86% 17.96% 16.80% 16.96%

MCAPM Method, ke = Rf + ( b x RPm ) + RPs + RPu Ibbotson D&P

Risk-Free Rate (Rf) 4.10% 4.10%

Beta (b) 1.30 1.30

Market Premium (RPm) 6.50% 3.84%Size Premium (RPs) 5.81% 6.00%Company Specific Risk Premium (RPu) 2.00% 2.00%

ke = 20.36% 17.09%

Range of ke = 16.80% 20.36%



Some Company, Inc. Cost of Equity (ke)

Valuation date: May 1, 2009

Build-up Method, ke = Rf + RPm + RPs + RPi + RPu Ibbotson D&P

Risk-Free Rate (Rf) 4.10% 4.10%Market Premium (RPm) 6.50% Size Premium (RPs) 5.81% 11.00% 1Industry Risk Premium (RPi)? 1.45% 0.86% 2

Company Specific Risk Premium (RPu) 2.00% 2.00%

ke = 19.86% 17.96%




Build-up Method, ke = Rf + RPm + RPs + RPi + RPu

D&PD&P Risk 4

Risk-Free Rate (Rf) 4.10% 4.10%Market Premium (RPm) 3.84%Size Premium (RPs) 6.00% 10.00%Industry Risk Premium (RPi)? 0.86% 3 0.86% 5Company Specific Risk Premium (RPu) 2.00% 2.00% 5

ke = 16.80% 16.96%






MCAPM Method, ke = Rf + ( b x RPm ) + RPs + RPuIbbotson D&P

Risk-Free Rate (Rf) 4.10% 4.10%Beta (b) 1.30 1.30 Market Premium (RPm) 6.50% 3.84%Size Premium (RPs) 5.81% 6.00%

Company Specific Risk Premium (RPu) 2.00% 2.00%

ke = 20.36% 17.09%



1 Risk premiums over the risk free rate; total of ERP and size premiums; A Exhibits

2 Converts Ibbotson IRP to D&P IRP; not beta adjusted3 Converts Ibbotson IRP to D&P IRP; beta adjusted using

separately calculated ERP and size premiums; B Exhibits4 Risk based on operating margin, CV(operating margin) and

CV(ROE); D Exhibits5 Based on assessment that the subject company risk is

meaningfully different from the average risk of the companies in the guideline portfolio (more risky or less risky than the average). The company-specific volatility is capturing risk (at least along that one dimension of risk) already.

Footnotes

Ibbotson D&P Case 5/1/09Some Company, Inc. Comparison to Historical Equity Risk Premiums by CharacteristicBased on the 2009 Duff & Phelps, LLC Risk Premium Report

SmoothedPrem.

Subject Implied Smoothed Over CAPMCharacteristic Company Category Premium

Market Value of Equity 25 12.40% 7.10%Book Value of Equity 25 10.90% 5.70%5-Year Ave. Net Income 25 11.70% 6.40%Market Value of Invested Capital 25 12.00% 6.70%Total Assets 25 11.20% 5.90%5-Year Ave. EBITDA 25 11.40% 6.10%Sales 25 10.50% 5.40%Number of Employees 25 10.60% 5.90%

Min 10.50% 5.40%Max 12.40% 7.10%

Mean 11.34% 6.15%Median 11.30% 6.00%

Selected 11.00% 6.00%© 2009 Valuation Products and Services, LLC© 2009 Valuation Products and Services, LLC 1414



CharacteristicSubject

Co.Implied

CategorySmoothed Ave.

Premium

Operating Margin Number 21 10.00%

CV of Operating Margin Number 3 10.32%

CV of Return on Book Equity Number 2 9.15%

Mean 9.82%

Median 10.00%

Selected 10.00%

Cost of Capital Corner

1010 10b10bRf Rf (3)(3) 4.8%4.8% 4.8%4.8%RPm RPm (4)(4) 7.1%7.1% 7.1%7.1%RPs RPs (5)(5) 6.4%6.4% 9.8%9.8%Cost of Equity Cost of Equity (6)(6) 18.3%18.3%21.7%21.7%

Ibbotson decile (1)

Equity Invested Capital SalesRf (3) 4.8% 4.8% 4.8%ERP (7) 13.7% 13.4% 12.2%Cost of Equity (8) 18.5% 18.2% 17.0%

Duff & Phelps 25th size criteria (2)

Gross Domestic Inflation Product

Historical (1926-2005) (9) 3.1% 3.4%10 yr. forecast (10) 2.5% 3.2%

Financial Valuation and Litigation Expert – Issue 3, Oct./Nov., 2006


1010 10b10bRf Rf (3)(3) 4.9%4.9% 4.9%4.9%RPm RPm (4)(4) 7.1%7.1% 7.1%7.1%RPs RPs (5)(5) 6.3%6.3% 9.7%9.7%Cost of Equity Cost of Equity (6)(6) 18.3%18.3%21.7%21.7%

Ibbotson decile (1)





