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- 1. Cost of Capital (Equity Capital)
- 2. Topics Covered <ul><li>72 Years of Capital Market History </li></ul><ul><li>Measuring Risk, Beta and Unique Risk </li></ul><ul><li>CAPM and Cost of Capital </li></ul><ul><li>Introduction to WACC & Capital Structure </li></ul>
- 3. The Future Value of an Investment of $1 in 1925 $59.70 $17.48 Source: © Stocks, Bonds, Bills, and Inflation 2003 Yearbook™ , Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved. $1,775.34
- 4. Historical Returns, 1926-2002 Source: © Stocks, Bonds, Bills, and Inflation 2003 Yearbook™ , Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved. – 90% + 90% 0% Average Standard Series Annual Return Deviation Distribution Large Company Stocks 12.2% 20.5% Small Company Stocks 16.9 33.2 Long-Term Corporate Bonds 6.2 8.7 Long-Term Government Bonds 5.8 9.4 U.S. Treasury Bills 3.8 3.2 Inflation 3.1 4.4
- 5. Average Stock Returns and Risk-Free Returns <ul><li>The Risk Premium is the additional return (over and above the risk-free rate) resulting from bearing risk. </li></ul><ul><li>One of the most significant observations of stock market data is this long-run excess of stock return over the risk-free return. </li></ul><ul><ul><li>The average excess return from large company common stocks for the period 1926 through 1999 was 8.4% = 12.2% – 3.8% </li></ul></ul><ul><ul><li>The average excess return from small company common stocks for the period 1926 through 1999 was 13.2% = 16.9% – 3.8% </li></ul></ul><ul><ul><li>The average excess return from long-term corporate bonds for the period 1926 through 1999 was 2.4% = 6.2% – 3.8% </li></ul></ul>
- 6. The Risk-Return Tradeoff
- 7. Rates of Return 1926-2002 Source: © Stocks, Bonds, Bills, and Inflation 2000 Yearbook™ , Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
- 8. Measuring Total Risk <ul><li>There is no universally agreed-upon definition of risk. </li></ul><ul><li>The measures of risk that we discuss are variance and standard deviation. </li></ul><ul><li>Variance - A measure of volatility. Average value of squared deviations from mean. </li></ul><ul><li>Standard Deviation - The standard deviation is the standard statistical measure of the spread of a sample (the square root of the variance). It is the measure of total risk that we use most of the time. </li></ul>
- 9. Stock Market Volatility 1926-2004 Std Dev 2004
- 10. Country Risk Premia (%)
- 11. Measuring Risk <ul><li>Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments. </li></ul><ul><li>Unique Risk - Risk factors affecting only that firm. Also called “diversifiable risk.” </li></ul><ul><li>Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.” </li></ul>
- 12. Measuring Risk
- 13. Capital Asset Pricing Model R = r f + B ( r m - r f ) CAPM Security Market Line (SML) RP = Risk Premium
- 14. Security Market Line Expected Return BETA r f Risk Free Return = Market Return = r m 1.0 Security Market Line (SML)
- 15. The Formula for Beta Covariance with the market Variance of the market
- 16. Beta Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market. Beta - Sensitivity of a stock’s return to the return on the market portfolio.
