VALCON Morningstar v. Duff & Phelps

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1 VALCON 2010 Size Premia: Morningstar v. Duff & Phelps Roger J. Grabowski, ASA Duff & Phelps, LLC Co-author with Shannon Pratt of Cost of Capital: Applications and Examples, 3 rd ed. (Wiley 2008) and 4th ed. (Wiley, forthcoming 2010) roger.grabowski@duffandphelps.com February 24, 2010 Disclaimer Any opinions presented in this seminar are those of Roger J. Grabowski and do not represent the official position of Duff & Phelps, LLC. This material is offered for educational purposes with the understanding that neither the author or Duff & Phelps, LLC are not engaged in rendering legal, accounting or any other professional service through presentation of this material. The information presented in this seminar has been obtained with the greatest of care from sources believed to be reliable, but is not guaranteed to be complete, accurate or timely. The author and Duff & Phelps LLC expressly disclaim any liability, including incidental or consequential damages, arising from the use of this material or any errors or omissions that may be contained in it. 2 1

2 The Size Effect Empirical evidence suggests that investments in small capitalization (small market value) companies have earned greater historical rates of return than investments t in large capitalization ti companies over the longterm. Empirical evidence suggests that CAPM (beta - adjusted return) tends to underestimate historical rates of return on small companies (i.e., beta - adjusted return too low) SBBI Yearbook has documented this effect: Size-based (where size is measured by market value) premiums over return predicted using textbook CAPM Based on 10 size (where size is measured by market value) deciles Correction to textbook CAPM: add premium to the return predicted by the textbook CAPM to adjust expected return for smaller companies. 3 The Size Effect SBBI Valuation Edition 2000 Yearbook In the (textbook) CAPM, only systematic or beta risk is rewarded; small company stocks have had returns in excess of those implied by their betas. calendar annual return differences between small and large companies are serially correlated. the firm size effect is seasonal. the excess return is especially pronounced for micro cap stocks (deciles 9-10). The size-related phenomenon has prompted a revision to the CAPM, which includes a size premium. 4 2

3 Why Do Companies With Small Equity Value Get High Returns? Reward for risk of smaller companies? Losers? Big companies with high risk Financial distress? Big or small companies in trouble High leverage? Big or small companies with high financial risk New companies? Speculative new technology or new market entrants 5 Berk Critique of Size Premium Berk, A Critique of Size Related Anomalies, Review of Financial Studies (1995) and Does Size Really Matter?, Financial Analyst Journal (Sept./Oct. 1997). Riskier companies have higher discount rates Higher discount rates results in lower market values Therefore: low market value portfolios get high returns This does not mean small size is rewarded with high returns Berk s argument concerns ranking by market value Ranking by other criteria eliminates possible bias 6 3

4 Are Small Companies Riskier Than Comparable Large Companies? Long and Zhang, Growth Options, Unwritten Call Discounts and Valuing Small Firms, working paper (March 2004). Research shows that t small public cos earn higher h rates of return and have lower multiples than large, widely-held cos Risks include lack of liquidity and lack of information But valuing small co is not same as valuing scaled down large co Potential competitor can more easily enter real market and take value from small co Large cos have resources to better adjust to competition and avoid bankruptcy Small cos undertake less R&D, spend less on advertising, giving less control over product demand and potential competition Small cos have fewer resources to fend off competition and redirect themselves after changes in market occurs 7 Are Small Companies Riskier Than Comparable Large Companies? (cont d) Define: Value = E 1 / k + PVGO Call where: E 1 / k = value of assets in place PVGO = present value of future growth options Call = unwritten call - value that can be taken by potential competition that can enter the market and destroy value Small companies have larger unwritten call against their value from prospective new competition vs. larger firms Value of unwritten call option increases with volatility; unsystematic risk (variance of returns) of small companies > than unsystematic risk of large companies, increasing value of unwritten call Study survival of small companies find large companies can better handle change in competitive environment over time Though size and variance of returns highly correlated, find unwritten call option against small company value larger than predicted by variance (i.e., find size premium) 8 4

5 Build-Up Method and Adjustment for Size Three alternative formulations: Risk-Free Rate Risk-Free Rate Risk-Free Rate + RP m + RP m + D&P Risk + Size Premium + Small Stock Premium Beta Adj. Premium (Exh A-1 to A-8) + Other Factors + Other Factors + Other Factors = Cost of Equity = Cost of Equity = Cost of Equity How do we measure size? 9 Build-up Method: How do we Measure Size? Market value: only SBBI measure - Data options: CRSP 9-10 CRSP 10 CRSP 10a (10w and 10x) and 10b (10y and 10z) Small Cap Series D&P Risk Premium Report-Size Study - 8 size measures and 25 risk premium categories Calculation options: Returns in excess of returns expected given beta (return in excess of CAPM) beta - adjusted size premium Small stock returns in excess of large stock returns - small stock premium Total risk premium in excess of T-bonds (RP m plus size premium) 10 5

