This Document Contains Chapters 12 to 13 Solutions to Chapter 12 1. a. False. Investors require higher expected rates of return on investments with high market risk, not high total risk. Variability of returns is a measure of total risk. Stocks with high total risk (highly variable returns) can have low market risk. That is, their returns have low correlation with the market. b. False. If beta = 0, the asset’s expected return should equal the risk-free rate, not zero. c. False. The portfolio is one-third invested in Treasury bills and two-thirds in the market. Its beta will be 1/3 × 0 + 2/3 × 1.0 = 2/3. d. True. High exposure to macroeconomic changes cannot be diversified away in a portfolio. Thus stocks with higher sensitivity to macroeconomic risks have higher market risk and higher expected returns when compared to stocks with lower sensitivity to macroeconomic changes. e. True. For similar reasons as in (d). Sensitivity to fluctuations in the stock market cannot be diversified away. Such stocks have higher systematic risk and higher expected rates of return. 2. The risks of deaths of individual policyholders are largely independent, and therefore are diversifiable. Therefore, the insurance company is satisfied to charge a premium that reflects actuarial probabilities of death, without an additional risk premium. In contrast, flood damage is not independent across policyholders. If my coastal home floods in a storm, there is a greater chance that my neighbor's will too. Because flood risk is not diversifiable, the insurance company may not be satisfied to charge a premium that reflects only the expected value of payouts. 3. The actual returns on the Snake Oil fund exhibit considerable variation around the regression line. This indicates that the fund is subject to diversifiable risk: it is not well diversified. The variation in the fund's returns is influenced by more than just market-wide events. 4. Investors would buy shares of firms with high degrees of diversifiable risk, and earn high risk premiums. But by holding these shares in diversified portfolios, they would not necessarily bear a high degree of portfolio risk. This would represent a profit opportunity, however. As investors seek these shares, we would expect their prices to rise, and the expected rate of return to investors buying at these higher prices to fall. This process would continue until the reward for bearing diversifiable risk dissipated. 11-1 This Document Contains Chapters 12 to 13 5. a. Required return = rf + β(rm – rf) = 4% + .6 (11% – 4%) = 8.2% With an IRR of 14%, the project is attractive. b. If beta = 1.6, required return increases to: 4% + 1.6 (11% – 4%) = 15.2% which is greater than the project IRR. You should now reject the project. c. Given its IRR, the project is attractive when its risk and therefore its required return are low. At a higher risk level, the IRR is no longer higher than the expected return on comparable risk assets available elsewhere in the capital market. 6. a. The expected cash flows from the firm are in the form of a perpetuity. The discount rate is: rf + β(rm – rf) = 5% + .4×7% = 7.8%. Therefore, the value of the firm would be: P0 = Cash flow r = .078 $10,000 = $128,205 b. If the true beta is actually .6, the discount rate should be: rf + β(rm – rf) = 5% + .6×7% = 9.2% Therefore, the value of the firm is: P0 = Cash flow r = $10,000 .092 = $108,696 By underestimating beta, you would overvalue the firm by $128,205 – 108,696 =$19,509 11-2 7. Required return = rf + β(rm – rf) = 4% + 1.25(11% – 4%) = 12.75% Expected return = 11% The stock’s expected return is less than the required return given its risk. Thus the stock is overpriced. Why? Given the stock’s future cash flows and its current price, investors can expect to earn only 11%. Comparable risk investments earn 12.75%. At the current price, investors are better off investing in these other investments. This lack of demand will cause the stock price to fall until its expected return increases to the required return of 12.75%. 8. Required return = risk free rate + beta × [expected return on market – risk free rate] = rf + β(rm – rf) For the stock, we know that 12% = rf + .8 ( 14% - rf ) Using the CAPM, solve for the risk free rate of interest: rf = (Required return - β × rm) / ( 1 - β) = (12% - .8 × 14%) / (1 - .8) = 4% We assume that the risk free rate is not changed. Therefore, if the market return turns out to be 10%, we expect that the stock’s return will be 4% + .8(10% - 4%) = 8.8%. 9. a. A diversified investor will find the highest-beta stock most risky. This is Ford, which has a beta of 2.46. b. Ford has the highest total volatility; the standard deviation of its returns is 34.6%. c. Portfolio beta, β = (2.46 + .84 + 1.45)/3 = 1.58 d. This portfolio will have the same beta as Ford, 2.46. The total risk of the portfolio will be 1.58 times the total risk of the market portfolio because the effect of firm-specific risk will be diversified away. The standard deviation of the portfolio is therefore 2.46 × 20% = 49.2%. e. Using the CAPM, we compute the expected rate of return on each stock from the equation r = rf + β × (rm – rf). In this case, rf = 4% and (rm – rf) = 8%. Ford: r = 4% + 2.46(8%) = 23.68% Newmont Mining: r = 4% + .84(8%) = 10.72% McDonald’s: r = 4% + 1.45(8%) = 15.6% 11-3 10. The following table shows the average return on Tumblehome for various values of the market return. It is clear from the table that, when the market return increases by 1%, Tumblehome’s return increases on average by 1.5%. Therefore, β = 1.5. If you prepare a plot of the return on Tumblehome as a function of the market return, you will find that the slope of the line through the points is 1.5. Market return(%) Average return on Tumblehome(%) −2 −3.0 −1 −1.5 0 0.0 1 1.5 2 3.0 Note: If your calculator supports statistics then you can estimate this. Enter points as X,Y values. In stats linear mode you see that b = 1.5 which is the slope of the line. Using the SLOPE function in Excel will also calculate the slope of 1.5. 