Fluent Essays - CLA 2 Paper & PPT - Financial Management

CLA 2 PAPER &AMP; PPT - FINANCIAL MANAGEMENT

CLA 2 Paper & PPT - Financial Management - Business & Finance

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Question for CLA 2 Paper: This is a complete written report of your portfolio formation in a Word file. Your historical data and relevant derived values in tables can be pasted from your previous calculations in the Excel file. Please provide explanations of all calculations and the justifications in the Word format. Also, make sure to paste all underlying Excel formulae that you used for calculations in the Word file. Provide once again the data that you presented in answering part 2 of professional assignment 2. Calculate the mean, variance, and the standard deviation of each security’s annual rate of return. Calculate the correlation coefficient between every possible pair of securities’ annual rates of return. Choose percentages of your initial investment that you want to allocate amongst the five (5) securities (weights in the portfolio). Create embedded formulae which generate statistical properties of the portfolio upon insertion of the weights. Observe the mean, the standard deviation, and the CV of the annual rate of return of the portfolio. Find the combination of the weights that minimizes CV of the portfolio. How the CV of the optimal portfolio compares with the CV’s of its constituents. What is the expected rate of return and standard deviation of the rate of return of the portfolio? Choose different values within the range of the standard deviation of the portfolio, and for each chosen value locate the corresponding point on the efficient frontier by finding the weights that maximize the expected rate of return of the portfolio. Subsequently, construct the efficient frontier of your portfolio. Assume that you initially invested $1,000,000 in the portfolio and that the distribution of the annual rate of return of the portfolio is normal. What is the distribution of the return of the portfolio 20 years after its formation? Provide the graph of the distribution of the return of the portfolio. Provide your explanations and definitions in detail and be precise. Comment on your findings. Provide references for content when necessary. Provide your work in detail and explain in your own words. Support your statements with six (6) peer-reviewed in-text citation(s) and reference(s). Question for CLA 2 Presentation: In addition to your CLA 2 report, please prepare a professional PowerPoint presentation summarizing your findings for CLA 2. The presentation will consist of your major findings, analysis, and recommendations in a concise presentation of 15 slides (minimum). You should use content from your CLA 2 report as material for your PowerPoint presentation. In addition, you should include learning outcomes from all your major assignments. This would include PA 1, CLA 1, PA 2, and of course, CLA 2 (unless otherwise specified by your Professor). An agenda, executive summary, and references slides should also be included. Please keep in mind that the university is moving towards a more digital footprint for our students. Requirement for CLA 2 Paper: 1. Explain your work in detail and provide an in-text citation. 2. Paper needs to be formatted in APA 7th edition 3. Include the initial situation and the initial assumptions in your answers 4. At least 6 peer-reviewed references are required (Recommend to find the articles from proquest.) 5. Needs to include formulas, calculations, and tables. Please use Excel if it is needed. 6. Need to include introduction and conclusion. 7. Please find PA 2 Paper assignment and the data that I used in the attachment to complete this assignment. 8. Please find the class PPTs and Textbook in the attachment. 9. Please find the previous assignment: Activity 1, Activity 2, PA 1, PA 2, and CLA 1 in the attachment 10. Need to include the textbook as the references. 11. Textbook Information: Bowerman, B., Drougas, A. M., Duckworth, A. G., Hummel, R. M. Moniger, K. B., & Schur, P. J. (2019). Business statistics and analytics in practice (9th ed.). McGraw-Hill ISBN 9781260187496 14. Please find the Course Learning Outcome list of this course in the attachment Requirement for PPT 1. Create 15 slides PPT based on the material you write on the CLA2 paper. 2. Please add the scripts of the presentation in the speaker note section of PPT. 3.Time Length: Within 15 minutes 4. Need to include in-text citations and reference page. 5. Include calculations and tables with the explanation. 6. Do not put too many words on the slides. The slides should look simple and clear with main points. 7. Need to include the summary of the previous paper assignment which are: PA 1, PA 2, CLA 1 (Please find them in the attachment) 2 2 Professional Assignment 2 The annual rate of return is the amount earned on a fund throughout the year (Carvajal & Popovici 2020). Investors will view an average rate of return of 10\% or more as a good return on investment for long-term investments in the stock market (Sim & Wright, 2017). It is important to know that in some instances, the returns may be low and high, as they fluctuate with the stock prices. I have chosen five corporations from which to analyze their annual rate of return (Carvajal & Popovici, 2021). These companies are; · Walmart · eBay · Toyota · Thor Industries · McDonalds Walmart is an American multinational retail corporation that operates a chain of hypermarkets, stores, grocery stores. Walmart operates thousands of stores in the United States and expanded internationally by the means of innovation. eBay is a global commerce leader that connects millions of buyers and sellers in 190 markets around the world. The organization exists to enable community opportunities for individuals, entrepreneurs, businesses, and organizations of all sizes. eBay has approximately 1.7 billion live listings, 187 million active buyers worldwide, and 20 million sellers on the eBay marketplace. Toyota is a multinational automotive manufacturer headquartered in Japan. It is known for manufacturing high-quality, high-value cars, vans, and trucks that set the standard for long-term resale value and durability. Thor Industries is an American manufacturer of recreational vehicles. The organization sells towable and motorized recreational vehicles through its subsidized brands. McDonald’s is an American fast-food company that is known for its hamburgers. Each industry has its annual rate of return which is different for each corporation. Companies will be assessed based on their annual rates of return as shareholders will assess their strengths using the data on selling and purchase of shares (Carvajal & Popovici 2020; Gniadkowska-Szymanska, 2017). With the aid of Yahoo-finance, the historical data for these companies can be derived and the annual rate of return evaluated. Organizations such as these, have different rates of return. However, these rates have not deviated so much from one another. From the graph, it is evident that several organizations are at the same rates of return. WACC The information has been derived from the income statement of the organization. It will be helpful in the calculation of the WACC. 2021 2020 Debt 1976 2262 Finance, capital lease, and financing obligations 339 337 Total Interest Expense 2315 2599 Current Debt and Capital Lease Obligation 5,296 8,241 Long-term debt 41,194 43,714 Long-term operating lease obligations 12,909 16,171 Long-term finance lease obligations 3,847 4,307 Total Debt 63,246 72,433 Cost of Debt 3.66\% 3.59\% Equity: 400,258.52 2021 2020 2019 Income before income taxes 20,564 20,116 11,460 Provision for income taxes 6,858 4,915 4,281 Tax Rate 33.35\% 24.43\% 37.36\% Weight of Equity 0.863548256 Weight of Debt 0.136451744 Cost of Equity 7.08\% Cost of Debt 3.66\% Tax Rate (1-tax rate) 66.65\% WACC 6.45\% The WACC for Walmart as of January 31, 2021, is 6.45\%. Beta Beta is a measure of how individual asset moves when the overall stock market increases or decreases (Gajurel & Chowdhury, 2021). Beta is a useful measure of the contribution of an individual asset to the risk of the market portfolio when it is added in a small quantity. Beta is calculated as follows; Beta Calculated 1.92 Data source 0.47 Annual Rate of Return for Five corporations Walmart eBay McDonalds Thor Industries Toyota Corporation Date Adj Close Annual Rate Adj Close Annual Rate Adj Close Annual Rate Adj Close Annual Rate Adj Close Annual Rate 2021-1-4 $ 145.35 1.638\% $ 51.18 2.457\% $ 207.79 -2.053\% $ 93.18 0.867\% $ 153.29 -0.832\% 2020-12-31 $ 142.99 -0.021\% $ 49.94 -0.595\% $ 212.10 1.417\% $ 92.37 -3.715\% $ 154.57 0.311\% 2020-1-2 $ 116.04 0.084\% $ 35.56 0.525\% $ 193.63 1.596\% $ 71.76 -0.594\% $ 142.24 1.202\% 2019-12-31 $ 115.95 -0.470\% $ 35.38 0.862\% $ 190.57 0.355\% $ 72.18 0.405\% $ 140.54 -0.050\% 2019-1-2 $ 89.26 0.204\% $ 27.84 2.741\% $ 165.79 -0.854\% $ 49.51 0.460\% $ 116.28 0.172\% 2018-12-31 $ 89.08 1.101\% $ 27.09 -0.604\% $ 167.21 1.138\% $ 49.28 1.277\% $ 116.08 -0.224\% 2018-1-2 $ 92.09 -0.162\% $ 36.73 0.844\% $ 159.08 0.637\% $ 144.27 3.032\% $ 128.37 0.939\% 2017-12-29 $ 92.24 -0.656\% $ 36.43 -0.476\% $ 158.07 -0.568\% $ 139.96 -1.508\% $ 127.17 -0.861\% 2017-1-3 $ 62.52 -0.668\% $ 28.80 0.504\% $ 107.10 -1.740\% $ 92.21 0.429\% $ 118.55 1.145\% 2016-12-30 $ 62.94 -0.202\% $ 28.66 -0.972\% $ 108.98 -0.875\% $ 91.82 -0.677\% $ 117.20 0.137\% 2016-1-4 $ 54.39 0.261\% $ 25.51 -3.896\% $ 102.12 -0.475\% $ 49.96 -1.453\% $ 117.42 -1.292\% 2015-12-31 $ 54.24 -0.618\% $ 26.52 -0.978\% $ 102.61 -1.086\% $ 50.69 -2.062\% $ 118.95 -0.146\% 2015-1-2 $ 73.96 0.023\% $ 22.83 0.160\% $ 78.30 -0.471\% $ 49.10 -0.700\% $ 118.14 0.151\% 2014-12-31 $ 73.94 -1.054\% $ 22.80 -1.941\% $ 78.67 -0.585\% $ 49.44 0.233\% $ 117.96 -0.342\% 2014-1-2 $ 66.28 0.279\% $ 21.91 -1.709\% $ 78.25 -0.641\% $ 47.78 -0.490\% $ 110.17 -1.064\% 2013-12-31 $ 66.09 0.076\% $ 22.29 1.580\% $ 78.75 0.021\% $ 48.01 0.709\% $ 111.35 0.460\% 2013-1-2 $ 56.76 1.469\% $ 21.77 4.954\% $ 70.83 2.142\% $ 32.29 2.689\% $ 85.82 2.896\% 2012-12-31 $ 55.93 0.913\% $ 20.72 2.361\% $ 69.33 0.717\% $ 31.43 1.589\% $ 83.37 1.273\% 2012-1-3 $ 48.27 0.949\% $ 12.73 3.276\% $ 75.27 -1.496\% $ 21.94 1.232\% $ 59.59 2.464\% 2011-12-30 $ 47.81 -0.384\% $ 12.32 -0.099\% $ 76.40 -0.477\% $ 21.67 0.512\% $ 58.14 1.324\% 2011-1-3 $ 42.49 1.161\% $ 11.65 3.009\% $ 56.62 -0.209\% $ 26.40 0.265\% $ 68.67 1.012\% 2010-12-31 $ 42.00 -0.259\% $ 11.30 -1.072\% $ 56.74 0.000\% $ 26.33 -0.147\% $ 67.98 0.357\% 2010-1-4 $ 41.28 1.449\% $ 9.71 1.560\% $ 44.94 0.543\% $ 23.84 -0.992\% $ 72.31 1.087\% 2009-12-31 $ 40.69 -1.578\% $ 9.56 -1.141\% $ 44.69 -0.718\% $ 24.08 -0.477\% $ 71.53 -0.297\% 2009-1-2 $ 42.60 1.978\% $ 5.96 4.893\% $ 44.07 2.477\% $ 10.09 2.695\% $ 55.40 1.411\% 2008-12-31 $ 41.77 1.818\% $ 5.67 0.000\% $ 42.99 0.726\% $ 9.82 4.104\% $ 54.62 1.323\% 2008-1-2 $ 34.34 -1.334\% $ 13.20 -2.132\% $ 39.05 -1.385\% $ 27.65 -0.978\% $ 86.41 0.273\% 2007-12-31 $ 34.80 -1.151\% $ 13.48 -1.762\% $ 39.59 -0.997\% $ 27.92 -0.446\% $ 86.18 -0.404\% 2007-1-3 $ 34.16 2.924\% $ 12.26 0.332\% $ 28.73 -1.043\% $ 31.05 1.400\% $ 107.81 0.734\% 2006-12-29 $ 33.18 0.369\% $ 12.21 -0.795\% $ 29.03 -0.068\% $ 30.61 0.182\% $ 107.02 0.037\% 2006-1-3 $ 32.73 -1.225\% $ 18.06 2.829\% $ 21.43 -0.595\% $ 27.42 1.437\% $ 83.73 2.109\% 2005-12-30 $ 33.14 -1.443\% $ 17.56 -1.219\% $ 21.56 -1.238\% $ 27.03 -1.215\% $ 81.99 0.941\% 2005-1-3 $ 37.31 0.998\% $ 23.18 -1.935\% $ 19.93 -0.751\% $ 24.20 -2.045\% $ 62.85 -0.600\% 2004-12-31 $ 36.94 -0.453\% $ 23.63 -1.222\% $ 20.08 -0.993\% $ 24.70 0.270\% $ 63.23 1.501\% 2004-1-2 $ 36.23 -1.424\% $ 12.80 -2.523\% $ 15.25 -0.161\% $ 18.36 -1.668\% $ 52.66 0.305\% 2003-12-31 $ 36.75 0.510\% $ 13.12 0.512\% $ 15.27 0.202\% $ 18.67 -0.231\% $ 52.50 -0.189\% 2003-1-2 $ 35.51 2.135\% $ 7.04 2.231\% $ 10.02 2.881\% $ 12.09 5.811\% $ 40.66 1.517\% 2002-12-31 $ 34.76 -0.257\% $ 6.89 0.059\% $ 9.74 2.074\% $ 11.41 -0.896\% $ 40.04 -0.151\% 2002-1-2 $ 39.74 0.865\% $ 6.72 -1.097\% $ 15.82 0.076\% $ 6.25 1.872\% $ 38.37 0.470\% 2001-12-31 $ 39.40 -1.381\% $ 6.79 -1.616\% $ 15.81 -0.490\% $ 6.13 0.677\% $ 38.19 1.722\% 2001-2-1 $ 37.91 -1.956\% $ 4.90 -2.305\% $ 17.19 -1.096\% $ 4.27 3.537\% $ 51.36 1.226\% 2001-1-31 $ 38.66 $ 5.01 $ 17.38 $ 4.13 $ 50.73 Sources: https://finance.yahoo.com/quote/EBAY/history?p=EBAY, https://finance.yahoo.com/quote/THO/history?period1=980899200&period2=1612051200&interval=1d&filter=history&frequency=1d&includeAdjustedClose=true https://finance.yahoo.com/quote/TM/history?period1=980899200&period2=1612051200&interval=1d&filter=history&frequency=1d&includeAdjustedClose=true Income Statement Walmart