© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 7- 1 B Class #3  BM6 chapters 7, 8, 9  Based on slides created by Matthew Will  Modified 9/23/2001 by Jeffrey Wurgler

 Introduction to Risk, Return, and the Opportunity Cost of Capital Principles of Corporate Finance Brealey and Myers Sixth Edition Slides by Matthew Will, Jeffrey Wurgler Chapter 7 © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 7- 3 Topics Covered  72 Years of Capital Market History  Measuring Risk  Portfolio Risk and Diversification  Beta and Unique Risk  Diversification and Value Additivity

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 7- 4 The Value of an Investment of $1 in 1926 Source: Ibbotson Associates Index Year End Real returns

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 7- 5 Returns Source: Ibbotson Associates Year Percentage Return

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 7- 6 Measuring Risk Two standard measures of risk: Variance - Average value of squared deviations from mean. Standard Deviation – Square root of variance, I.e. square root of average value of squared deviations from mean.

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 7- 7 Measuring Risk Example: Calculating variance and standard deviation. Suppose four equally-likely outcomes:

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 7- 8 Measuring Risk Return % # of Years Histogram of Annual Stock Market Returns

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 7- 9 Measuring Risk Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments. Reduces risk but not expected return. Unique Risk - Risk factors affecting only that firm. Also called “diversifiable risk” or “idiosyncratic risk” Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “non- diversifiable risk” or “systematic risk”

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Measuring Risk + …

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Measuring Risk

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Measuring Risk

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Portfolio Risk In the two-asset case,

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Portfolio Risk Example Suppose you invest $55 in Bristol-Myers and $45 in McDonald’s. The s.d. of BM returns is 17.1% and the s.d. of McDonald’s is 20.8%. Assume they have a correlation of

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Portfolio Risk Example Suppose you invest $55 in Bristol-Myers and $45 in McDonald’s. The s.d. of BM returns is 17.1% and the s.d. of McDonald’s is 20.8%. Assume they have a correlation of

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Portfolio Risk The shaded boxes contain variance terms; the others contain covariance terms N N STOCK To calculate portfolio variance add up the boxes

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Beta and Unique Risk slope = beta Expected return Expected Market risk premium 10% -+ stock Copyright 1996 by The McGraw-Hill Companies, Inc -10% A security’s market risk is measured by beta, its expected sensitivity to the market.

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Beta and Unique Risk Market Portfolio - Portfolio of all investable 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.

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Beta and Unique Risk Covariance with the market risk premium Variance of the market risk premium

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Diversification & Value Additivity  Value additivity holds … PV(A,B) = PV(A) + PV(B)  … since investors can diversify on their own  They will not pay extra for firms that diversify  And they will not pay less for firms that do diversify, since they can “undo” its effect on their own account  Note: V.A. assumes no “synergies”

 Risk and Return Principles of Corporate Finance Brealey and Myers Sixth Edition Slides by Matthew Will, Jeffrey Wurgler Chapter 8 © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Topics Covered  Markowitz Portfolio Theory  Risk and Return Relationship  Testing the CAPM  CAPM Alternatives  Consumption CAPM (CCAPM)  Arbitrage pricing theory (APT)

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Markowitz Portfolio Theory  Can combine individual securities into portfolios that achieve at least a given expected return at the lowest possible variance. efficient portfolios  These are called the efficient portfolios.  a.k.a. mean-variance efficient portfolios.

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Markowitz Portfolio Theory 100% Bristol-Myers-Squibb 100% McDonald’s Portfolio Standard Deviation (%) Portfolio Expected Return (%) 45% McDonald’s, 55% Bristol-Myers-Squibb  Portfolio expected return and standard deviation depends on the weights you put on each stock.

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Efficient Frontier Portfolio Standard Deviation (%) Portfolio Expected Return (%) Each half egg shell represents the possible combinations of two stocks. As you add more stocks, you can construct more complex portfolios. The composite using all securities is the efficient frontier, and the portfolios on the frontier are efficient portfolios.

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Efficient Frontier Lending or Borrowing at the risk-free rate ( r f ) allows us to achieve combinations that are outside the efficient frontier. Would never choose T, for example, when could choose S and then borrow or lend rfrf Lending Borrowing S T Portfolio Expected Return (%) Portfolio Standard Deviation (%)

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Security Market Line Expected return Beta. rfrf rmrm Market Portfolio 1.0 SML

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Security Market Line / CAPM Expected return Beta rfrf 1.0 SML SML/CAPM: E[r i ] = r f + B i (E[r m ] - r f )

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Testing the CAPM Avg Portfolio Risk Premium Portfolio Beta 1.0 SML Beta decile portfolios Market Portfolio Beta vs. Average Risk Premium

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Testing the CAPM Avg Risk Premium Portfolio Beta 1.0 SML Investors Market Portfolio Beta vs. Average Risk Premium

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Testing the CAPM Average Return (%) Company size SmallestLargest Company Size vs. Average Return

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Testing the CAPM Average Return (%) Book-to-Market Ratio HighestLowest Book-to-Market vs. Average Return

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Consumption Betas vs Market Betas Stocks (and other risky assets) Wealth = market portfolio Market risk makes wealth uncertain. Standard CAPM

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Consumption Betas vs Market Betas Stocks (and other risky assets) Wealth = market portfolio Market risk makes wealth uncertain. Stocks (and other risky assets) Consumption Wealth Wealth is uncertain Consumption is uncertain Standard CAPM Consumption CAPM