11. a. Beta is the responsiveness of each stock's return to changes in the market return. Then: βA = ∆rA ∆rm = 32 – (−8) 38 – (−10) = 48 40 = 1.2 βD = ∆rD ∆rm = 32 – (−8) 24 – (−6) = 30 40 = .75 D is considered to be a more defensive stock than A because its return is less sensitive to the return of the overall market. In a recession, D will usually outperform both stock A and the market portfolio. b. We take an average of returns in each scenario to obtain the expected return. rm = (32% – 8%)/2 = 12% rA = (38%– 10%)/2 = 14% rD = (24% – 6%)/2 = 9% 11-4 c. According to the CAPM, the expected returns that investors will demand of each stock, given the stock betas and given the expected return on the market, are: r = rf + β(rm – rf) rA = 4% + 1.2(12% – 4%) = 13.6% rD = 4% + .75(12% – 4%) = 10.0% d. The return you actually expect for stock A, 14%, is above the fair return, 13.6%. The return you expect for stock D, 9%, is below the fair return, 10%. Therefore stock A is the better buy. 12. Figure follows below. Cost of capital = risk-free rate + beta × market risk premium Since the risk-free rate is 4% and the market risk premium is 7%, we can write the cost of capital as: Cost of capital = 4% + beta × 7% Cost of capital (from CAPM) Beta = 4% + beta × 7% .75 4% + .75 × 7% = 9.25% 1.75 4% + 1.75 × 7% = 16.25% beta r 1.0 4% 11% 7% = market risk premium SML 0 11-5 The cost of capital of each project is calculated using the above CAPM formula. Thus, for Project P, its cost of capital is: 4% + 1.0 × 7% = 11%. If the cost of capital is greater than IRR, then the NPV is negative. If the cost of capital equals the IRR, then the NPV is zero. Otherwise, if the cost of capital is less than the IRR, the NPV is positive. Project Beta Cost of capital IRR NPV P 1.0 11.0% 14% + Q 0.0 4.0 6 + R 2.0 18.0 18 0 S 0.4 6.8 7 + T 1.6 15.2 20 + 13. The appropriate discount rate for the project (opportunity cost of capital) is: r = rf + E(rm – rf) = 4% + 1.4(12% – 4%) = 15.2% Therefore: NPV = –100 + 15 uannuity factor(15.2%, 10 years) = –100 + 74.7112 = -$25.29 With negative NPV you should reject the project. 14. To calculate the IRR find the discount rate for which the net present value of the project is zero. Let r be the IRR. Find r such that: NPV = -100 + 15 uannuity factor(r, 10 years) = 0 Rearranging the equation: 15 uannuity factor(r, 10 years) = 100. So find the discount rate that makes the present value of the 15 annual cash flow equal to 100 To solve this equation on the calculator: N=10, PMT = 15, PV=-100, FV=0 and calculate I/Y. We find that the project IRR is 8.14%. The IRR is less than the opportunity cost of capital, 15.2% (from Question 13). Therefore you should reject the project, just as you found from the NPV rule. 15. From the CAPM, the appropriate discount rate is: r = rf + Ex market risk premium = 4% +.75 x 7% = 9.25% To solve for the price in one year, P1, use the rate of return equation and assume that the stock’s rate of return equals the appropriate discount rate: r = .0925 = DIV + capital gain price = 50 2 + (P1 – 50) So: P1 = 50 x .0925 - 2 + 50 = $52.625 11-6 16. If investors believe the year-end stock price will be $52, then the expected return on the stock is: Rate of return = (dividend + capital gain)/initial share price = [2 + (52 – 50)] / 50= .08 = 8%, which is less than the opportunity cost of capital. Alternatively, the “fair” current price of the stock (that is, the present value of the investor's expected cash flows) is (2 + 52)/1.0925 = $49.43, which is less than the current price. Some investors who own the stock will want to sell the stock to capture the high value. But the process of selling the stock will continue until the price reaches $49.43. At that point, the expected return is a “fair” 9.25%: [2 + (52 – 49.43)] / 49.43 = .0925 = 9.25%. 17. a. The expected return of the portfolio is the weighted average of the returns on the TSX and T-bills. Similarly, the beta of the portfolio is a weighted average of the beta of the TSX (which is 1.0) and the beta of T-bills (which is zero). (i) E(r) = 0 u13% + 1.0 u5% = 5% E= 0 u1 + 1 u0 = 0 (ii) E(r) = .25 u13% + .75 u5% = 7% E= .25 u1 + .75 u0 = .25 (iii) E(r) = .50 u13% + .50 u5% = 9% E= .50 u1 + .50 u0 = .50 (iv) E(r) = .75 u13% + .25 u5% = 11% E= .75 u1 + .25 u0 = .75 (v) E(r) = 1.00 u13% + 0 u5% = 13% E= 1.0 u1 + 0 u0 = 1.0 b. For every increase of .25 in the Eof the portfolio, the expected return increases by 2%. The slope of the relationship (additional return per unit of additional risk) is therefore 2%/.25 = 8%. c. The slope of the return per unit of risk relationship is the market risk premium: rM – rf = 13% – 5% = 8%, which is exactly what the SML predicts. The SML says that the risk premium equals beta times the market risk premium. 18. a. Call the weight in the TSX w and the weight in T-bills (1 – w). Then w must satisfy the equation: w u10% + (1 – w) u4% = 8% which implies that w = .67. The portfolio would be 67% in the TSX and 33% in T-bills. The beta of the portfolio would be the weighted average of the betas of the TSX and T-Bills. Since T-Bills are risk-free, their beta is zero. The beta of the portfolio is: .67×1 + .33×0 = .67 11-7 b. To form a portfolio with a beta of .4, use a weight of .40 in the TSX and a weight of .60 in T-bills. Then, the portfolio beta would be: E= .40 u1 + .60 u0 = .40 The expected return on this portfolio is .4 × 10% + .6 × 4% = 6.4% c. Security’s expected return = risk-free rate + security’s risk premium So: Security’s risk premium = Security’s expected return- risk-free rate Security risk premium for Portfolio with 8% expected return and 0.67 beta = 8% - 4% = 4% For this portfolio: Security risk premium/beta = .04/.67 = .06 Security risk premium for Portfolio with beta of .4 = 6.4% - 4% =2.4% For this portfolio: Security risk premium/beta = .024/.4 = .06 Both portfolios have the same ratio of risk premium to beta: (8% - 4%) / 0.67 = (6.4% - 4%) / .4 = 6%. Notice that the ratio of security risk premium to risk (i.e., beta) equals the market risk premium (6%) for both stocks. 19. Expected return on the market portfolio beta (with beta =1) = risk free rate + market portfolio beta expected x expected market risk premium = .05 + 1 x .07 = .12 = 12% If the systematic risk were comparable to that of the market, the discount rate would be 12.0%. The property would be worth $50,000/0.12 = $416,667. 20. The CAPM states that r = rf + E(rm – rf). If E< 0, then r < rf. Investors would invest in a security with an expected return below the risk-free rate because of the hedging value such a security provides for the rest of the portfolio. Investors get their “reward” in terms of risk reduction rather than in the form of high expected return. 