Inc. Consolidated Statements of Income Fiscal Years Ended January 31, (Amounts in millions, except per share data) 2021 2020 2019 Revenues: Net sales $ 555,233 $ 519,926 $ 510,329 Membership and other income 3,918 4,038 4,076 Total revenues 559,151 523,964 514,405 Costs and expenses: Cost of sales 420,315 394,605 385,301 Operating, selling, general and administrative expenses 116,288 108,791 107,147 Operating income 22,548 20,568 21,957 Interest: Debt 1,976 2,262 1,975 Finance, capital lease, and financing obligations 339 337 371 Interest income -121 -189 -217 Interest, net 2,194 2,410 2,129 Other (gains) and losses -210 -1,958 8,368 Income before income taxes 20,564 20,116 11,460 Provision for income taxes 6,858 4,915 4,281 Consolidated net income 13,706 15,201 7,179 Consolidated net income attributable to noncontrolling interest -196 -320 -509 Consolidated net income attributable to Walmart $ 13,510 $ 14,881 $ 6,670 Net income per common share: Basic net income per common share attributable to $ 4.77 $ 5.22 $ 2.28 Walmart Diluted net income per common share attributable to 4.75 5.19 2.26 Walmart Weighted-average common shares outstanding: Basic 2,831 2,850 2,929 Diluted 2,847 2,868 2,945 Dividends declared per common share $ 2.16 $ 2.12 $ 2.08 Consolidated net income $ 13,706 $ 15,201 $ 7,179 Consolidated net income attributable to noncontrolling -196 -320 -509 interest Consolidated net income attributable to Walmart 13,510 14,881 6,670 Other comprehensive income (loss), net of income taxes Currency translation and other 842 286 -226 Net investment hedges -221 122 272 Cash flow hedges 235 -399 -290 Minimum pension liability -30 -1,244 131 Other comprehensive income (loss), net of income taxes 826 -1,235 -113 Other comprehensive (income) losses attributable to 213 -28 188 noncontrolling interest Other comprehensive income (loss) attributable to Walmart 1,039 -1,263 75 Balance Sheet Walmart Inc. Consolidated Balance Sheets As of January 31, (Amounts in millions) 2021 2020 ASSETS Current assets: Cash and cash equivalents $ 17,741 $ 9,465 Receivables, net 6,516 6,284 Inventories 44,949 44,435 Prepaid expenses and other 20,861 1,622 Total current assets 90,067 61,806 Property and equipment, net 92,201 105,208 Operating lease right-of-use assets 13,642 17,424 Finance lease right-of-use assets, net 4,005 4,417 Goodwill 28,983 31,073 Other long-term assets 23,598 16,567 Total assets $ 252,496 $ 236,495 LIABILITIES AND EQUITY Current liabilities: Short-term borrowings $ 224 $ 575 Accounts payable 49,141 46,973 Accrued liabilities 37,966 22,296 Accrued income taxes 242 280 Long-term debt due within one year 3,115 5,362 Operating lease obligations due within one year 1,466 1,793 Finance lease obligations due within one year 491 511 Total current liabilities 92,645 77,790 Long-term debt 41,194 43,714 Long-term operating lease obligations 12,909 16,171 Long-term finance lease obligations 3,847 4,307 Deferred income taxes and other 14,370 12,961 Commitments and contingencies Equity: Common stock 282 284 Capital in excess of par value 3,646 3,247 Retained earnings 88,763 83,943 Accumulated other comprehensive loss -11,766 -12,805 Total Walmart shareholders equity 80,925 74,669 Noncontrolling interest 6,606 6,883 Total equity 87,531 81,552 Total liabilities and equity $ 252,496 $ 236,495 Conclusion Investor’s analysts will use the WACC to check whether there is a return on their investment. This will aid management in understanding whether an organization is adding value. The beta will be very useful in ascertaining the return that should be expected from an investment. References Carvajal, M. J., & Popovici, I. (2020). A Theoretical Framework for Estimating the Rate of Return to a Pharmacy Education Anywhere. Pharmacy, 8(3), 162. Carvajal, M. J., & Popovici, I. (2021). The rate of return to a pharmacy education investment in the US. Research in Social and Administrative Pharmacy, 17(5), 904-910. eBay (n.d.) Historical Statements. Retrieved from https://finance.yahoo.com/quote/EBAY/history?p=EBAY Gajurel, D., & Chowdhury, B. (2021). Realized volatility, jump, and beta: evidence from Canadian stock market. Applied Economics, 1-22. Gniadkowska-Szymanska, A. (2017). The multifactorial Pastor-Stambaugh model: Explaining the impact of liquidity on the rate of return based on the example of the Warsaw Stock Exchange. Equilibrium. Quarterly Journal of Economics and Economic Policy, 12(2), 211-228. McDonald (n.d.) Historical Statements. Retrieved from Prol, J. L., & Steininger, K. W. (2020). Photovoltaic self-consumption is now profitable in Spain: Effects of the new regulation on prosumers internal rate of return. Energy Policy, 146, 111793. Sim, T., & Wright, R. H. (2017). Stock valuation using the dividend discount model: An internal rate of return approach. In Growing Presence of Real Options in Global Financial Markets. Emerald Publishing Limited. Thor Industries (n.d.) Historical Statements. Retrieved from https://finance.yahoo.com/quote/THO/history?period1=980899200&period2=1612051200&interval=1d&filter=history&frequency=1d&includeAdjustedClose=true Toyota (n.d.) Historical Statements. Retrieved from https://finance.yahoo.com/quote/TM/history?period1=980899200&period2=1612051200&interval=1d&filter=history&frequency=1d&includeAdjustedClose=true Walmart (n.d.) Historical Statements. Retrieved from Annual Rate of Return … CLA_2 Walmart eBay McDonalds Thor Industries Toyota Date Adj Close Annual Rate Adj Close Annual Rate Adj Close Annual Rate Adj Close Annual Rate Adj Close Annual Rate 1/29/21 $ 139.36 -2.294\% $ 56.16 0.124\% $ 205.43 0.492\% $ 120.21 -0.445\% $ 140.52 -1.959\% 1/28/21 $ 142.59 -0.063\% $ 56.09 -3.328\% $ 204.43 -0.087\% $ 120.74 -1.186\% $ 143.30 0.462\% 1/27/21 $ 142.68 -2.519\% $ 57.99 -1.396\% $ 204.60 -3.969\% $ 122.18 1.706\% $ 142.64 -2.315\% 1/26/21 $ 146.32 0.892\% $ 58.80 3.299\% $ 212.89 0.952\% $ 120.12 4.898\% $ 145.98 -0.506\% 1/25/21 $ 145.02 -0.089\% $ 56.90 1.390\% $ 210.87 -0.019\% $ 114.38 5.480\% $ 146.72 -0.835\% 1/22/21 $ 145.15 1.017\% $ 56.11 0.106\% $ 210.91 -0.070\% $ 108.28 1.535\% $ 147.95 -2.265\% 1/21/21 $ 143.68 -0.455\% $ 56.05 0.409\% $ 211.06 -0.047\% $ 106.63 -0.585\% $ 151.34 0.903\% 1/20/21 $ 144.34 1.468\% $ 55.82 -1.432\% $ 211.16 2.148\% $ 107.25 0.473\% $ 149.98 1.241\% 1/19/21 $ 142.24 -0.868\% $ 56.63 2.776\% $ 206.67 -0.391\% $ 106.75 2.230\% $ 148.13 -0.189\% 1/15/21 $ 143.48 -1.598\% $ 55.08 0.271\% $ 207.48 0.674\% $ 104.39 -0.048\% $ 148.41 -1.955\% 1/14/21 $ 145.79 -0.326\% $ 54.93 -0.793\% $ 206.09 -1.707\% $ 104.44 2.115\% $ 151.34 0.457\% 1/13/21 $ 146.26 -1.026\% $ 55.37 -0.591\% $ 209.64 0.231\% $ 102.26 -0.339\% $ 150.65 -0.728\% 1/12/21 $ 147.77 1.134\% $ 55.69 3.838\% $ 209.15 -1.235\% $ 102.60 4.222\% $ 151.75 -1.075\% 1/11/21 $ 146.10 0.449\% $ 53.60 -1.015\% $ 211.75 -0.763\% $ 98.36 2.848\% $ 153.39 0.353\% 1/8/21 $ 145.45 -0.014\% $ 54.14 2.641\% $ 213.37 1.818\% $ 95.60 -5.567\% $ 152.85 0.118\% 1/7/21 $ 145.47 -0.007\% $ 52.73 -0.301\% $ 209.53 0.463\% $ 101.07 2.983\% $ 152.67 -0.562\% 1/6/21 $ 145.48 0.622\% $ 52.89 2.261\% $ 208.56 -0.227\% $ 98.10 3.053\% $ 153.53 0.085\% 1/5/21 $ 144.58 -0.534\% $ 51.71 1.024\% $ 209.03 0.598\% $ 95.15 2.099\% $ 153.40 0.072\% 1/4/21 $ 145.35 1.638\% $ 51.18 2.457\% $ 207.79 -2.053\% $ 93.18 0.867\% $ 153.29 -0.832\% 12/31/20 $ 142.99 -0.021\% $ 49.94 -0.595\% $ 212.10 1.417\% $ 92.37 -3.715\% $ 154.57 0.311\% 12/30/20 $ 143.02 -0.083\% $ 50.24 -0.611\% $ 209.11 -0.542\% $ 95.87 0.839\% $ 154.09 0.488\% 12/29/20 $ 143.14 -0.636\% $ 50.55 1.227\% $ 210.25 -0.614\% $ 95.07 -1.723\% $ 153.34 0.484\% 12/28/20 $ 144.05 1.191\% $ 49.93 0.239\% $ 211.54 1.236\% $ 96.72 -4.587\% $ 152.60 1.406\% 12/24/20 $ 142.34 0.195\% $ 49.81 -1.995\% $ 208.94 -0.298\% $ 101.26 0.117\% $ 150.47 -0.458\% 12/23/20 $ 142.07 -0.682\% $ 50.81 -0.954\% $ 209.57 0.047\% $ 101.14 0.766\% $ 151.16 0.258\% 12/22/20 $ 143.04 -1.220\% $ 51.30 0.097\% $ 209.47 0.118\% $ 100.37 1.539\% $ 150.77 -0.661\% 12/21/20 $ 144.79 0.014\% $ 51.25 -2.848\% $ 209.22 -1.598\% $ 98.84 4.388\% $ 151.77 -1.309\% 12/18/20 $ 144.77 -0.103\% $ 52.73 0.019\% $ 212.59 0.387\% $ 94.59 2.810\% $ 153.77 -0.564\% 12/17/20 $ 144.92 0.460\% $ 52.72 -1.125\% $ 211.77 0.210\% $ 91.97 -0.054\% $ 154.64 -0.291\% 12/16/20 $ 144.26 -0.103\% $ 53.32 2.970\% $ 211.33 -0.495\% $ 92.02 -4.519\% $ 155.09 1.455\% 12/15/20 $ 144.41 -0.048\% $ 51.76 4.940\% $ 212.37 1.378\% $ 96.28 5.220\% $ 152.85 -0.476\% 12/14/20 $ 144.48 -0.923\% $ 49.26 0.892\% $ 209.47 1.983\% $ 91.38 -2.975\% $ 153.58 1.694\% 12/11/20 $ 145.82 -0.027\% $ 48.83 -0.952\% $ 205.36 -0.135\% $ 94.14 2.124\% $ 151.00 5.395\% 12/10/20 $ 145.86 -0.468\% $ 49.29 0.202\% $ 205.63 -0.312\% $ 92.16 -1.025\% $ 143.07 1.543\% 12/9/20 $ 146.54 -0.793\% $ 49.19 -0.785\% $ 206.27 0.144\% $ 93.11 -1.633\% $ 140.88 1.531\% 12/8/20 $ 147.71 0.901\% $ 49.58 -0.280\% $ 205.98 -0.240\% $ 94.64 -2.874\% $ 138.74 0.426\% 12/7/20 $ 146.38 -0.539\% $ 49.72 -1.861\% $ 206.47 -0.882\% $ 97.40 2.728\% $ 138.15 -0.094\% 12/4/20 $ 147.17 -0.262\% $ 50.66 1.343\% $ 208.30 -0.365\% $ 94.78 0.649\% $ 138.28 1.040\% 12/3/20 $ 147.56 -0.814\% $ 49.98 -2.086\% $ 209.06 0.308\% $ 94.17 -0.806\% $ 136.85 0.373\% 12/2/20 $ 148.76 -1.399\% $ 51.03 1.630\% $ 208.42 -2.473\% $ 94.93 -3.240\% $ 136.34 0.147\% 12/1/20 $ 150.86 -0.098\% $ 50.21 0.178\% $ 213.64 -0.600\% $ 98.06 2.679\% $ 136.14 1.242\% 11/30/20 $ 151.01 0.782\% $ 50.12 -1.476\% $ 214.92 0.184\% $ 95.46 -0.217\% $ 134.46 -4.152\% 11/27/20 $ 149.83 -0.152\% $ 50.86 1.749\% $ 214.53 -0.462\% $ 95.67 1.647\% $ 140.16 -0.817\% 11/25/20 $ 150.06 0.310\% $ 49.98 -0.158\% $ 215.52 -0.169\% $ 94.11 -0.294\% $ 141.31 -1.775\% 11/24/20 $ 149.59 0.285\% $ 50.06 1.255\% $ 215.88 1.241\% $ 94.39 -1.910\% $ 143.84 0.404\% 11/23/20 $ 149.17 0.458\% $ 49.44 1.840\% $ 213.22 1.350\% $ 96.21 4.221\% $ 143.26 0.792\% 11/20/20 $ 148.49 -1.244\% $ 48.54 -1.600\% $ 210.36 -0.475\% $ 92.23 0.754\% $ 142.13 0.855\% 11/19/20 $ 150.35 2.012\% $ 49.32 2.543\% $ 211.36 -0.190\% $ 91.54 1.163\% $ 140.92 -0.644\% 11/18/20 $ 147.35 -0.188\% $ 48.08 0.413\% $ 211.77 -0.227\% $ 90.48 -0.665\% $ 141.83 -0.640\% 11/17/20 $ 147.63 -2.034\% $ 47.88 -0.454\% $ 212.25 -0.333\% $ 91.08 3.503\% $ 142.74 -0.955\% 11/16/20 $ 150.66 1.254\% $ 48.10 -0.247\% $ 212.96 1.605\% $ 87.95 2.448\% $ 144.11 1.743\% 11/13/20 $ 148.78 1.546\% $ 48.22 4.368\% $ 209.57 0.099\% $ 85.82 2.948\% $ 141.62 1.372\% 11/12/20 $ 146.50 0.169\% $ 46.16 -2.375\% $ 209.36 -2.297\% $ 83.33 -3.166\% $ 139.69 -1.978\% 11/11/20 $ 146.25 1.649\% $ 47.27 2.483\% $ 214.22 2.179\% $ 86.01 4.025\% $ 142.48 1.799\% 11/10/20 $ 143.86 1.397\% $ 46.11 -3.753\% $ 209.61 0.047\% $ 82.61 3.944\% $ 139.94 0.215\% 11/9/20 $ 141.87 -1.542\% $ 47.87 -4.788\% $ 209.51 -1.554\% $ 79.42 -9.995\% $ 139.64 1.763\% 11/6/20 $ 144.07 1.590\% $ 50.22 2.558\% $ 212.79 0.116\% $ 87.77 -1.887\% $ 137.20 0.095\% 11/5/20 $ 141.80 1.058\% $ 48.95 3.271\% $ 212.54 0.668\% $ 89.44 1.797\% $ 137.07 2.146\% 11/4/20 $ 140.30 -0.576\% $ 47.38 -2.274\% $ 211.13 -0.894\% $ 87.85 2.082\% $ 134.16 -1.267\% 11/3/20 $ 141.11 1.681\% $ 48.47 2.170\% $ 213.02 1.975\% $ 86.04 0.426\% $ 135.87 1.955\% 11/2/20 $ 138.76 1.182\% $ 47.43 0.503\% $ 208.86 -0.207\% $ 85.67 2.372\% $ 133.24 1.474\% 10/30/20 $ 137.13 -0.840\% $ 47.19 -3.406\% $ 209.29 -0.911\% $ 83.66 -2.821\% $ 131.29 -0.046\% 10/29/20 $ 138.29 -0.086\% $ 48.82 -7.748\% $ 211.21 0.121\% $ 86.06 -1.132\% $ 131.35 0.979\% 10/28/20 $ 138.41 -2.001\% $ 52.76 -0.562\% $ 210.95 -3.784\% $ 87.04 0.822\% $ 130.07 -1.821\% 10/27/20 $ 141.20 0.498\% $ 53.05 0.393\% $ 219.09 -0.581\% $ 86.32 -0.514\% $ 132.46 -0.294\% 10/26/20 $ 140.50 -1.182\% $ 52.85 -0.840\% $ 220.36 -1.960\% $ 86.77 -0.580\% $ 132.85 -0.323\% 10/23/20 $ 142.17 0.209\% $ 53.29 2.828\% $ 224.73 -0.192\% $ 87.27 -2.662\% $ 133.28 -0.105\% 10/22/20 $ 141.88 -0.590\% $ 51.81 -1.008\% $ 225.16 0.420\% $ 89.63 0.842\% $ 133.42 0.210\% 10/21/20 $ 142.72 0.347\% $ 52.33 -2.579\% $ 224.22 0.325\% $ 88.88 -6.363\% $ 133.14 1.384\% 10/20/20 $ 142.22 0.662\% $ 53.70 -0.221\% $ 223.49 0.640\% $ 94.72 2.548\% $ 131.31 0.328\% 10/19/20 $ 141.28 -1.224\% $ 53.82 -2.742\% $ 222.06 -1.480\% $ 92.33 -1.545\% $ 130.88 0.184\% 10/16/20 $ 143.02 0.124\% $ 55.31 0.773\% $ 225.38 -0.118\% $ 93.77 -1.387\% $ 130.64 -0.405\% 10/15/20 $ 142.84 0.409\% $ 54.89 -1.895\% $ 225.64 0.884\% $ 95.08 2.114\% $ 131.17 -0.274\% 10/14/20 $ 142.26 -1.578\% $ 55.94 -1.982\% $ 223.66 0.119\% $ 93.09 -1.000\% $ 131.53 -0.848\% 10/13/20 $ 144.52 1.363\% $ 57.06 3.913\% $ 223.39 0.547\% $ 94.03 0.525\% $ 132.65 0.643\% 10/12/20 $ 142.57 1.024\% $ 54.87 -0.126\% $ 222.17 0.568\% $ 93.53 -1.670\% $ 131.80 -0.212\% 10/9/20 $ 141.11 1.000\% $ 54.94 6.270\% $ 220.91 -0.431\% $ 95.11 -1.143\% $ 132.08 -0.657\% 10/8/20 $ 139.71 0.333\% $ 51.60 2.213\% $ 221.87 -0.301\% $ 96.20 -5.719\% $ 132.95 0.392\% 10/7/20 $ 139.25 0.185\% $ 50.47 2.545\% $ 222.54 1.061\% $ 101.86 1.441\% $ 132.43 0.887\% 10/6/20 $ 138.99 -0.829\% $ 49.20 -4.161\% $ 220.19 -0.880\% $ 100.41 -1.218\% $ 131.26 -0.638\% 10/5/20 $ 140.15 0.921\% $ 51.29 0.174\% $ 222.13 1.515\% $ 101.64 3.249\% $ 132.10 0.280\% 10/2/20 $ 138.86 -1.820\% $ 51.20 -1.345\% $ 218.79 1.393\% $ 98.39 1.320\% $ 131.73 -0.530\% 10/1/20 $ 141.41 2.240\% $ 51.89 0.536\% $ 215.77 0.046\% $ 97.10 3.456\% $ 132.43 -0.008\% 9/30/20 $ 138.28 2.000\% $ 51.62 -1.050\% $ 215.67 0.370\% $ 93.80 1.055\% $ 132.44 -1.357\% 9/29/20 $ 135.54 -0.080\% $ 52.16 -2.606\% $ 214.87 -0.720\% $ 92.81 -0.413\% $ 134.25 -1.302\% 9/28/20 $ 135.65 -0.015\% $ 53.54 2.929\% $ 216.42 0.949\% $ 93.20 1.533\% $ 136.01 2.260\% 9/25/20 $ 135.67 0.416\% $ 51.99 1.343\% $ 214.38 0.949\% $ 91.78 1.361\% $ 132.97 0.846\% 9/24/20 $ 135.11 0.521\% $ 51.30 2.147\% $ 212.36 0.534\% $ 90.54 -1.917\% $ 131.85 -1.086\% 9/23/20 $ 134.40 -1.692\% $ 50.21 -0.472\% $ 211.23 -0.668\% $ 92.29 -2.174\% $ 133.29 0.783\% 9/22/20 $ 136.70 0.901\% $ 50.45 1.544\% $ 212.64 0.000\% $ 94.32 4.856\% $ 132.25 0.782\% 9/21/20 $ 135.47 1.307\% $ 49.68 3.099\% $ 212.64 -1.768\% $ 89.85 1.290\% $ 131.22 -2.283\% 9/18/20 $ 133.71 -1.029\% $ 48.16 -0.062\% $ 216.43 -1.043\% $ 88.70 -1.411\% $ 134.25 -0.557\% 9/17/20 $ 135.10 0.315\% $ 48.19 -3.594\% $ 218.70 -0.997\% $ 89.96 2.527\% $ 135.00 0.721\% 9/16/20 $ 134.67 -0.804\% $ 49.95 -2.662\% $ 220.90 1.091\% $ 87.71 -6.812\% $ 134.03 0.000\% 9/15/20 $ 135.76 0.029\% $ 51.30 -0.999\% $ 218.50 0.817\% $ 93.90 -2.465\% $ 134.03 0.194\% 9/14/20 $ 135.72 0.453\% $ 51.82 -0.895\% $ 216.72 1.167\% $ 96.24 5.662\% $ 133.77 1.833\% 9/11/20 $ 135.11 -0.080\% $ 52.28 0.856\% $ 214.20 0.349\% $ 90.94 -3.217\% $ 131.34 0.887\% 9/10/20 $ 135.21 -2.226\% $ 51.83 -2.118\% $ 213.46 0.707\% $ 93.92 1.086\% $ 130.18 -0.727\% 9/9/20 $ 138.26 1.035\% $ 52.94 3.640\% $ 211.95 0.992\% $ 92.90 1.894\% $ 131.13 -0.076\% 9/8/20 $ 136.83 -3.115\% $ 51.05 -1.941\% $ 209.86 0.870\% $ 91.16 0.585\% $ 131.23 -1.468\% 9/4/20 $ 141.16 -1.190\% $ 52.05 -1.173\% $ 208.04 -0.973\% $ 90.63 2.219\% $ 133.17 2.448\% 9/3/20 $ 142.85 -2.149\% $ 52.67 -3.566\% $ 210.08 -1.130\% $ 88.64 -7.003\% $ 129.95 -1.958\% 9/2/20 $ 145.96 0.061\% $ 54.58 2.649\% $ 212.46 1.651\% $ 95.07 1.555\% $ 132.52 0.166\% 9/1/20 $ 145.87 6.104\% $ 53.15 -2.084\% $ 208.99 -0.389\% $ 93.60 0.665\% $ 132.30 -0.098\% 8/31/20 $ 137.23 -1.039\% $ 54.27 1.231\% $ 209.80 -0.066\% $ 92.98 -4.291\% $ 132.43 -1.119\% 8/28/20 $ 138.66 2.651\% $ 53.61 -3.690\% $ 209.94 1.274\% $ 97.06 -1.440\% $ 133.92 0.269\% 8/27/20 $ 135.04 4.437\% $ 55.62 -3.952\% $ 207.28 -0.737\% $ 98.47 -1.025\% $ 133.56 -0.991\% 8/26/20 $ 129.18 0.054\% $ 57.87 0.909\% $ 208.82 0.521\% $ 99.48 1.045\% $ 134.89 0.074\% 8/25/20 $ 129.11 -0.534\% $ 57.34 -1.250\% $ 207.73 0.014\% $ 98.45 -5.374\% $ 134.79 0.022\% 8/24/20 $ 129.80 -0.228\% $ 58.06 0.974\% $ 207.70 0.495\% $ 103.88 -1.654\% $ 134.76 0.693\% 8/21/20 $ 130.09 0.809\% $ 57.50 0.949\% $ 206.68 0.802\% $ 105.62 -0.789\% $ 133.83 -0.194\% 8/20/20 $ 129.05 -1.399\% $ 56.96 -0.087\% $ 205.03 0.176\% $ 106.45 -0.875\% $ 134.09 -0.832\% 8/19/20 $ 130.87 -1.722\% $ 57.01 1.185\% $ 204.66 -0.386\% $ 107.39 -0.785\% $ 135.21 -0.641\% 8/18/20 $ 133.14 -0.658\% $ 56.33 -0.560\% $ 205.46 0.788\% $ 108.23 -2.958\% $ 136.08 0.405\% 8/17/20 $ 134.02 2.237\% $ 56.65 1.866\% $ 203.84 0.789\% $ 111.48 4.628\% $ 135.53 0.971\% 8/14/20 $ 131.05 0.567\% $ 55.60 0.018\% $ 202.24 0.261\% $ 106.44 0.855\% $ 134.22 -1.052\% 8/13/20 $ 130.31 0.380\% $ 55.59 1.414\% $ 201.71 0.228\% $ 105.54 1.305\% $ 135.64 -0.588\% 8/12/20 $ 129.82 1.290\% $ 54.81 2.186\% $ 201.25 0.496\% $ 104.17 -2.105\% $ 136.44 1.991\% 8/11/20 $ 128.15 -1.282\% $ 53.63 -0.147\% $ 200.26 0.430\% $ 106.38 -0.240\% $ 133.75 2.406\% 8/10/20 $ 129.81 1.459\% $ 53.71 -1.533\% $ 199.40 -0.235\% $ 106.64 -1.576\% $ 130.57 0.468\% 8/7/20 $ 127.93 0.478\% $ 54.54 0.236\% $ 199.87 0.696\% $ 108.33 -0.472\% $ 129.96 1.254\% 8/6/20 $ 127.32 -0.355\% $ 54.41 -2.828\% $ 198.48 1.948\% $ 108.85 -6.505\% $ 128.34 2.781\% 8/5/20 $ 127.77 -1.400\% $ 55.97 0.584\% $ 194.65 -0.050\% $ 116.16 1.245\% $ 124.82 1.542\% 8/4/20 $ 129.57 1.794\% $ 55.64 -0.425\% $ 194.75 2.519\% $ 114.72 -3.566\% $ 122.91 1.616\% 8/3/20 $ 127.27 -0.077\% $ 55.88 2.307\% $ 189.90 0.062\% $ 118.89 5.753\% $ 120.94 1.332\% 7/31/20 $ 127.37 -0.555\% $ 54.61 1.018\% $ 189.79 -0.580\% $ 112.24 -1.489\% $ 119.34 -2.581\% 7/30/20 $ 128.08 -0.437\% $ 54.05 0.348\% $ 190.89 -0.409\% $ 113.93 -1.934\% $ 122.46 -1.242\% 7/29/20 $ 128.64 -0.815\% $ 53.87 -3.283\% $ 191.67 -0.015\% $ 116.15 1.762\% $ 123.99 -1.179\% 7/28/20 $ 129.69 0.418\% $ 55.66 -1.550\% $ 191.70 -2.521\% $ 114.12 -1.064\% $ 125.46 -1.668\% 7/27/20 $ 129.15 -0.023\% $ 56.53 3.757\% $ 196.60 1.265\% $ 115.34 4.827\% $ 127.57 1.867\% 7/24/20 $ 129.18 -0.304\% $ 54.45 -0.054\% $ 194.12 0.591\% $ 109.91 -0.438\% $ 125.21 -0.518\% 7/23/20 $ 129.57 -0.772\% $ 54.48 -2.135\% $ 192.98 -0.540\% $ 110.39 -5.053\% $ 125.86 -0.317\% 7/22/20 $ 130.58 0.249\% $ 55.65 -0.443\% $ 194.03 2.881\% $ 116.11 1.667\% $ 126.26 -0.008\% 7/21/20 $ 130.25 0.652\% $ 55.90 -3.268\% $ 188.52 0.712\% $ 114.19 3.778\% $ 126.27 -0.797\% 7/20/20 $ 129.40 -0.205\% $ 57.76 0.583\% $ 187.18 0.068\% $ 109.96 1.470\% $ 127.28 0.173\% 7/17/20 $ 129.67 -0.349\% $ 57.42 -0.891\% $ 187.05 0.293\% $ 108.35 -2.140\% $ 127.06 0.450\% 7/16/20 $ 130.12 0.151\% $ 57.93 0.444\% $ 186.50 -0.444\% $ 110.70 1.316\% $ 126.49 -0.662\% 7/15/20 $ 129.93 -0.008\% $ 57.68 -1.175\% $ 187.33 0.549\% $ 109.25 4.611\% $ 127.33 0.709\% 7/14/20 $ 129.94 1.904\% $ 58.36 1.329\% $ 186.31 3.088\% $ 104.33 4.715\% $ 126.43 1.098\% 7/13/20 $ 127.48 -0.892\% $ 57.59 -1.650\% $ 180.64 0.022\% $ 99.52 -0.769\% $ 125.05 0.064\% 7/10/20 $ 128.63 2.268\% $ 58.55 0.084\% $ 180.60 0.298\% $ 100.29 4.519\% $ 124.97 0.916\% 7/9/20 $ 125.74 2.625\% $ 58.50 1.617\% $ 180.07 -0.821\% $ 95.86 -4.165\% $ 123.83 -1.268\% 7/8/20 $ 122.48 -1.997\% $ 57.56 2.204\% $ 181.55 0.016\% $ 99.93 0.533\% $ 125.41 0.359\% 7/7/20 $ 124.96 6.559\% $ 56.31 1.467\% $ 181.52 -1.432\% $ 99.40 -1.981\% $ 124.96 -1.604\% 7/6/20 $ 117.02 -0.269\% $ 55.49 3.275\% $ 184.14 2.677\% $ 101.39 -3.277\% $ 126.98 0.466\% 7/2/20 $ 117.34 -0.402\% $ 53.70 2.609\% $ 179.28 -0.619\% $ 104.77 1.134\% $ 126.39 1.796\% 7/1/20 $ 117.81 -0.075\% $ 52.31 0.968\% $ 180.39 0.103\% $ 103.59 -1.256\% $ 124.14 -1.193\% 6/30/20 $ 117.90 0.603\% $ 51.81 2.197\% $ 180.20 0.909\% $ 104.90 -0.422\% $ 125.63 -0.998\% 6/29/20 $ 117.19 0.623\% $ 50.68 0.822\% $ 178.57 1.688\% $ 105.34 0.920\% $ 126.89 0.577\% 6/26/20 $ 116.46 -1.168\% $ 50.27 2.972\% $ 175.58 -1.666\% $ 104.37 -3.100\% $ 126.16 -1.268\% 6/25/20 $ 117.83 -0.492\% $ 48.80 1.284\% $ 178.53 -0.834\% $ 107.66 0.686\% $ 127.77 -0.023\% 6/24/20 $ 118.41 -0.638\% $ 48.18 -2.090\% $ 180.03 -1.256\% $ 106.93 -4.222\% $ 127.80 -1.004\% 6/23/20 $ 119.17 -0.503\% $ 49.19 1.293\% $ 182.30 -0.449\% $ 111.54 -0.666\% $ 129.09 0.746\% 6/22/20 $ 119.77 1.515\% $ 48.56 1.786\% $ 183.12 0.481\% $ 112.28 1.010\% $ 128.13 0.266\% 6/19/20 $ 117.97 1.564\% $ 47.70 -0.310\% $ 182.24 -1.558\% $ 111.15 -1.272\% $ 127.79 -1.035\% 6/18/20 $ 116.14 -0.878\% $ 47.85 0.021\% $ 185.11 -0.684\% $ 112.58 0.638\% $ 129.12 0.186\% 6/17/20 $ 117.16 -0.520\% $ 47.84 0.642\% $ 186.38 0.247\% $ 111.86 -0.341\% $ 128.88 -0.557\% 6/16/20 $ 117.77 1.321\% $ 47.53 0.479\% $ 185.92 0.437\% $ 112.24 0.596\% $ 129.60 1.712\% 6/15/20 $ 116.22 0.288\% $ 47.31 0.481\% $ 185.11 0.169\% $ 111.58 6.249\% $ 127.40 -0.329\% 6/12/20 $ 115.89 -1.976\% $ 47.08 -0.586\% $ 184.79 0.881\% $ 104.82 5.413\% $ 127.82 2.680\% 6/11/20 $ 118.20 -0.887\% $ 47.36 -2.696\% $ 183.17 -4.326\% $ 99.29 -8.273\% $ 124.44 -5.145\% 6/10/20 $ 119.26 -0.157\% $ 48.65 -1.010\% $ 191.27 -1.882\% $ 107.86 -0.725\% $ 131.01 0.321\% 6/9/20 $ 119.44 0.091\% $ 49.14 2.092\% $ 194.91 -1.557\% $ 108.64 -0.352\% $ 130.59 -1.127\% 6/8/20 $ 119.34 -0.264\% $ 48.13 -0.205\% $ 197.96 2.746\% $ 109.02 10.562\% $ 132.07 0.737\% 6/5/20 $ 119.65 -0.451\% $ 48.22 -1.100\% $ 192.60 2.008\% $ 98.10 0.864\% $ 131.10 2.268\% 6/4/20 $ 120.19 -1.108\% $ 48.76 6.076\% $ 188.77 -0.026\% $ 97.25 4.730\% $ 128.16 -0.444\% 6/3/20 $ 121.53 -0.380\% $ 45.88 1.017\% $ 188.82 2.993\% $ 92.76 5.600\% $ 128.73 1.763\% 6/2/20 $ 121.99 -0.016\% $ 45.42 1.711\% $ 183.25 0.096\% $ 87.71 2.445\% $ 126.48 0.024\% 6/1/20 $ 122.01 -0.081\% $ 44.65 -0.749\% $ 183.08 0.583\% $ 85.59 1.211\% $ 126.45 0.349\% 5/29/20 $ 122.11 0.299\% $ 44.98 3.281\% $ 182.01 -0.621\% $ 84.56 1.708\% $ 126.01 -1.848\% 5/28/20 $ 121.75 0.983\% $ 43.53 0.181\% $ 183.14 0.537\% $ 83.13 -3.775\% $ 128.36 1.215\% 5/27/20 $ 120.56 -1.120\% $ 43.45 1.806\% $ 182.16 1.546\% $ 86.32 3.492\% $ 126.81 2.152\% 5/26/20 $ 121.91 -0.379\% $ 42.68 -0.207\% $ 179.37 0.233\% $ 83.36 3.643\% $ 124.11 5.422\% 5/22/20 $ 122.38 -0.529\% $ 42.76 2.281\% $ 178.95 -0.363\% $ 80.38 0.502\% $ 117.56 -0.331\% 5/21/20 $ 123.03 -0.367\% $ 41.80 -0.564\% $ 179.60 0.531\% $ 79.98 0.665\% $ 117.95 -1.573\% 5/20/20 $ 123.48 0.399\% $ 42.04 0.728\% $ 178.65 2.491\% $ 79.45 3.429\% $ 119.82 1.344\% 5/19/20 $ 122.99 -2.146\% $ 41.73 -0.236\% $ 174.25 -0.145\% $ 76.77 1.144\% $ 118.22 -1.052\% 5/18/20 $ 125.65 1.356\% $ 41.83 0.922\% $ 174.51 3.405\% $ 75.90 7.848\% $ 119.47 2.183\% 5/15/20 $ 123.96 2.021\% $ 41.45 0.166\% $ 168.67 -0.916\% $ 70.17 5.992\% $ 116.89 -0.051\% 5/14/20 $ 121.48 -0.235\% $ 41.38 1.100\% $ 170.22 1.488\% $ 66.09 -1.034\% $ 116.95 -0.690\% 5/13/20 $ 121.77 -0.057\% $ 40.92 -1.005\% $ 167.70 -2.130\% $ 66.77 -6.910\% $ 117.76 -2.026\% 5/12/20 $ 121.84 0.089\% $ 41.34 -0.309\% $ 171.31 -2.429\% $ 71.55 -5.844\% $ 120.17 -2.830\% 5/11/20 $ 121.73 0.592\% $ 41.47 -0.047\% $ 175.53 -0.193\% $ 75.86 0.454\% $ 123.62 0.422\% 5/8/20 $ 121.01 0.858\% $ 41.49 1.868\% $ 175.87 0.061\% $ 75.51 11.133\% $ 123.10 1.292\% 5/7/20 $ 119.97 -0.711\% $ 40.72 1.020\% $ 175.76 2.318\% $ 67.56 3.909\% $ 121.52 -0.049\% 5/6/20 $ 120.83 -1.153\% $ 40.30 1.550\% $ 171.73 -1.275\% $ 64.97 2.044\% $ 121.58 -0.312\% 5/5/20 $ 122.23 0.829\% $ 39.68 1.223\% $ 173.93 -1.457\% $ 63.65 6.084\% $ 121.96 1.039\% 5/4/20 $ 121.22 0.633\% $ 39.20 1.467\% $ 176.49 -0.433\% $ 59.90 -3.032\% $ 120.70 -0.347\% 5/1/20 $ 120.46 1.121\% $ 38.63 -1.467\% $ 177.25 -2.647\% $ 61.74 -5.050\% $ 121.12 -2.019\% 4/30/20 $ 119.12 -1.672\% $ 39.20 2.029\% $ 182.01 -0.139\% $ 64.94 -5.995\% $ 123.59 -3.397\% 4/29/20 $ 121.13 -3.498\% $ 38.41 -0.128\% $ 182.26 1.011\% $ 68.95 6.282\% $ 127.86 1.871\% 4/28/20 $ 125.44 -0.234\% $ 38.46 -1.398\% $ 180.43 0.022\% $ 64.75 4.985\% $ 125.49 1.033\% 4/27/20 $ 125.73 -0.885\% $ 39.01 0.709\% $ 180.39 1.011\% $ 61.60 7.745\% $ 124.20 1.329\% 4/24/20 $ 126.85 0.706\% $ 38.73 3.728\% $ 178.57 1.082\% $ 57.01 6.707\% $ 122.56 0.721\% 4/23/20 $ 125.96 -2.353\% $ 37.31 -0.893\% $ 176.65 -2.410\% $ 53.32 3.635\% $ 121.68 0.206\% 4/22/20 $ 128.96 1.825\% $ 37.65 1.687\% $ 180.96 4.890\% $ 51.41 0.076\% $ 121.43 0.628\% 4/21/20 $ 126.62 -0.494\% $ 37.02 -0.080\% $ 172.32 -2.266\% $ 51.37 0.536\% $ 120.67 -0.858\% 4/20/20 $ 127.25 -1.733\% $ 37.05 0.479\% $ 176.27 -2.420\% $ 51.10 -2.240\% $ 121.71 -2.355\% 4/17/20 $ 129.47 -0.159\% $ 36.87 0.643\% $ 180.59 3.611\% $ 52.26 7.098\% $ 124.61 2.256\% 4/16/20 $ 129.68 2.735\% $ 36.63 2.806\% $ 174.19 0.929\% $ 48.68 4.873\% $ 121.83 -0.948\% 4/15/20 $ 126.18 -0.186\% $ 35.62 1.251\% $ 172.58 -3.400\% $ 46.36 -8.203\% $ 122.99 -1.333\% 4/14/20 $ 126.42 2.910\% $ 35.18 2.780\% $ 178.54 2.126\% $ 50.32 9.802\% $ 124.64 2.749\% 4/13/20 $ 122.79 2.833\% $ 34.21 2.712\% $ 174.79 -1.968\% $ 45.62 -9.880\% $ 121.26 -1.758\% 4/9/20 $ 119.36 -0.033\% $ 33.30 2.454\% $ 178.26 3.439\% $ 50.36 7.816\% $ 123.41 -0.105\% 4/8/20 $ 119.40 -0.123\% $ 32.49 4.302\% $ 172.24 1.076\% $ 46.58 8.456\% $ 123.54 1.336\% 4/7/20 $ 119.55 -3.290\% $ 31.12 1.401\% $ 170.39 -0.822\% $ 42.80 3.879\% $ 121.90 -0.418\% 4/6/20 $ 123.55 5.369\% $ 30.69 5.844\% $ 171.80 9.914\% $ 41.17 14.900\% $ 122.41 6.244\% 4/3/20 $ 117.09 0.697\% $ 28.95 0.751\% $ 155.58 -0.727\% $ 35.47 -6.814\% $ 115.00 -2.423\% 4/2/20 $ 116.27 3.875\% $ 28.73 1.415\% $ 156.72 2.083\% $ 37.97 2.405\% $ 117.82 0.947\% 4/1/20 $ 111.85 0.457\% $ 28.33 -4.351\% $ 153.49 -4.439\% $ 37.07 -10.037\% $ 116.71 -2.738\% 3/31/20 $ 111.34 -1.372\% $ 29.59 -3.690\% $ 160.46 -1.667\% $ 40.98 -0.520\% $ 119.95 -4.300\% 3/30/20 $ 112.88 4.993\% $ 30.70 3.292\% $ 163.15 2.481\% $ 41.20 -0.986\% $ 125.22 -1.600\% 3/27/20 $ 107.39 -0.219\% $ 29.70 0.066\% $ 159.16 -2.016\% $ 41.61 -6.902\% $ 127.24 0.710\% 3/26/20 $ 107.62 0.383\% $ 29.68 6.118\% $ 162.40 2.646\% $ 44.58 10.227\% $ 