6 Morningstar SBBI Studies Exhibit 13.1 Returns in CAPM with S&P 500 Benchmark Term Returns in CAPM Estimation for Decile Portfolios of the NYSE/AMEX/NASDAQ, Decile Beta * Arithmetic Mean Return Realized Riskless Estimated Riskless Size Premium ( Rate Rate CAPM) 1-Largest % 5.56% 5.91% 0.36% % 7.31% 6.69% 0.62% % 7.87% 7.13% 0.74% % 8.25% 7.28% 0.97% % 9.03% 7.49% 1.54% % 9.28% 7.65% 1.63% % 9.65% 8.03% 1.62% % 10.76% 8.41% 2.35% % 11.42% 8.71% 2.71% 10-Smallest % 14.93% 9.12% 5.81% Mid-Cap, % 8.18% 7.24% 0.94% 5 Low-Cap, % 9.66% 7.92% 1.74% 8 Micro-Cap, % 12.52% 8.79% 3.74% * Betas are estimated from monthly portfolio total returns in excess of the 30-day U.S. Treasury bill total return versus the S&P 500 total returns in excess of the 30-day U.S. Treasury bill, January 1926-December Historical riskless rate is measured by the 83-year arithmetic mean income return component of 20-year U.S. government bonds (5.20 percent). Source: Shannon Pratt and Roger Grabowski, Cost of Capital: Applications and Examples, 4th ed. (John Wiley & Sons, 2010). Used with permission. All Rights Reserved. 11 Returns in CAPM: Long-term Returns in CAPM Estimation for Decile Portfolios of the NYSE/ AMEX/ NASDAQ, Decile Beta * Arithmetic Mean Return Realized Risk-free Rate Estimated Risk-free Rate Size Premium ( CAPM) Standard Deviation of Realized Excess Return 1-Largest % 3.30% 3.74% 0.44% 17.05% % 4.59% 3.96% 0.63% 17.58% % 5.78% 4.18% 1.60% 18.66% % 5.79% 4.21% 1.58% 20.12% % 6.17% 4.19% 1.98% 20.82% % 7.06% 4.31% 2.75% 22.51% % 6.66% 4.43% 2.23% 23.58% % 7.82% 4.52% 3.30% 25.94% % 7.18% 4.39% 2.79% 27.39% % 856% 8.56% 412% 4.12% 4.44% 44% 32.30% 30% Smallest * Betas are estimated from monthly portfolio total returns in excess of the 30-day U.S. Treasury bill total return versus the S&P 500 total returns in excess of the 30-day U.S. Treasury bill, January 1959 December 2008, January 1969 December 2008, January 1979 December 2008, and January 1989 December Historical risk-free rate is measured by the arithmetic mean income return component of 20-year U.S. government bonds for each period. Calculated in the context of the CAPM by multiplying the equity risk premium by beta. The equity risk premium is estimated by the arithmetic mean total return of the S&P 500 minus the arithmetic mean income return component of 20-year U.S. government bonds for each period. Source: Calculated (or derived) based on CRSP data, Copyright 2009 Center for Research in Security Prices (CRSP ), Graduate School of Business, The University of Chicago. Calculations performed by Duff & Phelps LLC. Used with permission. All rights reserved. Source: Shannon Pratt and Roger Grabowski, Cost of Capital: Applications and Examples, 4th ed. (John Wiley & Sons, 2010). Used with permission. All Rights Reserved. 12 6

7 Returns in CAPM: Long-term Returns in CAPM Estimation for Decile Portfolios of the NYSE/AMEX/ NASDAQ, Decile Beta * Arithmetic Mean Return Realized Risk-free Rate Estimated Risk-free Rate Size Premium ( Ecessof Excess CAPM) Standard Deviation of Realized ed Excess Return 1-Largest % 2.77% 3.11% 0.34% 18.05% % 3.83% 3.30% 0.53% 18.76% % 4.71% 3.48% 1.23% 19.61% % 4.61% 3.50% 1.11% 20.82% % 4.70% 3.49% 1.21% 20.95% % 5.51% 3.56% 1.95% 22.85% % 4.96% 3.66% 1.30% 23.50% % 5.50% 3.75% 1.75% 25.22% % 4.76% 3.67% 1.09% 26.54% 10- Smallest % 5.13% 3.43% 1.70% 30.01% * Betas are estimated from monthly portfolio total returns in excess of the 30-day U.S. Treasury bill total return versus the S&P 500 total returns in excess of the 30-day U.S. Treasury bill, January 1959 December 2008, January 1969 December 2008, January 1979 December 2008, and January 1989 December Historical risk-free rate is measured by the arithmetic mean income return component of 20-year U.S. government bonds for each period. Calculated in the context of the CAPM by multiplying the equity risk premium by beta. The equity risk premium is estimated by the arithmetic mean total return of the S&P 500 minus the arithmetic mean income return component of 20-year U.S. government bonds for each period. Source: Shannon Pratt and Roger Grabowski, Cost of Capital: Applications and Examples, 4th ed. (John Wiley & Sons, 2010). Used with permission. All Rights Reserved. 13 Returns in CAPM: Long-term Returns in CAPM Estimation for Decile Portfolios of the NYSE/AMEX/ NASDAQ, Decile Beta * Arithmetic Mean Return Realized Risk-free Estimated Risk-free Size Premium ( Standard Deviation of Realized Rate Rate CAPM) Excess Return 1-Largest % 4.59% 4.86% -0.27% 17.89% % 6.01% 5.04% 0.97% 17.44% % 6.02% 5.30% 0.72% 17.97% % 6.13% 5.24% 0.89% 17.88% % 6.05% 5.20% 0.85% 18.28% % 6.96% 4.37% 1.59% 20.62% % 6.34% 5.41% 0.93% 20.27% % 6.97% 5.53% 1.44% 22.10% % 6.80% 5.31% 1.49% 23.64% 10- Smallest % 6.48% 4.81% 1.67% 27.27% * Betas are estimated from monthly portfolio total returns in excess of the 30-day U.S. Treasury bill total return versus the S&P 500 total returns in excess of the 30-day U.S. Treasury bill, January 1959 December 2008, January 1969 December 2008, January 1979 December 2008, and January 1989 December Historical risk-free rate is measured by the arithmetic mean income return component of 20-year U.S. government bonds for each period. Calculated in the context of the CAPM by multiplying the equity risk premium by beta. The equity risk premium is estimated by the arithmetic mean total return of the S&P 500 minus the arithmetic mean income return component of 20-year U.S. government bonds for each period. Source: Shannon Pratt and Roger Grabowski, Cost of Capital: Applications and Examples, 4th ed. (John Wiley & Sons, 2010). Used with permission. All Rights Reserved. 14 7

8 Returns in CAPM: Long-term Returns in CAPM Estimation for Decile Portfolios of the NYSE/ AMEX/ NASDAQ, Decile Beta * Arithmetic Mean Return Realized Risk-free Rate Estimated Risk-free Rate Size Premium ( CAPM) Standard Deviation of Realized Excess Return 1-Largest % 4.17% 4.10% 0.07% 20.43% % 5.08% 4.15% 0.93% 19.53% % 4.85% 4.46% 0.39% 20.55% % 4.73% 4.28% 0.45% 19.62% % 4.70% 4.34% 0.36% 20.02% % 5.45% 4.46% 0.99% 22.67% % 5.14% 4.38% 0.76% 21.65% % 5.64% 4.49% 1.25% 23.29% % 21% 6.00% 4.28% 1.72% 25.81% 10- Smallest % 6.92% 3.80% 3.12% 30.35% * Betas are estimated from monthly portfolio total returns in excess of the 30-day U.S. Treasury bill total return versus the S&P 500 total returns in excess of the 30-day U.S. Treasury bill, January 1959 December 2008, January 1969 December 2008, January 1979 December 2008, and January 1989 December Historical risk-free rate is measured by the arithmetic mean income return component of 20-year U.S. government bonds for each period. Calculated in the context of the CAPM by multiplying the equity risk premium by beta. The equity risk premium is estimated by the arithmetic mean total return of the S&P 500 minus the arithmetic mean income return component of 20-year U.S. government bonds for each period. Source: Shannon Pratt and Roger Grabowski, Cost of Capital: Applications and Examples, 4th ed. (John Wiley & Sons, 2010). Used with permission. All Rights Reserved. 15 Reasons for Size Effect - Betas Misspecified? Ibbotson, Kaplan and Peterson, Estimate of Small Stock Betas are Much Too Low, Journal of Portfolio Management (Summer, 1997). Betas estimates based on OLS regression of 60 months data severely biased downwards for small market value firms Traditional OLS beta found to be unrelated to future returns Adjusted estimates of beta provide better estimates of expected returns: Traditional OLS beta: R t -R ft = α + β x (R mt -R ft ) + e t Lagged beta: R t - R ft = α + β x (R mt - R ft ) + β -1 x (R mt-1 - R ft-1 ) + u t Sumβeta = β + β -1 Explains part of size effect, but not all. 16 8

