1. Calculate the cost of each capital component, after-tax cost of debt, cost of preferred, and cost of equity with the DCF method and CAPM method.

2. What do you estimate the company?s WACC?

Please use data from the provided worksheet. Let me know if you find anything wrong with the data if it interferes with solving the above problems. Please add a new worksheet to the workbook attached. Thank you!!

Group 1 Interim Report 1 Johnson & Johnson Company Overview For generations, almost every household in the United States has used some form of product from Johnso With a growing product line that dates back from 1886, Johnson & Johnson is one of the world's leading health The company started with the first commercially available first aid kit. With major acquisitions throughout history, they were able to introduce other products that became household items such as mass-producing san women. In the hospital and surgical rooms, they introduced the first coronary stent, which is a medical device to flow to the heart by keeping vessels open. This device revolutionized cardiology and helped treat patients w diseases. With over 250 subsidiary companies under Johnson & Johnson, the company is structured into 3 segments Pharmaceutical, and Medical Devices. Some of its most recognizable brands in the consumer segment, include Listerine, and Benadryl. In the pharmaceutical segment, their number selling medication is Remicade whic about 9.4% of Johnson & Johnson's 2015 total revenue. In this segment of Johnson & Johnson, they are also h other therapeutic areas such as oncology and immunology medicines. Their Medical Devices segment account of their revenue in 2015. While keeping this in mind, Johnson & Johnson's Medical Device segment is also the world in terms of revenue. Sustainability and growth is always a concern, even for this massive and historical company that has shown impressive growth rates. Some concerns come from the revenue decline of every category in the market devic other issue stems from the recent approval of a cheaper generic version of Remicade from federal health offi Johnson has been proactive and looks to combat declining growth by investing $9 billion into research and dev meet the evolving health care needs of the aging population in developing nations and to fuel long-term grow Johnson & Johnson was held privately for nearly 5 decades before going public in 1944. The company liste investors through the New York Stock Exchange. Since they began publicly trading, they have over 32 successiv earning increases and 54 years of uninterrupted years of increases in dividends. The following information is th quote for the company. Just in the last year, their 52-week low was at 89.90. Johnson & Johnson Last Price Volume Day Change *Friday Sep 9, 2016 4:02 PM 118.23 7.96 Million 1.24-1.04% References Blake, H. (n.d.). A history of... Johnson & Johnson - Pharmaphorum. Retrieved September 11, 2016, from http://pharmap and-analysis/a-history-of-johnson-johnson/ Johnson & Johnson. (2015). Retrieved September 11, 2016, from http://files.shareholder.com/downloads/JNJ/1709744668x0x881109/474857DD-8E67-43B1-BB380A9712D93545/2015_annual_report_.pdf MDDI Staff. (2014, November 21). Top 40 Medical Device Companies. Retrieved September 11, 2016, from http://www.mddionline.com/article/top-40-medical-device-companies NYSE. (2016, September 9). Johnson & Johnson. stock quote. Retrieved from https://www.nyse.com/quote/XNYS:JNJ The Associated Press. (2016, April 05). F.D.A. Clears Cheaper Version of Johnson & Johnson Biologic. Retrieved Septembe http://www.nytimes.com/2016/04/06/business/fda-clears-cheaper-version-of-johnson-johnson-biologic.html? rref=collection/timestopic/Johnson & Johnson e form of product from Johnson & Johnson. ne of the world's leading health care company. major acquisitions throughout its 130-year ms such as mass-producing sanitary products for tent, which is a medical device that allows blood ogy and helped treat patients with cardiovascular ny is structured into 3 segments: Consumer, the consumer segment, includes: Band-Aid, medication is Remicade which accounts for son & Johnson, they are also heavily vested in edical Devices segment account for about 35.7% ical Device segment is also the largest in the torical company that has shown a very ry category in the market device segment. The micade from federal health officials. Johnson & $9 billion into research and development to ons and to fuel long-term growth. blic in 1944. The company listed shares for public ng, they have over 32 successive years of . The following information is the most recent ber 11, 2016, from http://pharmaphorum.com/views- -43B1-BB38- mber 11, 2016, from ww.nyse.com/quote/XNYS:JNJ nson Biologic. Retrieved September 11, 2016, from n-johnson-biologic.html? Johnson & Johnson Financial Ratios vs Industry Averages BALANCE SHEET (IN THOUSANDS) Period Ending 1/3/2016 12/28/2014 Current Assets Cash And Cash Equivalents 13,732,000 14,523,000 Short Term Investments 24,644,000 18,566,000 Net Receivables 10,734,000 10,985,000 Inventory 8,053,000 8,184,000 Other Current Assets 3,047,000 3,486,000 Total Current Assets 60,210,000 55,744,000 Long Term Investments Property Plant and Equipment 15,905,000 16,126,000 Goodwill 21,629,000 21,832,000 Intangible Assets 25,764,000 27,222,000 Accumulated Amortization Other Assets 4,413,000 3,232,000 Deferred Long Term Asset Charges 5,490,000 6,202,000 Total Assets 133,411,000 130,358,000 Current Liabilities Accounts Payable 20,743,000 21,393,000 Short/Current Long Term Debt 7,004,000 3,638,000 Other Current Liabilities Total Current Liabilities 27,747,000 25,031,000 Long Term Debt 12,857,000 15,122,000 Other Liabilities 19,095,000 18,006,000 Deferred Long Term Liability Charges 2,562,000 2,447,000 Minority Interest Negative Goodwill Total Liabilities 62,261,000 60,606,000 Stockholders' Equity Misc. Stocks Options Warrants Redeemable Preferred Stock Preferred Stock Common Stock 3,120,000 3,120,000 Retained Earnings 103,879,000 97,245,000 Treasury Stock -22,684,000 -19,891,000 Capital Surplus Other Stockholder Equity -13,165,000 -10,722,000 Total Stockholder Equity 71,150,000 69,752,000 Net Tangible Assets 23,757,000 20,698,000 Total Liabilities and Equity 133,411,000 130,358,000 12/31/2013 20,927,000 8,279,000 15,320,000 7,878,000 4,003,000 56,407,000 16,710,000 22,798,000 27,947,000 4,949,000 3,872,000 132,683,000 20,823,000 4,852,000 25,675,000 13,328,000 15,638,000 3,989,000 58,630,000 3,120,000 89,493,000 -15,700,000 -2,860,000 74,053,000 23,308,000 132,683,000 INCOME STATEMENT (IN THOUSANDS) 1/3/2016 12/28/2014 70,074,000 74,331,000 21,536,000 22,746,000 48,538,000 51,585,000 Revenue Total Revenue Cost of Revenue Gross Profit Operating Expenses Research Development Selling General and Administrative Non Recurring Others Total Operating Expenses Operating Income or Loss Income from Continuing Operations Total Other Income/Expenses Net Earnings Before Interest and Taxes Interest Expense Income Before Tax Income Tax Expense Minority Interest Net Income From Continuing Ops Non-recurring Events Discontinued Operations Extraordinary Items Effect Of