- 17. Beta and CL 1. Market risk is measured by beta, the sensitivity to market changes. 2. The slope of the characteristic line is beta beta Expected return Expected market return 10% 10% - + <ul><li>10% </li></ul>+10% stock Copyright 1996 by The McGraw-Hill Companies, Inc -10%
- 18. Estimating with regression Security Returns Return on market % R i = i + i R m + e i Slope = i Characteristic Line
- 19. Measuring Betas <ul><li>The SML shows the relationship between return and risk. </li></ul><ul><li>CAPM uses Beta as the measure for risk. </li></ul><ul><li>Beta is the slope of the Characteristic Line (CL). </li></ul><ul><li>Other methods - Regression Analysis - can be employed to determine the slope of the CL and thus Beta. </li></ul>
- 20. Measuring Betas Hewlett Packard Beta Slope determined from 60 months of prices and plotting the line of best fit. Price data - Jan 78 - Dec 82 Market return (%) Hewlett-Packard return (%) R 2 = .53 B = 1.35
- 21. Measuring Betas Hewlett Packard Beta Slope determined from 60 months of prices and plotting the line of best fit. Price data - Jan 93 - Dec 97 Market return (%) Hewlett-Packard return (%) R 2 = .35 B = 1.69
- 22. Measuring Betas A T & T Beta Slope determined from 60 months of prices and plotting the line of best fit. Price data - Jan 78 - Dec 82 Market return (%) A T & T (%) R 2 = .28 B = 0.21
- 23. Measuring Betas A T & T Beta Slope determined from 60 months of prices and plotting the line of best fit. Price data - Jan 93 - Dec 97 Market return (%) R 2 = ..17 B = .90 A T & T (%)
- 24. Using the SML to Estimate the Risk-Adjusted Discount Rate for Projects <ul><li>An all-equity firm should accept a project whose IRR exceeds the cost of equity capital and reject projects whose IRRs fall short of the cost of capital. </li></ul>Project IRR Firm’s risk (beta) 5% Good project Bad project 30% 2.5 A B C
- 25. Extensions of the Basic Model <ul><li>The Firm versus the Project </li></ul><ul><li>The Cost of Capital with Debt </li></ul>
- 26. The Firm versus the Project <ul><li>Any project’s cost of capital depends on the use to which the capital is being put—not the source. </li></ul><ul><li>Therefore, it depends on the risk of the project and not the risk of the company . </li></ul>
- 27. Company Cost of Capital <ul><li>A company’s cost of capital can be compared to the CAPM required return. </li></ul>Required return Project Beta 1.26 Company Cost of Capital 13 5.5 0 SML Possible error Possible error
- 28. Capital Budgeting & Risk <ul><li>Modifying the CAPM </li></ul><ul><li>(account for proper risk) </li></ul><ul><li>Use COC unique to project, if possible, </li></ul><ul><li>rather than Company COC </li></ul><ul><li>Take into account Capital Structure (next </li></ul><ul><li>topic) </li></ul>
- 29. <ul><li>Capital Structure - the mix of debt & equity within a company </li></ul><ul><li>Expand CAPM to include CS </li></ul><ul><li>R = r f + B ( r m - r f ) </li></ul><ul><li>becomes </li></ul><ul><li>R equity = r f + B ( r m - r f ) </li></ul><ul><li>(because equity returns are observable ) </li></ul>Capital Structure RP = market risk premium
- 30. Capital Structure & COC r equity = r f + β equity ( r m - r f ) r debt = r f + β debt ( r m - r f ) IMPORTANT E, D, and V are all market values
- 31. Using an Industry Beta <ul><li>It is frequently argued that one can better estimate a firm’s beta by involving the whole industry. </li></ul><ul><li>If you believe that the operations of the firm are similar to the operations of the rest of the industry, you should use the industry beta. </li></ul><ul><li>If you believe that the operations of the firm are fundamentally different from the operations of the rest of the industry, you should use the firm’s beta. </li></ul><ul><li>Don’t forget about adjustments for financial leverage ( more details coming later in the course ). </li></ul>
- 32. Utility Example Pinnacle West Corp.
- 33. Example: Pinnacle West Corp R asset = r f + β ( r m - r f ) = .045 + .24(.08) = .064 or 6.4% (7.5% for Pinnacle’s beta = .38) Assumes riskfree rate of 4.5% and market risk premium of 8%
- 34. Other Methods of Estimating Cost of Equity Capital <ul><li>The EP Method </li></ul><ul><ul><li>r = EPS / Stock Price </li></ul></ul><ul><li>The Constant Growth (Gordon) Model </li></ul><ul><li>r = DIV 1 / P 0 + g </li></ul><ul><li>compute g from earnings, dividend, or cash flow growth or use the sustainable growth estimate </li></ul>
- 35. Conclusion <ul><li>Now compute the cost of capital for Ameritrade Corporation </li></ul><ul><li>Use the CAPM – compute the beta for comparable firms to Ameritrade </li></ul><ul><li>Compute asset betas from equity betas </li></ul><ul><li>What is the cost of capital for Ameritrade? </li></ul>

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