9 Reasons for Size Effect - Betas Misspecified? (cont d) SUMβ 1.4 Beta β Size Portfolios 17 Size Premium Using Sum Betas Table 14.1 Size Premium Using Sum Betas Long-term Returns in CAPM for Decile Portfolios of the NYSE/AMEX/NASDAQ, with sum Beta Decile Sum Beta * Arithmetic Mean Return Estimated Size Premium Riskless Rate Riskless Rate ( CAPM) 1-Largest % 5.56% 5.91% 0.35% % 7.31% 6.82% 0.49% % 7.87% 7.34% 0.53% % 8.25% 7.76% 0.48% % 9.03% 8.00% 1.03% Betas are estimated from monthly portfolio total returns in excess of the 30-day U.S. Treasury bill total return versus the S&P 500 Index total returns in excess of the 30-day U.S. Treasury bill, January 1926 December 2008 Historical riskless rate is measured by the 83-year arithmetic mean income return component of 20-year U.S. government bonds (5.20%) Calculated in the context of the CAPM by multiplying the equity risk premium by beta. The equity risk premium is estimated by the arithmetic mean total return of the S&P 500 (11.67%) minus the arithmetic mean income return component of 20-year U.S. government bonds (5.20%) from 1926 to

10 Size Premium Using Sum Betas (cont d) Decile Sum Beta * Arithmetic Mean Return Estimated Riskless Rate Size Premium Riskless Rate ( CAPM) % 9.28% 8.39% 0.88% % 9.65% 8.93% 0.71% % 10.76% 9.68% 1.08% % 11.42% 10.06% 1.37% 10- Smallest % 14.93% 11.06% 3.87% Betas are estimated from monthly portfolio total returns in excess of the 30-day U.S. Treasury bill total return versus the S&P 500 Index total returns in excess of the 30-day U.S. Treasury bill, January 1926 December 2008 Historical riskless rate is measured by the 83-year arithmetic mean income return component of 20-year U.S. government bonds (5.20%) Calculated in the context of the CAPM by multiplying the equity risk premium by beta. The equity risk premium is estimated by the arithmetic mean total return of the S&P 500 (11.67%) minus the arithmetic mean income return component of 20-year U.S. government bonds (5.20%) from 1926 to Size Premium Using Sum Betas (cont d) Decile Sum Beta * Arithmetic Mean Return Mid-Cap, 3 5 Low-Cap, 6 8 Micro-Cap, 9 10 Estimated Riskless Rate Size Premium Riskless Rate ( CAPM) % 8.18% 7.58% 0.59% % 9.66% 8.82% 0.83% % 12.52% 10.34% 2.18% Betas are estimated from monthly portfolio total returns in excess of the 30-day U.S. Treasury bill total return versus the S&P 500 Index total returns in excess of the 30-day U.S. Treasury bill, January 1926 December 2008 Historical riskless rate is measured by the 83-year arithmetic mean income return component of 20-year U.S. government bonds (5.20%) Calculated in the context of the CAPM by multiplying the equity risk premium by beta. The equity risk premium is estimated by the arithmetic mean total return of the S&P 500 (11.67%) minus the arithmetic mean income return component of 20-year U.S. government bonds (5.20%) from 1926 to Source: Ibbotson Stocks, Bonds, Bills, and Inflation 2009 Valuation Yearbook. Copyright 2009 Morningstar, Inc. All rights reserved. Used with permission. (Morningstar, Inc. acquired Ibbotson in 2006.) Calculated (or derived) based on CRSP data, Copyright 2006 Center for Research in Security Prices (CRSP ), Graduate School of Business, The University of Chicago. Source: Shannon Pratt and Roger Grabowski, Cost of Capital: Applications and Examples, 4th ed. (John Wiley & Sons, 2010). Used with permission. All Rights Reserved