Financial Valuation and Litigation Expert – April/May, 2007


1010 10b10bRf Rf (3)(3) 4.1%4.1% 4.1%4.1%RPm RPm (4)(4) 7.1%7.1% 7.1%7.1%RPs RPs (5)(5) 5.8%5.8% 9.7%9.7%Cost of Equity Cost of Equity (6) (6) 17.0%17.0% 20.9%20.9%

Ibbotson decile (1)





Financial Valuation and Litigation Expert – Oct./Nov. 2008


1010 10b10bRf Rf (3)(3) 3.8%3.8% 3.8%3.8%RPm RPm (4)(4) 6.5%6.5% 6.5%6.5%RPs RPs (5)(5) 5.8%5.8% 9.5%9.5%Cost of Equity Cost of Equity (6) (6) 16.1%16.1% 19.8%19.8%

Ibbotson decile (1)





Financial Valuation and Litigation Expert – April/May 2009


Sources(1)(1) Ibbotson Associates, Stocks, Bonds, Bills and Inflation, (SBBI), Valuation Ibbotson Associates, Stocks, Bonds, Bills and Inflation, (SBBI), Valuation

Edition 2006, www.ibbotson.comEdition 2006, www.ibbotson.com(2) Duff & Phelps, LLC (D&P), Risk Premium Report, 2006, www.ibbotson.com(2) Duff & Phelps, LLC (D&P), Risk Premium Report, 2006, www.ibbotson.com(3)(3)Risk-free rate, 20-year Treasury Bond Yield, Federal Reserve Statistical Risk-free rate, 20-year Treasury Bond Yield, Federal Reserve Statistical

Release, 9/27/06Release, 9/27/06(4) “Risk Premium in the Market,” Ibbotson, SBBI, inside back cover(4) “Risk Premium in the Market,” Ibbotson, SBBI, inside back cover(5)(5)“Size Premium,” Ibbotson, SBBI, pages 137 and 139“Size Premium,” Ibbotson, SBBI, pages 137 and 139(6)(6)Build up method illustration only; excludes industry risk premium and Build up method illustration only; excludes industry risk premium and

specific company riskspecific company risk(7)(7)Total Equity Risk Premium; includes RPm and RPs; D&P, Exhibits A-1, A-4, A-Total Equity Risk Premium; includes RPm and RPs; D&P, Exhibits A-1, A-4, A-

7, 7, smoothed averagesmoothed average

(8)(8)Build up method illustration only; excludes industry risk premium and Build up method illustration only; excludes industry risk premium and specific company riskspecific company risk

(9) Samuel H. Williamson and Lawrence Officer, “What is the Average Annual (9) Samuel H. Williamson and Lawrence Officer, “What is the Average Annual Growth Rate of Growth Rate of Various Historical Economic Series?” Economic History Services, March Various Historical Economic Series?” Economic History Services, March 2006, 2006, http://www.eh.net/hmit/growth/.http://www.eh.net/hmit/growth/.

(10)Consensus Median Average, Livingston Survey, Federal Reserve Bank of (10)Consensus Median Average, Livingston Survey, Federal Reserve Bank of Philadelphia, June 2006, p. 10Philadelphia, June 2006, p. 10Note: I highly recommend that all financial experts who rely on Ibbotson and Duff &

Phelps data purchase these books/studies and become familiar with how the data are compiled and the data choices available.


Sources(1)(1)Morningstar, Inc., Stocks, Bonds, Bills and Inflation, (SBBI), Valuation Morningstar, Inc., Stocks, Bonds, Bills and Inflation, (SBBI), Valuation

Edition 2007, www.global.morningstar.com/sbbiyrbksEdition 2007, www.global.morningstar.com/sbbiyrbks(2) Duff & Phelps, LLC (D&P), Risk Premium Report, 2006(2) Duff & Phelps, LLC (D&P), Risk Premium Report, 2006(3)(3)Risk-free rate, 20-year Treasury Bond Yield, Federal Reserve Statistical Risk-free rate, 20-year Treasury Bond Yield, Federal Reserve Statistical


specific company riskspecific company risk(7)(7)Total Equity Risk Premium; includes RPm and RPs; D&P, Exhibits A-1, A-Total Equity Risk Premium; includes RPm and RPs; D&P, Exhibits A-1, A-

4, A-7, 4, A-7, smoothed averagesmoothed average


(9) Samuel H. Williamson and Lawrence Officer, “Annualized Growth Rate (9) Samuel H. Williamson and Lawrence Officer, “Annualized Growth Rate of Various Historical Economic Series,” August 2006of Various Historical Economic Series,” August 2006www.measuringworth.comwww.measuringworth.com

(10)Consensus Median Average, Livingston Survey, Federal Reserve Bank (10)Consensus Median Average, Livingston Survey, Federal Reserve Bank of Philadelphia, December 2006, p. 10of Philadelphia, December 2006, p. 10Note: I highly recommend that all financial experts who rely on Morningstar-

Ibbotson and Duff & Phelps data purchase these books/studies and become familiar with how the data are compiled and the data choices available.








