Chapter 12 - McGrawHill Exercises

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Chapter 12 - Risk, Return and Capital Budgeting Basic 1. Risk and Return. True or false? Explain or qualify as necessary. a. Investors demand higher expected rates of return on stocks with more variable rates of return. ( LO3) b. The capital asset pricing model predicts that a security with a beta of zero will provide an expected return of zero. ( LO3) ¢. An investor who puts $10,000 in Treasury bills and $20,000 in the market portfolio will have a portfolio beta of 2. ( LO2) d. Investors demand higher expected rates of return from stocks with returns that are highly exposed to macroeconomic changes. ( LO3) e. Investors demand higher expected rates of return from stocks with returns that are very sensitive to fluctuations in the stock market. ( LO3) 2. Diversifiable Risk. In the light of what you've learned about market versus diversifiable (unique) risks, explain why an insurance company has no problem selling life insurance to individuals but is reluctant to issue policies insuring against flood damage to residents of coastal areas. Why don’t the insurance companies simply charge coastal residents a premium that reflects the actuarial probability of damage from hurricanes and other storms? ( LOT) 3. Unique Versus Market Risk. @F igure 12.10 plots monthly rates of return from 2006 to 2020 for the Snake Oil mutual fund and the S&P/TSX Composite Total Return Index. Was this fund well diversified? Explain. ( LO1) Monthly rates of return for the Snake Oil mutual fund and the S&P/TSX Composite Total Return Index (see problem 3) N Snake Oil return, 25 — & percent - ° @ .O 15 ® o ° @ [5) 10 E * ° ® o ® @ IS 5 - o ° ° @ PY [ [ | | | | | ] ® ® 30 20 10 ' ® 10 20 30 (s} @ ® -5 L4 . 0e® o Market return, ° @ 10 percent & o® ®e 7] ® o, s} -15 |- @ -20 o 25 L .

4. Risk and Return. Suppose that the risk premium on stocks and other securities did in fact rise with (that is, the variability of returns) rather than just market risk. Explain how investors could exploit the situation to create portfolios with high expected rates of return but low levels of risk. ( LO3) 5. CAPM and Hurdle Rates. A project under consideration has an internal rate of return of 14% and a beta of .6. The risk-free rate is 4% and the expected rate of return on the market portfolio is 11%. ( LO4) a. Should the project be accepted? b. Should the project be accepted if its beta is 1.6? ¢. Does your answer change? Why or why not? Intermediate 6. CAPM and Valuation. You are considering acquiring a firm that you believe can generate expected free cash flows of $10,000 a year forever. However, you recognize that those cash flows are uncertain. ( LO3) a. Suppose you believe that the beta of the firm is .4. How much is the firm worth if the risk-free rate is 5% and the expected market risk premium is 7%? b. By how much will you misvalue the firm if its beta is actually .6? Page 402 7. CAPM and Expected Return. If the risk-free rate is 4% and the expected market risk premium is 7%, is a security with a beta of 1.25 and an expected rate of return of 11% overpriced or underpriced? ( LO3) 8. Using Beta. 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? ( LO3) 9. Unique Versus Market Risk. [’ Figure 12.11 shows plots of monthly rates of return on three stocks versus the stock market index. The beta and standard deviation of each stock is given beside its plot. a. Which stock is riskiest to a diversified investor? (@ LOT) b. Which stock is riskiest to an undiversified investor who puts all her funds in one of these stocks? ( LO1T) ¢. Consider a portfolio with equal investments in each stock. What would this portfolio’s beta have been? ( LO2) d. Consider a well-diversified portfolio made up of stocks with the same beta as Ford. What are the beta and standard deviation of this portfolio’s return? The standard deviation of the market portfolio’s return is 20%. ( LO2) e. What is the expected rate of return on each stock? Use the capital asset pricing model with an expected market risk premium of 8%. The risk-free rate of interest is 4%. ( LO3)