Accounting Changes Other Items Net Income Net Income Preferred Stock And Other Adjustments Net Income Applicable To Common Sha EPS (Basic) Basic Shares Outstanding EPS (Diluted) Diluted Shares Outstanding EBITDA 9,046,000 21,203,000 733,000 - 12/31/2013 71,312,000 22,342,000 48,970,000 17,556,000 8,494,000 21,954,000 178,000 20,959,000 8,183,000 21,830,000 580,000 18,377,000 2,192,000 19,748,000 552,000 19,196,000 3,787,000 15,409,000 137,000 21,096,000 533,000 20,563,000 4,240,000 16,323,000 -2,424,000 15,953,000 482,000 15,471,000 1,640,000 13,831,000 - - - 15,409,000 15,409,000 5.56 2,770,000 5.48 2.81B 22,110,000 16,323,000 16,323,000 5.8 2,820,000 5.7 2.86B 24,820,000 13,831,000 13,831,000 4.92 2,810,000 4.81 2.88B 22,930,000 CASH FLOW (IN THOUSANDS) Period Ending 1/3/2016 12/28/2014 Net Income 15,409,000 16,323,000 Operating Activities, Cash Flows Provided By or Used In Depreciation 3,746,000 3,895,000 12/31/2013 13,831,000 4,104,000 Adjustments To Net Income -1,215,000 Changes In Accounts Receivables -433,000 Changes In Liabilities -3,000 Changes In Inventories -449,000 Changes In Other Operating Activities 2,224,000 Total Cash Flow From Operating Activiti 19,279,000 Investing Activities, Cash Flows Provided By or Used In Capital Expenditures -3,463,000 Investments -6,679,000 Other Cash flows from Investing Activiti 2,407,000 Total Cash Flows From Investing Activiti -7,735,000 Financing Activities, Cash Flows Provided By or Used In Dividends Paid -8,173,000 Sale Purchase of Stock -3,995,000 Net Borrowings 1,379,000 Other Cash Flows from Financing Activit -57,000 Total Cash Flows From Financing Activit -10,846,000 Effect Of Exchange Rate Changes -1,489,000 Change In Cash and Cash Equivalents -791,000 -681,000 -247,000 955,000 -1,120,000 -654,000 18,471,000 307,000 -632,000 1,821,000 -622,000 -1,395,000 17,414,000 -3,714,000 -10,794,000 2,203,000 -12,305,000 -3,595,000 -865,000 -643,000 -5,103,000 -7,768,000 -5,342,000 850,000 -57,000 -12,260,000 -310,000 -6,404,000 -7,286,000 -889,000 2,028,000 56,000 -6,091,000 -204,000 6,016,000 NYSE. (2016, September 9). Johnson & Johnson Stock Reports. Retrieved from http://finance.yahoo.com/quote/JNJ/financials?p=JNJ Liquidity Ratio Current ratio Quick Ratio Utilization Ratio Inventory Turnover Days Sales Outstanding Fixed Asset Turnover Total Asset Turnover Leverage Ratio Debt Ratio Times Interest Earned EBITDA Coverage Ratio Liabilities-to-assets ratio Profitability Net Profit Margin Gross Profit Margin Basic Earning Power Return on Assets Return on Equity Price-to Earnings Ratio Price-to-Cash Flow Ratio Market to Book Ratio Calculations 2015 2014 2.1699643205 2.2269985218 1.8797347461 1.9000439455 2.6742828759 55.9110369038 4.4057843445 0.5252490424 2.7793255132 53.941491437 4.6093885651 0.5702066617 0.1488707828 35.7753623188 40.0543478261 0.4666856556 0.1439113825 39.5797373358 46.5666041276 0.4649196827 0.2198961098 31.75% 0.1480237762 11.55% 21.66% 0.2195988215 31.64% 0.1618312647 12.52% 23.40% 18.4748201439 0.798858862 3.9990780042 17.7103448276 0.8854961832 4.1528615667 DU PONT EQUATION ROE = (net income / sales) * (sales / assets) * (assets / shareholders' equity) ROE = net profit margin asset turnover ROE = 0.2198961098 0.5252490424 ROE = 0.2165706254 the multiplier is what busting the ROE Johnson & Johnson. (2016, September 9). Financials. Reuters. Retrieved from http://www.reuters.com/finance/stocks/financialHighlights?symbol=JNJ.N Price Dec 31, 2015 102.72 s 2013 Industry 2.1969620253 2.85 1.8901265823 1.98 2.8359989845 78.4131702939 4.2676241771 0.5374614683 0.1370183068 33.0975103734 47.5726141079 0.441880271 s. Retrieved from symbol=JNJ.N 0.99 45.79 0.1939505273 28.24% 0.120233941 10.42% 18.68% 11.42 54.38 20.8780487805 0.7939129436 3.8977921219 37.08 26.94 (assets / shareholders' equity) equity multiplier 1.8750667604 ROE 2.48 61.87 11.23 15.4 Johnson & Johnson (JNJ) seems to be utilizing their asset well compared the industry. They are turning over their inventory faster the industry as well as collecting their accounts receivable faster too. JNJ is able to cover their debts however their current ratio is less than the industry. Investors expect growth from JNJ however not at the extent of the industry avg. JNJ is not highly leverage; therefore, it has more assets than it does debt. Johnson & Johnson Stock Data Price Shares Outstanding Average Volume Percent Change Beta Insider Ownership Percentage Owned By Insiders Percentage Owned By Institutions Percentage Owned By Investors $118.23 2.74 B 6,651,057 1.24% 0.07 0.02% 67.30% 32.68% *Date Obatined 09/09/2016 at 4:44 PM Insider Ownership Direct Holders Name GORSKY ALEX STOFFELS PAULUS CARUSO DOMINIC J COSGROVE STEPHEN J ULLMANN MICHAEL H FASOLO PETER DUATO JOAQUIN PRUDEN GARY J PETERSON SANDRA E KAPUSTA RONALD A Shares Date Reported 176,849 8-Feb-16 122,543 17-Feb-16 116,673 26-Jul-16 97,011 16-Jan-15 91,455 8-Feb-16 49,407 8-Feb-16 47,960 28-Apr-16 43,630 7-Jun-16 35,644 8-Feb-16 25,725 22-Jul-16 Options Septembe Calls Strike 113 114 115 116 117 118 119 120 121 122 Contract Name JNJ160909C00113000 JNJ160909C00114000 JNJ160909C00115000 JNJ160909C00116000 JNJ160909C00117000 JNJ160909C00118000 JNJ160909C00119000 JNJ160909C00120000 JNJ160909C00121000 JNJ160909C00122000 Last Price 6.7 6.3 4.55 2.68 2.11 0.72 0.01 0.01 0.04 0.04 Bid 6.2 5.25 3.1 2.15 1.02 0.12 0.01 0.02 0 0 Ask 6.35 5.45 3.6 2.55 1.55 0.55 0.01 0.02 0.04 0.05 123 124 125 126 127 128 129 JNJ160909C00123000 JNJ160909C00124000 JNJ160909C00125000 JNJ160909C00126000 JNJ160909C00127000 JNJ160909C00128000 JNJ160909C00129000 0.01 0.01 0.01 0.08 0.07 0.13 0.05 0 0.06 0.04 0 0.12 0.03 0 0.11 0.03 0 0.16 0.32 0 0.47 Puts Strike 95 100 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 127 Contract Name JNJ160909P00095000 JNJ160909P00100000 JNJ160909P00108000 JNJ160909P00109000 JNJ160909P00110000 JNJ160909P00111000 JNJ160909P00112000 JNJ160909P00113000 JNJ160909P00114000 JNJ160909P00115000 JNJ160909P00116000 JNJ160909P00117000 JNJ160909P00118000 JNJ160909P00119000 JNJ160909P00120000 JNJ160909P00121000 JNJ160909P00122000 JNJ160909P00123000 JNJ160909P00124000 JNJ160909P00125000 JNJ160909P00127000 Last Price 0.05 0.21 0.03 0.01 0.04 0.02 0.01 0.01 0.02 0.01 0.01 0.04 0.02 0.7 1.44 2.23 3.18 3.58 4.25 6.15 8 Bid 0 0 0 0 0.01 0.01 0 0 0 0 0 0.01 0.01 0.54 1.48 2.47 3.45 3.5 5.45 5.9 7.05 Ask 0.13 0.26 0.05 0.06 0.04 0.04 0.06 0.06 0.05 0.12 0.02 0.12 0.05 1 1.87 2.95 3.95 3.8 5.95 6.05 7.2 Repurchase Program I have attached an article from Johnson & Johnson with talking points on a stock repurchase program. http://www.jnj.comews/all/Johnson-Johnson-Announces-10-Billion-Share-Repurchase-Program Works Cited (n.d.). News. Retrieved September 09, 2016, from http://www.jnj.comews/all/Johnson-Johnson-Announces-10-Billion-Sh Repurchase-Program In, B. O. (n.d.). JNJ : Summary for Johnson & Johnson Common Stock - Yahoo Finance. Retrieved September 09, 2016, from http://finance.yahoo.com/quote/JNJ?p=JNJ Holder Vanguard Group, Inc. (The) State Street Corporation BlackRock Institutional Trust Company, N.A. FMR, LLC BlackRock Fund Advisors Bank of New York Mellon Corporation Wellington Management Company, LLP State