(9) Samuel H. Williamson and Lawrence Officer, “Annualized Growth Rate (9) Samuel H. Williamson and Lawrence Officer, “Annualized Growth Rate of Various Historical Economic Series,” as of 2007 of Various Historical Economic Series,” as of 2007 www.measuringworth.comwww.measuringworth.com

(10)Consensus Median Average, Livingston Survey, Federal Reserve Bank (10)Consensus Median Average, Livingston Survey, Federal Reserve Bank of Philadelphia, June 2008, p. 10of Philadelphia, June 2008, p. 10Note: I highly recommend that all financial experts who rely on Morningstar-









(9) Samuel H. Williamson and Lawrence Officer, “Annualized Growth Rate (9) Samuel H. Williamson and Lawrence Officer, “Annualized Growth Rate of Various Historical Economic Series,” as of 2008 of Various Historical Economic Series,” as of 2008 www.measuringworth.comwww.measuringworth.com

(10)Consensus Median Average, Livingston Survey, Federal Reserve Bank (10)Consensus Median Average, Livingston Survey, Federal Reserve Bank of Philadelphia, Dec. 2008, p. 4of Philadelphia, Dec. 2008, p. 4Note: I highly recommend that all financial experts who rely on Morningstar-



Morningstar/Ibbotson

Ibbotson SBBI 2009 Valuation Ibbotson SBBI 2009 Valuation YearbookYearbook

Market Results for Stocks, Bonds, Bills, Market Results for Stocks, Bonds, Bills, and Inflationand Inflation

1926-20081926-2008

Morningstar, Inc.Morningstar, Inc.


Risk PremiumsTreasury billTreasury bill Real rate + InflationReal rate + InflationTreasury notesTreasury notes Real rate + Inflation + Real rate + Inflation +

Intermediate horizon premiumIntermediate horizon premiumTreasury bondsTreasury bonds Real rate + Inflation + Real rate + Inflation +

Long horizon premiumLong horizon premiumCorporate bondsCorporate bonds Real rate + Inflation + Long Real rate + Inflation + Long

horizon premium + Default horizon premium + Default premiumpremium

Large capitalization Large capitalization Real rate + Inflation + Equity Real rate + Inflation + Equity riskrisk

stocks premiumstocks premiumSmall capitalization Small capitalization Real rate + Inflation + Equity Real rate + Inflation + Equity risk stocks premium + Size premiumrisk stocks premium + Size premium


Equity Risk Premium

Expected (Forward Looking) ERP defined as:Expected (Forward Looking) ERP defined as:– Additional return to compensate for Additional return to compensate for

additional riskadditional risk– Unobservable in the marketUnobservable in the market

Historical ERP calculation Historical ERP calculation – Long-term average stock market return Long-term average stock market return

(measured over the same period as that of (measured over the same period as that of the riskless asset)the riskless asset)

MINUSMINUS– Long-term average of the income return on Long-term average of the income return on

the riskless asset (Treasuries)the riskless asset (Treasuries)


Calculating the Historical Equity Risk Premium

DecisionsDecisions– Selecting the stock market Selecting the stock market

benchmarkbenchmark– Risk-free assetRisk-free asset– Arithmetic or a geometric averageArithmetic or a geometric average– Time period for measurementTime period for measurement


Supply ModelSupply of stock market returns generated by the Supply of stock market returns generated by the productivity of corporations in the real economyproductivity of corporations in the real economyEarnings and dividends have historically grown in Earnings and dividends have historically grown in tandem with the overall economy (GDP per capita)tandem with the overall economy (GDP per capita)The overall stock market price grew faster than The overall stock market price grew faster than GDP per capitaGDP per capitaPrimarily because the P/E ratio (one-year average Primarily because the P/E ratio (one-year average earnings) increased 1.9X (10.2 vs. 19.3) from 1926 earnings) increased 1.9X (10.2 vs. 19.3) from 1926 to 2008 times during the same period - an average to 2008 times during the same period - an average increase of 0.77 percent per yearincrease of 0.77 percent per yearPast supply of corporate growth forecasted to Past supply of corporate growth forecasted to continue - a change in investors’ predictions is notcontinue - a change in investors’ predictions is not


Supply side risk premiumsHistory

– Analysts generally assume that Analysts generally assume that historical historical behaviorbehavior of stock returns can be used to of stock returns can be used to predict investors’ expected returnspredict investors’ expected returns on on stockstock

– Ibbotson and ChenIbbotson and Chen** present an alternative present an alternative model that uses historical economic and model that uses historical economic and market data to forecast the equity risk market data to forecast the equity risk premiumpremium•Roger G. Ibbotson and Peng Chen, “Long -Run Stock Returns: Roger G. Ibbotson and Peng Chen, “Long -Run Stock Returns:

Participating in the Real Economy,” Participating in the Real Economy,” •Financial Analysts Journal,Financial Analysts Journal, 59, No. 1, (January/February 2003), 59, No. 1, (January/February 2003), Internet version, p. 12.Internet version, p. 12.