11 Returns in CAPM 10th Decile Split Exhibit 14.2 Returns in CAPM Tenth-Decile Split Long-term Returns in CAPM Estimation for Decile Portfolios of the NYSE/AMEX?NASDAQ, with 10 th Decile Split, Decile Beta * Arithmetic Mean Return Realized Riskless Rate Estimated Riskless Rate Size Premium ( CAPM) 1-Largest % 5.56% 5.91% 0.36% % 7.31% 6.69% 0.62% % 7.87% 7.13% 0.74% % 8.25% 7.28% 0.97% % 9.03% 7.49% 1.54% % 9.28% 7.65% 1.63% * Betas are estimated from monthly portfolio total returns in excess of the 30-day U.S. Treasury bill total return versus the S&P 500 total returns in excess of the 30-day U.S. Treasury bill, January 1926 December Historical riskless rate is measured by the 83-year arithmetic mean income return component of 20-year U.S. government bonds (5.20%). Calculated in the context of the CAPM by multiplying the equity risk premium by beta. The equity risk premium is estimated by the arithmetic mean total return of the S&P 500 (11.67%) minus the arithmetic mean income return component of 20-year U.S. government bonds (5.20%) from For Mid, Low and Micro Cap data see Exhibit Source: Stocks, Bonds, Bills, and Inflation 2009 Valuation Yearbook and 2009 Ibbotson SBBI Valuation Supplement. Copyright 2009 Morningstar, Inc. All rights reserved. Used with permission. (Morningstar, Inc. acquired Ibbotson in 2006.) Calculated (or derived) based on CRSP data, Copyright 2009 Center for Research in Security Prices (CRSP ), Graduate School of Business, The University of Chicago. 21 Returns in CAPM 10th Decile Split (cont d) Decile Beta * Arithmetic Mean Return Realized Riskless Estimated Riskless Size Premium ( Rate Rate CAPM) % 9.65% 8.03% 1.62% % 10.76% 8.41% 2.35% % 11.42% 8.71% 2.71% 10a % 13.29% 9.19% 4.11% 10b- Smallest % 18.48% 8.95% 9.53% * Betas are estimated from monthly portfolio total returns in excess of the 30-day U.S. Treasury bill total return versus the S&P 500 total returns in excess of the 30-day U.S. Treasury bill, January 1926 December Historical riskless rate is measured by the 83-year arithmetic mean income return component of 20-year U.S. government bonds (5.20%). Calculated in the context of the CAPM by multiplying the equity risk premium by beta. The equity risk premium is estimated by the arithmetic mean total return of the S&P 500 (11.67%) minus the arithmetic mean income return component of 20-year U.S. government bonds (5.20%) from For Mid, Low and Micro Cap data see Exhibit Source: Stocks, Bonds, Bills, and Inflation 2009 Valuation Yearbook and 2009 Ibbotson SBBI Valuation Supplement. Copyright 2009 Morningstar, Inc. All rights reserved. Used with permission. (Morningstar, Inc. acquired Ibbotson in 2006.) Calculated (or derived) based on CRSP data, Copyright 2009 Center for Research in Security Prices (CRSP ), Graduate School of Business, The University of Chicago. Source: Shannon Pratt and Roger Grabowski, Cost of Capital: Applications and Examples, 4th ed. (John Wiley & Sons, 2010). Used with permission. All Rights Reserved

12 Duff & Phelps (D&P) Risk Premium Report- Size Study Research into the relationship between company size and equity risk premiums realized Applications to cost of capital estimation using buildup method: measures historical realized risk premiums including size premium since 1963: market risk premium plus size premium (RP m plus size premium) Size is proxy for risk Complement/alternative to SBBI Yearbook data 23 Research on Company Size Initiated by Grabowski in 1990 Uses CRSP and Compustat databases Original article: June 95 Business Valuation Review Alternative measures of size rather than just market value Sept. 96 and March 97 Business Valuation Review D&P Risk Premium Report formerly published by Price Waterhouse, PricewaterhouseCoopers and Standard & Poor s Corporate Value Consulting Risk Premium Report annually updated at Morningstar: Business Valuation Resources: ValuSource:

13 D&P Research on Company Size Investigated relation between size and historical returns Sorted companies by size into 25 portfolios Used eight measures of size Average premiums over bonds since 1963 Result: Small companies have earned higher returns whether size is measured by market value or fundamental size measures 25 Data Base Created for Study Only look at the following types of companies: Publicly traded for 5 years Established history of sales (exclude companies with sales below $1 million in any of the previous five fiscal years) Positive operating profits (exclude companies with negative 5-year average EBIDA) 26 13

14 Data Base Created for Study (cont d) Isolate distressed or challenged companies and put into high-financial-risk portfolios: Bankrupt or liquidating Negative book value of equity History of net losses (companies with 5-year average not less than zero) High leverage (debt-to-total > 80%) 27 Data Base Created for Study (cont d) Company characteristics after the clean up Publicly traded for 5 years Established history of sales and profitability Positive book value Debt/MVIC < 80% 28 14

15 D&P Risk Premium Report Measures of Size Market value of equity (same as SBBI Yearbook) Book value of equity Net income Market value of Invested Capital ( MVIC ) Book value of Invested Capital EBITDA Sales Number of employees 29 Exhibit 13.7 Duff & Phelps Size Study : Risk Premiums for Use in Build-up Method: Companies Ranked by Market Value of Equity Historic Equity Risk Premium: Average Since 1963 Equity Risk Premium Study: Data through December 31, 2008 Data for Year Ending December 31, 2008 Data Smoothing with Regression Analysis Dependent Variable: Average 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 (SumBeta) Deviation Average Average Average Risk Average Risk Debt/ Regression Output: by Size ($mils.) Mkt Value 2008 Since '63 of Returns Return Return Premium Premium MVIC Constant % Std Err of Y Est 1.044% 1 127, % 9.63% 10.97% 3.93% 1.51% 14.76% R Squared 85% 2 36, % 9.92% 11.25% 4.21% 3.44% 21.09% No. of Observations , % 8.75% 10.11% 3.07% 4.25% 22.87% Degrees of Freedom , % 10.18% 11.63% 4.59% 4.70% 23.85% 5 12, % 9.99% 99% 11.34% 4.30% 5.11% 24.47% 47% X Coefficient(s) % 6 9, % 11.19% 12.60% 5.56% 5.53% 24.37% Std Err of Coef % 7 7, % 11.72% 13.32% 6.28% 5.95% 25.13% t-statistic , % 10.88% 12.43% 5.39% 6.33% 24.03% 9 4, % 12.30% 14.12% 7.08% 6.57% 23.52% Smoothed Premium = % % * Log(Market Value) 10 3, % 11.17% 12.76% 5.72% 6.86% 24.40% 11 3, % 12.69% 14.87% 7.83% 7.08% 22.99% 12 2, % 11.06% 12.76% 5.72% 7.32% 24.08% 13 2, % 11.88% 13.64% 6.60% 7.46% 20% Smoothed Premium vs. Unadjusted Average 24.10% 14 2, % 12.68% 14.81% 7.77% 7.66% 24.53% 18% 15 2, % 11.69% 13.58% 6.54% 7.84% 25.14% 16 1, % 13.15% 15.21% 8.17% 8.06% 24.32% 16% 17 1, % 14.48% 16.55% 9.51% 8.29% 24.06% 14% 18 1, % 13.05% 15.45% 8.41% 8.52% 24.68% 19 1, % 12.77% 15.13% 8.09% 8.73% 24.91% 12% % 13.30% 16.11% 9.07% 9.01% 25.28% 10% % 14.69% 17.22% 10.18% 9.25% 26.38% % 13.09% 15.71% 8.67% 9.53% 26.11% 8% % 14.29% 17.05% 10.01% 10.00% 26.14% 6% % 15.06% 17.78% 10.74% 10.67% 26.47% % 17.48% 21.63% 14.59% 12.36% 29.41% 4% Large Stocks (Ibbotson SBBI data) 9.39% 10.88% 3.84% 0% Small Stocks (Ibbotson SBBI data) 13.07% 15.96% 8.92% Log of Average Market Value of Equity Long-Term Treasury Income (Ibbotson SBBI data) 7.01% 7.04% Source: CRSP, Center for Research in Security Prices. Graduate School of Business, The University of Chicago used with permission. All rights reserved. Calculations by Duff & Phelps LLC. Duff and Phelps, LLC Equity Premium 2% Source: Shannon Pratt and Roger Grabowski, Cost of Capital: Applications and Examples, 4th ed. (John Wiley & Sons, 2010). Used with permission. All Rights Reserved