Farm Mutual Automobile Insurance Co Northern Trust Corporation Bank of America Corporation Top Institutional Holders Shares Date Reported 184,512,652 29-Jun-16 143,791,840 29-Jun-16 73,876,243 29-Jun-16 43,435,082 29-Jun-16 42,089,045 29-Jun-16 41,599,812 29-Jun-16 39,104,602 29-Jun-16 37,878,592 29-Jun-16 34,965,355 29-Jun-16 31,070,667 29-Jun-16 Insider Transactions Insider Purchases Last 6 Months Purchases Sales Net Shares Purchased (Sold) Total Insider Shares Held % Net Shares Purchased (Sold) Net Institutional Purchases Prior Quarter to Latest Quarter Net Shares Purchased (Sold) % Change in Institutional Shares Held Shares 5,000 0 5,000 492.46k 1.00% Shares -17,863,400 -0.98% Trans 2 0 2 N/A N/A % Change 0.00% -42.20% 0.00% -16.25% -28.23% -52.63% -98.28% -80.00% 0.00% 0.00% Volume 21 1 2 40 1 39 150 181 3 2 Here is a link to actual transactions: http://finance.yahoo.com/quote/JNJ/holders?p=JNJ Options September 9, 2016 Calls Change 0 -4.6 0 -0.52 -0.83 -0.8 -0.57 -0.04 0 0 -0.04 0.05 0 0 0 0 0 -80.00% 166.67% 0.00% 0.00% 0.00% 0.00% 0.00% 9 1 1 1 23 1 2 Change 0 0 0 0 0 -0.03 0 0 0 -0.02 0 0.02 -0.02 0.6 0.76 0.72 0.55 0 0 1.02 0 % Change 0.00% 0.00% 0.00% 0.00% 0.00% -60.00% 0.00% 0.00% 0.00% -66.67% 0.00% 100.00% -50.00% 600.00% 111.76% 47.68% 20.91% 0.00% 0.00% 19.88% 0.00% Volume 2 20 238 4 80 8 1 1 1 21 10 59 235 1,195 213 155 4 4 1 5 38 Puts repurchase program. urchase-Program son-Johnson-Announces-10-Billion-ShareRetrieved September 09, 2016, from % Out 6.71% 5.23% 2.69% 1.58% 1.53% 1.51% 1.42% 1.38% 1.27% 1.13% Value 22,381,385,241 17,441,950,623 8,961,188,497 5,268,675,576 5,105,401,284 5,046,057,320 4,743,388,339 4,594,673,323 4,241,297,666 3,768,872,000 Open Interest Implied Volatility 0 122.27% 3 112.60% 5 59.38% 40 44.63% 6 32.03% 37 17.24% 285 7.42% 847 16.80% 293 27.74% 254 36.72% 71 35 669 399 95 61 2 34.38% 58.98% 53.52% 67.19% 72.66% 84.77% 113.87% Open Interest Implied Volatility 2 196.09% 20 174.61% 239 79.69% 469 74.22% 93 65.63% 38 58.59% 18 52.73% 13 51.56% 130 41.80% 109 41.41% 44 20.70% 1,059 21.09% 360 5.47% 729 21.29% 402 25.00% 197 40.82% 218 50.29% 56 0.00% 39 67.97% 38 0.00% 38 0.00% A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 B Tool Kit C D E F G Chapter 9 H 12/8/2012 The Cost of Capital 9-1 The Weighted Average Cost of Capital The cost of capital is the weighted average cost of the debt, preferred stock, and common equity that the firm uses to finance its assets, or its WACC. Definitions WACC = Weighted average cost of capital = wd rd(1 - T) + wps rps + ws rs rd = Cost of debt rps = Cost of preferred stock rs = Cost of stock (common equity) wd = Percent of target capital structure financed with debt wps = Percent of target capital structure financed with preferred stock ws = Percent of target capital structure financed with stock (common equity) T = Tax rate 9-2 Choosing Weights for the Weighted Average Cost of Capital Figure 9-1 MicroDrive, Inc.: Selected Capital Structure Data (Millions of Dollars, December 31, 2013) Liabilities and Equity Accounts payable Notes payable Accruals Total C.L. Long-term debt Total liabilities Preferred stock Common stock Retained earnings Total common equity Total L&E $ ,200 ,280 ,300 $ ,780 1,200 $1,980 ,100 ,500 ,970 $1,470 $3,550 Percent of Total 5.6% 7.9% 8.5% 22.0% 33.8% Investor-Supplied Capital Book Market Book Percent Market Percent Value of Total Value of Total $ ,280 9.2% $ ,280 9.9% 1,200 39.3% 1,200 42.4% ,100 3.3% ,100 3.5% $1,470 $3,050 48.2% 100.0% $1,250 $2,830 44.2% 100.0% 55.8% 2.8% 14.1% 27.3% 41.4% 100.0% Other Data (Millions, except per share data): Number of common shares outstanding = Price per share of common stock = Number of preferred shares outstanding = 50 $25.00 1 A 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 B C D E F G H Price per share of preferred stock = $100.00 Notes: 1. The market value of the notes payable is equal to the book value. Some of the long-term bonds sell at a discount and some sell at a premium, but their aggregate market value is approximately equal to their aggregate book value. 2. The common stock price is $25 per share. There are 50 million shares outstanding, for a total market value of equity of $25(50) = $1,250 million. 3. The preferred stock price is $100 per share. There are 1 million shares outstanding, for a total market value of preferred of $100(1) = $100 million. 9-3 After-Tax Cost of Debt: rd (1 T) and rstd (1 T) The relevant cost of debt is the after-tax cost of new debt, taking account of the tax deductibility of interest. The after-tax cost is calculated by multiplying the interest rate (or the before-tax cost of debt) times one minus the tax rate. MicroDrive's Short-Term Debt MicroDrive has notes payable with the following interest rate: rstd = 10.000% MicroDrive's Actual Long-Term Debt MicroDrive has outstanding bonds with a 9% annual coupon rate, 15 years remaining until maturity, and a face value of $1,000. The bonds make semiannual coupon payments and currently are trading in the market at a price of $1000. To estimate the cost of debt, use the RATE function to find the yield on the bonds: Number of years to maturity Number of payments per year Annual coupon rate Par value Current price = PV = 15 2 9% $1,000 $1,000.00 N= PMT = FV = 30 $45 $1,000 I/YR = rd = 4.500% Annualized rd = 9.000% Hypothetical Example for a Bond not at Par A 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 B C D E F G Use the RATE function to find the yield on the bonds with the following information: Number of years to maturity Number of payments per year Annual coupon rate Par value Current price = PV = 15 2 9% $1,000 $923.14 N= PMT = FV = 30 $45 $1,000 I/YR = rd = 5.0% Annualized rd = 10.0% The Impact of a High Probability of Default Use the RATE function to find the yield on the bonds with the following information: Number of years to default Recovery percentage at default Number of payments per year Annual coupon rate Par value Current price = PV = 14 70% 2 9% $1,000 $1,000.00 N= PMT = FV = 28 $45 $700 I/YR = rd = 3.9% Annualized rd = 7.8% The After-Tax Cost of Debt Find the after-tax cost of debt; MicroDrive has a 40% marginal tax rate. Tax rate = Short-term debt: rstd = Long-term debt: rd = 40% 10% 9% After-tax cost of debt = r (1 - T) Short-term debt: rstd (1-T) = Long-term debt: rd (1-T) = Flotation Costs and the Cost of Debt 6.000% 5.400% H A 155 156 157 158 159 160 161 162 163 164 165 166 167 168 B C D E F G H Consider the issuance of a 30-year, $1,000 par value bond with a coupon rate of 9%, paid semiannually. The tax rate is 40%, and the flotation costs are 1% of the value of the issue. The bond will initially sell at its par value. Years to maturity = Flotation percentage cost (F) = Par value = Annual coupon payment = Tax rate = Maturity payment = Par = Number of payments per year = 30 1.00% $1,000 9.00% 40% $1,000 2 First, calculate the after-tax coupon payments and the net proceeds after the flotation costs. 