21. The historical risk premium on the market portfolio has been about 7%. Therefore, using this value and the assumed risk-free rate of 2%, we can use the CAPM to derive the cost of capital for these firms as 2% + E u7%. Beta Return Magna International 1.33 11.31% Open Text 0.62 6.34% Agnico-Eagle Mines 0.79 7.53% Tim Hortons 0.77 7.39% 11-8 22. Magna International: (TSX: MG.TO) Magna International Inc. operates as an automotive supplier in North America, Europe, and internationally. The company designs, develops, and manufactures automotive systems, assemblies, and modules and components, as well as engineers and assembles vehicles primarily for sale to original equipment manufacturers of cars and light trucks. The demand for automobiles is correlated to the economic cycle, as the economic is booming, the sale of vehicles increase rapidly, while during recessionary periods, the sales plummet. Therefore, the beta of 1.33 makes sense. Open Text: (Nasdaq: OTEX) (TSX: OTC) is the market leader in providing Collaboration, Enterprise Content Management software solutions. The stock beta is 0.62, indicating lower sensitivity to variations in the market. The customers of Open Text are other businesses. The demand for Open Text’s solutions will be higher when the economy is growing and businesses are investing in new technologies. Likewise, the demand will be low when the economy is down. This however, does not makes sense that a high tech company such as Open Text will have a stock beta of 0.62. Agnico-Eagle Mines: (TSX: AEM.TO) engages in the exploration, development, and production of mineral properties. It explores for gold, silver, zinc, copper, and lead. Since precious metals such as gold and silver are considered safe havens in times of recessions, mining companies such as Agnico-Eagle are less sensitive of market conditions than other companies. Therefore, the beta of 0.79 is reasonable. Tim Hortons: (TSX:THI.TO) Offers coffee and doughnuts in locations across Canada and the United States. The beta of Tim Hortons is a bit less than 1, indicating that the sensitivity of the return on Tim Hortons stock to changes in the market is less than average. This makes sense. The demand for coffee and doughnuts is not hugely variable with market conditions. 23. r = rf + E(rm – rf) 5 = rf + .5(rm – rf) (stock A) 13 = rf + 1.5(rm – rf) (stock B) Solve these simultaneous equations to find that rf = 1% and rm = 9%. Thus the market risk premium is 9% - 1%, or 8%. 11-9 24. r = rf + E(rm – rf) Stock: 13.6 = 3 + E×7 E= (13.6 – 3)/7 = 1.51 Bond: 5.5 = 3 + E×7 E= (5.5 – 3)/7 = 0.36 25. 3 month Treasury Bills yield 0.85% as of Aug 2011. 7% market premium. TD Bank: Beta = 1.37, r = 0.85%+1.37×7% = 10.44% The Toronto-Dominion Bank and its subsidiaries provides financial services in North America. It operates through four segments: Canadian Personal and Commercial Banking, Wealth Management, U.S. Personal and Commercial Banking, and Wholesale Banking. The Canadian Personal and Commercial Banking segment provides personal and business banking services. It offers various financial products and services to approximately 11 million personal and small business customers. This segment also provides financing, investment, cash management, international trade, and day-today banking services; and insurance products, including home and automobile coverage, life and health insurance, and credit protection coverage. As of October 31, 2007, it offered banking solutions through telephone and Internet banking, approximately 2,500 automated banking machines, and a network of 1,070 branches. The Wealth Management segment provides various investment products and services, including advisory, distribution, and asset management; trader program and long-term investor solutions; and discount brokerage, financial planning, and private client services to retail and institutional customers. The U.S. Personal and Commercial Banking segment provides personal and commercial banking products and services, insurance agency, wealth management, mortgage banking, and other financial services to approximately 1.5 million households. As of the above date, it offered products and services through a network of 617 branches and 761 automated banking machines. The Wholesale Banking segment provides various capital markets and investment banking products and services, which include underwriting and distribution of new debt and equity issues, providing advice on strategic acquisitions and divestitures, and executing daily trading and investment needs primarily to corporate, government, and institutional customers. The company was founded in 1855 and is headquartered in Toronto, Canada. Find 4 other Canadian firms the same way as it is done to TD. 11-10 26. IMAX: (TSX: IMX.TO) large-format film company. It specializes in digital and film-based motion picture technologies. It has a beta of 1.06, which means it has higher sensitivity to the market. This makes sense because consumers watch movies in booming economies, while demand drops in economic downturns as more movies are placed behind necessities. Research in Motion: (TSX:RIM.TO) RIM is a leader in wireless communications. Products include the BlackBerry™ wireless email solution, wireless handhelds and wireless modems. At a beta of 1.64, it is far more volatile than the market. This makes sense because a major component of its business is selling to other businesses and technology companies like RIM flourish when other businesses are doing well and investing in new technology. Furthermore, because smartphones are more of a luxury good for regular consumers, the sensitivity of the market is greater in good times and bad. Gildan Activewear: (TSX: GIL.TO) is a vertically-integrated marketer and manufacturer of quality branded basic apparel. The Company is the leading supplier of activewear for the wholesale imprinted sportswear market in the U.S. and Canada, and also a leading supplier to this market in Europe. The Company sells T- shirts, sport shirts and fleece in large quantities to wholesale distributors as undecorated “blanks”, which are subsequently decorated by screenprinters with designs and logos. A beta of 1.04 is reasonable because clothing is a necessity and moves with the markets. Barrick Gold: (TSX: ABX.TO) Barrick is the world’s pre-eminent gold producer, with a portfolio of 27 operating mines, many advanced exploration and development projects located across five continents, and large land positions on the most prolific and prospective mineral trends. The Company also has the largest reserves in the industry, with 124.6 million ounces of proven and probable gold reserves, 6.2 billion pounds of copper reserves and 1.03 billion ounces of contained silver within gold reserves as at December 31, 2007. Gold is very stable because it is able to retain its value in poor economic conditions and is treated as a safe haven. However, in times of economic prosperity, the return on gold is far less than the returns in most other industries. Therefore, a beta of 0.45 is very fitting. Cameco： (TSX: CCO.TO) is the world's largest publicly traded uranium company. The consumption of