126.34 4.079\% 3/25/20 $ 107.21 -5.018\% $ 27.92 2.498\% $ 158.16 0.634\% $ 40.25 9.942\% $ 121.29 4.158\% 3/24/20 $ 112.73 0.654\% $ 27.23 4.926\% $ 157.16 16.658\% $ 36.44 6.699\% $ 116.35 4.617\% 3/23/20 $ 111.99 0.272\% $ 25.92 -4.600\% $ 133.04 -7.981\% $ 34.08 -2.589\% $ 111.10 -4.712\% 3/20/20 $ 111.69 -4.696\% $ 27.15 -7.068\% $ 144.09 -0.678\% $ 34.97 -3.280\% $ 116.46 -1.508\% 3/19/20 $ 117.06 -2.145\% $ 29.13 -5.584\% $ 145.07 8.513\% $ 36.14 7.190\% $ 118.23 1.844\% 3/18/20 $ 119.60 2.746\% $ 30.81 -6.134\% $ 133.24 -7.247\% $ 33.63 -15.345\% $ 116.07 -2.401\% 3/17/20 $ 116.36 11.072\% $ 32.76 3.175\% $ 143.25 -0.937\% $ 39.21 0.821\% $ 118.89 9.145\% 3/16/20 $ 104.16 -6.649\% $ 31.73 -5.286\% $ 144.60 -17.287\% $ 38.89 -22.004\% $ 108.50 -6.882\% 3/13/20 $ 111.32 9.220\% $ 33.45 2.865\% $ 171.89 4.032\% $ 48.46 8.579\% $ 116.23 3.529\% 3/12/20 $ 101.52 -9.509\% $ 32.51 -5.306\% $ 165.09 -10.121\% $ 44.47 -13.737\% $ 112.20 -9.019\% 3/11/20 $ 111.64 -4.578\% $ 34.28 -3.415\% $ 182.68 -5.985\% $ 51.02 -8.135\% $ 122.79 -3.363\% 3/10/20 $ 116.87 2.220\% $ 35.47 1.453\% $ 193.94 6.726\% $ 55.35 10.524\% $ 126.99 3.363\% 3/9/20 $ 114.31 -0.060\% $ 34.96 -2.420\% $ 181.33 -6.224\% $ 49.82 -31.196\% $ 122.79 -3.458\% 3/6/20 $ 114.38 1.124\% $ 35.82 -2.255\% $ 192.97 0.272\% $ 68.06 0.300\% $ 127.11 -1.631\% 3/5/20 $ 113.10 -0.731\% $ 36.63 -3.355\% $ 192.45 -4.293\% $ 67.85 -12.009\% $ 129.20 -2.030\% 3/4/20 $ 113.93 3.362\% $ 37.88 4.708\% $ 200.89 3.695\% $ 76.51 3.937\% $ 131.85 0.685\% 3/3/20 $ 110.16 -2.596\% $ 36.14 2.091\% $ 193.60 -1.512\% $ 73.55 -2.414\% $ 130.95 -1.335\% 3/2/20 $ 113.06 7.339\% $ 35.39 3.740\% $ 196.55 4.225\% $ 75.35 2.798\% $ 132.71 1.488\% 2/28/20 $ 105.06 -2.495\% $ 34.09 -0.690\% $ 188.42 -2.833\% $ 73.27 -0.172\% $ 130.75 -0.496\% 2/27/20 $ 107.71 -3.016\% $ 34.33 -4.601\% $ 193.84 -4.428\% $ 73.40 -7.065\% $ 131.40 -2.799\% 2/26/20 $ 111.01 -0.535\% $ 35.95 0.629\% $ 202.61 -0.947\% $ 78.77 0.929\% $ 135.13 0.817\% 2/25/20 $ 111.61 -1.673\% $ 35.72 -2.170\% $ 204.54 -0.667\% $ 78.04 -0.966\% $ 134.03 -0.343\% 2/24/20 $ 113.49 -1.924\% $ 36.51 -2.492\% $ 205.91 -1.095\% $ 78.80 -5.843\% $ 134.49 -3.327\% 2/21/20 $ 115.69 0.753\% $ 37.43 1.344\% $ 208.18 0.367\% $ 83.54 -2.424\% $ 139.04 -0.050\% 2/20/20 $ 114.83 0.009\% $ 36.93 0.425\% $ 207.42 -0.255\% $ 85.59 3.101\% $ 139.11 0.917\% 2/19/20 $ 114.82 -1.643\% $ 36.77 -0.902\% $ 207.95 -0.241\% $ 82.98 0.070\% $ 137.84 -1.111\% 2/18/20 $ 116.72 1.465\% $ 37.10 -0.710\% $ 208.45 -0.434\% $ 82.92 -1.535\% $ 139.38 -0.551\% 2/14/20 $ 115.02 0.382\% $ 37.37 2.522\% $ 209.35 -0.152\% $ 84.20 -0.254\% $ 140.15 -0.676\% 2/13/20 $ 114.58 1.363\% $ 36.44 0.108\% $ 209.67 -0.018\% $ 84.42 1.589\% $ 141.10 -0.938\% 2/12/20 $ 113.03 0.389\% $ 36.40 1.930\% $ 209.71 0.799\% $ 83.09 3.741\% $ 142.43 0.225\% 2/11/20 $ 112.59 0.130\% $ 35.70 1.159\% $ 208.04 1.175\% $ 80.04 1.320\% $ 142.11 0.586\% 2/10/20 $ 112.44 -1.036\% $ 35.29 -0.498\% $ 205.61 0.753\% $ 78.99 0.074\% $ 141.28 -0.747\% 2/7/20 $ 113.62 0.120\% $ 35.47 -4.853\% $ 204.07 -0.594\% $ 78.93 -2.228\% $ 142.34 -1.055\% 2/6/20 $ 113.48 -0.429\% $ 37.23 2.316\% $ 205.28 -0.702\% $ 80.71 -0.875\% $ 143.85 1.492\% 2/5/20 $ 113.97 1.327\% $ 36.38 -0.751\% $ 206.73 -0.117\% $ 81.42 0.899\% $ 141.72 0.545\% 2/4/20 $ 112.46 0.871\% $ 36.65 8.417\% $ 206.97 -0.261\% $ 80.69 1.126\% $ 140.95 1.451\% 2/3/20 $ 111.49 -0.192\% $ 33.69 2.443\% $ 207.51 0.564\% $ 79.78 1.955\% $ 138.92 0.058\% 1/31/20 $ 111.70 -1.809\% $ 32.88 -4.373\% $ 206.35 -1.028\% $ 78.24 -1.650\% $ 138.84 -1.600\% 1/30/20 $ 113.74 0.594\% $ 34.35 1.379\% $ 208.48 0.808\% $ 79.54 0.748\% $ 141.08 -0.333\% 1/29/20 $ 113.07 -0.611\% $ 33.88 -4.606\% $ 206.80 1.907\% $ 78.95 -1.016\% $ 141.55 -0.725\% 1/28/20 $ 113.76 0.637\% $ 35.48 2.037\% $ 202.89 0.500\% $ 79.75 1.832\% $ 142.58 1.072\% 1/27/20 $ 113.04 1.294\% $ 34.76 0.339\% $ 201.88 -0.904\% $ 78.31 -1.012\% $ 141.06 -1.198\% 1/24/20 $ 111.59 -1.251\% $ 34.64 -0.705\% $ 203.71 -1.027\% $ 79.10 -2.463\% $ 142.76 -0.210\% 1/23/20 $ 112.99 -0.250\% $ 34.89 -0.783\% $ 205.81 0.932\% $ 81.08 1.400\% $ 143.06 1.054\% 1/22/20 $ 113.27 0.440\% $ 35.16 0.475\% $ 203.91 0.133\% $ 79.95 1.149\% $ 141.56 -0.578\% 1/21/20 $ 112.78 0.547\% $ 35.00 -0.280\% $ 203.64 -0.388\% $ 79.04 -0.613\% $ 142.38 1.657\% 1/17/20 $ 112.16 -0.814\% $ 35.09 -0.279\% $ 204.43 0.534\% $ 79.52 0.000\% $ 140.04 -0.043\% 1/16/20 $ 113.08 0.536\% $ 35.19 1.656\% $ 203.34 0.514\% $ 79.52 1.390\% $ 140.10 0.530\% 1/15/20 $ 112.47 -0.778\% $ 34.61 -0.057\% $ 202.29 1.175\% $ 78.42 3.994\% $ 139.36 -0.722\% 1/14/20 $ 113.35 0.259\% $ 34.63 1.769\% $ 199.93 0.391\% $ 75.35 4.862\% $ 140.37 -0.135\% 1/13/20 $ 113.06 -0.431\% $ 34.03 -0.460\% $ 199.15 -0.367\% $ 71.78 4.315\% $ 140.56 0.592\% 1/10/20 $ 113.55 -0.839\% $ 34.18 -0.828\% $ 199.88 -0.520\% $ 68.75 2.302\% $ 139.73 -0.557\% 1/9/20 $ 114.50 1.028\% $ 34.47 -1.187\% $ 200.93 1.178\% $ 67.18 -0.921\% $ 140.51 -0.462\% 1/8/20 $ 113.33 -0.344\% $ 34.88 -0.056\% $ 198.57 1.606\% $ 67.80 0.835\% $ 141.16 -0.248\% 1/7/20 $ 113.72 -0.931\% $ 34.90 -0.448\% $ 195.41 0.148\% $ 67.24 -2.427\% $ 141.51 0.524\% 1/6/20 $ 114.79 -0.204\% $ 35.06 -0.502\% $ 195.12 1.118\% $ 68.89 -2.383\% $ 140.77 0.014\% 1/3/20 $ 115.02 -0.887\% $ 35.23 -0.941\% $ 192.95 -0.354\% $ 70.55 -1.693\% $ 140.75 -1.053\% 1/2/20 $ 116.04 0.084\% $ 35.56 0.525\% $ 193.63 1.596\% $ 71.76 -0.594\% $ 142.24 1.202\% 12/31/19 $ 115.95 -0.470\% $ 35.38 0.862\% $ 190.57 0.355\% $ 72.18 0.405\% $ 140.54 -0.050\% 12/30/19 $ 116.49 -0.159\% $ 35.07 -0.751\% $ 189.89 -0.638\% $ 71.89 -0.553\% $ 140.61 -0.475\% 12/27/19 $ 116.68 0.059\% $ 35.34 -0.498\% $ 191.11 0.562\% $ 72.29 0.283\% $ 141.28 -0.177\% 12/26/19 $ 116.61 0.008\% $ 35.52 0.110\% $ 190.04 0.198\% $ 72.09 -1.405\% $ 141.53 0.134\% 12/24/19 $ 116.60 0.402\% $ 35.48 0.000\% $ 189.66 0.239\% $ 73.11 -1.163\% $ 141.34 -0.438\% 12/23/19 $ 116.13 -1.053\% $ 35.48 0.055\% $ 189.21 -0.478\% $ 73.96 2.850\% $ 141.96 -0.007\% 12/20/19 $ 117.36 0.175\% $ 35.46 0.415\% $ 190.12 0.041\% $ 71.88 1.640\% $ 141.97 -0.555\% 12/19/19 $ 117.16 0.183\% $ 35.31 1.116\% $ 190.04 0.728\% $ 70.72 1.044\% $ 142.76 0.260\% 12/18/19 $ 116.94 -1.178\% $ 34.92 -0.727\% $ 188.66 -0.454\% $ 69.98 4.405\% $ 142.39 -0.267\% 12/17/19 $ 118.33 0.612\% $ 35.17 1.403\% $ 189.52 -0.690\% $ 66.96 -0.446\% $ 142.77 0.168\% 12/16/19 $ 117.61 0.208\% $ 34.68 -0.226\% $ 190.83 0.385\% $ 67.26 1.084\% $ 142.53 0.302\% 12/13/19 $ 117.36 0.442\% $ 34.76 0.480\% $ 190.10 0.412\% $ 66.54 -0.550\% $ 142.10 0.352\% 12/12/19 $ 116.84 0.637\% $ 34.59 1.111\% $ 189.31 0.813\% $ 66.91 … Income Statement Walmart Inc. Walmart Inc. Consolidated Statements of Income Consolidated Balance Sheets Fiscal Years Ended January 31, As of January 31, (Amounts in millions, except per share data) 2021 2020 2019 (Amounts in millions) 2021 2020 Revenues: ASSETS Net sales $ 555,233 $ 519,926 $ 510,329 Current assets: Membership and other income 3,918 4,038 4,076 Cash and cash equivalents $ 17,741 $ 9,465 Total revenues 559,151 523,964 514,405 Receivables, net 6,516 6,284 Costs and expenses: Inventories 44,949 44,435 Cost of sales 420,315 394,605 385,301 Prepaid expenses and other 20,861 1,622 Operating, selling, general and administrative expenses 116,288 108,791 107,147 Total current assets 90,067 61,806 Operating income 22,548 20,568 21,957 Interest: Property and equipment, net 92,201 105,208 Debt 1,976 2,262 1,975 Finance, capital lease and financing obligations 339 337 371 Operating lease right-of-use assets 13,642 17,424 Interest income (121) (189) (217) Finance lease right-of-use assets, net 4,005 4,417 Interest, net 2,194 2,410 2,129 Goodwill 28,983 31,073 Other (gains) and losses (210) (1,958) 8,368 Other long-term assets 23,598 16,567 Income before income taxes 20,564 20,116 11,460 Total assets $ 252,496 $ 236,495 Provision for income taxes 6,858 4,915 4,281 Consolidated net income 13,706 15,201 7,179 LIABILITIES AND EQUITY Consolidated net income attributable to noncontrolling Current liabilities: interest (196) (320) (509) Short-term borrowings $ 224 $ 575 Consolidated net income attributable to Walmart $ 13,510 $ 14,881 $ 6,670 Accounts payable 49,141 46,973 Net income per common share: Accrued liabilities 37,966 22,296 Basic net income per common share attributable to $ 4.77 $ 5.22 $ 2.28 Accrued income taxes 242 280 Walmart Long-term debt due within one year 3,115 5,362 Diluted net income per common share attributable to 4.75 5.19 2.26 Operating lease obligations due within one year 1,466 1,793 Walmart Finance lease obligations due within one year 491 511 5,314 Weighted-average common shares outstanding: Total current liabilities 92,645 77,790 Basic 2,831 2,850 2,929 Diluted 2,847 2,868 2,945 Long-term debt 41,194 43,714 Long-term operating lease obligations 12,909 16,171 Dividends declared per common share $ 2.16 $ 2.12 $ 2.08 Long-term finance lease obligations 3,847 4,307 57,950 Consolidated net income $ 13,706 $ 15,201 $ 7,179 Deferred income taxes and other 14,370 12,961 Consolidated net income attributable to noncontrolling (196) (320) (509) interest Commitments and contingencies Consolidated net income attributable to Walmart 13,510 14,881 6,670 Equity: Other comprehensive income (loss), net of income taxes Common stock 282 284 Currency translation and other 842 286 (226) Capital in excess of par value 3,646 3,247 Net investment hedges (221) 122 272 Retained earnings 88,763 83,943 Cash flow hedges 235 (399) (290) Accumulated other comprehensive loss (11,766) (12,805) Minimum pension liability (30) (1,244) 131 Total Walmart shareholders equity 80,925 74,669 Noncontrolling interest 6,606 6,883 Other comprehensive income (loss), net of income taxes 826 (1,235) (113) Total equity 87,531 81,552 Other comprehensive (income) loss attributable to 213 (28) 188 Total liabilities and equity $ 252,496 $ 236,495 noncontrolling interest Other comprehensive income (loss) attributable to Walmart 1,039 (1,263) 75 Annual Rate of Return Walmart eBay Date Adj Close Annual Rate Adj Close Annual Rate Annual rate of return for security Expected Annual Rate of Return Date Interest Free rate 2021 2020 2021 2020 2019 1/29/21 $ 139.36 -2.294\% 56.161098 0.124\% 1.11\% -5.41\% 1/29/21 1.11\% Debt 1976 2262 Income before income taxes 20,564 20,116 11,460 1/28/21 $ 142.59 -0.063\% 56.091534 -3.328\% 1.07\% -1.10\% Beta 1/28/21 1.07\% Finance, capital lease and financing obligations 339 337 Provision for income taxes 6,858 4,915 4,281 1/27/21 $ 142.68 -2.519\% 57.989738 -1.396\% 1.04\% -5.78\% Calculated 1.92 1/27/21 1.04\% Total Interest Expense 2315 2599 Tax Rate 33.35\% 24.43\% 37.36\% 1/26/21 $ 146.32 0.892\% 58.804676 3.299\% 1.05\% 0.75\% Data source 0.47 1/26/21 1.05\% 1/25/21 $ 145.02 -0.089\% 56.896534 1.390\% 1.05\% -1.13\% 1/25/21 1.05\% Current Debt and Capital Lease Obligation 5,296 8,241 1/22/21 $ 145.15 1.017\% 56.111408 0.106\% 1.10\% 0.94\% 1/22/21 1.10\% Long-term debt 41,194 43,714 Weight of Equity 0.8635482562 1/21/21 $ 143.68 -0.455\% 56.051781 0.409\% 1.12\% -1.90\% 1/21/21 1.12\% Long-term operating lease obligations 12,909 16,171 Weight of Debt 0.1364517438 1/20/21 $ 144.34 1.468\% 55.823196 -1.432\% 1.10\% 1.80\% 1/20/21 1.10\% Long-term finance lease obligations 3,847 4,307 Cost of Equity 7.08\% 1/19/21 $ 142.24 -0.868\% 56.628197 2.776\% 1.10\% -2.67\% 1/19/21 1.10\% Total Debt 63,246 72,433 Cost of Debt 3.66\% 1/15/21 $ 143.48 -1.598\% 55.077827 0.271\% 1.11\% -4.08\% 1/18/21 ERROR:#N/A Tax Rate 66.65\% 1/14/21 $ 145.79 -0.326\% 54.928757 -0.793\% 1.15\% -1.68\% 1/15/21 1.11\% Cost of Debt 3.66\% 3.59\% WACC 6.45\% 1/13/21 $ 146.26 -1.026\% 55.366039 -0.591\% 1.10\% -2.97\% 1/14/21 1.15\% 1/12/21 $ 147.77 1.134\% 55.694004 3.838\% 1.15\% 1.12\% 1/13/21 1.10\% Equity: 400,258.52 1/11/21 $ 146.10 0.449\% 53.597031 -1.015\% 1.15\% -0.19\% 1/12/21 1.15\% 1/8/21 $ 145.45 -0.014\% 54.143635 2.641\% 1.13\% -1.06\% 1/11/21 1.15\% 1/7/21 $ 145.47 -0.007\% 52.732403 -0.301\% 1.08\% -1.00\% 1/8/21 1.13\% 1/6/21 $ 145.48 0.622\% 52.891415 2.261\% 1.04\% 0.24\% 1/7/21 1.08\% 1/5/21 $ 144.58 -0.534\% 51.708755 1.024\% 0.96\% -1.90\% 1/6/21 1.04\% 1/4/21 $ 145.35 1.638\% 51.18203 2.457\% 0.93\% 2.29\% 1/5/21 0.96\% 12/31/20 $ 142.99 -0.021\% 49.939751 -0.595\% 0.93\% -0.89\% 1/4/21 0.93\% 12/30/20 $ 143.02 -0.083\% 50.237896 -0.611\% 0.93\% -1.01\% 1/1/21 ERROR:#N/A 12/29/20 $ 143.14 -0.636\% 50.545982 1.227\% 0.94\% -2.08\% 12/31/20 0.93\% 12/28/20 $ 144.05 1.191\% 49.929813 0.239\% 0.94\% 1.42\% 12/30/20 0.93\% 12/24/20 $ 142.34 0.195\% 49.810551 -1.995\% 0.94\% -0.49\% 12/29/20 0.94\% 12/23/20 $ 142.07 -0.682\% 50.81432 -0.954\% 0.96\% -2.18\% 12/28/20 0.94\% 12/22/20 $ 143.04 -1.220\% 51.301289 0.097\% 0.93\% -3.19\% 12/25/20 ERROR:#N/A 12/21/20 $ 144.79 0.014\% 51.251598 -2.848\% 0.95\% -0.84\% 12/24/20 0.94\% 12/18/20 $ 144.77 -0.103\% 52.732403 0.019\% 0.95\% -1.07\% 12/23/20 0.96\% 12/17/20 $ 144.92 0.460\% 52.722462 -1.125\% 0.94\% 0.02\% 12/22/20 0.93\% 12/16/20 $ 144.26 -0.103\% 53.31876 2.970\% 0.92\% -1.04\% 12/21/20 0.95\% 12/15/20 $ 144.41 -0.048\% 51.758453 4.940\% 0.92\% -0.93\% 12/18/20 0.95\% 12/14/20 $ 144.48 -0.923\% 49.26395 0.892\% 0.90\% -2.59\% 12/17/20 0.94\% 12/11/20 $ 145.82 -0.027\% 48.826668 -0.952\% 0.90\% -0.88\% 12/16/20 0.92\% 12/10/20 $ 145.86 -0.468\% 49.293762 0.202\% 0.92\% -1.74\% 12/15/20 0.92\% 12/9/20 $ 146.54 -0.793\% 49.194382 -0.785\% 0.95\% -2.39\% 12/14/20 0.90\% 12/8/20 $ 147.71 0.901\% 49.581974 -0.280\% 0.92\% 0.88\% 12/11/20 0.90\% 12/7/20 $ 146.38 -0.539\% 49.721107 -1.861\% 0.94\% -1.89\% 12/10/20 0.92\% 12/4/20 $ 147.17 -0.262\% 50.655304 1.343\% 0.97\% -1.39\% 12/9/20 0.95\% 12/3/20 $ 147.56 -0.814\% 49.979504 -2.086\% 0.92\% -2.40\% 12/8/20 0.92\% 12/2/20 $ 148.76 -1.399\% 51.032959 1.630\% 0.95\% -3.55\% 12/7/20 0.94\% 12/1/20 $ 150.86 -0.098\% 50.208084 0.178\% 0.92\% -1.03\% 12/4/20 0.97\% 11/30/20 $ 151.01 0.782\% 50.118637 -1.476\% 0.84\% 0.73\% 12/3/20 0.92\% 11/27/20 $ 149.83 -0.152\% 50.864006 1.749\% 0.84\% -1.06\% 12/2/20 0.95\% 11/25/20 $ 150.06 0.310\% 49.982262 -0.158\% 0.88\% -0.21\% 12/1/20 0.92\% 11/24/20 $ 149.59 0.285\% 50.061516 1.255\% 0.88\% -0.26\% 11/30/20 0.84\% 11/23/20 $ 149.17 0.458\% 49.437359 1.840\% 0.86\% 0.09\% 11/27/20 0.84\% 11/20/20 $ 148.49 -1.244\% 48.535797 -1.600\% 0.83\% -3.14\% 11/26/20 ERROR:#N/A 11/19/20 $ 150.35 2.012\% 49.318466 2.543\% 0.86\% 3.07\% 11/25/20 0.88\% 11/18/20 $ 147.35 -0.188\% 48.080059 0.413\% 0.88\% -1.16\% 11/24/20 0.88\% 11/17/20 $ 147.63 -2.034\% 47.881916 -0.454\% 0.87\% -4.69\% 11/23/20 0.86\% 11/16/20 $ 150.66 1.254\% 48.099876 -0.247\% 0.91\% 1.57\% 11/20/20 0.83\% 11/13/20 $ 148.78 1.546\% 48.218761 4.368\% 0.89\% 2.15\% 11/19/20 0.86\% 11/12/20 $ 146.50 0.169\% 46.158047 -2.375\% 0.88\% -0.48\% 11/18/20 0.88\% 11/11/20 $ 146.25 1.649\% 47.267658 2.483\% ERROR:#N/A ERROR:#N/A 11/17/20 0.87\% 11/10/20 $ 143.86 1.397\% 46.108509 -3.753\% 0.98\% 1.78\% 11/16/20 0.91\% 11/9/20 $ 141.87 -1.542\% 47.872005 -4.788\% 0.96\% -3.83\% 11/13/20 0.89\% 11/6/20 $ 144.07 1.590\% 50.220032 2.558\% 0.83\% 2.29\% 11/12/20 0.88\% 11/5/20 $ 141.80 1.058\% 48.951904 3.271\% 0.79\% 1.30\% 11/11/20 ERROR:#N/A 11/4/20 $ 140.30 -0.576\% 47.376644 -2.274\% 0.78\% -1.82\% 11/10/20 0.98\% 11/3/20 $ 141.11 1.681\% 48.466442 2.170\% 0.90\% 2.40\% 11/9/20 0.96\% 11/2/20 $ 138.76 1.182\% 47.426178 0.503\% 0.87\% 1.47\% 11/6/20 0.83\% 10/30/20 $ 137.13 -0.840\% 47.188408 -3.406\% 0.88\% -2.41\% 11/5/20 0.79\% 10/29/20 $ 138.29 -0.086\% 48.823105 -7.748\% 0.85\% -0.94\% 11/4/20 0.78\% 10/28/20 $ 138.41 -2.001\% 52.756298 -0.562\% 0.79\% -4.56\% 11/3/20 0.90\% 10/27/20 $ 141.20 0.498\% 53.053516 0.393\% 0.79\% 0.23\% 11/2/20 0.87\% 10/26/20 $ 140.50 -1.182\% 52.845463 -0.840\% 0.81\% -3.01\% 10/30/20 0.88\% 10/23/20 $ 142.17 0.209\% 53.291294 2.828\% 0.85\% -0.38\% 10/29/20 0.85\% 10/22/20 $ 141.88 -0.590\% 51.805202 -1.008\% 0.87\% -1.93\% 10/28/20 0.79\% 10/21/20 $ 142.72 0.347\% 52.330288 -2.579\% 0.83\% -0.10\% 10/27/20 0.79\% 10/20/20 $ 142.22 0.662\% 53.697491 -0.221\% 0.81\% 0.53\% 10/26/20 0.81\% 10/19/20 $ 141.28 -1.224\% 53.816376 -2.742\% 0.78\% -3.06\% 10/23/20 0.85\% 10/16/20 $ 143.02 0.124\% 55.312382 0.773\% 0.76\% -0.46\% 10/22/20 0.87\% 10/15/20 $ 142.84 0.409\% 54.886368 -1.895\% 0.74\% 0.11\% 10/21/20 0.83\% 10/14/20 $ 142.26 -1.578\% 55.936539 -1.982\% 0.73\% -3.69\% 10/20/20 0.81\% 10/13/20 $ 144.52 1.363\% 57.056065 3.913\% 0.74\% 1.93\% 10/19/20 0.78\% 10/12/20 $ 142.57 1.024\% 54.86655 -0.126\% ERROR:#N/A ERROR:#N/A 10/16/20 0.76\% 10/9/20 $ 141.11 1.000\% 54.935902 6.270\% 0.79\% 1.19\% 10/15/20 0.74\% 10/8/20 $ 139.71 0.333\% 51.597145 2.213\% 0.78\% -0.08\% 10/14/20 0.73\% 10/7/20 $ 139.25 0.185\% 50.467716 2.545\% 0.81\% -0.39\% 10/13/20 0.74\% 10/6/20 $ 138.99 -0.829\% 49.199581 -4.161\% 0.76\% -2.28\% 10/12/20 ERROR:#N/A 10/5/20 $ 140.15 0.921\% 51.29002 0.174\% 0.78\% 1.05\% 10/9/20 0.79\% 10/2/20 $ 138.86 -1.820\% 51.200855 -1.345\% 0.70\% -4.13\% 10/8/20 0.78\% 10/1/20 $ 141.41 2.240\% 51.894367 0.536\% 0.68\% 3.67\% 10/7/20 0.81\% 9/30/20 $ 138.28 2.000\% 51.616959 -1.050\% 0.69\% 3.20\% 10/6/20 0.76\% 9/29/20 $ 135.54 -0.080\% 52.161865 -2.606\% 0.66\% -0.76\% 10/5/20 0.78\% 9/28/20 $ 135.65 -0.015\% 53.538975 2.929\% 0.67\% -0.64\% 10/2/20 0.70\% 9/25/20 $ 135.67 0.416\% 51.993435 1.343\% 0.66\% 0.19\% 10/1/20 0.68\% 9/24/20 $ 135.11 0.521\% 51.299927 2.147\% 0.67\% 0.38\% 9/30/20 0.69\% 9/23/20 $ 134.40 -1.692\% 50.210125 -0.472\% 0.68\% -3.86\% 9/29/20 0.66\% 9/22/20 $ 136.70 0.901\% 50.447899 1.544\% 0.68\% 1.10\% 9/28/20 0.67\% 9/21/20 $ 135.47 1.307\% 49.675133 3.099\% 0.68\% 1.88\% 9/25/20 0.66\% 9/18/20 $ 133.71 -1.029\% 48.159317 -0.062\% 0.70\% -2.61\% 9/24/20 0.67\% 9/17/20 $ 135.10 0.315\% 48.189041 -3.594\% 0.69\% -0.03\% 9/23/20 0.68\% 9/16/20 $ 134.67 -0.804\% 49.952534 -2.662\% 0.69\% -2.17\% 9/22/20 0.68\% 9/15/20 $ 135.76 0.029\% 51.299927 -0.999\% 0.68\% -0.57\% 9/21/20 0.68\% 9/14/20 $ 135.72 0.453\% 51.815109 -0.895\% 0.68\% 0.24\% 9/18/20 0.70\% 9/11/20 $ 135.11 -0.080\% 52.28075 0.856\% 0.67\% -0.77\% 9/17/20 0.69\% 9/10/20 $ 135.21 -2.226\% 51.834919 -2.118\% 0.68\% -4.89\% 9/16/20 0.69\% 9/9/20 $ 138.26 1.035\% 52.944538 3.640\% 0.71\% 1.33\% 9/15/20 0.68\% 9/8/20 $ 136.83 -3.115\% 51.05225 -1.941\% 0.69\% -6.60\% 9/14/20 0.68\% 9/4/20 $ 141.16 -1.190\% 52.052883 -1.173\% 0.72\% -2.94\% 9/11/20 0.67\% 9/3/20 $ 142.85 -2.149\% 52.667133 -3.566\% 0.63\% -4.69\% 9/10/20 0.68\% 9/2/20 $ 145.96 0.061\% 54.579239 2.649\% 0.66\% -0.49\% 9/9/20 0.71\% 9/1/20 $ 145.87 6.104\% 53.152592 -2.084\% 0.68\% 11.07\% 9/8/20 0.69\% 8/31/20 $ 137.23 -1.039\% 54.272114 1.231\% 0.72\% -2.65\% 9/7/20 ERROR:#N/A 8/28/20 $ 138.66 2.651\% 53.60833 -3.690\% 0.74\% 4.40\% 9/4/20 0.72\% 8/27/20 $ 135.04 4.437\% 55.623451 -3.952\% 0.74\% 7.82\% 9/3/20 0.63\% 8/26/20 $ 129.18 0.054\% 57.865784 0.909\% 0.69\% -0.53\% 9/2/20 0.66\% 8/25/20 $ 129.11 -0.534\% 57.342239 -1.250\% 0.69\% -1.66\% 9/1/20 0.68\% 8/24/20 $ 129.80 -0.228\% 58.063339 0.974\% 0.65\% -1.03\% 8/31/20 0.72\% 8/21/20 $ 130.09 0.809\% 57.500286 0.949\% 0.64\% 0.96\% 8/28/20 0.74\% 8/20/20 $ 129.05 -1.399\% 56.956993 -0.087\% 0.65\% -3.28\% 8/27/20 0.74\% 8/19/20 $ 130.87 -1.722\% 57.006386 1.185\% 0.68\% -3.92\% 8/26/20 0.69\% 8/18/20 $ 133.14 -0.658\% 56.334671 -0.560\% 0.67\% -1.87\% 8/25/20 0.69\% 8/17/20 $ 134.02 2.237\% 56.650772 1.866\% 0.69\% 3.65\% 8/24/20 0.65\% 8/14/20 $ 131.05 0.567\% 55.603699 0.018\% 0.71\% 0.44\% 8/21/20 0.64\% 8/13/20 $ 130.31 0.380\% 55.593819 1.414\% 0.71\% 0.08\% 8/20/20 0.65\% 8/12/20 $ 129.82 1.290\% 54.81345 2.186\% 0.69\% 1.84\% 8/19/20 0.68\% 8/11/20 $ 128.15 -1.282\% 53.628082 -0.147\% 0.64\% -3.04\% 8/18/20 0.67\% 8/10/20 $ 129.81 1.459\% 53.707104 -1.533\% 0.59\% 2.25\% 8/17/20 0.69\% 8/7/20 $ 127.93 0.478\% 54.536865 0.236\% 0.57\% 0.39\% 8/14/20 0.71\% 8/6/20 $ 127.32 -0.355\% 54.408451 -2.828\% 0.55\% -1.18\% 8/13/20 0.71\% 8/5/20 $ 127.77 -1.400\% 55.969189 0.584\% 0.55\% -3.18\% 8/12/20 0.69\% 8/4/20 $ 129.57 1.794\% 55.643211 -0.425\% 0.52\% 2.96\% 8/11/20 0.64\% 8/3/20 $ 127.27 -0.077\% 55.880283 2.307\% 0.56\% -0.66\% 8/10/20 0.59\% 7/31/20 $ 127.37 -0.555\% 54.60601 1.018\% 0.55\% -1.57\% 8/7/20 0.57\% 7/30/20 $ 128.08 -0.437\% 54.052837 0.348\% 0.55\% -1.34\% 8/6/20 0.55\% 7/29/20 $ 128.64 -0.815\% 53.865154 -3.283\% 0.58\% -2.09\% 8/5/20 0.55\% 7/28/20 $ 129.69 0.418\% 55.662964 -1.550\% 0.59\% 0.26\% 8/4/20 0.52\% 7/27/20 $ 129.15 -0.023\% 56.532234 3.757\% 0.62\% -0.61\% 8/3/20 0.56\% 7/24/20 $ 129.18 -0.304\% 54.447964 -0.054\% 0.59\% -1.12\% 7/31/20 0.55\% 7/23/20 $ 129.57 -0.772\% 54.477596 -2.135\% 0.59\% -2.02\% 7/30/20 0.55\% 7/22/20 $ 130.58 0.249\% 55.653088 -0.443\% 0.60\% -0.07\% 7/29/20 0.58\% 7/21/20 $ 130.25 0.652\% 55.90004 -3.268\% 0.61\% 0.69\% 7/28/20 0.59\% 7/20/20 $ 129.40 -0.205\% 57.757118 0.583\% 0.62\% -0.96\% 7/27/20 0.62\% 7/17/20 $ 129.67 -0.349\% 57.421265 -0.891\% 0.64\% -1.25\% 7/24/20 0.59\% 7/16/20 $ 130.12 0.151\% 57.934929 0.444\% 0.62\% -0.28\% 7/23/20 0.59\% 7/15/20 $ 129.93 -0.008\% 57.678089 -1.175\% 0.64\% -0.60\% 7/22/20 0.60\% 7/14/20 $ 129.94 1.904\% 58.359684 1.329\% 0.63\% 3.07\% 7/21/20 0.61\% 7/13/20 $ 127.48 -0.892\% 57.589195 -1.650\% 0.64\% -2.29\% 7/20/20 0.62\% 7/10/20 $ 128.63 2.268\% 58.547367 0.084\% 0.65\% 3.75\% 7/17/20 0.64\% 7/9/20 $ 125.74 2.625\% 58.497974 1.617\% 0.62\% 4.46\% 7/16/20 0.62\% 7/8/20 $ 122.48 -1.997\% 57.559555 2.204\% 0.67\% -4.44\% 7/15/20 0.64\% 7/7/20 $ 124.96 6.559\% 56.305042 1.467\% 0.65\% 11.97\% 7/14/20 0.63\% 7/6/20 $ 117.02 -0.269\% 55.485157 3.275\% 0.69\% -1.15\% 7/13/20 0.64\% 7/2/20 $ 117.34 -0.402\% 53.697231 2.609\% 0.68\% -1.39\% 7/10/20 0.65\% 7/1/20 $ 117.81 -0.075\% 52.314297 0.968\% 0.69\% -0.78\% 7/9/20 0.62\% 6/30/20 $ 117.90 0.603\% 51.810516 2.197\% 0.66\% 0.55\% 7/8/20 0.67\% 6/29/20 $ 117.19 0.623\% 50.684414 0.822\% 0.64\% 0.61\% 7/7/20 0.65\% 6/26/20 $ 116.46 -1.168\% 50.269535 2.972\% 0.64\% -2.82\% 7/6/20 0.69\% 6/25/20 $ 117.83 -0.492\% 48.797707 1.284\% 0.68\% -1.56\% 7/3/20 ERROR:#N/A 6/24/20 $ 118.41 -0.638\% 48.175385 -2.090\% 0.69\% -1.85\% 7/2/20 0.68\% 6/23/20 $ 119.17 -0.503\% 49.192825 1.293\% 0.72\% -1.62\% 7/1/20 0.69\% 6/22/20 $ 119.77 1.515\% 48.560627 1.786\% 0.71\% 2.25\% 6/30/20 0.66\% 6/19/20 $ 117.97 1.564\% 47.701237 -0.310\% 0.70\% 2.36\% 6/29/20 0.64\% 6/18/20 $ 116.14 -0.878\% 47.849403 0.021\% 0.71\% -2.33\% 6/26/20 0.64\% 6/17/20 $ 117.16 -0.520\% 47.839531 0.642\% 0.74\% -1.67\% 6/25/20 0.68\% 6/16/20 $ 117.77 1.321\% 47.533306 0.479\% 0.75\% 1.84\% 6/24/20 0.69\% 6/15/20 $ 116.22 0.288\% 47.30611 0.481\% 0.71\% -0.10\% 6/23/20 0.72\% 6/12/20 $ 115.89 -1.976\% 47.078915 -0.586\% 0.71\% -4.44\% 6/22/20 0.71\% 6/11/20 $ 118.20 -0.887\% 47.355503 -2.696\% 0.66\% -2.30\% 6/19/20 0.70\% 6/10/20 $ 119.26 -0.157\% 48.649529 -1.010\% 0.75\% -0.99\% 6/18/20 0.71\% 6/9/20 $ 119.44 0.091\% 49.143436 2.092\% 0.84\% -0.60\% 6/17/20 0.74\% 6/8/20 $ 119.34 -0.264\% 48.125992 -0.205\% 0.88\% -1.31\% 6/16/20 0.75\% 6/5/20 $ 119.65 -0.451\% 48.224773 -1.100\% 0.91\% -1.70\% 6/15/20 0.71\% 6/4/20 $ 120.19 -1.108\% 48.75819 6.076\% 0.82\% -2.87\% 6/12/20 0.71\% 6/3/20 $ 121.53 -0.380\% 45.883671 1.017\% 0.77\% -1.43\% 6/11/20 0.66\% 6/2/20 $ 121.99 -0.016\% 45.419399 1.711\% 0.68\% -0.65\% 6/10/20 0.75\% 6/1/20 $ 122.01 -0.081\% 44.648911 -0.749\% 0.66\% -0.76\% 6/9/20 0.84\% 5/29/20 $ 122.11 0.299\% 44.984764 3.281\% 0.65\% -0.02\% 6/8/20 0.88\% 5/28/20 $ 121.75 0.983\% 43.532684 0.181\% 0.70\% 1.24\% 6/5/20 0.91\% 5/27/20 $ 120.56 -1.120\% 43.453953 1.806\% 0.68\% -2.77\% 6/4/20 0.82\% 5/26/20 $ 121.91 -0.379\% 42.676403 -0.207\% 0.69\% -1.36\% 6/3/20 0.77\% 5/22/20 $ 122.38 -0.529\% 42.764988 2.281\% 0.66\% -1.62\% 6/2/20 0.68\% 5/21/20 $ 123.03 -0.367\% 41.800434 -0.564\% 0.68\% -1.33\% 6/1/20 0.66\% 5/20/20 $ 123.48 0.399\% 42.036648 0.728\% 0.68\% 0.14\% 5/29/20 0.65\% 5/19/20 $ 122.99 -2.146\% 41.731541 -0.236\% 0.70\% -4.75\% 5/28/20 0.70\% 5/18/20 $ 125.65 1.356\% 41.82996 0.922\% 0.73\% 1.93\% 5/27/20 0.68\% 5/15/20 $ 123.96 2.021\% 41.44611 0.166\% 0.64\% 3.29\% 5/26/20 0.69\% 5/14/20 $ 121.48 -0.235\% 41.377213 1.100\% 0.63\% -1.03\% 5/25/20 ERROR:#N/A 5/13/20 $ 121.77 -0.057\% 40.924465 -1.005\% 0.64\% -0.69\% 5/22/20 0.66\% 5/12/20 $ 121.84 0.089\% 41.337845 -0.309\% 0.69\% -0.46\% 5/21/20 0.68\% 5/11/20 $ 121.73 0.592\% 41.465794 -0.047\% 0.73\% 0.47\% 5/20/20 0.68\% 5/8/20 $ 121.01 0.858\% 41.485481 1.868\% 0.69\% 1.01\% 5/19/20 0.70\% 5/7/20 $ 119.97 -0.711\% 40.717773 1.020\% 0.63\% -1.94\% 5/18/20 0.73\% 5/6/20 $ 120.83 -1.153\% 40.304394 1.550\% 0.72\% -2.87\% 5/15/20 0.64\% 5/5/20 $ 122.23 0.829\% 39.684334 1.223\% 0.66\% 0.98\% 5/14/20 0.63\% 5/4/20 $ 121.22 0.633\% 39.202057 1.467\% 0.64\% 0.63\% 5/13/20 0.64\% 5/1/20 $ 120.46 1.121\% 38.631195 -1.467\% 0.64\% 1.56\% 5/12/20 0.69\% 4/30/20 $ 119.12 -1.672\% 39.202057 2.029\% 0.64\% -3.79\% 5/11/20 0.73\% 4/29/20 $ 121.13 -3.498\% 38.414665 -0.128\% 0.63\% -7.28\% 5/8/20 0.69\% 4/28/20 $ 125.44 -0.234\% 38.463879 -1.398\% 0.62\% -1.02\% 5/7/20 0.63\% 4/27/20 $ 125.73 -0.885\% 39.005215 0.709\% 0.67\% -2.31\% 5/6/20 0.72\% 4/24/20 $ 126.85 0.706\% 38.729622 3.728\% 0.60\% 0.80\% 5/5/20 0.66\% 4/23/20 $ 125.96 -2.353\% 37.312325 -0.893\% 0.61\% -5.07\% 5/4/20 0.64\% 4/22/20 $ 128.96 1.825\% 37.646969 1.687\% 0.63\% 2.92\% 5/1/20 0.64\% 4/21/20 $ 126.62 -0.494\% 37.017056 -0.080\% 0.58\% -1.48\% 4/30/20 0.64\% 4/20/20 $ 127.25 -1.733\% 37.046577 0.479\% 0.63\% -3.90\% 4/29/20 0.63\% 4/17/20 $ 129.47 -0.159\% 36.869419 0.643\% 0.65\% -0.90\% 4/28/20 0.62\% 4/16/20 $ 129.68 2.735\% 