These plots show monthly rates of return for (a) Ford, (b) Newmont Mining, and (c) McDonald’s, plus the market portfolio. (See (@ problem 9.) (a) Beta = 2.46 Standard deviation = 34.6% 15 20 Ford return (%) Market return

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(b) (c) Newmont Mining return (%) McDonald’s return (%) Beta = .84 Standard deviation = 28.6% Market return Beta =145 Standard deviation = 20.3% . 10 Market return

10. Calculating Beta. Following are several months’ rates of return for Tumblehome Canoe Company. Prepare a plot like @ Figure 12.1. What is Tumblehome’s beta? Check your answers using the Excel SLOPE function. ( LO1) Month Market Return, % Tumblehome Return, % 1 0 +1 2 0 -1 3 -1 -2.5 4 -1 -5 5 +1 +2 6 +1 +1 7 +2 +4 8 +2 +2 9 -2 -2 10 -2 -4 11. Expected Returns. An economy has two scenarios: boom or bust. The returns in each scenario for the market portfolio, an aggressive stock A, and a defensive stock D are in this chart. Rate of Return Scenario Market Aggressive Stock A Defensive Stock D Bust -8% -10% -6% Boom 32 38 24 a. Find the beta of each stock. In what way is stock D defensive? ( LO1) b. If each scenario is equally likely, calculate the expected rate of return on the market portfolio and on each stock. ¢. If the Treasury bill rate is 4%, what does the CAPM say about the fair expected rate of return on the two stocks? ( LO3) d. Which stock seems to be a better buy based on your answers to (a) through (c)? ( LO3) 12. CAPM and Cost of Capital. Draw the security market line when the Treasury bill rate is 4% and the market risk premium is 7%. ‘What are the project costs of capital for new ventures with betas of .75 and 1.75? Which of the following capital investments have positive NPVs? ( LO4) Project Beta Internal Rate of Return, % P10 14 Q 0 6 20 18 N 4 7

13. CAPM and Valuation. You are a consultant to a firm evaluating an expansion of its current business. The annual cash flow LO4) forecasts (in millions of dollars) for the project are: Years Annual Cash Flow 0 -100 Based on the behaviour 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% and that the expected rate of return on the market portfolio is 12%, what is the net present value of the project? 14. CAPM and Cost of Capital. Reconsider the project in the preceding problem. What is the project IRR? What is the cost of capital for the project? Does the accept-reject decision using IRR agree with the decision using NPV? ( LO4) Page 404 { 15. CAPM and Valuation. 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 Treasury bill rate is 4%, and the market risk premium is 7%. If the stock is perceived to be fairly priced today, what must be investors’ expectation for the price of the stock at the end of the year? ( LO3) 16. CAPM and Expected Return. Reconsider the stock in the preceding problem. Suppose investors actually believe the stock will sell for $52 at year-end. Is the stock a good or bad buy? What will investors do? At what point will the stock reach an “equilibrium” at which it again is perceived as fairly priced? (& LO3) 17. Portfolio Risk and Return. Suppose that the TSX, with a beta of 1.0, has an expected return of 13% and Treasury bills provide a riskree return of 5%. (& L02, @ LO3) a. What would be the expected return and beta of portfolios constructed from these two assets with weights in the TSX of (i) 0: (ii) .25; (iii) .5; (iv) .75: (v) 1.0? b. Based on your answer to (a), what is the trade-off between risk and return, that is, how does expected return vary with beta’ ¢. What does your answer to (b) have to do with the security market line relationship? 18. Portfolio Risk and Return. Suppose that the S&P/TSX Composite Index, with a beta of 1.0, has an expected return of 10% and Treasury bills provide a risk-free return of 4%. ( LO2) a. Construct a portfolio from these two assets with an expected return of 8%. What is the beta of this portfolio? b. Construct a portfolio from these two assets with a beta of .4. Calculate the portfolio’s expected return. ¢. Show that the risk premiums of the portfolios in (a) and (b) are proportional to their betas. 19. CAPM and Valuation. You are considering the purchase of real estate that will provide perpetual income that should average $50.000 per year. How much will you pay for the property if you believe its market risk is the same as the market portfolio’s? The Treasury bill rate is 5%, and the expected market risk premium is 7%. (@ LO4) 20. Risk and Return. According to the CAPM, would the expected rate of return on a security with a beta less than zero be more or less than the risk-free interest rate? Why would investors be willing to invest in such a security? Hint: Look back to the auto and gold example in (5’ Chapter 11. ( LO3)