Supply Side SupportSome analysts are now reducing the Morningstar Some analysts are now reducing the Morningstar equity risk premium by equity risk premium by 1.25% (2006/2007 1.25% (2006/2007 SBBI was .8%; 2008 was .9%; 2009 SBBI was .8%; 2008 was .9%; 2009 was .8%)was .8%) to adjust to the supply side model to adjust to the supply side model

Others are reluctant, particularly given the rather Others are reluctant, particularly given the rather flat endorsement in the flat endorsement in the Valuation YearbookValuation Yearbook ““This section has briefly reviewed some of This section has briefly reviewed some of the more common arguments that seek to the more common arguments that seek to reduce the equity risk premium. While reduce the equity risk premium. While some of these theories are compelling in an some of these theories are compelling in an academic framework, most do little to academic framework, most do little to prove that the equity risk premium is too prove that the equity risk premium is too high.”*high.”*

****Morningstar Morningstar Stocks, Bonds, Bills, and Inflation, SBBI, Valuation Edition, 2009 Stocks, Bonds, Bills, and Inflation, SBBI, Valuation Edition, 2009 Yearbook,Yearbook, 70. 70.


Supply Side – Another Quote

Goetzmann and Ibbotson, “History of the Goetzmann and Ibbotson, “History of the Equity Risk Premium,” Yale International Equity Risk Premium,” Yale International Center for Finance Working paper no. 05-04 Center for Finance Working paper no. 05-04 (April 2005)(April 2005)““These forecasts tend to give somewhat These forecasts tend to give somewhat lower forecasts than historical risk premiums, lower forecasts than historical risk premiums, primarily because part of the total returns of primarily because part of the total returns of the stock market have come from price-the stock market have come from price-earnings ratio expansion. earnings ratio expansion. This expansion This expansion is not predicted to continue indefinitely, is not predicted to continue indefinitely, and should logically be removed from and should logically be removed from the expected risk premiumthe expected risk premium.” (p. 8).*.” (p. 8).*

*FCG University 2008, Roger Grabowski.


SSERP and Size

Morningstar size premiums are “in excess of Morningstar size premiums are “in excess of CAPM”CAPM”(Actual return) – (expected CAPM return) = (Actual return) – (expected CAPM return) =

(in excess of CAPM) = (size premium)(in excess of CAPM) = (size premium)Size premiums are not based on SSERP Size premiums are not based on SSERP but traditional ERPbut traditional ERPThe lower SSERP is offset by the higher size The lower SSERP is offset by the higher size premium since the “in excess of CAPM’ would premium since the “in excess of CAPM’ would be lower using the SSERPbe lower using the SSERPBeta may affect calculations as wellBeta may affect calculations as wellAlternate viewAlternate view is that it doesn’t matter is that it doesn’t matter


Size Risk Premiums - RPs

10 primary choices10 primary choices

Range is approximately Range is approximately 2% to 10%?2% to 10%?

Analyst must be able to explain and Analyst must be able to explain and support choicesupport choice

Choices for RPs are all Choices for RPs are all “in excess of “in excess of CAPM”CAPM” rate differentials as defined by rate differentials as defined by MorningstarMorningstar


EXHIBIT: TEN CHOICES FOR RPS SIZE PREMIUM

1.1. 10th decile monthly beta S&P10th decile monthly beta S&P2.2. 10th decile annual beta S&P10th decile annual beta S&P3.3. 10th decile sum beta S&P10th decile sum beta S&P4.4. 10A monthly beta S&P10A monthly beta S&P5.5. 10B monthly beta S&P10B monthly beta S&P6.6. Micro-cap annual beta S&PMicro-cap annual beta S&P7.7. Micro-cap monthly beta S&PMicro-cap monthly beta S&P8.8. Micro-cap sum beta S&PMicro-cap sum beta S&P9.9. 10th decile monthly beta NYSE10th decile monthly beta NYSE10.10. Micro-cap monthly beta NYSE*Micro-cap monthly beta NYSE*

*Ibbotson *Ibbotson Stocks, Bonds, Bills, and Inflation, SBBI, Valuation Stocks, Bonds, Bills, and Inflation, SBBI, Valuation Edition, 2009 Yearbook, 94-98Edition, 2009 Yearbook, 94-98..

Size Premium Choices

Size Category

No. of Companies

Minimum Cap.

MaximumCap.

Mean Average

Cap.

Micro-Cap 2,229 $1.6 million $453 million $139 million

10th Decile 1,626 $1.6 million $219 million $79 million

10a 409 $137 million $219 million $191 million

10b 1,182 $1.6 million $137 million $64 million


Size Category

No. of Companies

MinimumCap.

MaximumCap.

Mean Average

Cap.