169 After-tax coupon payment = (Coupon pmt.) 170 171 172 173 174 175 176 177 178 179 180 181 182 183 After-tax coupon payment = Net proceeds after flotation costs = Net proceeds after flotation costs = (1 - Tax rate) $45 60% = $27.00 (Par value) $1,000 (1 - F) 99% = $990 Now find the rate that the company pays, based on its net proceeds after flotation costs and its after-tax payments. Ignoring the tax shield due to amortization of flotation costs: Number of coupon payments = After-tax coupon payment = N= 60 27.00 A 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 B C D Net proceeds after flotation costs = Payment of face value at maturity = E F G H PV= $990.00 FV= $1,000.0 Periodic after-tax cost of debt = Rate = Nominal annual after-tax cost of debt = 2.734% 5.468% Now find the rate that the company pays, based on its net proceeds after flotation costs (including the amortization of flotation costs) and its after-tax payments. Incorporating the tax shield due to amortization of flotation costs: Number of coupon payments = After-tax coupon payment = Amortized flotation cost/period = Tax shield from flotation/period = Net payment, after tax = Net proceeds after flotation costs = Payment of face value at maturity = N= 60 27.00 $0.17 $0.07 PMT= $26.93 PV= $990.00 FV= $1,000.0 Periodic after-tax cost of debt = Rate = Nominal annual after-tax cost of debt = 2.727% 5.455% Notice that this after-tax cost of debt is only slightly higher than the after-tax cost of debt where flotation costs are ignored. Therefore, analysts often ignore the flotation costs of debt. 9-4 Cost of Preferred Stock, rps The cost of preferred stock is simply the preferred dividend divided by the price the company will receive if it issues new preferred stock. No tax adjustment is necessary, as preferred dividends are not tax deductible. What is the cost of preferred stock for a company that pays a preferred dividend of $8 per share if the company could sell new preferred with a par value of $100 and a flotation cost of 2%? Pref. Dividend Par value Flotation % Net preferred issue price rps = rps = DivPref $8.00 $8.00 $100.00 2.0% $98.00 Net Pref. Price $98.00 = 8.16% A 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 B D E F G H 9-5 Cost of Common Stock: The Market Risk Premium, RPM Before addressing the required return of an individual stock, what is the required return for the stock market? What is the Market Risk Premium (RPM), which is excess return investor require to induce them to invest in the stock market rather than a long-term T-bond? There are 3 methods to estimate the market risk premium. (1) Use historical market data as an estimate for the current risk premium. (2) Ask experts. (3) Estimate a forward looking risk premium, found as the differential between expected returns on the S&P 500 over some forecasted future period and the current long-term bond rate. Historical Risk Premiums Many analysts use data provided by Ibbotson Associates, which has collected data from 1926. Ibbotson publishes information annually that enables use of different periods and thus different historical risk premiums. Ibbotson recommends using the longest set of data, but others disagree, arguing that events that occurred back in the period of say 1926 to 1966 are less relevant than events that occurred during the last 50 or so years. Ibbotson Historical Risk Premium: 1926-Current Date Stock market return (return on large stocks) Risk-free rate: 20-year T-bond yield at beginning of year Average ArithmeticGeometric 11.80% 9.80% 5.20% 5.10% 6.60% 4.70% Historical risk premium: RM minus T-bond yield = Our Historical Risk Premium: 1968-Current Date (Data shown results) Average Arithmetic Geometric Stock market return (S&P 500) 10.85% 9.34% 6.96% 6.93% 3.90% 2.36% Risk-free rate: 10-year Treasury contestant maturity yield at beginning of year Historical risk premium: RM minus T-bond yield = Data for Our Historical Risk Premium: 1968-Current Date 277 278 C S&P 500 Year Index Level Total Return, rM Capital Gains Return on 10-Year T-bond (Treasury 10-year constant maturity) Actual Reported First Day of Year, Return yield on Required During Year, A 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 B C D E F on G H on yield Total Return, Dividend last day of Required During Year, rM rRF Actual rRF Index Level Capital Gains s year 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991 1990 1989 1988 1987 1986 1985 1984 1983 1982 1981 1980 1979 1978 1977 1976 1975 1974 1973 1972 1971 1970 1969 1968 1967 Arithmetic average Geometric average 1257.60 1257.64 1115.1 903.25 1468.36 1418.3 1248.29 1211.92 1111.92 879.82 1148.08 1320.28 1469.25 1229.23 970.43 740.74 615.93 459.27 466.45 435.71 417.09 330.22 353.4 277.72 247.08 242.17 211.28 167.24 164.93 140.64 122.55 135.76 107.94 96.11 95.1 107.46 90.19 68.56 97.55 118.05 102.09 92.15 92.06 103.86 96.47 2.11% 15.06% 26.46% -37.00% 5.49% 15.79% 4.91% 10.88% 28.70% -22.10% -11.88% -9.11% 21.04% 28.58% 33.36% 23.07% 37.43% 1.31% 9.99% 7.67% 30.55% -3.17% 31.49% 16.81% 5.23% 18.47% 32.16% 6.27% 22.51% 21.41% -4.91% 32.42% 18.44% 6.56% -7.18% 23.84% 37.20% -26.47% -14.66% 18.98% 14.31% 3.10% -8.36% 10.66% 0.00% 12.78% 23.45% -38.49% 3.53% 13.62% 3.00% 8.99% 26.38% -23.37% -13.04% -10.14% 19.53% 26.67% 31.01% 20.26% 34.11% -1.54% 7.06% 4.46% 26.31% -6.56% 27.25% 12.40% 2.03% 14.62% 26.33% 1.40% 17.27% 14.76% -9.73% 25.77% 12.31% 1.06% -11.50% 19.15% 31.55% -29.72% -17.37% 15.63% 10.79% 0.10% -11.36% 7.66% 2.11% 2.28% 3.01% 1.49% 1.96% 2.17% 1.91% 1.89% 2.32% 1.27% 1.16% 1.03% 1.51% 1.91% 2.35% 2.81% 3.32% 2.85% 2.93% 3.21% 4.24% 3.39% 4.24% 4.41% 3.20% 3.85% 5.83% 4.87% 5.24% 6.65% 4.82% 6.65% 6.13% 5.50% 4.32% 4.69% 5.65% 3.25% 2.71% 3.35% 3.52% 3.00% 3.00% 3.00% 10.85% 9.34% 7.46% 6.01% 3.39% 3.38% 1.89% 3.30% 3.85% 2.25% 4.04% 4.71% 4.39% 4.24% 4.27% 3.83% 5.07% 5.12% 6.45% 4.65% 5.75% 6.43% 5.58% 7.84% 5.83% 6.70% 6.71% 8.08% 7.93% 9.14% 8.83% 7.23% 9.00% 11.55% 11.82% 10.36% 13.98% 12.43% 10.33% 9.15% 7.78% 6.81% 7.76% 7.40% 6.90% 6.41% 5.89% 6.50% 7.88% 6.16% 5.70% 1.89% 3.30% 3.85% 2.25% 4.04% 4.71% 4.39% 4.24% 4.27% 3.83% 5.07% 5.12% 6.45% 4.65% 5.75% 6.43% 5.58% 7.84% 5.83% 6.70% 6.71% 8.08% 7.93% 9.14% 8.83% 7.23% 9.00% 11.55% 11.82% 10.36% 13.98% 12.43% 10.33% 9.15% 7.78% 6.81% 7.76% 7.40% 6.90% 6.41% 5.89% 6.50% 7.88% 6.16% 5.70% 16.9% 8.9% -11.1% 21.6% 10.9% 1.6% 2.9% 4.5% 0.0% 16.9% 5.6% 19.2% -10.2% 16.2% 12.8% -1.8% 30.5% -10.7% 14.9% 6.8% 21.2% 6.6% 20.7% 6.1% -6.2% 26.3% 37.4% 14.3% -2.0% 52.4% -0.6% -6.9% -0.9% -3.8% -1.5% 16.7% 4.2% 2.5% 2.1% 1.3% 12.2% 21.1% -8.1% 1.6% 6.96% 6.93% 8.48% 7.73% A 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 B C D E F G H Expert Opinions for Estimates of the Risk Premium Surveys of experts (CFO's, analysts, professors) are another way to estimate the risk premium. Forward-Looking Risk Premiums Historical risk premiums look at past data and assume that investors think the best estimate of the current risk premium is the historical differential between earned returns on stocks and bonds. Forward-looking risk premiums assume that investors expect equities to earn a rate that is equal to the expected dividend yield plus the expected capital gains (growth) rate and the current yield on Treasury securities. If we make these two assumptions, we can use the constant dividend growth model to estimate the expected