fuel such as uranium is largely dependent on production in the economy. As the economy suffers, so do companies such as Cameco. Therefore, 1.51 beta does make sense. Canadian Pacific Railway: (TSX: HCH.TO) connects the Atlantic and the Pacific coasts with the heart of North America. The Canadian Pacific Railway boasts a beta less than one because it is less sensitive to market movements. As the economy 11-11 worsens, travellers look for cheaper means of transportation than airplanes. Resulting, in a lesser impact in recessionary periods. Royal Bank : (TSX: RY-PR-L.TO) RBC provides personal and commercial banking, wealth management services, insurance, corporate, investment banking and transaction processing services on a global basis. RBC employs more than 70,000 full and part-time employees who serve more than 15 million personal, business, public sector and institutional clients through offices in Canada, the U.S. and 46 other countries. Since banking services are necessities and given the nature of security in the Canadian banking operations, a beta of 0.86 is logical. Loblaw Companies: (TSX:L-PA.TO) is Canada’s largest food distributor, with grocery stores across the country. Since food is an essential for survival, it is expected that a grocery chain’s earnings won’t vary much with the business cycle. It is not surprising the beta of the Loblaw is the lowest of the group and is far less than 1. The sensitivity of the return on Loblaw stock to changes in market is low. We say that the market risk of a grocery chain is low. TransCanada Corp 🙁 TSX: TRP.TO) TransCanada is a leader in the responsible development and reliable operation of North American energy infrastructure. Similar to Loblaws, energy is a necessity and is essential to survival. Therefore, a beta of 0.40 is no surprise. 27. Cara Operations should use the beta of Tim Horton’s (which is 0.77) to find that the required rate of return is 7.39%. The project is an investment in a chain of coffee shops and the beta of Tim Horton’s reflects the risk of a firm in the coffee shop business. The beta of Cara Operations reflects the risk of a coffee shop business. 28. a. False. The stock’s risk premium, not its expected rate of return, is twice as high as the market’s. b. True. The stock’s unique risk does not affect its contribution to portfolio risk but its market risk does. c. False. A stock plotting below the SML offers too low an expected return relative to the expected return indicated by the CAPM. The stock is overpriced. Investors will not want to pay that price to receive the stock’s cash flows. The price must fall to increase the stock’s rate of return. d. True. If the portfolio is diversified to such an extent that it has negligible unique risk, then the only source of volatility is its market exposure. A beta of 2 then implies twice the volatility of the market portfolio. e. False. An undiversified portfolio has more than twice the volatility of the market. In addition to the fact that it has double the sensitivity to market risk, it also has volatility due to unique risk. 11-12 29. The CAPM implies that the expected rate of return that investors will demand of the portfolio is: r = rf + E(rm – rf) = 4% + .8(11% – 4%) = 9.6% If the portfolio is expected to provide only a 9% rate of return, it’s an unattractive investment. The portfolio does not provide an expected return that is sufficiently high relative to its risk. 30. A portfolio invested 80% in a stock market index fund (with a beta of 1.0) and 20% in a money market fund (with a beta of zero) would have the same beta as this manager's portfolio: E= .80 u1.0 + .20 u0 = .80 However, it would provide an expected return of .80 u11% + .20 u4% = 9.6% which is better than the portfolio manager's expected return. 31. The security market line provides a benchmark expected return that an investor can earn by mixing index funds with money market funds. Before you place your funds with a professional manager, you will need to be convinced that he or she can earn an expected return (net of fees) in excess of the expected return available on an equally risky index fund strategy. 32. a. r = rf + E(rm rf) = 5% + [–.2 u(12% – 5%)] = 3.6% b. Portfolio beta = .90 u Emarket + .10 u Elaw firm = .90 u1.0 + .10 u( .2) = .88 33. Expected income on stock fund: $2 million u.12 = .24 million Interest paid on borrowed funds: $1 million u.04 = .04 million Net expected earnings: $0.20 million Expected rate of return on the $1 million you invest is: $.20 million $1 million = .20 = 20% Risk premium = 20% – 4% = 16% 11-13 This is double the risk premium of the market index fund (which is 8%, = 12% - 4%) The risk is also double that of holding a market index fund. You have $2 million at risk, but the net value of your portfolio is only $1 million. A 1% change in the rate of return on the market index will change your profits by .01 u$2 million = $20,000. But this changes the rate of return on your portfolio by $20,000/$1,000,000 = 2%, double that of the market. So your risk is in fact double that of the market index. 34. a. Expected rate of return = rf + E(rm rf) = .04 + .9 × (.11 - .04) = .103 = 10.3% b. The appropriate discount rate to evaluate ChemCo is one that reflects the riskiness of ChemCo’s cash flows. Since we know that ChemCo's current beta is 1.4, it is reasonable to use this in the calculation of the appropriate discount rate. Note that the discount rate of BigCo is irrelevant because BigCo has three different divisions, of which only one is in the same business of ChemCo. Discount rate = rf + E(rm rf) = .04 + 1.4 × (.11 - .04) = .138 = 13.8% c. Assuming that these are after-tax cash flows and using the constant dividend growth model, the value of ChemCo is Value of ChemCo = $9 million .138 - .04 = $91.837 million d. Think of BigCo as a portfolio consisting of the original three divisions plus the new ChemCo division. Thus, the new beta of BigCo will equal the weighted average of its old beta and the beta ChemCo, with the weights based on the market values of three original divisions, ChemCo and the new combined BigCo. The value of BigCo is its original $1,000 million plus the value of ChemCo, for a total of $1,091.837 million. Weight for ChemCo division = ChemCo value New BigCo value = 91.837 1091.837 = .084 = 8.4% Weight for original BigCo = Original BigCo value New BigCo value = 1000 1091.837 = .916 = 91.6% New beta of BigCo = .084 × 1.4 + .916 × .9 = .942 As expected, adding ChemCo, with its higher beta, causes the beta of BigCo to increase. 