Chapter 11 and 12

1. Chapter 11 and 12 Capital Asset Pricing Model and Estimating the Cost of Capital

2. 11.7 The Capital Asset Pricing Model • Market Portfolio • The portfolio of all stocks and securities in the market • The expected return of any traded security is determined by its beta with the efficient portfolio.

3. The CAPM Assumptions • Three Main Assumptions • Assumption 1 • Investors can buy and sell all securities at competitive market prices (without incurring taxes or transactions costs) and can borrow and lend at the risk-free interest rate.

4. The CAPM Assumptions (cont'd) • Three Main Assumptions • Assumption 2 • Investors hold only efficient portfolios of traded securities—portfolios that yield the maximum expected return for a given level of volatility.

5. The CAPM Assumptions (cont'd) • Three Main Assumptions • Assumption 3 • Investors have homogeneous expectations regarding the volatilities, correlations, and expected returns of securities. • Homogeneous Expectations • All investors have the same estimates concerning future investments and returns.

6. Security Demand Must Equal Supply • Given homogeneous expectations, all investors will demand the same efficient portfolio of risky securities. • The combined portfolio of risky securities of all investors must equal the efficient portfolio. • Thus, if all investors demand the efficient portfolio, and the supply of securities is the market portfolio, the demand for market portfolio must equal the supply of the market portfolio.

7. Example Assume the assumption of the CAPM hold. There are 1000 people with $100 each and there are two securities A and B. If Mr. Smith invests 40% of his risky portfolio in A, (a) what is the value of B given that the market capitalization value of A is $20,000, (b) what is the total investment in the riskless asset in the market?

8. Figure 11.11 The Capital Market Line

9. Example

10. The Capital Market Line Offers the Best Possible Risk–Return Combinations

11. 11.8 Determining the Risk Premium • Market Risk and Beta • Given an efficient market portfolio, the expected return of an investment is: • The beta is defined as:

12. Example

13. Example Assume the risk-free return is 5% and the market portfolio has an expected return of 12% and a standard deviation of 44%. • ATP Oil and Gas has a standard deviation of 68% and a correlation with the market of 0.91. • What is ATP’s beta with the market? • Under the CAPM assumptions, what is its expected return?

14. Figure 11.12 The Capital Market Line and the Security Market Line, panel (a)

15. Figure 11.12 The Capital Market Line and the Security Market Line, panel (b)

16. Figure 12.3 The Capital Market Line and the Security Market Line

17. Example

18. Example Suppose the stock of the 3M Company (MMM) has a beta of 0.69 and the beta of Hewlett-Packard Co. (HPQ) stock is 1.77. • Assume the risk-free interest rate is 5% and the expected return of the market portfolio is 12%. • What is the expected return of a portfolio of 40% of 3M stock and 60% Hewlett-Packard stock, according to the CAPM?

19. 12. The Equity Cost of Capital • The appropriate risk premium for an investment can be determined from its beta with the Market portfolio: • Cost of Capital for Investment i • The cost of capital of investment i is equal to the expected return of the best available portfolio in the market with the same sensitivity to systematic risk.

20. Alternative Example 12.1 • Problem • Suppose you estimate that Wal-Mart’s stock has a volatility of 16.1% and a beta of 0.20. A similar process for Johnson &Johnson yields a volatility of 13.7% and a beta of 0.54. Which stock carries more total risk? Which has more market risk? If the risk-free interest rate is 4% and you estimate the market’s expected return to be 12%, calculate the equity cost of capital for Wal-Mart and Johnson & Johnson. Which company has a higher cost of equity capital?

21. 12.2 The Market Portfolio • Value-Weighted Portfolio • A portfolio in which each security is held in proportion to its market capitalization

22. Investing in a Market Index • Index funds – mutual funds that invest in the S&P 500, the Wilshire 5000, or some other index. • Exchange-traded funds (ETFs) – trade directly on an exchange but represent ownership in a portfolio of stocks. • Example: SPDRS (Standard and Poor’s Depository Receipts) represent ownership in the S&P 500

23. Example

24. Common Stock Market Indexes (cont'd) • Example of a Price-Weighted Index • DJIA • Example of a Value-Weighted Index • S&P 500 • Wilshire 5000

25. 12.3 Determining Beta • Estimating Beta from Historical Returns • Recall, beta is the expected percent change in the excess return of the security for a 1% change in the excess return of the market portfolio. • Consider Cisco Systems stock and how it changes with the market portfolio.