return on the market: (1) growth is expected to be constant, (2) the firm pays out all available funds as dividends (i.e., there are no stock repurchases or purchases of short-term securities). rM = (D1/P0) + g To use this model, we need estimates of the expected dividend yield and the expected growth rate in the stock price (recall that in a constant growth model, the expected growth in stock price is also the expected growth in dividends). Simplified Illustration of Estimating a Forward-Looking Risk Premium Estimating the Year-1 Dividend Yield (See source at right) D1/P0 = 2.16% Estimating the Long-Term Growth Rate Since 1926, the average dividend growth for the S&P 500 has been about: g= 4.40% Estimated Forward-Looking Expected Market Return rM = rM = (D1/P0) + g 6.56% Estimated Forward-Looking Premium rRF = RPM = rM - rRF = 2.19%Yield on 10-year T-bond 4.37% Assumes constant growth and no stock repurchases. A 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 B C D E F G H 9-6 Using the CAPM to Estimate the Cost of Common Stock, rs rs = risk-free rate + (Market risk premium) (Beta) = rRF + (RPM) bi (Recall that: RPM is the expected return on the market minus the risk-free rate.) The Risk-Free Rate The risk-free rate is often proxied by the yield on a long-term Treasury bond. When we wrote this, the rate on a 10-year T-bond was: Date of data: Yield on 10-year T-bond = rRF = 4/5/2012 2.19% The Market Risk Premium The market risk premium is the return in excess of the risk-free rate that is required to induce investors to invest in the stock market. Assumed market risk premium = RPM = 6.00% Estimating Beta Beta can be estimated from historical stock returns using the following formula, where im is the correlation between Stock i and the market, i is the standard deviation of Stock i, and M is the standard deviation of the market. Beta for Stock i = bi = r iM(s i/s M) The same estimate for beta can be obtained as the estimated slope coefficient in a regression, with the company's stock returns on the y-axis and market returns on the x-axis. Beta can also be obtained from many Web sources. MicroDrive's beta: bi = 1.43 An Illustration of the CAPM Approach: MicroDrive's Cost of Equity, r s Assuming the risk-free rate (i.e., the current yield on a long-term Treasury bond) equals 5%, the market risk premium is 6%, and the MicroDrive's beta is 1.43, what is MicroDrive's cost of stock? Risk-free rate Market risk premium Beta rs = rs = rRF 5.0% 5.0% 6.0% 1.43 + + (RPM) (bi) 6.0% 1.43 A 431 432 433 434 435 rs = rs = B C D 5.0% 13.58% + 8.6% E F G 9-7 Dividend-Yield-Plus-Growth-Rate, or Discounted Cash 436 Flow (DCF), Approach 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 rs = D1/P0 + g. The simplest DCF model assumes that growth is expected to remain constant, and Estimating Inputs for the DCF Approach The next expected dividend is easy to estimate, and the stock price can be determined readily. However, it is not easy to determine the marginal investor's expected future growth rate. Three approaches are commonly used: (1) historical growth rates, (2) retention growth model, and (3) analysts' forecasts. 1. Historical Growth Rates Historical growth estimates are usually not good estimates of expected future growth except for a few very stable and mature companies. 2. Retention Growth Model Another method for finding the growth is utilizing the sustainable growth rate, found by multiplying the expected future return on equity (ROE) times the expected future retention ratio (i.e., the percentage of net income that is not paid out as dividends). This is: g = (Retention rate) (ROE) = (1 - Payout rate) (ROE) Suppose a firm's expected ROE is 14.5% and it pays out 63% of its earnings. What is the firm's sustainable growth rate? Payout rate = ROE = 63% 14.50% g = (1 - Payout rate) x (ROE) g= 37% x g= 5.4% 14.50% H A 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 B C E F G H A third method for estimating the growth rate is to use analysts' forecasts. Value Line provides estimated dividends. IBES, Zack's, and many brokerage firms provide estimates of growth rates, which can be used as proxies for dividend growth. These often have a forecast for the next five years and then a long-term forecast for the period after five years, which requires the use of a nonconstant multi-stage growth model, as described in the Web Extension. An Illustration of the DCF Approach Suppose a firm's stock trades at $32 and its next dividend is expected to be $1.82. If the expected growth rate is 5.5%, what is the firm's cost of equity? P0 = D1 = g= $32.00 $1.82 5.4% rs = rs = rs = D1 $1.82 11.1% P0 $32.00 + + g 5.4% 9-8 The Weighted Average Cost of Capital (WACC) The weighted average cost of capital (WACC) is calculated using the firm's target capital structure together with its after-tax cost of long-term debt, after-tax cost of short-term debt, cost of preferred stock, and cost of common equity. WACC = Weighted average cost of capital = wd rd(1 - T) + wstd(1 - T)rstd + wps rps + ws rs A firm's target capital structure consists of the following capital structure. Using the relevant costs calculated previously, what is the firm's weighted average cost of capital? T= wd = wstd = wps = ws = 40% 28% 2% 3% 67% rd = rstd = rps = rs = 9.0% 10.0% 8.2% 13.6% Sources of Capital ShortLong-term Preferred Common term Debt Stock Stock Debt 514 515 516 517 518 519 520 521 D 3. Analysts' Forecasts Pre-tax cost of capital source, ri: After-tax cost of debt, (1-T)(ri): Cost of capital component for WACC: Target capital structure weight, wi: 9.00% 10.00% 5.40% 6.00% 5.40% 28.00% 6.00% 2.00% 8.16% 13.58% 8.16% 3.00% 13.58% 67.00% 100% A 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 B C D Weighted component cost: WACC = 1.51% E 0.12% F G H 0.24% 9.10% 10.98% 10.98% 9-9 Adjusting the Cost of Equity for Flotation Costs A company's stock sells for $32 and its next dividend is expected to be $1.82, with constant growth of 5.5%. What is the cost of equity using the DCF model? P0 = D1 = g= $32.00 $1.82 5.4% rs = rs = rs = D1 $1.82 11.1% P0 $32.00 + + g 5.4% If the firm in the preceding question incurred a flotation cost of 12.5% for issuing new stock, how much higher is its cost of equity from having to issue new common stock? Flotation percentage cost (F) = Stock price = 12.5% $32.00 Net proceeds after flotation costs = (Stock Price) Net proceeds after flotation costs = $32.00 Net proceeds after flotation costs = $28.00 Net proceeds after flotation costs = D1 = g= (1 - F) 88% $28.00 $1.82 5.4% 555 rs = D1 556 557 558 559 560 561 562 563 564 565 566 rs = rs = rs = $1.82 6.5% Net Proceeds $28.00 + g + + 5.4% 5.4% 11.9% Notice that this cost of stock is quite different than the cost of stock without flotation costs. To find the cost of perpetual preferred stock, simply use the procedure above with g = 0. If the preferred stock has a fixed maturity, then use the same procedure as for debt, except that the preferred dividend is not tax deductible. A 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 B C F G H A privately held firm often estimates its own beta as the average beta of publicly traded companies