36.633202 2.806\% 0.61\% 4.68\% 4/27/20 0.67\% 4/15/20 $ 126.18 -0.186\% 35.619438 1.251\% 0.63\% -0.93\% 4/24/20 0.60\% 4/14/20 $ 126.42 2.910\% 35.176537 2.780\% 0.76\% 4.88\% 4/23/20 0.61\% 4/13/20 $ 122.79 2.833\% 34.211983 2.712\% 0.76\% 4.73\% 4/22/20 0.63\% 4/9/20 $ 119.36 -0.033\% 33.29665 2.454\% 0.73\% -0.73\% 4/21/20 0.58\% 4/8/20 $ 119.40 -0.123\% 32.489574 4.302\% 0.77\% -0.94\% 4/20/20 0.63\% 4/7/20 $ 119.55 -3.290\% 31.12149 1.401\% 0.75\% -6.99\% 4/17/20 0.65\% 4/6/20 $ 123.55 5.369\% 30.688429 5.844\% 0.67\% 9.67\% 4/16/20 0.61\% 4/3/20 $ 117.09 0.697\% 28.946333 0.751\% 0.62\% 0.77\% 4/15/20 0.63\% 4/2/20 $ 116.27 3.875\% 28.729801 1.415\% 0.63\% 6.85\% 4/14/20 0.76\% 4/1/20 $ 111.85 0.457\% 28.326265 -4.351\% 0.62\% 0.31\% 4/13/20 0.76\% 3/31/20 $ 111.34 -1.372\% 29.586086 -3.690\% 0.70\% -3.27\% 4/10/20 ERROR:#N/A 3/30/20 $ 112.88 4.993\% 30.698271 3.292\% 0.70\% 8.92\% 4/9/20 0.73\% 3/27/20 $ 107.39 -0.219\% 29.704193 0.066\% 0.72\% -1.08\% 4/8/20 0.77\% 3/26/20 $ 107.62 0.383\% 29.684507 6.118\% 0.83\% -0.03\% 4/7/20 0.75\% 3/25/20 $ 107.21 -5.018\% 27.922728 2.498\% 0.88\% -10.42\% 4/6/20 0.67\% 3/24/20 $ 112.73 0.654\% 27.233767 4.926\% 0.84\% 0.48\% 4/3/20 0.62\% 3/23/20 $ 111.99 0.272\% 25.924732 -4.600\% 0.76\% -0.18\% 4/2/20 0.63\% 3/20/20 $ 111.69 -4.696\% 27.145184 -7.068\% 0.92\% -9.84\% 4/1/20 0.62\% 3/19/20 $ 117.06 -2.145\% 29.133337 -5.584\% 1.12\% -5.13\% 3/31/20 0.70\% 3/18/20 $ 119.60 2.746\% 30.806536 -6.134\% 1.18\% 4.18\% 3/30/20 0.70\% 3/17/20 $ 116.36 11.072\% 32.755318 3.175\% 1.02\% 20.27\% 3/27/20 0.72\% 3/16/20 $ 104.16 -6.649\% 31.731716 -5.286\% 0.73\% -13.40\% 3/26/20 0.83\% 3/13/20 $ 111.32 9.220\% 33.454132 2.865\% 0.94\% 16.80\% 3/25/20 0.88\% 3/12/20 $ 101.52 -9.509\% 32.509258 -5.306\% 0.88\% -19.02\% 3/24/20 0.84\% 3/11/20 $ 111.64 -4.578\% 34.280888 -3.415\% 0.82\% -9.52\% 3/23/20 0.76\% 3/10/20 $ 116.87 2.220\% 35.471809 1.453\% 0.76\% 3.56\% 3/20/20 0.92\% 3/9/20 $ 114.31 -0.060\% 34.960003 -2.420\% 0.54\% -0.61\% 3/19/20 1.12\% 3/6/20 $ 114.38 1.124\% 35.816292 -2.255\% 0.74\% 1.48\% 3/18/20 1.18\% 3/5/20 $ 113.10 -0.731\% 36.633202 -3.355\% 0.92\% -2.24\% 3/17/20 1.02\% 3/4/20 $ 113.93 3.362\% 37.883183 4.708\% 1.02\% 5.50\% 3/16/20 0.73\% 3/3/20 $ 110.16 -2.596\% 36.141087 2.091\% 1.02\% -5.91\% 3/13/20 0.94\% 3/2/20 $ 113.06 7.339\% 35.393066 3.740\% 1.10\% 13.05\% 3/12/20 0.88\% 2/28/20 $ 105.06 -2.495\% 34.093876 -0.690\% 1.13\% -5.81\% 3/11/20 0.82\% 2/27/20 $ 107.71 -3.016\% 34.330093 -4.601\% 1.30\% -6.97\% 3/10/20 0.76\% 2/26/20 $ 111.01 -0.535\% 35.946659 0.629\% 1.33\% -2.24\% 3/9/20 0.54\% 2/25/20 $ 111.61 -1.673\% 35.721321 -2.170\% 1.33\% -4.42\% 3/6/20 0.74\% 2/24/20 $ 113.49 -1.924\% 36.505119 -2.492\% 1.38\% -4.95\% 3/5/20 0.92\% 2/21/20 $ 115.69 0.753\% 37.426079 1.344\% 1.46\% 0.11\% 3/4/20 1.02\% 2/20/20 $ 114.83 0.009\% 36.926403 0.425\% 1.52\% -1.38\% 3/3/20 1.02\% 2/19/20 $ 114.82 -1.643\% 36.76965 -0.902\% 1.56\% -4.58\% 3/2/20 1.10\% 2/18/20 $ 116.72 1.465\% 37.102757 -0.710\% 1.55\% 1.39\% 2/28/20 1.13\% 2/14/20 $ 115.02 0.382\% 37.36729 2.522\% 1.59\% -0.72\% 2/27/20 1.30\% 2/13/20 $ 114.58 1.363\% 36.436539 0.108\% 1.61\% 1.14\% 2/26/20 1.33\% 2/12/20 $ 113.03 0.389\% 36.397354 1.930\% 1.62\% -0.74\% 2/25/20 1.33\% 2/11/20 $ 112.59 0.130\% 35.701736 1.159\% 1.59\% -1.21\% 2/24/20 1.38\% 2/10/20 $ 112.44 -1.036\% 35.290241 -0.498\% 1.56\% -3.41\% 2/21/20 1.46\% 2/7/20 $ 113.62 0.120\% 35.466595 -4.853\% 1.59\% -1.23\% 2/20/20 1.52\% 2/6/20 $ 113.48 -0.429\% 37.230122 2.316\% 1.65\% -2.33\% 2/19/20 1.56\% 2/5/20 $ 113.97 1.327\% 36.37775 -0.751\% 1.66\% 1.02\% 2/18/20 1.55\% 2/4/20 $ 112.46 0.871\% 36.652077 8.417\% 1.61\% 0.20\% 2/17/20 ERROR:#N/A 2/3/20 $ 111.49 -0.192\% 33.69326 2.443\% 1.54\% -1.78\% 2/14/20 1.59\% 1/31/20 $ 111.70 -1.809\% 32.880081 -4.373\% 1.51\% -4.85\% 2/13/20 1.61\% 1/30/20 $ 113.74 0.594\% 34.349689 1.379\% 1.57\% -0.30\% 2/12/20 1.62\% 1/29/20 $ 113.07 -0.611\% 33.879414 -4.606\% 1.60\% -2.63\% 2/11/20 1.59\% 1/28/20 $ 113.76 0.637\% 35.476395 2.037\% 1.65\% -0.29\% 2/10/20 1.56\% 1/27/20 $ 113.04 1.294\% 34.761177 0.339\% 1.61\% 1.01\% 2/7/20 1.59\% 1/24/20 $ 111.59 -1.251\% 34.643616 -0.705\% 1.70\% -3.95\% 2/6/20 1.65\% 1/23/20 $ 112.99 -0.250\% 34.88855 -0.783\% 1.74\% -2.07\% 2/5/20 1.66\% 1/22/20 $ 113.27 0.440\% 35.16288 0.475\% 1.77\% -0.78\% 2/4/20 1.61\% 1/21/20 $ 112.78 0.547\% 34.996323 -0.280\% 1.78\% -0.58\% 2/3/20 1.54\% 1/17/20 $ 112.16 -0.814\% 35.094292 -0.279\% 1.84\% -3.24\% 1/31/20 1.51\% 1/16/20 $ 113.08 0.536\% 35.192261 1.656\% 1.81\% -0.63\% 1/30/20 1.57\% 1/15/20 $ 112.47 -0.778\% 34.61422 -0.057\% 1.79\% -3.13\% 1/29/20 1.60\% 1/14/20 $ 113.35 0.259\% 34.633812 1.769\% 1.82\% -1.17\% 1/28/20 1.65\% 1/13/20 $ 113.06 -0.431\% 34.026371 -0.460\% 1.85\% -2.52\% 1/27/20 1.61\% 1/10/20 $ 113.55 -0.839\% 34.183136 -0.828\% 1.83\% -3.28\% 1/24/20 1.70\% 1/9/20 $ 114.50 1.028\% 34.467262 -1.187\% 1.85\% 0.28\% 1/23/20 1.74\% 1/8/20 $ 113.33 -0.344\% 34.87875 -0.056\% 1.87\% -2.37\% 1/22/20 1.77\% 1/7/20 $ 113.72 -0.931\% 34.898346 -0.448\% 1.83\% -3.46\% 1/21/20 1.78\% 1/6/20 $ 114.79 -0.204\% 35.055103 -0.502\% 1.81\% -2.05\% 1/20/20 ERROR:#N/A 1/3/20 $ 115.02 -0.887\% 35.231457 -0.941\% 1.80\% -3.35\% 1/17/20 1.84\% 1/2/20 $ 116.04 0.084\% 35.564568 0.525\% 1.88\% -1.56\% 1/16/20 1.81\% 12/31/19 $ 115.95 -0.470\% 35.378418 0.862\% 1.92\% -2.66\% 1/15/20 1.79\% 12/30/19 $ 116.49 -0.159\% 35.074699 -0.751\% 1.90\% -2.04\% 1/14/20 1.82\% 12/27/19 $ 116.68 0.059\% 35.33923 -0.498\% 1.88\% -1.61\% 1/13/20 1.85\% 12/26/19 $ 116.61 0.008\% 35.515579 0.110\% 1.90\% -1.72\% 1/10/20 1.83\% 12/24/19 $ 116.60 0.402\% 35.476395 0.000\% 1.90\% -0.97\% 1/9/20 1.85\% 12/23/19 $ 116.13 -1.053\% 35.476395 0.055\% 1.93\% -3.78\% 1/8/20 1.87\% 12/20/19 $ 117.36 0.175\% 35.456795 0.415\% 1.92\% -1.42\% 1/7/20 1.83\% 12/19/19 $ 117.16 0.183\% 35.309837 1.116\% 1.92\% -1.41\% 1/6/20 1.81\% 12/18/19 $ 116.94 -1.178\% 34.917938 -0.727\% 1.92\% -4.01\% 1/3/20 1.80\% 12/17/19 $ 118.33 0.612\% 35.172676 1.403\% 1.89\% -0.56\% 1/2/20 1.88\% 12/16/19 $ 117.61 0.208\% 34.682804 -0.226\% 1.89\% -1.33\% 1/1/20 ERROR:#N/A 12/13/19 $ 117.36 0.442\% 34.761177 0.480\% 1.82\% -0.82\% 12/31/19 1.92\% 12/12/19 $ 116.84 0.637\% 34.594624 1.111\% 1.90\% -0.52\% 12/30/19 1.90\% 12/11/19 $ 116.10 -0.118\% 34.212524 0.574\% 1.79\% -1.86\% 12/27/19 1.88\% 12/10/19 $ 116.24 -0.184\% 34.016579 0.433\% 1.85\% -2.05\% 12/26/19 1.90\% 12/9/19 $ 116.45 -0.351\% 33.869621 -0.835\% 1.83\% -2.35\% 12/25/19 ERROR:#N/A 12/6/19 $ 116.86 0.939\% 34.15374 0.201\% 1.84\% 0.12\% 12/24/19 1.90\% 12/5/19 $ 115.77 0.422\% 34.085167 -0.516\% 1.80\% -0.84\% 12/23/19 1.93\% 12/4/19 $ 115.28 0.017\% 34.261517 0.631\% 1.77\% -1.59\% 12/20/19 1.92\% 12/3/19 $ 115.26 -0.513\% 34.045971 -0.431\% 1.72\% -2.56\% 12/19/19 1.92\% 12/2/19 $ 115.86 0.159\% 34.192936 -1.761\% 1.83\% -1.37\% 12/18/19 1.92\% 11/29/19 $ 115.67 0.277\% 34.800369 -0.533\% 1.78\% -1.10\% 12/17/19 1.89\% 11/27/19 $ 115.35 -0.361\% 34.986519 0.279\% 1.77\% -2.31\% 12/16/19 1.89\% 11/26/19 $ 115.77 0.227\% 34.888927 -0.279\% 1.74\% -1.16\% 12/13/19 1.82\% 11/25/19 $ 115.51 -0.369\% 34.986519 2.057\% 1.76\% -2.32\% 12/12/19 1.90\% 11/22/19 $ 115.93 -0.418\% 34.274101 0.514\% 1.77\% -2.42\% 12/11/19 1.79\% 11/21/19 $ 116.42 0.611\% 34.098442 0.229\% 1.77\% -0.45\% 12/10/19 1.85\% 11/20/19 $ 115.71 -0.636\% 34.020367 -0.572\% 1.73\% -2.80\% 12/9/19 1.83\% 11/19/19 $ 116.45 -0.300\% 34.215549 -0.114\% 1.79\% -2.21\% 12/6/19 1.84\% 11/18/19 $ 116.80 1.154\% 34.254581 -0.483\% 1.81\% 0.55\% 12/5/19 1.80\% 11/15/19 $ 115.46 -1.486\% 34.420486 0.883\% 1.84\% -4.53\% 12/4/19 1.77\% 11/14/19 $ 117.19 -0.273\% 34.117958 0.920\% 1.82\% -2.19\% 12/3/19 1.72\% 11/13/19 $ 117.51 1.549\% 33.805664 -1.234\% 1.88\% 1.25\% 12/2/19 1.83\% 11/12/19 $ 115.70 0.067\% 34.225307 -0.512\% 1.92\% -1.63\% 11/29/19 1.78\% 11/11/19 $ 115.62 -0.335\% 34.400974 0.313\% ERROR:#N/A ERROR:#N/A 11/28/19 ERROR:#N/A 11/8/19 $ 116.01 -0.659\% 34.293625 0.714\% 1.94\% -3.04\% 11/27/19 1.77\% 11/7/19 $ 116.78 0.609\% 34.049641 -1.733\% 1.92\% -0.59\% 11/26/19 1.74\% 11/6/19 $ 116.07 0.537\% 34.644947 0.056\% 1.81\% -0.63\% 11/25/19 1.76\% 11/5/19 $ 115.45 1.091\% 34.625427 0.197\% 1.86\% 0.39\% 11/22/19 1.77\% 11/4/19 $ 114.20 -0.043\% 34.557117 0.453\% 1.79\% -1.72\% 11/21/19 1.77\% 11/1/19 $ 114.24 0.307\% 34.400974 0.000\% 1.73\% -1.00\% 11/20/19 1.73\% 10/31/19 $ 113.89 -0.714\% 34.400974 -1.716\% 1.69\% -2.91\% 11/19/19 1.79\% 10/30/19 $ 114.71 0.808\% 34.996281 -0.695\% 1.78\% -0.08\% 11/18/19 1.81\% 10/29/19 $ 113.79 -1.752\% 35.240257 0.472\% 1.84\% -5.04\% 11/15/19 1.84\% 10/28/19 $ 115.80 0.151\% 35.074352 0.279\% 1.85\% -1.40\% 11/14/19 1.82\% 10/25/19 $ 115.62 -0.050\% 34.976761 0.616\% 1.80\% -1.74\% 11/13/19 1.88\% 10/24/19 $ 115.68 -0.210\% 34.762054 -9.577\% 1.77\% -2.02\% 11/12/19 1.92\% 10/23/19 $ 115.93 -0.193\% 38.255833 0.665\% 1.77\% -1.99\% 11/11/19 ERROR:#N/A 10/22/19 $ 116.15 -0.134\% 38.002087 -0.818\% 1.78\% -1.89\% 11/8/19 1.94\% 10/21/19 $ 116.30 0.502\% 38.314388 1.127\% 1.80\% -0.69\% 11/7/19 1.92\% 10/18/19 $ 115.72 -0.586\% 37.884983 -0.693\% 1.76\% -2.73\% 11/6/19 1.81\% 10/17/19 $ 116.40 0.351\% 38.148483 0.436\% 1.76\% -0.94\% 11/5/19 1.86\% 10/16/19 $ 115.99 -0.092\% 37.982578 0.103\% 1.75\% -1.78\% 11/4/19 1.79\% 10/15/19 $ 116.10 0.302\% 37.943542 1.346\% 1.77\% … Sheet1 Walmart Company Consolidated balance sheet as at January 31st 2019 and 2020 2020 2019 Millions $ Millions $ (Amounts in millions) 2020 2019 ASSETS Current assets: Cash and cash equivalents(Basics of financial statement analysis, 2019). $9,465 $7,722 Receivables, net 6,284 6,283 Inventories 44,435 44,269 Prepaid expenses and other 1,622 3,623 Total current assets 61,806 61,897 Non current assets Property and equipment, net 105,208 104,317 Operating lease right-of-use assets(Basics of financial statement analysis, 2019). 17,424 — Finance lease right-of-use assets, net 4,417 — Property under capital lease and financing obligations, net — 7,078 Goodwill 31,073 31,181 Other long-term assets 16,567 14,822 Total assets 236,495 219,295 LIABILITIES AND EQUITY Current liabilities: Short-term borrowings $575 $5,225 Accounts payable 46,973 47,060 Accrued liabilities(Basics of financial statement analysis, 2019). 22,296 22,159 Accrued income taxes 280 428 Long-term debt due within one year 5,362 1,876 Operating lease obligations due within one year 1,793 Finance lease obligations due within one year 511 — Capital lease and financing obligations due within one year — 729 Total current liabilities 77,790 77,477 Long-term debt 43,714 43,520 Long-term operating lease obligations 16,171 — Long-term finance lease obligations 4,307 — Long-term capital lease and financing obligations (Basics of financial statement analysis, 2019). — 6,683 Deferred income taxes and other 12,961 11,981 Commitments and contingencies Equity: Common stock 284 288 Capital in excess of par value 3,247 2,965 Retained earnings 83,943 80,785 Accumulated other comprehensive loss -12,805 -11,542 Total Walmart shareholders equity 74,669 72,496 Noncontrolling interest(Basics of financial statement analysis, 2019). 6,883 7,138 Total equity 81,552 79,634 Total liabilities and equity $ 236,495 219,295 Wal-mart company Income statement for the period ending 31st January 2019 and 2020 2020 2019 (Amounts in millions, except per share data) 2020 2019 Revenues: Net sales 519,926 510,329 Membership and other income 4,038 4,076 4, Total revenues, 523,964 510,329 Costs and expenses: Cost of sales 394,605 385,301 Operating, selling, general and administrative expenses 108,791 107,147 Operating income 20,568 21,957 Interest: Debt 2,262 1,975 Finance, capital lease and financing obligations(Basics of financial statement analysis, 2019). 337 371 Interest income -189 -217 Interest, net 2,410 2,129 Loss on extinguishment of debt — — Other (gains) and losses— -1,958 8,368 Income before income taxes(Basics of financial statement analysis, 2019). 20,116 11,460 Provision for income taxes 4,915 4,281 Consolidated net income 15,201 7,179 Consolidated net income attributable to noncontrolling interest -320 -509 Consolidated net income attributable to Walmart 14,881 6,670 (n.d.). 