16 Exhibit 13.8 Duff & Phelps Size Study : Risk Premiums for Use in Build-up Method: Companies Ranked by Book Value of Equity Historic Equity Risk Premium: Average Since 1963 Equity Risk Premium Study: Data through December 31, 2008 Data for Year Ending December 31, 2008 Data Smoothing with Regression Analysis Dependent Variable: Average Premium Independent Variable: Log of Average Book Value of Equity Portfolio Average Log of Number Beta Standard Geometric Arithmetic Arithmetic Smoothed Average Rank Book Val. Average as of (SumBeta) Deviation Average Average Average Risk Average Risk Debt/ Regression Output: by Size ($mils.) Book Val Since '63 of Returns Return Return Premium Premium MVIC Constant % Std Err of Y Est 0.917% 1 37, % 10.10% 11.35% 4.31% 2.87% 24.52% R Squared 79% 2 11, % 10.37% 11.64% 4.60% 4.34% 29.42% No. of Observations , % 12.01% 13.46% 6.42% 4.81% 30.55% Degrees of Freedom , % 10.50% 11.82% 4.78% 5.23% 29.87% 5 4, % 10.92% 12.54% 5.50% 5.60% 27.52% X Coefficient(s) % 6 3, % 10.31% 11.99% 4.95% 599% 5.99% 27.39% Std Err of Coef % 7 2, % 10.99% 12.61% 5.57% 6.26% 26.21% t-statistic , % 11.05% 12.68% 5.64% 6.50% 25.81% 9 1, % 12.01% 13.73% 6.69% 6.69% 25.49% Smoothed Premium = % % * Log(Book Value) 10 1, % 11.52% 13.17% 6.13% 6.83% 26.43% 11 1, % 10.96% 12.54% 5.50% 6.99% 26.88% 12 1, % 12.46% 14.39% 7.35% 7.19% 27.11% 13 1, % 12.41% 14.31% 7.27% 7.34% 25.90% Smoothed Premium vs. Unadjusted Average 20% % 13.23% 15.03% 7.99% 7.47% 25.32% % 13.30% 15.13% 8.09% 7.61% 24.82% 18% % 12.56% 14.47% 7.43% 7.76% 25.73% 16% % 11.99% 14.06% 7.02% 7.93% 24.26% % 12.70% 14.65% 7.61% 8.11% 14% 25.11% % 11.77% 13.91% 6.87% 8.28% 26.53% 12% % 14.36% 16.64% 9.60% 8.43% 26.05% 10% % 14.25% 16.33% 9.29% 8.57% 25.42% % 13.63% 16.13% 9.09% 8.82% 24.70% 8% % 12.87% 15.56% 8.52% 9.17% 25.53% 6% % 15.19% 18.14% 11.10% 9.64% 25.67% % 15.06% 19.04% 12.00% 10.88% 25.71% 4% Large (Ibbotson data) Stocks SBBI 9.39% 10.88% 3.84% 0% Small Stocks (Ibbotson SBBI data) 13.07% 15.96% 8.92% Log of Average Book Value of Equity Long-Term Treasury Income (Ibbotson SBBI data) 7.01% 7.04% Source: CRSP, Center for Research in Security Prices. Graduate School of Business, The University of Chicago used with permission. All rights reserved. Calculations by Duff & Phelps LLC. Duff and Phelps, LLC Equity Premium 2% Source: Shannon Pratt and Roger Grabowski, Cost of Capital: Applications and Examples, 4th ed. (John Wiley & Sons, 2010). Used with permission. All Rights Reserved. 31 CAPM and Adjustment for Size Three alternative formulations: Risk-Free Rate Risk-Free Rate Risk-Free Rate + OLS βeta x RP m + Sumβeta x RP m + Sumβeta x RP m + Size Prem-SBBI + Size Prem-SBBI + Size Prem-D&P OLS βeta Adj Sumβeta Adj Sumβeta Adj + Other Factors + Other Factors + Other Factors = Cost of Equity = Cost of Equity = Cost of Equity How do we measure size? 32 16