in the same industry. Own-Bond-Yield-Plus-Judgmental-Risk-Premium Approach This approach consists of adding a judgmental risk premium to the yield on the firm's own long-term debt. It is logical that a firm with risky, low-rated debt would also have risky, high-cost equity. Historically, we have observed that the risk premium for equity is in the range of 3 to 5 percentage points. In addition to applications to privately held firms, this method is used primarily in utility rate case hearings. Example: Judgmental over-own-bond-yield risk premium = Bond yield or rd = rs = 586 587 588 589 590 591 592 rs = rs = 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 E 9-10 Privately Owned Firms and Small Businesses 585 593 D Extra Premium 4.0% 14.0% 4.0% 10.0% + rd + 10.0% 9-11 Managerial Issues and the Cost of Capital There is a relationship between the cost of capital and risk--the higher a project's risk, the higher its cost of capital. When adjusting for risk, firms usually begin by estimating a divisional cost of capital, and then adjusting this estimate for the risk of individual projects. Consider a company with a single division, steel production. The risk-free rate of interest is 5%, and the market risk premium is 6%. If the firm has a beta of 1.1, what is the firm's cost of equity? Risk-free rate Market risk premium Steel Beta 5% 6.0% 1.1 rSteel = 11.6% Suppose the firm undertakes a new operation (a barge project). The average beta of companies that only have barge operations (I.e., pure-play companies) is 1.5. What is the cost of equity for the new division? Risk-free rate Market risk premium Barge Beta 5% 6.0% 1.5 rBarge = 14.0% Now suppose the firm undertakes a new low-risk operation (a distribution center). The average beta of companies that only have distribution centers (I.e., pure-play companies) is 0.5. What is the cost of equity for the new division? A 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 B Risk-free rate Market risk premium Distribution Beta C D 5% 6.0% 0.5 E rCenter = F G 8.0% After adding the two new divisions, the Steel division will make up 70% of the company's value, the Barge division will make up 20%, and the Distribution division will make up 10%. What is the new beta for the entire company? (Hint: the beta of the firm is a weighted average of the divisional betas.) What rate of return will equity holders require the firm as a whole to provide? Beta of Steel Division % of the firm 1.1 70% Beta of Barge Division % of the firm 1.5 20% Beta of Distribution Division % of the firm 0.5 10% New corp. beta = 1.12 Risk-free rate Market risk premium Beta 5% 6.0% 1.12 New rs = 11.72% H I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 J Target Capital Structure wstd = 2% wd = 28% wps = 3% ws = 67% 100% K L M N O P Q R I J 50 51 52 53 the long-term bonds sell at a discount and qual to their aggregate54 book value. 55 standing, for a total market 56 value of equity 57 tstanding, for a total market 58 value of 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 K L M N O P Q R I 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 J K L M N O P Q R I 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 J K L M N O P Q R I 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 J K L M N O P Q R I 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 J K L M N O P Q R Note: Ibbotson actually uses the bond's return due to income as a proxy for the yield. Premium return rM of 10Requi For calculation of geometric mean: wealth relative Return Reported First Day Return Total on yield on of Year, During Return, Capital Required Year, Gains rM Required rRF I 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 Requi red rRF of J10year bond ### -14.79% ### 6.13% ### 37.55% ### -58.63% ### -5.45% ### 14.24% ### 2.01% ### 6.34% ### 28.75% ### -39.02% ### -17.45% ### -28.31% ### 31.28% ### 12.39% ### 20.61% ### 24.84% ### 6.94% ### 11.97% ### -4.87% ### 0.87% ### 9.32% ### -9.76% ### 10.83% ### 10.73% ### 11.38% ### -7.83% ### -5.20% ### -8.01% ### 24.46% ### -30.99% ### -4.30% ### 39.31% ### 19.36% ### 10.36% ### -5.64% ### 7.14% ### 32.99% ### -28.97% ### -16.76% ### 17.66% ### 2.16% ### -18.04% ### -0.22% ### 9.01% ### 2.37% ### -0.01% K L M Return, rM Capital Gains 1.02 1.15 1.26 0.63 1.05 1.16 1.05 1.11 1.29 0.78 0.88 0.91 1.21 1.29 1.33 1.23 1.37 1.01 1.10 1.08 1.31 0.97 1.31 1.17 1.05 1.18 1.32 1.06 1.23 1.21 0.95 1.32 1.18 1.07 0.93 1.24 1.37 0.74 0.85 1.19 1.14 1.03 0.92 1.11 1.00 1.13 1.23 0.62 1.04 1.14 1.03 1.09 1.26 0.77 0.87 0.90 1.20 1.27 1.31 1.20 1.34 0.98 1.07 1.04 1.26 0.93 1.27 1.12 1.02 1.15 1.26 1.01 1.17 1.15 0.90 1.26 1.12 1.01 0.88 1.19 1.32 0.70 0.83 1.16 1.11 1.00 0.89 1.08 N O on P Q R on yield rM Required Year, Dividend last day Required rRF Actual rRF rRF s of year 1.02 1.02 1.03 1.01 1.02 1.02 1.02 1.02 1.02 1.01 1.01 1.01 1.02 1.02 1.02 1.03 1.03 1.03 1.03 1.03 1.04 1.03 1.04 1.04 1.03 1.04 1.06 1.05 1.05 1.07 1.05 1.07 1.06 1.05 1.04 1.05 1.06 1.03 1.03 1.03 1.04 1.03 1.03 1.03 1.02 1.03 1.04 1.02 1.04 1.05 1.04 1.04 1.04 1.04 1.05 1.05 1.06 1.05 1.06 1.06 1.06 1.08 1.06 1.07 1.07 1.08 1.08 1.09 1.09 1.07 1.09 1.12 1.12 1.10 1.14 1.12 1.10 1.09 1.08 1.07 1.08 1.07 1.07 1.06 1.06 1.07 1.08 1.06 1.057 1.03 1.04 1.02 1.04 1.05 1.04 1.04 1.04 1.04 1.05 1.05 1.06 1.05 1.06 1.06 1.06 1.08 1.06 1.07 1.07 1.08 1.08 1.09 1.09 1.07 1.09 1.12 1.12 1.10 1.14 1.12 1.10 1.09 1.08 1.07 1.08 1.07 1.07 1.06 1.06 1.07 1.08 1.06 1.06 1.17 1.09 0.89 1.22 1.11 1.02 1.03 1.05 1.00 1.17 1.06 1.19 0.90 1.16 1.13 0.98 1.30 0.89 1.15 1.07 1.21 1.07 1.21 1.06 0.94 1.26 1.37 1.14 0.98 1.52 0.99 0.93 0.99 0.96 0.98 1.17 1.04 1.03 1.02 1.01 1.12 1.21 0.92 1.02 0.99 1.11 1.24 0.59 1.01 1.11 1.01 1.07 1.25 0.73 0.83 0.84 1.16 1.23 1.27 1.17 1.30 0.95 1.03 1.01 1.22 0.89 1.22 1.08 0.98 1.09 1.21 0.94 1.12 1.07 0.83 1.22 1.09 0.99 0.86 1.16 1.30 0.67 0.79 1.13 1.08 0.95 0.85 1.05 I J K L M N 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 For current estimates from Standard & Poor's, go to www.standardandpoors.com and select SP 500 under Categories and Index Earnings under Download Data. Look at the worksheet named ESTIMATES&PEs. Look for the item named \"Dividend yield (indicated rate).