Micro-Cap 2,416 $1.9 million $723 million $201 million

10th Decile 1,775 $1.9 million $363 million $114 million

10a 386 $212 million $363 million $281 million

10b 1,405 $1.9 million $212 million $102 million

2009

2008

© 2009 Valuation Products © 2009 Valuation Products and Services, LLCand Services, LLC 3636

Exhibit: Equity Size Exhibit: Equity Size Premiums (%) (2009)Premiums (%) (2009)

DecilesDecilesCategory Category Micro-Cap* Micro-Cap* 10 10 10A 10A 10B10B

S&P 500 (Monthly Beta) S&P 500 (Monthly Beta) 3.7 3.7 5.8 5.8 4.1 4.1 9.59.5

NYSE NYSE (Monthly Beta) (Monthly Beta) 4.24.2 6.3 6.3 N/A N/A N/AN/A

S&P 500 (Sum Beta) S&P 500 (Sum Beta) 2.22.2 3.9 3.9 N/A N/A N/A N/A

S&P 500 (Annual Beta) S&P 500 (Annual Beta) 2.82.8 4.4 4.4 N/A N/A N/A N/A

* 9th & 10th Deciles* 9th & 10th Deciles

Morningstar Stocks, Bonds, Bills and Inflation, 2009 Yearbook, Valuation Edition, pp. 94-98


Exhibit: Equity Size Premiums Exhibit: Equity Size Premiums (%) (2008)(%) (2008)







Morningstar Ibbotson, Stocks, Bonds, Bills and Inflation, 2008 Yearbook, Valuation Edition, pp. 137-145

© 2009 Valuation Products © 2009 Valuation Products and Services, LLCand Services, LLC 3838FVAM2 172FVAM2 172 3838

Exhibit: Equity Size Premiums Exhibit: Equity Size Premiums (%) (2005)(%) (2005)







Ibbotson Associates, Inc., Stocks, Bonds, Bills and Inflation, 2005 Yearbook, Valuation Edition,, (312) 616-1620, pp. 135-143


EXHIBIT: NUMBER OF COMPANIES IN THE 10TH DECILE BY SPECIFIC YEAR/DECADE

YearYear Tenth Decile Tenth Decile CompaniesCompanies

19261926 525219301930 727219401940 787819501950 10010019601960 10910919701970 86586519801980 685685 19901990 1,8141,814 20002000 1,9271,927 20082008 1,6261,626* Morningstar Stocks, Bonds, Bills, and Inflation, * Morningstar Stocks, Bonds, Bills, and Inflation,

SBBI, Valuation Edition, 2009 YearbookSBBI, Valuation Edition, 2009 Yearbook, 96, 96..


New Size and Liquidity

Capitalization Capitalization is not necessarilyis not necessarily the the underlying cause of the higher returns for underlying cause of the higher returns for smaller companiessmaller companies– (Zhiwu Chen and Roger G. Ibbotson demonstrate in their (Zhiwu Chen and Roger G. Ibbotson demonstrate in their

Zebra Capital working paper, “Illiquidity as an Investment Zebra Capital working paper, “Illiquidity as an Investment Style,” that liquidity strongly predicts stock returns. Style,” that liquidity strongly predicts stock returns. www.zebracapm.com ) )

The size premium The size premium can serve as a partial can serve as a partial measuremeasure of the increased cost of capital of a of the increased cost of capital of a less liquid stockless liquid stock– Does notDoes not represent the full cost of capital represent the full cost of capital

for non-traded companiesfor non-traded companiesThe valuation for a non-publicly traded The valuation for a non-publicly traded company should also reflect a discount for the company should also reflect a discount for the very fact that it is not tradedvery fact that it is not traded


NewLiquidity and Valuation

Liquidity affects stock returns and the cost of Liquidity affects stock returns and the cost of capitalcapitalTo some extent, size is correlated with To some extent, size is correlated with liquidityliquidity– Smaller companies have fewer shares Smaller companies have fewer shares

outstanding, and consequently fewer outstanding, and consequently fewer shares tradedshares traded

Size does not fully cover the impact of Size does not fully cover the impact of liquidityliquidity– Liquidity is a much stronger affectLiquidity is a much stronger affectLiquidity impacts the valuation of a company Liquidity impacts the valuation of a company by affecting the firm’s cost of capitalby affecting the firm’s cost of capital


Liquidity and Valuation

All deciles are comprised of relatively liquid All deciles are comprised of relatively liquid stockstock

Clear link between an illiquidity premium in a Clear link between an illiquidity premium in a cost of capital calculation and an illiquidity cost of capital calculation and an illiquidity discount applied to a valuationdiscount applied to a valuation

V = c/r where, c = the annual cash flow, and r V = c/r where, c = the annual cash flow, and r = the discount rate of a liquid security= the discount rate of a liquid security

If a valuation is reduced by one minus an If a valuation is reduced by one minus an illiquidity discount (1 – illiquidity discount (1 – LDLD), it would have the ), it would have the same impact as if the discount rate were same impact as if the discount rate were raised by an illiquidity premium, raised by an illiquidity premium, LPLP

