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1. 1. Chapter 11 – Risk, Return and Capital Budgeting +
2. 2. Measuring Market Risk <ul><li>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. </li></ul><ul><li>Beta - Sensitivity of a stock’s return to the return on the market portfolio. </li></ul>
3. 3. Measuring Market Risk <ul><li>Example - Turbo Charged Seafood has the following % returns on its stock, relative to the listed changes in the % return on the market portfolio. The beta of Turbo Charged Seafood can be derived from this information. </li></ul>
4. 4. <ul><li>When the market was up 1%, Turbo average % change was +0.8% </li></ul>(.08 + 1.8 -.02)/3 = .08
5. 5. <ul><li>When the market was down 1%, Turbo average % change was -0.8% </li></ul>(.08 + 1.8 -.02)/3 = .08 (-1.8 + 0.2 – 0.8)/3 = -.08
6. 6. <ul><li>The average change of 1.6 % (-0.8 to 0.8) divided by the 2% (-1.0 to 1.0) change in the market produces a beta of 0.8. </li></ul>(.08 + 1.8 -.02)/3 = .08 (-1.8 + 0.2 – 0.8)/3 = -.08
7. 7. Measuring Market Risk Actual returns Smooth regression returns
8. 8. Portfolio Betas <ul><li>Diversification decreases variability from unique risk , but not from market risk . </li></ul><ul><li>The beta of your portfolio will be an average of the betas of the securities in the portfolio. </li></ul><ul><li>If you owned all of the S&P Composite Index stocks, you would have an average beta of 1.0 </li></ul>
9. 9. Stock Betas HP Beta = 2.00
10. 10. Mutual Funds – Actively-Managed Vanguard Windsor II Beta of this conservative fund was .66 +1
11. 11. Mutual Funds – Actively-Managed Beta of this conservative fund was .66 But investors still had some unique risk
12. 12. Index Mutual Fund Vanguard 500 Beta = 1.0 Investors had no unique risk – only market risk
13. 13. Security Market Line shows the greater the systematic (non-diversifiable) risk, the greater the market risk premium demanded by investors Security Market Line + 1
14. 14. Security Market Line shows the greater the systematic (non-diversifiable) risk, the greater the market risk premium demanded by investors <ul><li>Market Risk Premium Difference between market return and return on risk-free Treasury bills. </li></ul>Security Market Line Risk-Free (T-bill) Rate
15. 15. Capital Asset Pricing model <ul><li>CAPM - Theory of the relationship between risk and return which states that the expected risk premium on any security equals its beta times the market risk premium. </li></ul>
16. 16. Capital Asset Pricing model <ul><li>CAPM - Theory of the relationship between risk and return which states that the expected risk premium on any security equals its beta times the market risk premium. </li></ul>Example: If the Treasury bill rate is 3%, the expected market return is 10% and a stock has a Beta of 1.2, what is its expected return and risk premium?