17 CAPM: How do we measure size? Market value - only SBBI measure - Data options: CRSP 9-10 CRSP 10 CRSP 10a (10w and 10x) and 10b (10y and 10z) D&P Risk Premium Report-Size Study - 8 size measures and 25 risk premiums Calculation options: Returns in excess of returns predicted given beta (return in excess of return predicted by CAPM) 33 Exhibit Duff & Phelps Size Study : Risk Premiums for Use in CAPM: Companies Ranked by Market Value of Equity: Premium over CAPM Historical Equity Risk Premium: Average Since 1963 Equity Risk Premium Study: Data through December 31, 2008 Data for Year Ending December 31, 2008 Data Smoothing with Regression Analysis Dependent Variable: Premium over CAPM Independent Variable: Log of Average Market Value of Equity Smoothed Portfolio Average Log Beta Arithmetic Arithmetic Indicated Premium Premium Rank Mkt Value of (SumBeta) Average Average Risk CAPM over over Regression Output: by Size ($mils.) Size Since '63 Return Premium Premium CAPM CAPM Constant % Std Err of Y Est 1.048% 1 127, % 3.93% 3.29% 0.64% -1.72% R Squared 78% 2 36, % 4.21% 3.55% 0.67% -0.15% No. of Observations , % 3.07% 3.72% -0.65% 0.52% Degrees of Freedom , % 4.59% 3.76% 0.83% 0.88% 5 12, % 4.30% 3.71% 0.59% 1.22% X Coefficient(s) % 6 9, % 5.56% 3.99% 1.58% 1.56% Std Err of Coef % 7 7, % 6.28% 3.97% 2.31% 1.91% t-statistic , % 5.39% 3.99% 1.40% 2.21% 9 4, % 7.08% 4.25% 2.83% 2.41% Smoothed Premium = % % * Log(Market Value ) 10 3, % 5.72% 4.13% 1.60% 2.65% 11 3, % 7.83% 4.40% 3.43% 2.83% 12 2, % 5.72% 4.31% 1.41% 3.03% Smoothed Premium vs. Unadjusted Average 13 2, % 6.60% 4.19% 2.41% 3.14% 12% 14 2, % 7.77% 4.31% 3.46% 3.31% 15 2, % 6.54% 4.47% 2.07% 3.45% 10% 16 1, % 8.17% 4.42% 3.75% 3.63% 8% 17 1, % 9.51% 4.55% 4.96% 3.82% 18 1, % 8.41% 4.58% 3.83% 4.00% 6% 19 1, % 8.09% 4.59% 3.50% 4.18% % 9.07% 4.83% 4.24% 4.41% 4% % 10.18% 4.79% 5.39% 4.60% 2% % 8.67% 4.83% 3.84% 4.83% % 10.01% 4.71% 5.29% 5.21% 0% % 10.74% 4.88% 5.85% 5.77% % 14.59% 4.94% 9.65% 7.15% -2% Premium over CAPM Large Stocks (Ibbotson SBBI data) 10.88% 3.84% Small Stocks (Ibbotson SBBI data) 15.96% 8.92% -4% Log of Average Market Value of Equity Long-Term Treasury Income (Ibbotson SBBI data) 7.04% Source: CRSP, Center for Research in Security Prices. Graduate School of Business, The University of Chicago used with permission. All rights reserved. Calculations by Duff & Phelps LLC. Duff and Phelps, LLC Source: Shannon Pratt and Roger Grabowski, Cost of Capital: Applications and Examples, 4th ed. (John Wiley & Sons, 2010). Used with permission. All Rights Reserved

18 Exhibit Duff & Phelps Size Study : Risk Premiums for Use in CAPM: Companies Ranked by Book Value of Equity: Premium over CAPM Historical Equity Risk Premium: Average Since 1963 Equity Risk Premium Study: Data through December 31, 2008 Data for Year Ending December 31, 2008 Data Smoothing with Regression Analysis Dependent Variable: Premium over CAPM Independent Variable: Log of Average Book Value of Equity Smoothed Portfolio Average Log Beta Arithmetic Arithmetic Indicated Premium Premium Rank Book Val. of (SumBeta) Average Average Risk CAPM over over Regression Output: by Size ($mils.) Size Since '63 Return Premium Premium CAPM CAPM Constant 9.353% Std Err of Y Est 0.953% 1 37, % 4.31% 3.11% 1.20% -0.16% R Squared 65% 2 11, % 4.60% 3.26% 1.34% 0.91% No. of Observations , % 6.42% 3.45% 2.97% 1.25% Degrees of Freedom , % 4.78% 3.55% 1.23% 1.55% 5 4, % 5.50% 3.89% 1.61% 1.82% X Coefficient(s) % 6 3, % 4.95% 3.88% 1.07% 2.11% Std Err of Coef % 7 2, % 5.57% 3.99% 1.58% 2.31% t-statistic , % 5.64% 4.15% 1.49% 2.48% 9 1, % 6.69% 4.05% 2.64% 2.61% Smoothed Premium = 9.353% % * Log(Book Value) 10 1, % 6.13% 4.12% 2.01% 2.72% 11 1, % 5.50% 4.13% 1.38% 2.83% 12 1, % 7.35% 4.08% 3.27% 2.98% Smoothed Premium vs. Unadjusted Average 13 1, % 7.27% 4.20% 3.07% 3.09% 12% % 7.99% 4.25% 3.73% 3.19% % 8.09% 4.24% 3.85% 3.29% 10% % 7.43% 4.50% 2.93% 3.39% 8% % 7.02% 4.55% 2.47% 3.52% % 7.61% 4.52% 3.09% 3.65% 6% % 6.87% 4.62% 2.25% 3.77% % 9.60% 4.71% 4.89% 3.88% 4% % 9.29% 4.66% 4.63% 3.98% 2% % 9.09% 4.65% 4.45% 4.16% % 8.52% 4.74% 3.78% 4.42% 0% % 11.10% 4.86% 6.24% 4.76% % 12.00% 4.99% 7.00% 5.66% -2% Premium over CAPM Large Stocks (Ibbotson SBBI data) 10.88% 3.84% Small Stocks (Ibbotson SBBI data) 15.96% 8.92% -4% Log of Average Book Value of Equity Long-Term Treasury Income (Ibbotson SBBI data) 7.04% Source: CRSP, Center for Research in Security Prices. Graduate School of Business, The University of Chicago used with permission. All rights reserved. Calculations by Duff & Phelps LLC. Duff and Phelps, LLC Source: Shannon Pratt and Roger Grabowski, Cost of Capital: Applications and Examples, 4th ed. (John Wiley & Sons, 2010). Used with permission. All Rights Reserved. 35 Duff & Phelps Risk Premium Report Risk Study Research the relationship between company risk and return on equity risk premiums Applications to cost of capital estimation using buildup method Measures historical realized risk premiums: market risk premium plus company-specific risk Articles: September 1999 and March 2000, Business Valuation Review Formerly Standard & Poor s CVC Risk Premium Study 36 18

19 Duff & Phelps Measures of Risk Profitability (operating profit margin) Operating profit / revenue Volatility of Earnings Volatility of operating profit margin Volatility of ROE (NI/book value of equity) 37 Measuring Volatility: Coefficient of Variation Coefficient of Variation = Standard Deviation / Mean Example: Coefficient of Variation in Operating Income Margin Average Margin = 15% Standard Deviation of Margin = 5% CV (Op.Inc. Margin) = 5/15 = 33% 38 19