26. Figure 12.1 Monthly Returns for Cisco Stock and for the S&P 500, 1996–2009

27. Figure 12.2 Scatterplot of Monthly Excess Returns for Cisco Versus the S&P 500, 1996–2009

28. Using Linear Regression • Linear Regression • The statistical technique that identifies the best-fitting line through a set of points. • αi is the intercept term of the regression. • Βi(RMkt – rf) represents the sensitivity of the stock to market risk. • εi is the error term and represents the deviation from the best-fitting line and is zero on average.

29. The CAPM in Practice • Forecasting Beta • Time Horizon • For stocks, common practice is to use at least two years of weekly return data or five years of monthly return data. • The Market Proxy • In practice the S&P 500 is used as the market proxy. Other proxies include the NYSE Composite Index and the Wilshire 5000.

30. 12.6 The CAPM in Practice (cont'd) • Forecasting Beta • Beta Extrapolation • Many practitioners prefer to use average industry betas rather than individual stock betas. • The beta estimates obtained from linear regression can be very sensitive to outliers. • 1.0 over time. • In addition, evidence suggests that betas tend to regress toward the average beta of Outliers

31. Beta Estimation with and without Outliers for Genentech Using Monthly Returns for 2002–2004

32. The Risk-Free Interest Rate • Make sense to use risk-free rate corresponding to the investment horizon (term-structure). • When surveyed, the vast majority of large firms and financial analysts report using the yields of long-term (10- to 30-year) Treasury bonds to determine the risk-free rate.

33. The Market Risk Premium • Use the historical average excess return of the market over the risk-free interest rate

34. 12.4 The Debt Cost of Capital • Debt Yields • Yield to maturity is the IRR an investor will earn from holding the bond to maturity and receiving its promised payments. • If there is little risk the firm will default, yield to maturity is a reasonable estimate of investors’ expected rate of return. • If there is significant risk of default, yield to maturity will overstate investors’ expected return.

35. 12.5 A Project’s Cost of Capital • All-equity comparables • Find an all-equity financed firm in a single line of business that is comparable to the project. • Use the comparable firm’s equity beta and cost of capital as estimates • Levered firms as comparables

36. 12.5 A Project’s Cost of Capital (cont’d) • Asset (unlevered) cost of capital • Expected return required by investors to hold the firm’s underlying assets. • Weighted average of the firm’s equity and debt costs of capital

37. 12.5 A Project’s Cost of Capital (cont’d) • Asset (unlevered) beta

38. Textbook Example 12.5

39. Cash and Net Debt • Some firms maintain high cash balances • Cash is a risk-free asset that reduces the average risk of the firm’s assets • Since the risk of the firm’s enterprise value is what we’re concerned with, leverage should be measured in terms of net debt. Net Debt = Debt – Excess Cash and short-term investments

40. Textbook Example 12.6

41. Textbook Example 12.7

42. Textbook Example 12.7 (cont’d)

43. Figure 12.4 Industry Asset Betas

44. 12.6 Project Risk Characteristics and Financing • Differences in project risk • Firm asset betas reflect market risk of the average project in a firm. • Individual projects may be more or less sensitive to market risk.

45. 12.6 Project Risk Characteristics and Financing (cont’d) • Another factor that can affect market risk of a project is its degree of operating leverage • Operating leverage is the relative proportion of fixed versus variable costs • A higher proportion of fixed costs increases the sensitivity of the project’s cash flows to market risk • The project’s beta will be higher • A higher cost of capital should be assigned

46. Textbook Example 12.8

47. Financing and the Weighted Average Cost of Capital • How might the project’s cost of capital change if the firm uses leverage to finance the project? • Perfect capital markets • In perfect capital markets, choice of financing does not affect cost of capital or project NPV • Taxes – A Big Imperfection • When interest payments on debt are tax deductible, the net cost to the firm is given by: • Effective after-tax interest rate = r(1-τC)

48. The Weighted Average Cost of Capital Weighted Average Cost of Capital (WACC) Given a target leverage ratio:

49. Textbook Example 12.9

50. 12.7 Final Thoughts on the CAPM There are a large number of assumptions made in the estimation of cost of capital using the CAPM. How reliable are the results?