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Arbitrage Pricing Theory  Besides CCAPM, APT is another alternative to CAPM Expected Risk Premium = r - r f = B factor1 (r factor1 - r f ) + B f2 (r f2 - r f ) + … Return= a + b factor1 (r factor1 ) + b f2 (r f2 ) + …

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Arbitrage Pricing Theory  APT, like CCAPM, is an alternative to CAPM  If Return = a + b 1 *r factor 1 + b 2 *r factor 2 + …  Then Expected Return (risk premium) = = r i – r f = b 1 *(r factor 1 - r f ) + b 2 *(r factor 2 - r f ) + …

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Arbitrage Pricing Theory Estimated risk premiums for taking on risk factors ( data)

 Capital Budgeting and Risk Principles of Corporate Finance Brealey and Myers Sixth Edition Slides by Matthew Will, Jeffrey Wurgler Chapter 9 © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Topics Covered  Measuring Betas  Capital Structure and COC  Discount Rates for International Projects  Estimating Discount Rates – What if no beta?  Risk and DCF

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Company Cost of Capital  Value-additivity: Total firm value is the sum of the value of its various assets.  Note each PV on the right is evaluated at its own discount rate

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Company Cost of Capital  Company’s average cost of capital versus individual project cost of capital. (CAPM) Required Return (%) Project Beta 1.26 “Company Cost of Capital” SML “Average Company Beta”

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Measuring Betas  The SML shows the equilibrium relationship between expected return and risk (beta) according to the CAPM.  How to measure beta?  Typical approach: Regression analysis

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Measuring Betas Hewlett-Packard Stock Beta Slope (beta) estimated from a regression over 60 months of return data. Returns - Jan 88 to Dec 92 Market return (%) Hewlett-Packard return (%) R 2 = 0.45 B = 1.70

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Measuring Betas Returns - Jan 93 - Dec 97 Market return (%) R 2 = 0.35 B = 1.69 Hewlett-Packard Stock Beta Hewlett-Packard return (%) Slope (beta) estimated from a regression over 60 months of return data.

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Measuring Betas AT&T Stock Beta Returns - Jan 88 - Dec 92 Market return (%) R 2 = 0.28 B = 0.90 A T & T (%) Slope (beta) estimated from a regression over 60 months of return data.

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Measuring Betas AT&T Stock Beta Returns - Jan 93 - Dec 97 Market return (%) R 2 = 0.17 B = 0.90 A T & T (%) Slope (beta) estimated from a regression over 60 months of return data.

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Beta Stability % IN SAME % WITHIN ONE RISK CLASS 5 CLASS 5 CLASS YEARS LATER YEARS LATER 10 (High betas) (Low betas) Source: Sharpe and Cooper (1972)

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Company Cost of Capital simple approach The overall company cost of capital is based on the weighted- average beta of the individual asset / project betas. The weights in the weighted average are determined by the % of firm value attached to each asset / project. Example: Say firm value is split as: 1/3 New ventures investment (B=2.0) 1/3 Expand existing business investment (B=1.3) 1/3 Plant efficiency investment (B=0.6) Average asset beta = (1/3)*2.0 + (1/3)*1.3 + (1/3)*0.6 = 1.3 This average beta determines the company cost of capital.

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Capital Structure & COC  So we’ve established how to estimate the company cost of capital.  If you owned all of firm’s securities – 100% of its equity and 100% of its debt – you would own all its assets  Think of company cost of capital as expected return on this hypothetical portfolio.

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Capital Structure & COC Company cost of capital = r portfolio = r assets r assets = r debt (D) + r equity (E) (V) (V) B assets = B debt (D) + B equity (E) (V) (V) r equity = r f + B equity ( r m - r f ) IMPORTANT E, D, and V are all market values

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Capital Structure & COC  Changing capital structure can change the risk of the debt relative to the risk of the equity, but does not change the overall risk of the firm.  Changing capital structure therefore does not change the company cost of capital.  Let’s see how changes in capital structure change the costs of equity vs. debt…

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Capital Structure & COC Expected return (%) B debt B assets B equity r debt =8 r assets =12.2 r equity =15 Expected Returns and Betas before refinancing

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Capital Structure & COC Expected return (%) B debt B assets B equity r debt =7.3 r assets =12.2 r equity =14.3 Expected Returns and Betas after refinancing

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Capital Structure & COC  Go from estimated B equity (say, from regression) and assumed / estimated B debt to compute B assets  This is called unlevering beta  To unlever beta, just remember: B assets = B debt (D) + B equity (E) (V) (V)

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Pinnacle West Corp.

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Pinnacle West Corp. R equity = r f + B equity ( r m - r f ) = (8.0) = 8.58% (Used industry average B equity since PW’s B equity was measured with lots of error) R debt = can estimate as YTM on PW bonds (Bond returns often hard to observe, so hard to estimate B debt ) = 6.90 %

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Pinnacle West Corp.

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill COC for International Projects  Same principles apply, with complications  If project is owned by US investors, they care more about project’s beta with US market. Not about project’s beta with local market.  The theory is clearest if investors are globally diversified. Then relevant beta is beta with world market.

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill What if can’t calculate Beta?  Suppose a new project doesn’t match the risk of traded securities… how to discount?  Need judgment. General advice:  Avoid fudge factors in discount rate. Make unbiased cash flow forecast (i.e. right on average).  Think about determinants of asset betas. Are project cash flows more or less cyclical than usual industry project?

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Risk and DCF: Putting it all together Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market risk premium of 8%, and an asset beta of.75, what is the PV of the project?

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Risk and DCF: Putting it all together Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market risk premium of 8%, and an asset beta of.75, what is the PV of the project?