11-14 35. a. We take advantage of the formula for the present value of a growing annuity, found in Chapter 4: rC1 - g × [1 - ( 1 + g 1 + r ) T ] for valuing the Year 2 to 5 cash flows and recognize that starting in Year 6, each stock has a constant perpetual growth rate and can be valued using the constant dividend growth model, DIV/(r – g). Food Express (FE) Required rate of return = rf + E(rm rf) = .04 + .85 × (.07) = .10 Value of FE today: = 7 1.10 + 1 1.10 × 7 × 1.03 .10 - .03 × [1 - ( 1.03 1.10 ) 4 ] + 1 1.105 × .10 - .03 7 × (1.03)5 = $100.00 million Note: Since FE has the same growth rate for Years 2 and onward, the constant growth formula can be used to value the stock: Value of FE today: = .10 7- .03 = $100.00 million Computer Power (CP) Required rate of return = rf + E(rm rf) = .04 + .95 × (.07) = .107 Value of CP today: = 2 1.107 + 1 1.107 × 2 × 1.08 .107 - .08 × [1 - ( 1.08 1.107 ) 4 ] + 1 1.1075 × 2 × (1.08)4 × (1.04) .107 - .04 = $34.00 million Bridge Steel (BS) Required rate of return = rf + E(rm rf) = .04 + 1.3 × (.07) = .131 Value of BS today: = 10 1.131 + 1 1.131 × 10 × 1.02 .131 - .02 × [1 - ( 1.02 1.131 ) 4 ] + 1 1.1315 × 10 × (1.02)4 × (1.03) .131 - .03 = $96.00 million 11-15 b. Total portfolio value = $100.00 + 34.00 + 96.00 = 230.00 million Company Weight in Portfolio E Weight × E FE 100 230 = .4348 .85 .3696 CP 34 230 = .1478 .95 .1404 BS 96 230 = .4174 1.3 .5426 Total 1.0526 The portfolio beta is the weighted average of the individual stocks’ betas and is about 1.05. 36. a. This question is most easily handled with a spreadsheet but can be done using the formulas. State of the Economy Probability Division A Division B Division C Division D Firm Market Recession 0.2 8% -10% -1% -4% -1.75% -3% Normal 0.6 8% 15% 7% 15% 11.25% 11% Boom 0.2 9% 30% 10% 20% 17.25% 22% Expected return 8.2% 13.0% 6.0% 12.2% 9.9% 10.4% Standard deviation 0.40% 12.88% 3.69% 8.33% 6.25% 7.94% b. Using the formula Ej = corrjm × σj σm , where corrjm is the correlation between stock j’s return and the market return, σj is the standard deviation of stock j’s return and σm is the standard deviation of the market return: Emarket = corrmm × σm σm = 1 × .0794 .0794 = 1 EA = corrAm × σA σm = .73 × .004 .0794 = .0368 EB = corrBm × σB σm = .995 × .1288 .0794 = 1.61 11-16 EC = corrCm × σC σm = .97 × .0369 .0794 = .451 ED = corrDm × σD σm = .945 × .0833 .0794 = .991 Since each of the four divisions is worth about ¼ of the firm’s market value, the beta of the firm is the equal-weighted average of the four divisions’ betas: EFirm = EA + EB + EC + ED 4 = (.0368 + 1.61 + .451 + .991)/4 = .77 c. According to the CAPM, the required rate of return is rj = rf + Ej (rm rf) Assuming the riskfree rate is 4 percent, and using the expected return on the market calculated in (a), the required rate of return to each division is: rA = .04 + .0368 × (.104 - .04) = .0424 = 4.24% rB = .04 + 1.61 × (.104 - .04) = .143 = 14.3% rC = .04 + .451 × (.104 - .04) = .0689 = 6.89% rD = .04 + .991 × (.104 - .04) = .103 = 10.3% d. Compare each division’s expected return, calculated in (a), with its required return, calculated according to the CAPM and reported in (c). Divisions with expected return at least equal to or greater than the required return are generating positive NPV. Those whose expected return is less than the required return are underperforming and provide negative NPV. Conglomerate should a buyer who can improve the performance of these negative NPV divisions. Hopefully, Conglomerate will sell these poorly performing divisions for more than they are worth under its control, capturing some of gains from the improved performance (See Chapter 23 for more on how companies share gains from mergers). Both Divisions A and D have expected returns greater than the CAPM required rate of return. However, Division B, with a required rate of return of 14.3%, has an expected return of 13%. Likewise, Division C has a required rate of return of 6.89% but its expected rate of return is 6%. This means Divisions B and C are likely candidates for sale. However, Conglomerate may want to consider whether improvements in performance can be made to increase the expected rates of return, without resorting to selling the divisions. 11-17 Brealey 5CE Solutions to Chapter 13 1. The yield to maturity on the bonds (since maturity is now 19 years) is the interest rate that solves the following equation: 90 × annuity factor(r, 19 years) + 1000/(1 + r)19 = 1050 The solution can be obtained most easily from a financial calculator: Set n = 19, FV = 1000, PV = (-)1050, PMT = 90. Compute the interest rate as 8.46%. The after-tax cost of debt is therefore 8.46% × (1 – .30) = 5.92%. 2. r = DIV/P0 = $4/$40 = .10 = 10% 3. WACC = VD × rdebt × (1 – Tc) + VP × rpreferred + VE × requity = .3 × 8.46% × (1 – .30) + .2 × 10% + .5 × 12.5% = 10.03% 4. r = DIV1/P0 + g = DIV0(1 + g) P0 + g = 5 × 1.05 60 + .05 = .1375 = 13.75% 5. The total value of the firm is $80 million. The weights for each security class are: Debt: D/V = 20/80 = .250 Preferred: P/V = 10/80 = .125 Common: E/V = 50/80 = .625 WACC = VD × rdebt × (1 – Tc) + VP × rpreferred + VE × requity = .25 × 6% × (1 – .35) + .125 × 8% + .625 × 12% = 9.475% 6. Executive Fruit should use the WACC of Geothermal, not its own WACC, when evaluating an investment in geothermal power production. The risk of the project determines the discount rate, and in this case, Geothermal’s WACC is more reflective of the risk of the project in question. The proper discount rate, therefore, is not 12.3%. It is more likely to be 11.4%. 7. a. First calculate the company’s WACC 12-1 WACC = 30% × (1 - 40%) × 6% + 70% × 11% = 8.78% Free cash flow = operating cash flow - investment = 68 – 30 million = 38 million Value of business = 38 /(8.78% - 4%) = 794.98 million b. Equity = Value of business - Debt = 794.98 × (1-30%) = 556.49 million 8. The rate on Buildwell’s debt is 5 percent. The cost of equity capital is the required rate of return on equity, which can be calculated from the CAPM as 4% + .80 × 7% = 9.6%. The weighted average cost of capital, with a tax rate of 35%, is WACC = VD × rdebt × (1 – Tc) + VE × requity = .30 × 5% × (1 – .35) + .70 × 9.6% = 7.695% 9. IRR, which is 12%, exceeds the cost of capital. Therefore, BCCI should accept the project. The present value of the project cash flows is $100,000 × annuity factor(7.695%, 7 years) = $526,112. Thus the most BCCI should pay for the project is $526,112. If it does, the project’s NPV will be zero but the project will earn enough to meet the cost of capital. If BCCI pays $526,112 for the project, then the project’s IRR will be 7.695%, just equal to the cost of capital. 