20 How Do These Risk Measures Relate to Rates of Return? Sort companies into 25 portfolios, ranked by risk measures: Operating income margin (Exhibit D-1) CV (operating income margin) (Exhibit D-2) CV (ROE) (Exhibit D-3) Same procedure as used when ranking by size Results: Lower profitability gives higher equity returns Higher earnings volatility gives higher equity returns 39 Exhibit 15.1 Duff & Phelps' Risk Study : Risk Premiums for Use in Build-up Method: Companies Ranked by Operating Margin Historical Equity Risk Premium: Average Since 1963 Equity Risk Premium Study: Data through December 31, 2008 Data for Year Ending December 31, 2008 Data Smoothing with Regression Analysis Dependent Variable: Average Premium Independent Variable: Log of Median Operating Margin Median Log of Number Beta Standard Geometric Arithmetic Arithmetic Smoothed Average Portfolio Operating Median as of (SumBeta) Deviation Average Average Average Risk Average Risk Debt/ Regression Output: Rank Margin Op Margin 2008 Since '63 of Returns Return Return Premium Premium MVIC Constant 1.744% Std Err of Y Est 0.965% % % 11.07% 12.50% 5.46% 4.42% 26.93% R Squared 82% % % 9.31% 10.67% 3.63% 5.23% 29.58% No. of Observations % % 11.09% 12.51% 5.47% 5.81% 28.00% Degrees of Freedom % % 11.53% 12.93% 5.89% 6.16% 24.44% % % 11.54% 13.04% 6.00% 6.45% 20.85% X Coefficient(s) % % % 12.54% 14.24% 7.20% 6.76% 17.75% Std Err of Coef % % % 11.53% 13.19% 6.15% 6.98% 17.76% t-statistic % % 11.41% 13.25% 6.21% 7.23% 19.55% % % 13.83% 15.63% 8.59% 7.44% 19.22% Smoothed Premium = 1.744% % * Log(Operating Margin) % % 13.21% 15.37% 8.33% 7.65% 21.09% % % 11.51% 13.49% 6.45% 7.83% 21.49% % % 12.26% 14.03% 6.99% 8.03% 21.90% % % 12.51% 14.76% 7.72% 8.20% 21.91% Smoothed Premium vs. Unadjusted Average % % 13.38% 15.79% 8.75% 8.38% 22.96% 20% % % 14.30% 16.75% 9.71% 8.59% 23.56% 18% % % 14.59% 16.83% 9.79% 8.80% 25.30% 16% % % 13.96% 16.65% 9.61% 8.96% 25.85% % % 14.04% 16.64% 9.60% 9.18% 26.10% 14% % % 14.00% 16.83% 9.79% 9.37% 27.56% 12% % % 14.75% 17.61% 10.57% 9.66% 29.28% 10% % % 15.76% 18.52% 11.48% 10.00% 29.94% 8% % % 14.12% 17.09% 10.05% 10.44% 30.21% % % 15.10% 18.20% 11.16% 11.00% 31.75% 6% % % 15.39% 18.73% 11.69% 11.67% 32.34% 4% % % 14.39% 18.09% 11.05% 13.08% 31.38% 2% Equity Premium Large Stocks (Ibbotson SBBI data) 9.39% 10.88% 3.84% Small Stocks (Ibbotson SBBI data) 13.07% 15.96% 8.92% 0% Log of Median Operating Margin Long-Term Treasury Income (Ibbotson SBBI data) 7.01% 7.04% Source: CRSP, Center for Research in Security Prices. Graduate School of Business, The University of Chicago used with permission. All rights reserved. Calculations by Duff & Phelps LLC. Duff and Phelps, LLC Source: Shannon Pratt and Roger Grabowski, Cost of Capital: Applications and Examples, 4th ed. (John Wiley & Sons, 2010). Used with permission. All Rights Reserved

21 Is the Subject Company more or less risky than comparable size firms? Small companies are believed to have higher rates of return than large companies because small companies are inherently more risky. Is this true? Yes, as measured by the stock-market based indicators of beta and price volatility. D&P data also demonstrates that as company size decreases, fundamental measures of accounting risk increase showing that small companies are inherently more risky. Exhibits C-1 to C-8 41 Exhibit Duff & Phelps Study: Comparative Risk Statistics Companies Ranked by Market Value of Equity: Comparative Risk Characteristics Data for Year Ending December 31, 2008 Portfolio Statistics for 2008 Portfolio Statistics for Portfolio Average Log Arithmetic Average Average Average Beta Average Average Average Rank Mkt Value of Number Average Risk Debt to Debt to Market Unlevered (SumBeta) Unlevered Operating CV(Operating Average by Size ($mils.) Size of Firms Premium MVIC Value of Equity Risk Premium Since '63 Beta Margin Margin) CV(ROE) 1 127, % 14.76% 17.3% 3.3% % 9.7% 15.1% 2 36, % 21.09% 26.7% 3.3% % 10.8% 19.1% 3 21, % 22.87% 29.7% 2.4% % 11.1% 18.4% 4 16, % 23.85% 31.3% 3.5% % 12.1% 20.5% 5 12, % 24.47% 32.4% 3.3% % 13.2% 21.0% 6 9, % 24.37% 32.2% 4.2% % 13.0% 19.4% 7 7, % 25.13% 33.6% 4.7% % 14.1% 22.4% 8 5, % 24.03% 31.6% 4.1% % 13.2% 21.8% 9 4, % 23.52% 30.8% 5.4% % 14.1% 21.3% 10 3, % 24.40% 32.3% 4.3% % 14.7% 22.8% 11 3, % 22.99% 29.8% 6.0% % 14.8% 21.8% 12 2, % 24.08% 31.7% 4.3% % 14.6% 20.7% 13 2, % 24.10% 31.8% 5.0% % 15.4% 21.9% 14 2, % 24.53% 32.5% 5.9% % 15.7% 22.0% 15 2, % 25.14% 33.6% 4.9% % 17.2% 23.8% 16 1, % 24.32% 32.1% 6.2% % 16.7% 24.4% 17 1, % 24.06% 31.7% 7.2% % 18.2% 25.3% 18 1, % 24.68% 32.8% 6.3% % 20.0% 26.7% 19 1, % 24.91% 33.2% 6.1% % 20.7% 26.9% % 25.28% 33.8% 6.8% % 23.5% 31.2% % 26.38% 35.8% 7.5% % 22.8% 30.7% % 26.11% 35.3% 6.4% % 25.3% 34.1% % 26.14% 35.4% 7.4% % 26.9% 35.0% % 26.47% 36.0% 7.9% % 29.5% 38.6% % 29.41% 41.7% 10.3% % 41.8% 56.2% Note: CV(X) = Standard deviation of X divided by mean of X calculated over 5 fiscal years. Source: Shannon Pratt and Roger Grabowski, Cost of Capital: Applications and Examples, 4th ed. (John Wiley & Sons, 2010). Used with permission. All Rights Reserved