403 Forbidden. https://s2.q4cdn.com/056532643/files/doc_financials/2020/ar/Walmart_2020_Annual_Report.pdf Basics of financial statement analysis. (2019). Financial Statements. https://doi.org/10.24053/9783739880143-73 https://s2.q4cdn.com/056532643/files/doc_financials/2020/ar/Walmart_2020_Annual_Report.pdf https://doi.org/10.24053/9783739880143-73 Sheet2 Sheet3 Running head: WALMART FINANCIAL ANALYSIS 1 WALMART FINANCIAL ANALYSIS 2 Wal-Mart financial analysis Student’s name Professor’s name Date Any investor in the business, must measure how his/her business is performing financially. It is a dream of every investor to stay in the business and make good profits thus every effort put into the business works towards this business goal of continuity and profitability (Tracy, 2012). For this reason the investor must ensure that his business is healthy financially and to be sure, a financial analysis must be done. This analysis will help the investor evaluate his business to determine whether the business is solvent and profitable or otherwise. This analysis is done using ratios like profitability ratios, liquidity ratios, leverage ratios etc. Wal-Mart Company is an American company that deals with retailing of different merchandise like food staff, clothing, toys etc. it was founded in 1950 by Sam Walton in Bentonville (Tracy, 2012). The company has its operations in different countries globally. It is a listed company in NYSE trading in many shares in the market. The following are financial analysis of the company for the year 2020. i) Debt ratio Debt ratio shows how much the company’s assets are financed through debt. A higher percentage shows that the company is highly leveraged. It is express as a percentage (Drake & Fabozzi, 2012). A ratio that is greater than 100\% indicates that most of the company’s assets are funded through debts in other words the company has more debts as compared to assets. It is calculated as shown: i) Debt ratio Debt ratio= Total debts/Assetsx100 Total debt = (236495-81552) =154,943 Total assets=236495 Debt ratio = 154,943/236495x100 = 65\% In the year 2020 Wal-Mart Company had more assets than debts thus its risk level was low. ii) Debt to equity ratio The debt to equity ratio indicates how the company is able to finance its debt using the owner net worth. It also shows how stable a company is in terms of financing its debt through equity (Drake & Fabozzi, 2012). The ideal ratio is believed to be between 1 and 1.5. However, the ratio varies from one industry to another depending on the operations. A ratio of 2 would be good for a company in manufacturing industry. It is calculated as shown. Debt to equity ratio= total debt / equity 154,943/81552 = 1.8 This means that Wal-Mart need to reduce its borrowing as it is already highly leveraged. iii) Return on assets The ratio indicates how the company’s assets were used to generate profits (Tracy, 2012). A higher number shows how efficient the management is in terms of using the company’s assets to ensure the company remains profitable. Return on asset is calculated as a percentage of net profit to total assets’ ROA = Net profit/ total assets 14881/236495 x100 = 6.3\% This means that Wal-Mart Company earned $6.3 cent for every dollar invested in 2020. Iv) Return on equity A good ratio is between 10\% and 14\%. However it is important to know the ROE for the other competing companies. In this case it the best ROE should be the same or slightly higher than the competing companies’ (Tracy, 2012). A higher ROE of a company compared to its peer indicates that the stock of a company is likely to grow. It is calculated as shown. ROE= Net income/ total equity =14881/81552x100 =18.24\% In 2020 Wal-Mart Company had a very good Return On equity above the recommended. For an investor this ratio is enticing. v) Current ratio It is a liquidity ratio that indicates how well the company is able to meet its short term obligations. It shows the number of time a company is able to settles it short term debts (Tracy, 2012). A very high ratio will indicate that a company is holding too much idle cash. The ideal ratio is 2. It is calculated as below. Current assets/current liabilities =61806/77790 =0.79 This ratio is not very good for Wal-Mart as it is below 1, it means that Wal-Mart does is not liquid enough to finance its short term obligations. vi) Quick ratio It is also a liquidity ratio; it involves the assets that are easily convertible to generate cash (Tracy, 2012). It indicates the number of times an entity can pay its short term debts using its most liquid assets. The ideal ratio is 1, however, the greater the number the more the company is able to cater for its short term debt. Quick ratio= Current asset – closing stock/Current liability 61806-44435=17,371 = 17371/77790 =0.2 This shows that Wal-Mart Company is at risk of not being able to meet its current obligation vii) Inventory turn over This shows the number of times a company is able to convert its inventory into cash (Tracy, 2012). This ratio helps the company make better decision on pricing, marketing, producing and purchasing. This will reduce over stocking and may help in reducing the storage cost. Inventory turnover= COS/ average stock Average stock = Opening stock + closing stock/2 44435+44269/2= 44,352 394605/44,352 =9 times This means that the company turned its stock into cash or sales 9 times viii) Days in inventory This ratio show how many days the stock remained in the company (Tracy, 2012). A better ratio indicates few days that the stock remained in the business. It is calculated as below. Average stock / COS X365 44,352/394605x365=41 days This means that Wal-Mart holds it stock for 41 days ix) Accounts receivable turn over This ratio show how many times the company was able to collect the accounts receivable. In other word the number of times a business entity is able to convert its credit sales to sales. Accounts receivables turn over = Credit sales/ Av debtors Average debtors = opening debtors + closing debtors /2 6283+6284/2=6283.5 6284/6283.5=1 This ratio indicates a very low turn ratio as it is below 7.8 which is the most preferable ratio. x) Accounts receivable cycle in days This show how long the business allowed its debtors to pay the debts (Quiry et al., 2011). The longer the period may put the business in liquidity risk. A shorter period is better. Receivable cycle = average debtors/credit sales x365 =6283.5/6284 x365= 364 This means the company gave its debtors 364 days to pay their debts. This ratio is not very healthy. xi) Accounts payable turnover This ratio shows that the business entity is more efficient when the rate at which the firm pays its creditors is high (Ittelson, 2009,). It shows the number of times the business paid its creditors. Accounts payable turnover = credit purchases/ average creditors 46973+47060/2=47016.5 46973/47016.5= 0.99 This means that the company was not able to pay its creditors on time. xii) Accounts payable cycle This indicates the period in which the creditors allowed the business to pay for the supplies (Basics of financial statement analysis, 2019). When this period is slightly higher than accounts receivable cycle it enables the company have a better circulation of cash in the business. Accounts payable cycle = Av Creditors / credit purchasex365 47061.5/46973x365=365 days The time taken to pay the debtors is equal to the time taken to pay the creditors xiii) Earnings per share This ratio shows how well a company is able to reward its shareholders. When the ratio is higher it means that the company is profitable and worth investing in. it is calculated as below EPS = Net profit/ outstanding shares 14881/81552 =0.2 This ratio is not enticing to the investors. xiv) Price to earnings ratio This ratio shows a share’s market value as compared to its peer (Drake & Fabozzi, 2012,). When this ratio is high it means that the share price may be overvalued. A low ratio indicates that the share may be undervalued. It is calculated as under. PE = share price/ earnings per share 0.7/0.2=0.3 This ratio shows that the stock was overvalued. xv) Cash conversion cycle This ratio show the time an entity requires to makes sales the time taken to collect its debts and time taken its bills. A steady CCC shows a good sign. CCC= DIO + DSO –DPO CCC=41+364-365=40 xvi) Working capital This ratio shows the business liquidity. A good working capital is a sign that the company has a potential of future growth (Drake & Fabozzi, 2012). When the currents assets are more than the current liabilities then the company is able to pay its obligations. Working capital = Current asset- current liabilities 61806-77790= -15,984 It means that this company is almost going to bankruptcy. xvii) DuPont Identity This analysis shows the factors that affect Return on Equity (Collis, 2016). These factors are profit margin; equity multiplier and asset turn over. This analysis helps the mangers to identify the cause of declining or rising of ROE, from the three factors. DuPont = G.P x asset turn over x equity multiplier G.P.M= G.P/ sales Equity multiplier = total assets/ equity 236497/81552 = 2.9 20568/519926x100= 4\% 0.04x0.063x 2.9= 7.3 Conclusion From the analysis performed above, we realize that in the year 2020, Wal-Mart Company did not have very good liquidity (Tracy, 2012). This may be a serious problem as it may lead to the company’s insolvency. This problem could be attributed to the many days the stocks are held within the business and the many days that debtors stay with the money. It is therefore important for the company to improve in these areas to increase its liquidity. References Basics of financial statement analysis. (2019). Financial Statements. https://doi.org/10.24053/9783739880143-73 Collis, J. (2016). Introduction to financial accounting. Financial Accounting, 1-14. https://doi.org/10.1007/978-1-137-54023-2_1 Drake, P. P., & Fabozzi, F. J. (2012). Analysis of financial statements. John Wiley & Sons. Ittelson, T. R. (2009). Financial statements: A step-by-step guide to understanding and creating financial reports. Red Wheel/Weiser. Quiry, P., Vernimmen, P., Dallocchio, M., Fur, Y. L., & Salvi, A. (2011). Corporate finance: Theory and practice. John Wiley & Sons. Tracy, A. (2012). Ratio analysis fundamentals: How 17 financial ratios can allow you to analyse any business on the planet. RatioAnalysis.net Wal-Mart link (n.d.). 403 Forbidden. https://s2.q4cdn.com/056532643/files/doc_financials/2020/ar/Walmart_2020_Annual_Report.pdf Running head: PROJECT APPRAISAL 1 PROJECT APPRAISAL 15 Project appraisal Student’s name Professor’s name Date A Project appraisal entails assessing the project at hand to determine its viability. A business manager should perform a mathematical test on a project or proposal to determine its profitability before funding the project. This assessment is normally done using a decision making technique and comparing the results with the results of other possibilities (Bowerman et al., 2016). The techniques used for a project appraisal are discussed under capital budgeting, where the best projects are chosen. Capital budgeting considers all the costs from the scratch to the very end and the revenues collected from the project. To determine the viability of the following project, we shall use capital budgeting technique. a) Payback Period year cash flows 0 -5000000 1 1500000 2 1500000 3 1500000 4 1500000 5 1500000 6 1500000 7 2000000 5000000 4500000 500000 3 Payback period 3.1 The project will take 3 years and 1 month to recoup the money injected in the project NPV project A The NPV is positive therefore accept the project The IRR is 23.8\% therefore accept the project. PI The profitability index is above 1 therefore the project should accepted PROJECT B a). Payback Period year cash flows 0 -5000000 1 1250000 2 1250000 3 1250000 4 1250000 5 1250000 6 1250000 7 1250000 8 1600000 5000000 3750000 1250000 3 Payback period 3.78125 The project will take 3 years and 7months to recoup the cash out lay a) NPV The NPV is positive thus accept the project c). IRR The IRR is positive therefore accept the project. d). MIRR The MIRR is more than RRR of the company thus accept the project. e). PI The profitability index is more than 1 thus accepts the project Decision Making under NPV The NPV for Project A is more than that of Project B thus the right project under these criteria is project A (Clayman et al., 2012). A higher NPV indicates that the project is more profitable, thus project A is more profitable than project B. Decision Making under IRR Project A has a higher IRR of 23\% than project B which has 17\% , which means project A is to be preferred (Farag & Johan, 2021). The IRR for both projects are higher than required rate of return thus both projects are profitable. However, project A is more profitable, as its IRR is above both the IRR for project B and the RRR of the company. Decision Making under MIRR The MIRR for both projects are above the RRR for the company thus they should be accepted (Richard T OConnell et al., 2018). However, Project A has a higher MIRR of 19.2\% as compared to 17\% of Project B thus project A is more preferable. The best MIRR should be above the RRR for the company. Decision Making under PI A profitable project should have a Profitability