\" O P Q R I 382 383 384 he market minus the risk-free 385 rate.) 386 387 388 When we wrote this, the 389rate on a 390 391 392 393 394 395 396 397 equired to induce investors 398 to 399 400 401 402 403 404 405 ula, where im is the correlation 406 M is the standard deviation of the 407 408 409 410 t in a regression, with411 the can also be obtained from many 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 J K L M N O P Q R I 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 J K L M N O P Q R I 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 = Sum J K L M N O P Q R I 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 = Sum J K L M N O P Q R I 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 J K L M N O P Q R I 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 J K L M N O P Q R S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 S 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 S 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 S 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 S 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 S 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 rM Actual 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 S rM Actual return of 10year bond 0.85 1.06 1.38 0.41 0.95 1.14 1.02 1.06 1.29 0.61 0.83 0.72 1.31 1.12 1.21 1.25 1.07 1.12 0.95 1.01 1.09 0.90 1.11 1.11 1.11 0.92 0.95 0.92 1.24 0.69 0.96 1.39 1.19 1.10 0.94 1.07 1.33 0.71 0.83 1.18 1.02 0.82 1.00 1.09 S 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 S 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 S 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 S 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 S 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 S 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 S 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 B C D E F G 12/8/2012 Web Extension 9A: The Required Return Assuming Nonconstant Dividends and Stock Repurchases As we explained in the chapter, two assumptions underlie the constant dividend growth model: (1) firms do not repurchase any stock, and (2) growth in dividends will be constant. We now explain how to estimate the required return when those assumptions are violated. Estimating the Long-Term Growth Rate The long-term constant growth rate should be approximately equal to the long-term growth rate in sales revenue, which depends on prices and units sold. Prices will be determined by inflation in the long-term, and units sold will depend on sustainable population growth. The forward estimated inflation rate is the difference between yields on a regular 10-year Treasury bond and an inflation protected 10-year Treasury bond, called a TIPS. Yield on 10-year Treasury bond: Yield on 10-year TIPS: Forward estimate of inflation: 2.19% -0.08% 2.27% Ibbotson provides the average inflation rate since 1926. The Fed also provides inflation data. Historical inflation rate: 3.00% Range in expected long-term inflation: Forward estimate of inflation 2.27% to to Historical inflation rate 3.00% We estimate expected inflation as the average of the inflation premium from the TIPS and the historical average: Our estimate of expected inflation: 2.64% Estimates of long-term population growth range from: Low estimate of population growth 1.00% High estimate of population growth 2.50% Average of estimated population growth: 1.75% Estimates of long-term sales growth rate (inflation plus population growth rate): Low range 3.27% High range 5.50% Average of range as an estimate of long-term sales growth, g: 4.39% A 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 B C D E F G The Impact of Stock Repurchases on the Estimated Price When there are repurchases, the growth rate in dividends per share changes. - (r - g) r 1 g g DPS (r - g) 1 g The constant growth model is: D 0 1 g DPS P 0 r - g DPS This can be rearranged to give this formula: 1 D 1 g P0 0 r - g The two formulas are equivalent, as shown in the following example. g= = rs = D0 = 5.0% 80.0% 12.0% $2.00 - (r - g) r 1 g g DPS (r - g) 1 g = 6.329% D 0 1 g DPS P 0 rs - g DPS = $37.50 1 D 0 1 g P 0 rs - g = $37.50 Alternatively: Estimating the Required Return In the textbook, we assumed constant growth and no repurchases. We now consider cases with repurchases and a period of nonconstant growth, beginning with the case of repurchases but constant growth. 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 In the textbook, we assumed constant growth and no repurchases. We now consider cases with repurchases beginning butG A and a periodBof nonconstant growth, C Dwith the case E of repurchases F constant growth. Repurchases and Constant Growth If there are repurchase but still constant growth, then we can invert the constant growth formula to solve for r. D 1 g r 0 g P0 Repurchases and a Period of Nonconstant Growth It is often the case that a period of nonconstant growth is expected before growth becomes constant. The valuation model for this situation is: D1 Dt D2 P _0 1 2 1 r 1 r t = 1 r D t (1 g) r g 1 r t Estimating the Required Market Return when there are Repurchases and a Period of Nonconstant Growth In recent years, companies in the S&P 500 aggregately have distributed as much cash to shareholders in the form of stock repurchases as in the form of dividends. This implies that about 50% of distributions are in the form of dividends. Percent of total distribution in the form of cash dividends = = 50.0% The next step is to estimate the total S&P dividend payouts for the next 2 years. S&P provides historical data for earnings per share, and dividends per share. They also provide data for estimated earnings per share for the next 2 years. We can use the historical data to estimate a relationship between EPS and DPS, and then use that model and the estiamted EPS to estimate DPS. We obtained data from the Standard and Poor's Web site: http://www.standardandpoors.com/home/en/us Under Categories, we selected S&P500. We then selected Download Index Data and Index Earnings. This downloaded an Excel file with quarterly data for the S&P 500. We summed up the quarterly data to get annual data. We also summed up the quarterly forecasted EPS to get the next 2 years annual forecast of EPS. The data is shown below. A 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 B C D E F G Annualized Data Date 12/31/88 12/31/89 12/31/90 12/31/91 12/31/92 12/31/93 12/31/94 12/31/95 12/31/96 12/31/97 12/31/98 12/31/99 12/31/00 12/31/01 12/31/02 12/31/03 12/31/04 12/31/05 12/31/06 12/31/07 12/31/08 12/31/09 12/31/10 12/30/11 Forecast Year 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Month 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 Annual S&P Price Annual EPS DPS Data for Regression Model 277.72 $23.75 $9.75 Annual DPS 353.40 $22.87 $11.06 $11.06 330.22 $21.34 $12.09 $12.09 417.09 $15.97 $12.20 $12.20 435.71 $19.09 $12.39 $12.39 466.45 $21.89 $12.58 $12.58 459.27 $30.60 $13.17 $13.17 615.93 $33.96 $13.79 $13.79 740.74 $38.73 $14.90 $14.90 970.43 $39.72 $15.50 $15.50 1229.23 $37.71 $16.20 $16.20 1469.25 $48.17 $16.69 $16.69 1320.28 $50.00 $16.27 $16.27 1148.08 $24.69 $15.74 $15.74 879.82 $27.59 $16.07 $16.07 1111.92 $48.74 $17.39 $17.39 1211.92 $58.55 $19.44 $19.44 1248.29 $69.83 $22.22 $22.22 1418.30 $81.51 $24.88 $24.88 1468.36 $66.18 $27.73 $27.73 903.25 $14.88 $28.39 $28.39 1115.10 $50.97 $22.41 $22.41 1257.64 $77.35 $22.73 $22.73 1257.60 $86.95 $26.43 $26.43 $97.83 $111.42 We estimated the following model: Dt = a + b Dt-1 + c EPSt + d (Change in EPS) As shown by the regression results below, this model does a good job of predicting the dividend. SUMMARY OUTPUT Regression Statistics Multiple R 0.9867169499 R Square 0.9736103392 Adjusted R Square 0.9694435506 Standard Error 0.9382693216 Observations 23 ANOVA df Regression Residual Total SS MS F Significance F 3 617.1063324011 205.7021108 233.65965 4E-015 19 16.7266370772 0.88034932 22 633.8329694783 A 212 213 214 215 216 217 218 219 220 Intercept X Variable 1 X Variable 2 X Variable 3 B C Coefficients Standard Error 1.5389305368 0.6787053577 0.6964328403 0.0507954154 0.1080987128 0.0141273704 -0.0945057351 