10. The company has 35% tax rate on its taxable income. To calculate free cash flow need to calculate taxes paid as if the firm was unlevered. This is because the cost and tax benefit of debt are in the WACC (WACC has the after-tax cost of debt in it) Unlevered Taxable income is EBITDA – Deprecation = EBIT Unlevered Taxes = tax rate x EBIT. The annual forecasted free cash flows are: Year 1 2 3 4 1. EBITDA 80 100 115 120 2. Unlevered taxes = .35 x EBIT 21 24.5 28 28 3. Investment 12 15 18 20 4. Free cash flow = 1-2-3 47 60.5 69 72 12-2 Since free cash flow from year 5 onward will remain unchanged at year-4 levels, so the free cash flow growth rate is zero. The horizon value at year 4 is: Horizon value = Free cash flow at year 5 $72 million $935.67 r - g = 0.07695 - 0 = million The company’s total value at the beginning of Year 1 is: 2 3 4 4 PV $47 $60.5 $69 $72 $935.67 $900.14 = 1.07695 + (1.07695) + (1.07695) + (1.07695) + (1.07695) = million Since the capital structure is 30% debt, the value of the firm’s debt is: 0.30× $900.14 million = $270.042 million The value of the equity is: 0.70 × $900.14 million = $630.098 million 11. Security Market value Explanation Debt $ 5.5 million 1.10 × par value of $5 million Equity $15.0 million $30 per share × 500,000 shares* Total $20.5 million *Number of shares = $10 million book value $20 book value per share = 500,000 WACC = VD (1 – Tc) × rdebt + VE × requity = 5.5 20.5 × (1 – .3) × 9% + 15 20.5 × 15% = 12.67% 12. Because the firm is all-equity financed, asset beta = equity beta = .8. The WACC is the same as the cost of equity which may be calculated using the CAPM: requity = rf + β(rm – rf) = 5% + .8 × 10% = 13% 13. The 12.5% value calculated by the analyst is the current yield of the firm’s outstanding debt: interest payments/bond value. This calculation neglects the fact that bonds selling at discounts from or premiums over par value provide expected returns determined in part by expected price appreciation or depreciation. The analyst should be using yield to maturity instead of current yield to calculate cost of debt. [This answer assumes the value of the debt provided is the market value. If it is the book value, then 12.5% would be the average coupon rate of outstanding debt, which also would be a poor estimate of the required rate of return on the firm’s debt. The coupon rate was set when the debt was issued. We have no idea how long ago the debt was issued. Don’t use the coupon rate as an estimate of the bond’s required rate of return!] 12-3 14. a. Using the recent growth rate of 30% and the dividend yield of 2%, one estimate would be: DIV1/P0 + g = .02 + .30 = .32 = 32% In this calculation, we’ve assumed that the current dividend yield is the next expected dividend divided by the current price, DIV1/P0. However, if the dividend yield was the most recent past dividend, DIV0/P0, then with 30% dividend growth, DIV1/P0 would be .02 × 1.3 = .026 and the estimated required rate of return would be .026 + .3 = .326, or 32.6%. Another estimate, based on the CAPM, would be r = rf + β(rm – rf) = 4% + 1.2 × 8% = 13.6% b. The estimate of 32% seems far less reasonable. It is based on an historic growth rate that is impossible to sustain. No company can grow at 30% forever. The [DIV1/P0 + g] rule requires that the growth rate of dividends per share must be viewed as highly stable over the foreseeable future. In other words, it requires us to use the sustainable growth rate. 15. a. The 9% coupon bond has a yield to maturity of 10% and sells for 93.86% of face value: n = 10, i = 10%, PMT = 90, FV = 1000, compute PV = $938.55 The market value of the issue is therefore .9386 × $20 million = $18.77 million The 10% coupon bond sells for 92.8% of par value, and has a yield to maturity of 11.0%: n = 15, PV = (−)928, PMT = 100, FV = 1000, compute i = 11.00% The market value of the issue is .928 × $25 million = $23.20 million The weighted average before-tax cost of debt is therefore 18.77 18.77 + 23.20 × 10% + 23.20 18.77 + 23.20 × 11% = 10.55% b. The after-tax cost of debt is (1 – .30) × 10.55% = 7.39% 12-4 16. The bonds must be selling below par value, because the YTM is greater than the coupon rate. The price per $1000 par value is 80 × annuity factor(9%, 10 years) + 1000/1.0910 = $935.82 The total market value of the bonds is $10 million par value × $935.82 market value $1000 par value = $9.36 million Book value of the preferred shares is $2 million and the par value per share is $20. Thus there are 100,000 shares of preferred stock (=$2 million/$20 per share). Preferred shares are selling at $15 per share, for total market value of $1.5 million. The market value of 1 million common shares selling at $20/share is $20 million. The book value of the common shares is sum of the common stock plus retained earnings, which also happens to equal $20 million. Therefore, the market value capital structure is: Dollars Percent Bonds 9.36 million 30.3% Preferred Stock 1.50 million 4.9% Common Stock 20.00 million 64.8% Total 30.86 million 100.0% 17. The yield to maturity on debt is rdebt = 9% The rate on preferred stock is rpreferred = $2/$15 = .133 = 13.3% The rate on common stock is requity = rf + β(rm – rf) = 4% + 1.5 × 7% = 14.5% Using the capital structure derived in the previous problem, we can calculate WACC as: WACC = VD (1 – Tc) × rdebt + VE × requity + VP × rpreferred = .303 × (1 – .4) × 9% + .648 × 14.5% + .049 × 13.3% = 11.68% 12-5 18. The discount rate for a project is determined by the risk of the project. If the venture in home computer is unlike any other projects in the personal computer industry and shares the same risk characteristics as University Products, then it is appropriate to use University Product’s WACC. However, if the new venture is similar to other projects in the personal computer industry, then the average WACC of firms in the personal computer industry should be used. Depending on the assumptions, the appropriate WACC will determine whether or not the project should be pursued. If the IRR on the computer project is greater than the WACC used, then the project should be accepted. If the IRR on the computer project is less than the WACC used, then the project should be rejected. 