Thus: V(1 – LD) = c/(r + LP)Thus: V(1 – LD) = c/(r + LP)


NewLiquidity and Stock Returns

Cannot measure the return of completely Cannot measure the return of completely illiquid securities because they are not tradedilliquid securities because they are not traded

Can measure the impact on relative levels of Can measure the impact on relative levels of liquidity for various publicly traded securitiesliquidity for various publicly traded securities

Split the universe of NYSE/AMEX/NASDAQ Split the universe of NYSE/AMEX/NASDAQ stocks into quartiles based on their share stocks into quartiles based on their share turnover ratesturnover rates

More liquid the stock, the less the historical More liquid the stock, the less the historical returnreturn

Conversely, less liquid stocks have higher Conversely, less liquid stocks have higher returnsreturns


Table 7-16: Liquidity Quartiles of the NYSE/AMEX/NASDAQ Annualized

Returns (%)

– Quartile 1-IlliquidQuartile 1-Illiquid Arithmetic Mean Arithmetic Mean 17.23%17.23%

– Quartile 2Quartile 2 Arithmetic Mean Arithmetic Mean 15.44%15.44%

– Quartile 3Quartile 3 Arithmetic Mean Arithmetic Mean 14.14%14.14%

– Quartile 4-LiquidQuartile 4-Liquid Arithmetic Mean Arithmetic Mean 10.73%10.73%

– Less liquid stocks have consistently higher Less liquid stocks have consistently higher returns over the period 1972-2008returns over the period 1972-2008


Table 7-17: Size and Liquidity Quartiles of the

NYSE/AMEX/NASDAQ: Stocks Independently Sorted Each Year Compound Annual Returns (%)

LiquidityLiquidity Low MinusLow MinusSizeSize 1-Low1-Low 22 33 4-High High Liq.4-High High Liq.

------------------------------------------------------------------------------------------------------------------------------------------------------------------1-Small1-Small 17.35%17.35% 15.99%15.99% 12.42%12.42% 4.09%4.09% 13.27%13.27%22 16.2416.24 14.1014.10 10.5510.55 4.664.66 11.5711.5733 14.4814.48 13.8813.88 11.9811.98 7.897.89 6.696.694-Large4-Large 11.8911.89 11.0111.01 10.7810.78 8.478.47 3.423.42

------------------------------------------------------------------------------------------------------------------------------------------------------------------Small MinusSmall Minus

LargeLarge 5.465.46 4.984.98 1.651.65 -4.38-4.38

Data from 1972-2008Data from 1972-2008


Duff & Phelps, LLC Risk Premium Duff & Phelps, LLC Risk Premium ReportReport

(Formerly the Standard & Poor’s Corporate Value

Consulting Risk Premium Report) 2009 now out Roger Grabowski and David King

BiographyMr. Grabowski, ASA, is a Managing Director in the Duff & Phelps valuation practice

Mr. King, CFA, is National Technical Director of Valuation Services at Mesirow Financial Consulting

Size Study Exhibits and tables - data updated through Exhibits and tables - data updated through Dec. 31, 2008Dec. 31, 2008 Exhibits A-1 through A-8 – Risk premiums Exhibits A-1 through A-8 – Risk premiums

vs. company size (25 portfolios and eight vs. company size (25 portfolios and eight measures of size)measures of size)

(A-1 and A-2 included in this presentation)(A-1 and A-2 included in this presentation) Exhibits B-1 through B-9 – Premiums over Exhibits B-1 through B-9 – Premiums over CAPM vs. company size (25 portfolios CAPM vs. company size (25 portfolios and eight measures of size)and eight measures of size) (B-1 and B-2 included in this presentation)(B-1 and B-2 included in this presentation)


Estimating Required Rates Estimating Required Rates of Returnsof Returns

If we are using a “build-up” method, we want to determine a premium over the riskless rate


Estimating Required Rates Estimating Required Rates of Returnsof Returns

Must use “in Must use “in excess of excess of CAPM” size CAPM” size premium when premium when using the using the MCAPMMCAPM


Risk Study

Exhibits C-1 through C-8 – Relation between Exhibits C-1 through C-8 – Relation between size and company risk (25 size portfolios and size and company risk (25 size portfolios and eight measures of size)eight measures of size)– Shows relationship of size to beta, unlevered Shows relationship of size to beta, unlevered

beta, operating margin, CV (operating margin, beta, operating margin, CV (operating margin, CV (ROE), risk premium, debt to MVIC, etc.CV (ROE), risk premium, debt to MVIC, etc.