17. 17. Example: If the Treasury bill rate is 3%, the expected market return is 10% and a stock has a Beta of 1.2, what is its expected return and risk premium? Expected Return = 3% + 1.2(10% - 3%) = 3% + 8.4% = 11.4%
18. 18. Example: If the Treasury bill rate is 3%, the expected market return is 10% and a stock has a Beta of 1.2, what is its expected return and risk premium? Expected Return = 3% + 1.2(10% - 3%) = 3% + 8.4% = 11.4% Risk Premium = 11.4% - 3% = 8.4%
19. 19. <ul><li>Example: If the Treasury bill rate is 3%, the expected market return is 10% and a stock has a Beta of 1.2, what is its expected return and risk premium? </li></ul>Expected Return r f = 3% Beta 1.0 r m = 10% Security Market Line +2
20. 20. <ul><li>Example: If the Treasury bill rate is 3%, the expected market return is 10% and a stock has a Beta of 1.2, what is its expected return and risk premium? </li></ul>Expected Return r f = 3% Beta 1.0 r m = 10% 1.2 r = 11.4% Security Market Line +1
21. 21. <ul><li>Example: If the Treasury bill rate is 3%, the expected market return is 10% and a stock has a Beta of 1.2, what is its expected return and risk premium? </li></ul>Expected Return r f = 3% Beta 1.0 r m = 10% 1.2 r = 11.4% Security Market Line Added risk Added return
22. 22. Capital Budgeting & Project Risk <ul><li>The project cost of capital depends on the use to which the capital is being put. Therefore, it depends on the risk of the project and not the risk of the company . </li></ul>
23. 23. <ul><li>Example - Based on the CAPM, ABC Company has a cost of capital of 17%. (4 + 1.3(14-4)). A breakdown of the company’s investment projects is illustrated below. What is the company’s cost of capital for a new dog food plant? </li></ul><ul><li>1/3 Nuclear Parts Mfr.. β =2.0 </li></ul><ul><li>1/3 Computer Hard Drive Mfr.. β =1.3 </li></ul><ul><li>1/3 Dog Food Production β =0.6 </li></ul><ul><li>AVG. β of assets = 1.3 </li></ul>
24. 24. <ul><li>Example - Based on the CAPM, ABC Company has a cost of capital of 17%. (4 + 1.3(14-4)). A breakdown of the company’s investment projects is listed below. When evaluating a new dog food production investment, which cost of capital should be used? </li></ul><ul><li>Go with the which has a Beta of .6 </li></ul><ul><li>r = 4 + 0.6 (14 - 4 ) = 10% </li></ul><ul><li>10% reflects the opportunity cost of capital on an investment given the unique risk of the project. </li></ul>
25. 25. <ul><li>You are considering acquiring a firm that you believe can generate expected cash flows of \$10,000 a year forever. However, you recognize that those cash flows are uncertain a) Suppose you believe that the beta of the firm is .4. How much is the firm worth if the risk-free rate is 4% and the expected rate of return on the market portfolio is 12% </li></ul>
26. 26. <ul><li>You are considering acquiring a firm that you believe can generate expected cash flows of \$10,000 a year forever. However, you recognize that those cash flows are uncertain a) Suppose you believe that the beta of the firm is .4. How much is the firm worth if the risk-free rate is 4% and the expected rate of return on the market portfolio is 12% </li></ul>The expected cash flows from the firm are in the form of a perpetuity. The discount rate is: r f +  (r m – r f ) = 4% + 0.4  (12% – 4%) = 7.2% Therefore, the value of the firm would be:
27. 27. <ul><li>You are considering acquiring a firm that you believe can generate expected cash flows of \$10,000 a year forever. However, you recognize that those cash flows are uncertain a) Suppose you believe that the beta of the firm is .4. How much is the firm worth if the risk-free rate is 4% and the expected rate of return on the market portfolio is 12% b) By how much will you overvalue the firm if the beta is actually .6? </li></ul>If the true beta is actually 0.6, the discount rate should be: r f +  (r m – r f ) = 4% + 0.6  (12% – 4%) = 8.8% Therefore, the value of the firm is:
28. 28. <ul><li>You are considering acquiring a firm that you believe can generate expected cash flows of \$10,000 a year forever. However, you recognize that those cash flows are uncertain a) Suppose you believe that the beta of the firm is .4. How much is the firm worth if the risk-free rate is 4% and the expected rate of return on the market portfolio is 12% b) By how much will you overvalue the firm if the beta is actually .6? </li></ul>If the true beta is actually 0.6, the discount rate should be: r f +  (r m – r f ) = 4% + 0.6  (12% – 4%) = 8.8% Therefore, the value of the firm is:
29. 29. <ul><li>You are considering acquiring a firm that you believe can generate expected cash flows of \$10,000 a year forever. However, you recognize that those cash flows are uncertain a) Suppose you believe that the beta of the firm is .4. How much is the firm worth if the risk-free rate is 4% and the expected rate of return on the market portfolio is 12% b) By how much will you overvalue the firm if the beta is actually .6? </li></ul>If the true beta is actually 0.6, the discount rate should be: r f +  (r m – r f ) = 4% + 0.6  (12% – 4%) = 8.8% Therefore, the value of the firm is: By underestimating beta, you would overvalue the firm by: \$138,888.89 – \$113,636.36 = \$25,252.53
30. 30. 8. Investors expect the market rate of return this year to be 14%. A stock with a beta of .8 has an expected rate of return of 12%. If the market return this year turns out to be 10%, what is your best guess as to the rate of return on the stock?