22 Exhibit Duff & Phelps Study: Comparative Risk Statistics Companies Ranked by Book Value of Equity: Comparative Risk Characteristics Data for Year Ending December 31, 2008 Portfolio Statistics for 2008 Portfolio Statistics for Average Log Average Average Average Portfolio Arithmetic Average Average Average Beta Rank Book Value of Number Average Risk Debt to Debt to Market Unlevered (SumBeta) Unlevered Operating CV(Operating Average by Size ($mils.) Size of Firms Premium MVIC Value of Equity Risk Premium Since '63 Beta Margin Margin) CV(ROE) 1 37, % 24.52% 32.5% 3.3% % 12.5% 20.2% 2 11, % 29.42% 41.7% 3.2% % 13.0% 18.6% 3 7, % 30.55% 44.0% 4.5% % 12.0% 20.5% 4 5, % 29.87% 42.6% 3.4% % 12.4% 22.0% 5 4, % 27.52% 38.0% 4.0% % 13.2% 22.5% 6 3, % 27.39% 37.7% 3.6% % 13.1% 23.1% 7 2, % 26.21% 35.5% 4.1% % 13.5% 22.6% 8 2, % 25.81% 34.8% 4.2% % 14.0% 23.5% 9 1, % 25.49% 34.2% 5.0% % 14.5% 21.5% 10 1, % 26.43% 35.9% 4.5% % 14.6% 21.8% 11 1, % 26.88% 36.8% 4.0% % 14.5% 23.4% 12 1, % 27.11% 37.2% 5.4% % 14.9% 22.0% 13 1, % 25.90% 34.9% 5.4% % 15.3% 23.3% % 25.32% 33.9% 6.0% % 15.3% 21.9% % 24.82% 33.0% 6.1% % 15.8% 23.0% % 25.73% 34.6% 5.5% % 17.6% 25.2% % 24.26% 32.0% 5.3% % 16.6% 24.7% % 25.11% 33.5% 5.7% % 17.9% 26.2% % 26.53% 36.1% 5.0% % 18.4% 28.3% % 26.05% 35.2% 7.1% % 20.5% 30.2% % 25.42% 34.1% 6.9% % 21.9% 31.5% % 24.70% 32.8% 6.8% % 23.5% 31.4% % 25.53% 34.3% 6.3% % 23.9% 34.6% % 25.67% 34.5% 8.2% % 25.3% 36.0% % 25.71% 34.6% 8.9% % 36.9% 52.2% Note: CV(X) = Standard deviation of X divided by mean of X divided by mean of X, calculated over 5 fiscal years. Source: Compiled from data from the Center for Research in Security Prices. Source: 2009 CRSP, Center for Research in Security Prices. Graduate School of Business, The University of Chicago. Used with permission. All rights reserved. wwwcrsp.chicagogsb.edu. Calculations by Duff & Phelps LLC. 43 Exhibits C-1 to 8 vs. Exhibits D-1 to 3 Not the same risk statistics. Exhibits C: reported statistics are calculated for portfolios grouped according to size and are averages since Shows relationship between size and accounting risk measures. Exhibits D: reported statistics are calculated for portfolios grouped according to risk, independent of size, and are trailing 5-year averages. Calculate alternative risk premium for build-up method

23 What kind of Companies make-up 10y? Exhibit 14.3 Breakdown of Decile 10y Companies as of September 30, 2008: Market Value between $74.9 and $136.5 Million ($ millions) Size: Market Value of Equity Book value of Equity MVIC * 95th percentile $132 $246 $461 $828 75th percentile $117 $113 $146 $229 Median $100 $67 $102 $123 25th percentile $86 $35 $79 $63 5th percentile $77 $6 $35 $20 * MVIC = Market Value of Equity + Book Value of Preferred Stock + Book Value of Debt Total Assets Profitability: Sales 5-yr avg Net Income before Extra Ordinary 5-yr avg EBITDA 95th percentile $779 $14 $51 36% 75th percentile $204 $5 $17 10% Median $86 $0 $7 0% 25th percentile $29 $ 10 $ 3 26% 5th percentile $zero $ 36 $ % Latest Fiscal Year Return on Book Equity 45 What kind of Companies make-up 10y? (cont d) Measures of Risk (NYSE + AMEX + NASDAQ companies): ($ millions) Size: Market Value of Equity OLS Beta 95th percentile $ th percentile $ Median $ th percentile $ th percentile $ Measures of Risk (NYSE companies): ($ millions) Size: Market Value of Equity OLS Beta 95th percentile $ Sum Beta Sum Beta 75th percentile $ Median $ th percentile $ th percentile $ Source: Compiled from Standard & Poor's Capital IQ. Beta calculations use data from Standard and Poor s Research Insight. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved. Source: Shannon Pratt and Roger Grabowski, Cost of Capital: Applications and Examples, 4th ed. (John Wiley & Sons, 2010). Used with permission. All Rights Reserved

24 What kind of Companies make-up 10z? Exhibit 14.4 Breakdown of Decile 10z Companies as of September 30, 2008: Market Value between $1.575 and $74.9 Million ($ millions) Size: Market Value of Book Value of Equity Equity MVIC * 95th percentile $68 $111 $203 $373 75th percentile $50 $47 $56 $93 Median $32 $24 $31 $46 25th percentile $17 $11 $15 $24 5th percentile $6 $2 $zero $7 * MVIC = Market Value of Equity + Book Value of Preferred Stock + Book Value of Debt Profitability: Sales 5-yr avg Net Income before Extra Ordinary 5-yr avg EBITDA Total Assets 95th percentile $325 $6 $23 31% 75th percentile $86 $2 $5 7% Median $37 $-1 $1-8% 25th percentile $13 $ 7 $ 3 47% 5th percentile $zero $ 31 $ % Latest Fiscal Year Return on Book Equity 47 What kind of Companies make-up 10z? (cont d) Measures of Risk (NYSE + AMEX + NASDAQ companies): ($ millions) Size: Market Value of Equity OLS Beta Sum Beta 95th percentile $ th percentile $ Median $ th percentile $ th percentile $ Measures of Risk (NYSE companies): ($ millions) Size: Market Value of Equity OLS Beta Sum Beta 95th percentile $ th percentile $ Median $ th percentile $ th percentile $ Source: Compiled from Standard & Poor's Capital IQ. Beta calculations use data from Standard and Poor s Research Insight. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved. Source: Shannon Pratt and Roger Grabowski, Cost of Capital: Applications and Examples, 4th ed. (John Wiley & Sons, 2010). Used with permission. All Rights Reserved