Exhibits D-1 through D-3 – Risk premiums vs. Exhibits D-1 through D-3 – Risk premiums vs. company risk (25 portfolios and three measures company risk (25 portfolios and three measures of risk) ranked by risk indicatorof risk) ranked by risk indicator (D-1 included in this presentation)(D-1 included in this presentation)


New and Supplemental ExhibitsExhibit E Exhibit E (new in 2009)(new in 2009)– Eight size measures in portfolio 25 onlyEight size measures in portfolio 25 only

Percentiles 5, 25, 50, 75 and 95Percentiles 5, 25, 50, 75 and 95Summaries after exhibit ESummaries after exhibit E– Premiums over long-term riskless rate (premium and Premiums over long-term riskless rate (premium and

smoothed premium)smoothed premium)Eight measures of sizeEight measures of sizeThree accounting measures of riskThree accounting measures of risk

– Premiums over CAPM (premium and smoothed Premiums over CAPM (premium and smoothed premium)premium)

Eight measures of sizeEight measures of size


Duff & Phelps Size Duff & Phelps Size PremiumPremium

Categorizes public companies into 25 size-Categorizes public companies into 25 size-ranked portfolios for ranked portfolios for eight different eight different measuresmeasures of size: of size: 1.1.Market value of common equityMarket value of common equity2.2.Book value of common equityBook value of common equity3.3.5-year average net income5-year average net income4.4.Market value of invested capitalMarket value of invested capital5.5.Total assetsTotal assets6.6.5-year average EBITDA5-year average EBITDA7.7.Net salesNet sales8.8.Number of employeesNumber of employees


Description of the Data

Study made use of the CRSP database together with Standard & Poor's Compustat database (1963)

NYSE/AMEX/NASDAQ

Intersection of the CRSP universe and the Compustat universe

Excluded financial service companies (SIC 6) – Some of the financial data used in the study are

difficult to apply in the financial sector – Companies in the financial services sector were

poorly represented during the early years of the Compustat database


Description of the Data

For each year since 1963, filtered the universe of companies to exclude the following:– Companies lacking 5 years of publicly traded

price history– Companies with sales below $1 million in any of

the previous five fiscal years– Companies with a negative 5-year-average

EBITDA for the previous five fiscal years


High Financial Risk CompaniesSeparate portfolio was created for companies with any one of the following characteristics:– In bankruptcy or in liquidation– 5-year-average net income available to common

equity for the previous five years less than zero– 5-year-average operating income for the

previous five years– Negative book value of equity at any of the

previous five fiscal year-ends– Debt-to-total capital of more than 80%


Build-Up MethodUse the historical risk premiums over the long-term risk-free rate in exhibits A-1 through A-8

The "smoothed" average risk premium is the most appropriate indicator for most of the portfolio groups

At the largest-size and smallest-size ends of the range, the average historical risk premiums tend to jump off of the smoothed line– Particularly ranked by market value


Build-Up Method

Required rate of return for a company that is significantly smaller than the 25th portfolio?

It may be appropriate to extrapolate the risk premium to smaller sizes using the regression relationships used in deriving the “smoothed” premiums

As a general rule one should be cautious about extrapolating a statistical relationship far beyond the range of the data used in the analysis


Estimating Required Rates of Return - Build Up

EXAMPLE: Assume the subject company has the following characteristics:

Market Value of Equity $120 million

Book Value of Equity $100 million

5-year Average Net Income $ 10 million

Market Value of Invested Capital $180 million

Total Assets $300 million

5-year Average EBITDA $ 30 million

Sales $250 million

Number of Employees 200


Build-Up Method

Exhibits A-1 through A-8

Risk Premiums (Market plus Size) over Risk-free Rate: Using Guideline Portfolios(EXAMPLE 1) Company Relevant Guideline Premium

Size Exhibit Portfolio Over Risk freeMarket Value of Equity $120 mil. A-1 25 12.4%Book Value of Equity $100 mil. A-2 25 10.9%5-year Average Net Income $10 mil. A-3* 24 10.5%Market Value of Invested Capital $180 mil. A-4* 25 12.0%Total Assets $300 mil. A-5* 24 10.0%5-year Average EBITDA $30 mil. A-6* 24 10.2%Sales $250 mil. A-7* 24 9.6%Number of Employees 200 A-8* 25 10.6%

Mean premium over risk-free rate 10.8%Median premium over risk-free rate 10.6%


Build-Up MethodWith a risk-free rate as of the valuation date of 4.5% (say)

Premiums would indicate a required rate of return on equity ranging from 14.1% to 16.9%

Mean average of 15.3%

Median average of 15.1%.