31. 31. Beta tells us how sensitive the stock return is to changes in market performance. The market return was 4 percent less than your prior expectation (10% versus 14%). Therefore, the stock would be expected to fall short of your original expectation by: 0.8  4% = 3.2% The ‘updated’ expectation for the stock return is: 12% – 3.2% = 8.8% 8. Investors expect the market rate of return this year to be 14%. A stock with a beta of .8 has an expected rate of return of 12%. If the market return this year turns out to be 10%, what is your best guess as to the rate of return on the stock?
32. 32. <ul><li>You are a consultant to a firm evaluating an expansion of its current business. The cash-flow forecasts (in millions of dollars) for the project are: </li></ul><ul><li>Years Cash Flow </li></ul><ul><li> 0 -100 </li></ul><ul><li>1-10 +15 </li></ul><ul><li>Based on the behavior of the firm’s stock, you believe that the beta of the firm is 1.4. Assuming that the rate of return available on risk-free investments is 4 percent and that the expected rate of return on the market portfolio is 12%, what is the net present value of the project? </li></ul>
33. 33. The appropriate discount rate for the project is: r = r f +  (r m – r f ) = 4% + 1.4  (12% – 4%) = 15.2% The initial investment = 100 and the annual cash flow for 10 years = 15 <ul><li>You are a consultant to a firm evaluating an expansion of its current business. The cash-flow forecasts (in millions of dollars) for the project are: </li></ul><ul><li>Years Cash Flow </li></ul><ul><li> 0 -100 </li></ul><ul><li>1-10 +15 </li></ul><ul><li>Based on the behavior of the firm’s stock, you believe that the beta of the firm is 1.4. Assuming that the rate of return available on risk-free investments is 4 percent and that the expected rate of return on the market portfolio is 12%, what is the net present value of the project? </li></ul>
34. 34. <ul><li>The appropriate discount rate for the project is: </li></ul><ul><li>r = r f +  (r m – r f ) = 4% + 1.4  (12% – 4%) = 15.2% </li></ul><ul><li>The initial investment = 100 and the annual cash flow for 10 years = 15 </li></ul><ul><li>Calculate PV of the cash flow =PV(15.2%,10,-15) = 74.71 </li></ul><ul><li>Subtract investment to get NPV = 74.71 – 100 = -25.289 REJECT </li></ul>
35. 35. 15. A share of stock with a Beta of .75 now sells for \$50. Investors expect the stock to pay a year-end dividend of \$2. The T-bill rate is 4%, and the market risk premium is 8%. If the stock is perceived to be fairly priced today, what must be investors’ expectation of the price of the stock at the end of the year?
36. 36. From the CAPM, the appropriate discount rate is: r = r f +  (r m – r f ) = 4% + (0.75  8%) = 10%  P 1 = \$53 15. A share of stock with a Beta of .75 now sells for \$50. Investors expect the stock to pay a year-end dividend of \$2. The T-bill rate is 4%, and the market risk premium is 8%. If the stock is perceived to be fairly priced today, what must be investors’ expectation of the price of the stock at the end of the year? 5 = 2 + P 1 – 50 P 1 = 5 – 2 + 50
37. 37. Chapter 11 – Risk, Return and Capital Budgeting +