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21. CAPM and Expected Return. The table here shows betas for several Canadian companies from [ yahoo.finance.com. Calculate each stock’s expected rate of return using the CAPM. Assume the risk-free rate of interest is 2%. Use a 7% risk premium for the market portfolio. ( LO3) Company Listing Beta Magna International TSX. NYSE 119 Open Text TSX, Nasdaq .92 Agnico-Eagle Mines TSX NYSE -.38 Second Cup Ltd TSX 34 22. Internet. Go to either (5 www.theglobeandmail.com/globe-investor or (% ca.finance.yahoo.com and look up the companies listed in @ problem 21. Briefly describe the main businesses of each company. Do you think that beta estimates make sense, given the nature of the businesses? ( LO1) 23. CAPM and Expected Return. Stock A has a beta of .5 and investors expect it to return 5%. Stock B has a beta of 1.5 and investors expect it to return 13%. Use the CAPM to find the expected market risk premium and the expected rate of return on the market. ( LO3) 24. CAPM and Expected Return. If the expected market risk premium is 7% and Treasury bills yield 3%, what must be the betas of a stock that investors expect to return 13.6% and a bond with a 5.5% expected return? ( LO3) 25. Internet. Free online betas are hard to find for Canadian stocks unless they are also listed on a U.S. stock exchange such as the NYSE or Nasdag. You can find stocks listed on the NYSE from its Web site, (5 www.nyse.com/listings_directory/stock. For Nasdag-listed companies, go to @ www.nasdaq.com/screening/company-list.aspx. For a Canadian U.S-listed company’s beta, go to @ finance.yahoo.com, enter the stock’s ticker symbol, then click on “Statistics” to find the beta. If you have access to Financial Post Advisor, betas of Canadian companies are found in Corporate Analyzer (click on “market data”). Using one of these methods, find the beta estimates for 5 different Canadian stocks and estimate their required rates of return. Use the current 3-month Treasury bill yield, available at (%) www.bankofcanada.ca/rates/interest-rates/t-bill- vields, as the risk-free rate and a 7% market risk premium. Also, record the main business activities of the firms. ( LO3) 26. Internet. Using Internet resources such as @ www.theglobeandmail.com/globe-investor or (5’ ca.finance.yahoo.com, look up the companies listed in (@ Table 12.2. What are the main businesses of each? On what stock exchanges are they listed? Do their betas make sense? (@ LO1) 27. Project Cost of Capital. Suppose Recipe Unlimited, (5 www.recipeunlimited.com, is considering opening a chain of coffee shops. ‘Which of the betas shown in (%’ problem 21 is most relevant in determining the required rate of return for this venture? Explain why the others are ot appropriate. (&) LO4) 28. Risk and Return. True or false? Explain or qualify as necessary. ( LO3) a. The expected rate of return on an investment with a beta of 2 is twice as high as the expected rate of return of the market portfolio. b. The contribution of a stock to the risk of a diversified portfolio depends on the market risk of the stock. c. If a stock’s expected rate of return plots below the security market line, it is underpriced. d. A diversified portfolio with a beta of 2 is twice as volatile as the market portfolio. e. An undiversified portfolio with a beta of 2 is twice as volatile as the market portfolio. 29. CAPM and Expected Return. A mutual fund manager expects her portfolio to earn a rate of return of 11% this year. The beta of her portfolio is .8. If the rate of return available on risk-free assets is 4% and you expect the rate of return on the market portfolio to be 14%, should you invest in this mutual fund? ( LO3) 30. Required Rate of Return. Reconsider the mutual fund manager in the previous problem. Explain how you would use a stock index mutual fund and a risk-free position in Treasury bills (or a money market mutual fund) to create a portfolio with the same risk as the manager’s but with a higher expected rate of return. What is the rate of return on that portfolio? ( LO2, LO3) 31. Required Rate of Return. In view of your answer to the preceding problem, explain why a mutual fund must be able to provide an expected rate of return in excess of that predicted by the security market line for investors to consider the fund an attractive investment opportunity. ( LO3)