Ibbotson Industry Risk Premiums (IRPs)

Can you use the D&P Size Study in conjunction with the industry risk premium data as published in the SBBI Valuation Edition Yearbook

The SBBI formula for the industry risk premia is as follows:

IRP = (FI-beta x RPm ) – RPm

where:– IRP = Industry Risk Premium– FI-beta = Full-information beta for industry

– RPm = ERP estimate used in calculating IRP


IRPsIbbotson uses the long-term, historical risk premiums measured from 1926 through the most recent period – 6.5%For 1963 through 2007 averaged 3.84%

Need to adjust for the differences in the estimated equity premium

Example: Assume that the SBBI IRP equaled -2.19 percent

Assume your ERP estimate is 6.0% vs. SBBI 6.5%


IRPs

New IRP = SBBI IRP x (New ERP estimate / SBBI historical ERP estimate)

-2.02 = -2.19 x (6.0% / 6.5%)


IRPsContinuing with example above, one can then use that industry risk premium and the risk premium data from exhibits A-1 through A-8 as follows:

Risk-free rate 4.5%Risk premium (ERP plus Size Premium) 12.76% (median from Example 1)Industry risk premium -2.02%Indicated cost of equity capital

(before consideration of RPu , if any) 15.24%

Caution the user that this may result in double counting of the beta effect

Preferable use of the IRP on the next slide


Risk Premiums over CAPM: Using Guideline Portfolios Company Relevant Guideline Premium

Size Exhibit Portfolio over CAPM

Market Value of Equity $120 mil. B-1 25 7.1%

Book Value of Equity $100 mil. B-2 25 5.7%

5-year Average Net Income $10 mil. B-3* 24 5.5%

Market Value of Invested

Capital $180 mil. B-4* 25 6.7%

Total Assets $300 mil. B-5* 24 5.0%

5-year Average EBITDA $30 mil. B-6* 24 5.2%

Sales $250 mil. B-7* 24 4.8%

Number of Employees 200 B-8* 25 5.9%

Mean risk premium over CAPM 5.7%

Median risk premium over CAPM 5.6%


IRPsAssume the size premium derived from exhibits B-1 through B-8 is 5.6% (from exhibit 3)

Risk-free rate 4.5%ERP estimate from Risk Premium Report 6.0%Industry risk premium -2.02%Industry CAPM 8.48%Size premium 5.6%Indicated cost of equity capital (before consideration of RPu , if any) 14.08%

Eliminates any double counting of beta risk that may be included in the size premium


Historical Risk Premiums and Company Risk

Part II of the report examines three separate measures of risk:– Operating margin (the lower the operating margin,

the greater the risk)– Coefficient of variation in operating margin (the

greater the coefficient of variation, the greater the risk)

– Coefficient of variation in return on equity (the greater the coefficient of variation, the greater the risk)

Coefficient of variation is the standard deviation divided by the mean - It measures volatility


Historical Risk Premiums and Company Risk

Are they mixing a "size" effect with a "risk" effect when measuring company size by "market value“

Market value is not just a function of "size"; it is also a function of the discount rate

Therefore, some companies will not be risky (high discount rate) because they are small, but instead will be "small" (low market value) because they are risky

This motivated D&P to consider alternative measures of "size" in previous articles and reports


Coefficient of Variation of Operating Margin:

(Standard Deviation of Operating Margin)/

(Average Operating Margin)

2008 2007 2006 2005 2004

Net Sales $900 $800 $850 $750 $900

Operating Income $150 $120 $130 $ 80 $140

Operating Margin 16.7% 15.0% 15.3% 10.7% 15.6%

Standard Deviation of Op. Margin 2.3%

Average Operating Margin 14.6%

Coefficient of Variation 15.8%


Coefficient of Variation of Return on Book Value of Equity:

(Standard Deviation of ROE) / (Average of ROE)(Example 5)

2008 2007 2006 2005 2004

Book Value $820 $710 $630 $540 $500

Net Income before

extraordinary items $110 $ 80 $ 90 $ 40 $100

Return on Book Equity

(BOE) 13.4% 11.3% 14.3% 7.4% 20.0%

Standard Deviation of ROE 4.6%

Average ROE 13.3%

Coefficient of Variation 34.7%


Risk Premiums over Risk-free Rate: Using Guideline Portfolios(Example 6)

Company Relevant Guideline Premium

Indicator Exhibit Portfolio over

Risk-free

Operating Margin 14.6% D-1 8 7.2%

CV (Operating margin) 15.8% D-2* 14 8.1%

CV (ROE) 34.7% D-3* 13 8.1%

Mean risk premium over risk-free rate 7.8%

Median risk premium over risk-free rate 8.1%


Application

Assume a risk-free rate of 4.5% and in Assume a risk-free rate of 4.5% and in isolation from other factorsisolation from other factors– Equity returns ofEquity returns of

11.7% based on operating margin (OM)11.7% based on operating margin (OM)12.6% based on CV of OM12.6% based on CV of OM12.6% based on CV of ROE12.6% based on CV of ROE

Mean average of 12.3%Mean average of 12.3%Median average of 12.6%Median average of 12.6%


AdjustmentsThe risk premiums are historical averages since 1963

Also report the average historical risk premium over the same period for the SBBI Large Company stocks (essentially the S&P 500)– This average was 3.84% over the period 1963-2008

If one’s estimate of the equity risk premium for the S&P 500 on a forward-looking basis (“ERP”) were materially different from the average historical risk premium since 1963– May be reasonable to assume that the other historical

portfolio returns reported here would differ on a forward-looking basis by approximately a similar differential

risk premium data: ibbotson vs. duff

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