19. a. r = rf + β(rm – rf) = 4% + 1.5 × 7% = 14.5% b. Total market value of Muskoka Real Estate is $6 million and the market value of the debt is $2 million. Thus the market value of its equity is $6 - $2, or $4 million. The current capital structure is 1/3 debt, 2/3 equity. Weighted average beta = 31 × 0 + 32 × 1.5 = 1.0 c. WACC = VD (1 – Tc) × rdebt + VE × requity = 31 × (1 – .4) × 4% + 32 × 14.5% = 10.47% d. If the company wishes to expand its present business then the WACC is a reasonable estimate of the discount rate since the risk of the proposed project is similar to the risk of the existing projects. Use a discount rate of 10.47%. e. The WACC of optical projects should be based on the risk of those projects. Using a beta of 1.2, the discount rate for the new venture is r = 4% + 1.2 × 7% = 12.4% 20. a. Equity Market value = 10 million shares × $15/share = $150 million rE = rf + rf + β(rm – rf) = 2.5% + 1.2 × 6.5% = 10.3% Debt Market value per bond = semi-annual coupon payment × PVIFA(6-month rB, no. of payments) + face value × PVIF(6-month rB, no. of periods to maturity) rB = required rate of return on 10-year Gov't debt +150 basis points Required rate of return on 10-year Gov't debt = (1 + .04/2)2 - 1 =.0404 rB = .0404 + .0150 = 0.0554 = 5.54% 12-6 6-month required rate of return = (1.0554)1/2 - 1 = .0273 Face value = 1000 Coupon payment= .06/2 × 1000 = 30 No. of payments = 2 payments/year × 10 years = 20 Market value per bond = 30 x PVIFA(.0273,20) + 1000 × PVIF(.0273, 20) = $1,041.2 Market value of all bonds = 20,000 bonds × $1,041.2 = $20,824,000 WACC Calculation Market Value Market Weight Before-tax Required Rate of Return After-tax Required Rate of Return Weight × After-tax Return Debt $ 20,824,000 .122 5.54% (1-.35)×5.54% = 3.6% .439% Equity $150,000,000 .878 10.3% 10.3% 9.043% Total $170,824,000 9.48% b. βU = βlevered + βdebt × D/E × (1 - TC) 1+D/E × (1 - TC) To find βdebt, use the CAPM: rdebt = rf + βdebt(rm – rf) βdebt = rdebt - rf rm – rf = .0554 - .025 .065 = .468 βU = βlevered + βdebt × D/E × (1 - TC) 1 + D/E × (1 - TC) = 1.2 + .468 × .122/.878 × (1 - .35) 1 + .122/.878 × (1 - .35) = 1.14 As expected, the unlevered beta is lower than the levered equity beta. With no debt in the capital structure, the equity is less risky. c. Relever the equity beta to reflect the new capital structure of 50% debt: βlevered = βU + [βU - βdebt] × D/E × (1 - TC) = 1.14 + [1.14 - .468] × .5/.5 × (1 - .35) = 1.58 As expected, moving from a debt/equity ratio of .122/.878, or about .139 to .5/.5, or 1, increases the riskiness of the equity. The levered equity beta increases from 1.2 to 1.58. The new required rate of return to equity is: rE = rf + β(rm – rf) = 2.5% + 1.58×6.5% = 12.77% 12-7 The new WACC is: WACC = VD × rdebt × (1 - TC) + VE × requity = .5 × 5.54% (1 - .35) + .5 × 12.77% = 8.19% 21. a. The annual free cash flows expected from Premier Pizza are: Calculation of Annual Cash Flow Annual Cash Flow 1. Revenues $10 million 2. Operating costs .7 × 10 million = $ 7.0 million 3. EBITDA (=1-2) $ 3.0 million 4. Depreciation .05 ×10 million = $ 0.5 million 5. EBIT (=3-4) $ 2.5 million 6. Tax at 35% .35×$2.5 million= $ 0.875 million 7. Profit after tax (=5 – 6) $ 1.625 million 8. Operating cash flow (= 4 + 7) $ 2.125 million 9.Capital expenditures .05×$10 million= $ 0.5 million 10. Free cash flow (=8 - 9) $ 1.625 million The annual cash flows from Premier Pizza are a constant growing perpetuity. Using the perpetuity formula, the present value of the cash flows is: PV(annual cash flows) = annual cash flow required rate of return - growth rate Required rate of return on cash flows: WACC = VD × rdebt × (1 - TC) + VE × requity = .25 × .06 × (1-.35) + .75 × .15 = .12225 PV(annual cash flows) = $1.625 million = $19.76 million .12225 - .04 If Boris and Isabelle offer $19.76 million for Premier Pizza, the NPV of their investment will be zero. The offer is the investment in the firm: NPV = - investment + PV(future firm’s free cash flows) = -19.76 million + 19.76 million = 0 The project will earn the required rate of return, just enough return to compensate all investors. This is the maximum amount they should offer. If they can purchase Premier Pizza for less than $19.76 million, the investment will earn more than the required rate of return, with the bulk of the extra return going to the equity investors in the project. 12-8 b. Fresh Foods current WACC rEQUITY = rf + β(rm – rf) = .03 + .8 × .07 = .086 rDEBT = .05 D/V = .4, E/V = .6 WACC = VD × rdebt × (1 - TC) + VE × requity = .4 × .05 × (1 - .35) + .6 × .086 = .0646 Using Fresh Food's current WACC as the required rate of return on Premier Pizza gives a valuation of: PV(annual cash flows) = $1.625 million = $66.06 million .0646 - .04 This says that Premier Pizza is worth over 3 times more owned by Fresh Foods than by Boris and Isabelle, even though both groups expect the same cash flows! The difference comes solely from the different discount rates. Question: What is the appropriate discount rate for Fresh Foods to use in valuing Premier Pizza? If you use Fresh Foods' current WACC, you are assuming that riskiness of the pizza manufacturing business is the same as the riskiness of the grocery retail business. Why should it necessarily be the case? Without further investigation, the better assumption would be that the appropriate discount rate for Fresh Foods to use for Premier Pizza's cash flows is 12.225%, the rate used by Boris and Isabella. We know that Boris and Isabelle investigated the risks of the business before determining the appropriate discount rate. Under this assumption, the maximum Fresh Foods should be willing to pay is also $19.76 million. 22. a. The current promised YTM if there is no default is YTM = (1000+60-569)/569 = 86.3% b. If default occurs, YTM = [.3 × (1000+60) - 569]/569 = -44.1% c. The current expected YTM is YTM = probability of default × YTM if default occurs + probability of no default × YTM if no default = .6 × -44.1% + .4× 86.3% = 8.06% Obviously when the probability of default is high, the promised YTM is too high, 86.3% in this case compared to 8.06% of expected return, so it is not a good measure of expected return. 12-9 23. The Big Oil WACC with taxes is shown in Table 13.4 (10.46%). If Big Oil does not pay taxes, the after-tax and before-tax costs of debt are identical because no tax savings on the interest expense. WACC would then become: WACC = VD × rdebt + P V × rpreferred + VE × requity = .277 × 9% + .07 x 10%.+.703 × 12% = 11.63% So, without taxes the firm’s WACC is higher because of the loss of tax savings. If Big Oil issues new equity (common stock) and uses the proceeds to pay off all of its debt, the cost of equity will fall. There is no longer any leverage, so the equity becomes safer and commands a lower risk premium. But the firm’s WACC is the same in this situation of no taxes. Assume the firm still has the preferred equity equal to 7% of the firm’s value and the preferred equity rate of return is unchanged. Now, with no debt the equity financing is 93% of the firm’s financing (NOTE the original percentage debt financing was 22.7% and the original common stock financing was 70.3%. Noted 22.7% + 70.3% =93%). Now given that WACC is 11.63%, cost of preferred stock is 10% the new cost of equity can be calculated by rearranging the new WACC equation: Without debt WACC = P V × rpreferred + VE × requity = 11.63% = .07 x 10% +.93x requity = 11.63% requity = (11.63% - .07 x 10%)/.93 = 10.93/.93 = 11.75% So the cost of equity is lower without the debt financing. (We use the WACC derived in the absence of interest tax shields since, for the all- equity firm, there is no interest tax shield.) 