32. CAPM. We Do Bankruptcies is a law firm that specializes in providing advice to firms in financial distress. It prospers in recessions when other firms are struggling. Consequently, its beta is negative, —.2. a. If the interest rate on Treasury bills is 5% and the expected return on the market portfolio is 12%, what is the expected return on the shares of the law firm according to the CAPM? (@ LO3) b. Suppose you invested 90% of your wealth in the market portfolio and the remainder of your wealth in the shares in the law firm. What would be the beta of your portfolio? (@ LO2) Challenge 33. Leverage and Portfolio Risk. [ Footnote 7 in the chapter asks you to consider a borrow-and-invest strategy in which you use $1 million of your own money and borrow another $1 million at the risk-free rate to invest $2 million in a market index fund. If the risk-free interest rate is 4% and the expected rate of return on the market index fund is 12%, what is the risk premium and expected rate of return on the borrow-and-invest strategy? Why is the risk of this strategy twice that of simply investing your $1 million in the market index fund? ( LO3) 34. Integrative. BigCo has a market value of $1 billion and a beta of .9. It has three divisions: chemical processing, oil and gas distribution, and plastic products. The company is thinking about buying another chemical producer, ChemCo. ChemCo is expected to earn cash flows of $9 million this year and cash flows are expected to grow 4% per year thereafter. The beta of ChemCo is 1.4. Currently, the risk-free rate is 4% and the expected rate of return on the market portfolio is 11%. ( LO4) a. What is the expected rate of return for BigCo? b. What discount rate should BigCo use to evaluate ChemCo and why? ¢. How much is ChemCo worth? d. Suppose BigCo acquires ChemCo for the price in (¢). What will be BigCo’s new beta after adding ChemCo? 35. Integrative. Food Express is a well-established grocery chain. Computer Power is an up-and-coming computer software developer for business. Bridge Steel is an integrated steel producer, focusing on steel for buildings and bridges. Some information about the companies was provided by an investment banking company as in the table below. a. If the risk-free rate is 4% and the expected market risk premium is 7%, what is each firm worth? ( LO3) b. If you owned all 3 companies, what would be the beta of your stock portfolio? ( LO2)

Expected Cash Flow Expected Cash Flow Growth Rate Firm Beta Year 1 Years 2to 5 Year 6 and On Food Express 85 $ 7 million 3% 3% Computer Power .95 2 million 8% 4% Bridge Steel 1.3 10 million 2% 3% Page 406 36. Comprehensive. Conglomerated Industries has 4 divisions, each worth about one-quarter of the firm’s market value. The table below summarizes the possible returns on the divisions as well as on the market portfolio. ( LO3) a. Calculate the expected rate of return and standard deviation of return for each division, the firm, and the market. b. What is the beta of the divisions, the firm, and the market? (&) LO1) ¢. According to the CAPM, what rate of return do investors require for each division, if the risk-free rate is 4% and the expected rate of return for the market is as calculated in (a)? ( LO3) d. If the company was thinking of selling the underperforming divisions, which one(s) should it consider selling? Explain your answer. LO4) Division Internal Rates of Return State of the Economy Probability A B C D Market Portfolio Recession .20 8% -10% -1% -4% -3% Normal .60 8% 15% 7% 15% 1% Boom .20 9% 30% 10% 20% 22% Correlation with the market portfolio 730 995 970 945 1

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