0.0148118684 t Stat 2.267450108 13.71054523 7.651722118 -6.38040606 Year 2012 2013 Predicted dividend, D $29.49 $32.84 Estimated intercept, a 1.539 1.539 Estimated coefficient for lagged dividend, b 0.696 0.696 F G P-value Lower 95% Upper 95% 0.0352196 0.11838 2.9594771762 2.646E-011 0.59012 0.8027488665 3.225E-007 0.07853 0.137667639 4.042E-006 -0.1255 -0.0635041382 Estimat ed coeffici ent for Lagged D EPS, c $26.43 0.108 $29.49 0.108 Forecast EPS $97.83 $111.42 Create a time line showing the predicted dividends for each year until growth in payouts becomes constant. To do this, obtain estimates of the next 2 year's projected dividends for the market and the long-term growth rate in CASH FLOWS after year 2. Find the horizon value on the time line assuming constant growth and an initial assumption for the required return on the market. Find the present value of the annual payouts and the present value of the horizon value; this is the estimate of the value of the market index. If the difference between the actual current value of the market index and the estimated value is not zero, adjust the input for the required market return until the difference is zero. Figure 9A-1: Estimating the Forward-Looking Market Risk Premium INPUTS: Projected Year 1 dividend for S&P 500 = Projected Year 2 dividend for S&P 500 = Projected portion of distributions as dividends, = Projected long-term constant growth rate in cash flow, gL = $29.49 $32.84 50.0% 4.39% Actual price level of S&P 500 = $1,257.60 Key Input/Output: Estimate of rM 250 Key Input and Output: Estimate of rM = 8.84% 251 Price level of S&P 500: Actual - Estimated = -$95.79 252 253 254 255 256 257 258 E We then used the regression coefficients to estimate the predicted dividends. 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 D Use Goal Seek to set the blue cell to zero by changing the orange cell. Time Line: Year 0 1 Estimated dividend = $29.49 Estimated P at Year 2 = [(D2/ ) (1+gL) ] / (rM gL) = Estimate price level of S&P 500 = (PV of dividends and P2) = $1,353.40 2 $32.84 $1,538.36 stimate of population H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 growth 40 41 42 43 44 45 46 47 48 49 50 51 52 I J K L M N O H 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 I J K L M N O 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 a Period of Nonconstant Growth 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 H I J K L M N O H I J K L M N O 159 160 161 162 Data for Regression Model Lagged DPS Annual EPS 163 $9.75 $22.87 164 $11.06 $21.34 165 $12.09 $15.97 166 $12.20 $19.09 167 $12.39 $21.89 168 $12.58 $30.60 169 $13.17 $33.96 170 $13.79 $38.73 171 $14.90 $39.72 172 $15.50 $37.71 173 $16.20 $48.17 174 $16.69 $50.00 175 $16.27 $24.69 176 $15.74 $27.59 177 $16.07 $48.74 178 $17.39 $58.55 179 $19.44 $69.83 180 $22.22 $81.51 181 $24.88 $66.18 182 $27.73 $14.88 183 $28.39 $50.97 184 $22.41 $77.35 185 $22.73 $86.95 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 Change in EPS -$0.88 -$1.53 -$5.37 $3.12 $2.80 $8.71 $3.36 $4.77 $0.99 -$2.01 $10.46 $1.83 -$25.31 $2.90 $21.15 $9.81 $11.28 $11.68 -$15.33 -$51.30 $36.09 $26.38 $9.60 Date 12/31/89 12/31/90 12/31/91 12/31/92 12/31/93 12/31/94 12/31/95 12/31/96 12/31/97 12/31/98 12/31/99 12/31/00 12/31/01 12/31/02 12/31/03 12/31/04 12/31/05 12/31/06 12/31/07 12/31/08 12/31/09 12/31/10 12/30/11 Year 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 Month 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 op esp $5.84 $5.01 $4.63 $5.61 $7.16 $8.80 $9.78 $11.01 $11.29 $11.47 $13.77 $13.11 $9.94 $11.94 $14.88 $17.95 $20.19 $21.99 $15.22 -$0.09 $17.16 $21.93 $23.73 H 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 I Lower 95.0% Upper 95.0% 0.1183838973 2.9594771762 0.590116814 0.8027488665 0.0785297867 0.137667639 -0.1255073319 -0.0635041382 Estimated coefficient for change in EPS, d -0.095 -0.095 Forecast change in EPS $10.88 $13.59 J K L M N O P 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 Q R S T P 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 Q R S T P 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 Q R S T P Q R S T 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 eps $4.80 $4.40 $2.55 $3.60 $5.08 $8.35 $7.13 $9.86 $8.94 $8.56 $12.77 $9.07 $5.45 $3.00 $13.16 $13.94 $17.30 $20.24 $7.82 -$23.25 $15.18 $20.67 $20.64 div $2.86 $3.12 $3.04 $3.03 $3.09 $3.34 $3.55 $3.79 $3.95 $4.00 $4.05 $3.98 $3.98 $4.26 $5.06 $5.33 $6.08 $6.87 $7.62 $7.15 $5.66 $6.03 $7.28 salespers bookvalu hare e $191.03 $189.10 $165.94 $178.85 $210.14 $232.52 $248.20 $268.16 $230.21 $236.02 $252.73 $272.64 $290.68 $325.80 $338.37 $321.72 $367.17 $414.75 $453.06 $504.39 $529.59 $451.37 $513.58 $579.14 $613.14 Index 353.40 330.22 417.09 435.71 466.45 459.27 615.93 740.74 970.43 1,229.23 1,469.25 1,320.28 1,148.08 879.82 1,111.92 1,211.92 1,248.29 1,418.30 1,468.36 903.25 1,115.10 1,257.64 1,257.60 P 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 Q R S T SECTION 9-3 SOLUTIONS TO SELF-TEST A company has outstanding long-term bonds with a face value of $1,000, a 10% coupon rate, 25 years remaining until maturity, and a current market value of $1,214.82. If it pays interest semiannually, what is the nominal annual pre-tax cost of debt? If the company's tax rate is 40%, what is the after-tax cost of debt? Number of years to maturity Number of payments per year Annual coupon rate Face value Tax rate N= PV = PMT = FV = 25 2 10% $1,000 40% 50 ($1,214.82) $50 $1,000 I/YR = rd = 4.000% Annualized rd = 8.000% A-T rd = 4.800% SECTION 9-4 SOLUTIONS TO SELF-TEST A company's preferred stock currently trades at $50 per share and it pays a $3 annual dividend. Flotation costs are equal to 3% of the gross proceeds. If the company issues preferred stock, what is the cost of that stock? Preferred stock price Dividend per share Flotation percentage rps $50 $3 3% 6.19% SECTION 9-6 SOLUTIONS TO SELF-TEST A company's beta is 1.4, the yield on a 10-year T-bond is 5%, and the market risk premium is 5.5%. What is rs? Beta 10-year T-bond yield Market risk premium rs 1.40 4.0% 4.5% 10.30% SECTION 9-7 SOLUTIONS TO SELF-TEST A company's estimated growth rate in dividends is 6%. Its current stock price is $40, and its expected annual dividend is $2. Using the DCF approach, what is r s? Growth Stock price Expected dividend rs 6.0% $40.00 $2.00 11.00% SECTION 9-8 SOLUTIONS TO SELF-TEST A firm has the following data: Target capital structure of 25% debt, 10% preferred stock, and 65% common equity; Tax rate = 40%; rd = 7%; rps = 7.5%; and rs = 11.5%. Assume the firm will not isssue new stock. What is this firm's WACC? wd 25% wps 10% ws 65% 40% Tax rate rd 7.0% rps 7.5% rs 11.5% 9.28% WACC SECTION 9-9 SOLUTIONS TO SELF-TEST A firm has common stock with D1 = $3.00; P0 = $30; g = 5%; and F = 4%. If the firm must issue new stock, what is its cost of external equity, re? D1 $3.00 P0 $30.00 5.0% 4.0% g F re 15.42% ssue new stock, SECTION 9-10 SOLUTIONS TO SELF-TEST A company's bond yield is 7%. If the appropriate over-own-bond-yield risk premium is 3.5%, what is rs, based upon the bond--yield-plus-judgmental-risk-premium approach? Bond yield Bond risk premium rs 7.0% 3.5% 10.50%