24. The net effect of Big Oil’s transaction is to leave the firm with $200 million more debt (because of the borrowing) and $200 million less equity (because of the dividend payout). Total assets and business risk are unaffected. The WACC will remain unaffected, since business risk is unchanged. Assume that the same preferred equity financing exists and the preferred equity rate of return is still 10%. However, the cost of equity will rise. With the now higher leverage, the business risk is spread over a smaller equity base, so each share is now riskier. The new financing mix for the firm would be E = 1,000, D = 388.3+200=588.3 and P=120 So total firm value = 1000 + 588.3 + 120 = 1,708.3. You can see that there’s an error in Table 13.3. The total there, 1,788.3 should be replaced with 1,708.3. With the new financing mix the percentage of financing of each source of financing is now:, 12-10 VD = 588.3 .344 1708.3 = and E V = 1000 .585 1708.3 = and P 120 .07 V = 1708.3 = If the cost of debt is still 9%, then we can solve for the new cost of equity as follows. We use the fact that, even at the new financing mix, WACC must still be 11.63%. WACC = VD × rdebt + VE × requity+ P V × rpreferred = .344 × 9% + .585 × requity + .07x10% = 11.63% requity = (11.63% - .344 x 9% - .07 x 10%)/.585 = 7.834/.585 = 13.4% We solve to find that requity = 13.40%. So issuing the new debt does increase the cost of equity. 25. Even if the WACC were lower when the firm’s tax rate is higher, this does not imply that the firm would be worth more. The after-tax cash flows that the firm would generate for its owners also would be lower and this would reduce the value of the firm, even if those cash flows were discounted at a lower rate. If the tax authority is collecting more income from the firm, the value of the firm will fall. 26. This reasoning is faulty in that it implicitly treats the discount rate for the project as the cost of debt if the project is debt financed, and as the cost of equity if the project is equity financed. In fact, if the project poses risk comparable to the risk of the firm’s other projects, the proper discount rate is the firm’s cost of capital, which is a weighted average of the costs of both debt and equity. 27. Internet: Calculating WACC of Canadian Companies Expected results: This question gives students enough information to get a rough estimate of companies' current WACC. TD Bank WACC From Chapter 12, Question 25: 3 month Treasury Bill yield 2.22% as of Oct 2008. 7% market premium. TD Equity Beta = 1.13 requity = 2.22% + 1.13 × 7% = 10.13% Using information from yahoo finance and government bond yield, and DBRS, which gave the debt an AA low rating, the WACC of TD is found to be 6.9% 7 yr gov bond yield = 1.89% 12-11 rdebt = 7 yr gov bond yield + AA-rated corporate bond spread = 1.89% +.44% = 2.33% Market Value Weight After-tax Cost Component Cost Equity (billion $) 67.27 .422 .1013 .422×.1013 Debt (billion $) 92.26 .578 .0233×(1-.30) .578×.0233 Firm Value 159.53 1.000 0.056 12-12 Solution to Minicase for Chapter 13 Bernice needs to explain to her boss, Mr. Brinestone, that appropriate rates of return for cost of capital calculations are the rates of return that investors can earn on comparable risk investments in the capital market. Mr. Brinestone’s estimate of the cost of equity is his target value for the book return on equity; it is not the expected rate of return that investors demand on shares of stock with the same risk as Sea Shore Salt. Bernice’s CAPM calculation indicates that the correct value for the equity rate is 10.5%. This value is broadly consistent with the rate one would infer from the constant growth dividend discount model (which seems appropriate for a mature firm like this one with stable growth prospects). The dividend discount model implies a cost of equity of a bit more than 10.5 percent: requity = DIV1 P0 + g = $2 $40 + .067 = .117 = 11.7% This value is close to Bernice's value. It is not surprising that the different methods for estimating the cost of equity yield different values. However, it is reassuring that the values are similar. For the rest of the solution we will use 11% as the cost of equity. Mr. Brinestone’s returns for other securities should be modified to reflect the expected returns these securities currently offer to investors. The bank loan and bond issue offer pre-tax rates of 7.75% and 8%, respectively, as in Mr. Brinestone’s memo. It is acceptable to use the interest rates on the loan and the debt as the required rates of return given the information provided. We are told the "bank charged interest at the current rate", which implies that the bank loan rate is a floating rate and hence changes when market rates change. We are told that the bonds were just issued. The convention is to set the bond coupon rate at the bond's required rate of return so that the bond will be sold at par value. The preferred stock, however, is not selling at par, so Mr. Brinestone’s assertion that the rate of return on preferred is 6% is incorrect. In fact, with the preferred selling at $70 per share, the rate of return is rpreferred = DIV P0 = $6 $70 = .086 = 8.6% This makes sense: the pre-tax return on preferred should exceed that on the firm’s debt. Finally, the weights used to calculate the WACC should reflect market, not book, values. These are the prices that investors would pay to acquire the securities. The market value weights are computed as follows: 12-13 Amount Percent Rate of Comment (millions) of total return (%) Bank loan valued at face amount $120 17.91 7.75 Bond issue valued at par 80 11.94 8.0 Pfd. stock $70 × 1 million shares 70 10.45 8.6 Common stock $40 × 10 million shares 400 59.70 10.5 $670 100.00 Therefore, the WACC, which serves as the corporate hurdle rate, should be 9%: WACC = .1791 × 7.75% × (1 – .35) + .1194 × 8% × (1 – .35) + .1045 × 8.6% + .5970 × 10.5 = 8.69% 12-14 Solution Manual for Fundamentals of Corporate Finance Richard A. Brealey, Stewart C. Myers, Alan J. Marcus, Elizabeth Maynes, Devashis Mitra 9780071320573, 9781259272011
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