index above 1 (Vernimmen et al., 2017). Both projects A and B have a PI that is above 1, thus these projects are profitable. However, the PI for project A is 1.28 more than that of Project B which 1.14, this means project A is better thus accept project A. Decision Making under payback period Project A is to e preferred since the capital out lay will be recouped in years and one month while as project B will take 3 year and 7 months (Vernimmen et al., 2017). The shorter the duration the more better the project becomes. Part Two a). Initial cost The initial cost of the project Zither is the total of market the survey, the cost of production machine, and the land cost (Taillard, 2012). All those cost that are incurred to get the production of Zither moving are the initial cost for the project, i.e. the total capital. The total cost for the project is $5725, 000. b). The Sunk Cost Sunk cost is the amount of money spent on a project that cannot be recovered. It includes the cost of land $2,100,000, the research cost, of $125,000 and the machinery cost $3,500,000 (Taillard, 2012). In many cases these costs are not considered for decision making. These costs remain to have been spent regardless of the decision made. The total sunk cost for our project is $5725, 000 c). Determining operating cash flows To determine the annual revenues, multiply the total units produced by the selling price, and then deduct the variable cost, the fixed cost, and the depreciation. The figure arrived at will be subjected to tax and then the depreciation amount will be added back (Vernimmen et al., 2017). The figure arrived at will be the operating cash flows. As shown in table three of the workings d). Determining terminal cash flows To determine the terminal cash flows, add all the incremental cash flows then deduct all the expenses and i.e. depreciation and tax (Vernimmen et al., 2017). This is the amount the company will get after disposing all its assets. As shown in working 4 Workings Determine cash outlay Cost Amt in $ Survey cost 125,000 Machine 3.500,000 Land 2,100,000 5725,000 Determine the cash flows Table One Year Units CPU Total 1 3600 750 2700000 2 4300 750 3225000 3 5200 750 3900000 4 3900 750 2925000 Variable cost Table two Year Revenue 15\% 1 2700000 405000 2 3225000 483750 3 3900000 585000 4 2925000 438750 Depreciation 3,500,000/3= 1,166,667 Determining cash flows Table three Year 1 2 3 4 Revenues 2700000 3225000 3900000 2925000 Less variable cost Less fixed cost Less depreciation (405000) (415,000) (1,166,667) (483750) (415000) (1,166,667) (585000) (415000) (1,166,667) (438750) (415000) (1,166,667) Total revenue before tax Less tax 713333 (256799.9) 1159583 (417449.9) 1733333 (623999.9) 904583 (325649.9) Revenues after tax Add depreciation 456533.1 1,166,667 742133.1 1,166,667 1109333 1,166,667 578933.1 1,166,667 Net cash flows 1623200.1 1908800.1 2276000.1 1745600.1 Terminal cash flows Working 4 Equipment $ Revenue 350,000 Less NBV 0______ Net revenue before tax 350,000 Tax (133,000) Terminal cash flow after tax 217,000 Land 2,400,000 Less initial cost (2,100,000) 300,000 Less tax (114,000) 186,000 di). NPV dii).IRR IRR=13.5\% diii). Decision The project is acceptable since the IRR of 13.5\% is more than the required rate of return and the NPV of 61440 is positive (Taillard, 2012). When the IRR is above the required rate of return it means the project is profitable. In our case the project is profitable and the NPV is showing profits. e) Implication in the Stock Market A company with good returns will tread well in the capital market. Our company is making a profit according to the analysis; this means that many people will be interested in the company’s stock increasing its demand in the market (Taillard, 2012,). This will eventually result in an increase in price for the stock. According to the analysis all the parameters are favorable thus very attractive to potential investors Conclusion From the above analysis it is easy to tell the best project to invest in. The capital appraisal will ensure that the investor chooses the best investment, thereby avoiding losses in terms of money and time (Taillard, 2012,). It is therefore important for all investors to undertake this type of analysis before injecting money to any project. References Bowerman, B., OConnell, R., & Murphree, E. (2016). Business statistics in practice: Using data, modeling, and analytics. McGraw-Hill Education. Clayman, M. R., Fridson, M. S., & Troughton, G. H. (2012). Corporate finance: A practical approach. John Wiley & Sons. Farag, H., & Johan, S. (2021). How alternative finance informs central themes in corporate finance. Journal of Corporate Finance, 67, 101879. https://doi.org/10.1016/j.jcorpfin.2020.101879 Richard T OConnell, P., Bowerman, B. L., & Emilly S. Murphree, P. (2018). Loose leaf for business statistics in practice. McGraw-Hill Education. Taillard, M. (2012). Corporate finance for dummies. John Wiley & Sons. Vernimmen, P., Quiry, P., Dallocchio, M., Fur, Y. L., & Salvi, A. (2017). Corporate finance: Theory and practice. John Wiley & Sons. 1 Week #1 VCS Alternative Assignment (VCSA) Miku Anraku Westcliff University BUS 550 – SU6-209-C Dr. John Knight July 7, 2021 2 Week #1 VCSA Assignment Corporate finance majorly deals with how corporations deal with funding sources, capital structuring, and investment decisions. There are different types of financial management decisions. It also involves the different actions taken by the management in increasing the value of the company. This also involves the tools and the analysis that is utilized in the distribution of the financial resources. Main Class Content Review Professor talked about the different types of financial management decisions. They include investing decisions, financing, and dividend decision. Finance can help in determining the long-term investment, where a company may get the long-term financing to pay for the investments, and how we can manage the everyday financial activities of the company. There are different investments or projects that the business may decide to take on. According to the professor, capital management is the everyday finances in the firm with the current assets and liabilities (Cloyne et al., 2018). There are different goals of financial management, however, the main goal of the corporation is maximizing the current value of the company stock which is shareholder maximization. According to the professors, increasing the value of the stock will help in maximizing profits, minimizing costs and maximizing the market share, and protecting the environment as this also reflects on how the corporation treats its employees (Yogasnumurti et al., 2021). Increasing the value of the firm makes a positive contribution to society which increases the stock price as the firm may now hire more employees and spend more money on disaster relief. Most of the American companies hire more people like Amazon, which reduces 3 unemployment, increases more money in the economy, and improves technology as all these are part of financial management. Total value = Stock value+ debts Tesla has more cash bonds outstanding that can be turned into cash profits. As much as they are not making any profits currently, but they are borrowing money on account of their credits and their future cash flows. If you look at an organization, the more they borrow, the riskier they get, if the debt increases, the total values will also increase as borrowing too much also increases the credit price increases as these costs a higher percentage of borrowing money. Company borrowing too much will make investors nervous, price of debt increases, costs increase, and the stock price falls. The agency relationship occurs where the principal hires an agent in representing their interests, stockholders hire managers to help in running the company. An agent problem occurs when there exists a conflict of interest between principal and agent (Michiels & Molly, 2017). Responses to Professor Questions On the question of what the course is all about, I think corporate finance deals with the capital structure of an organization including the funding and the different actions that the management takes to increase the value of the company (Handriani & Robiyanto, 2018). The major concept is understanding how to maximize the value of a business by utilizing different resources. With the example of Tesla, the company makes some losses as this is evident that their major goal is not making profits as their market value in the recent period has been lowering. The company however has a better market, customers love Tesla due to the products that they produce. According to the professor, the company is overvalued but however the value is based 4 on future cash flows and speculations as most of the shareholders base this information on their basis of success, this is why the company is in the position that they are currently. However in the future, the company would face stiff competition from other company and their products, this would affect Tesla negatively as it may decrease its market share On the question of how much we borrow, I guess we look at the risks that are involved in borrowing. On this aspect, we may have to understand different aspects such as the debt ratio and the competitors. This may involve analyzing the company financials and understand the stock prices and the risks that are involved, for instance, the more you borrow, the riskier you get. If the debt increases, the total value will also increase, however, borrowing too many increases the cost of credit as the creditors would start feeling nervous. Most firms have about a 40\% debt ratio and the other percentage is equity. Borrowing more leads to a fall in stock prices. This means that the cost of borrowing also increases. However, most borrowing is always the best option as debt is the cheapest way of financing the firm (Michiels & Molly, 2017). Future Use The different types of financial management include the following: investment decisions which are concerned with the way an organizations firm funds are invested in the different assets known as the investment decisions. The second one is financing decisions as this concerns the amount of finance that should be raised from different long-term sources of funds such as equity shares, preference shares, debentures, and bank loans. The third one is the dividend decision as this is a financial decision that determines the profit earned by an organization that should be distributed among shareholders (Seru & Sufi, 2021). Just as noted, as much as the organization aims at maximizing its profits and minimizing the costs involved, the major aim is maximizing the current value of the company stock. This is 5 the same way just as the United States follows corporate management or the shareholder value in attaining shareholder maximization. Increasing the value of the stock will increase the company profits, minimize the costs and maximize the market share at the same time and also protect the environment as the company would have a better reputation such better treatment of the employees which helps in maintaining the stock value of the company. Some companies try to maximize their profits by dumping their wastes in the river which is pollution to the environment. Doing the right thing by increasing the value of the firm would increase the stock price of the firm and impact society positively this would also increase the number of employees in the firm, the organization should also spend some money on disastrous relief. Increasing the company value has different advantages as this increases more money in the economy, just as Amazon, more people would be employed as this also helps in decreasing the rate of unemployment in the society and improve technology. This shows that the major aim of financial management is far beyond making profits and also it includes making the right decisions (Seru & Sufi, 2021). Conclusion In conclusion, corporate finance entails the capital structure and the funding of the organization. This information is useful for the management in making some decisions. The major aim of organizations is generating profits reason why an organization gets funding to increase its pool of resources reason why management should consider the risks involved in different funding before making that decision. 6 References Cloyne, J., Ferreira, C., Froemel, M., & Surico, P. (2018). Monetary policy, corporate finance and investment (No. w25366). National Bureau of Economic Research. Handriani, E., & Robiyanto, R. (2018). Corporate finance and firm value in the Indonesian manufacturing companies. International Research Journal of Business Studies, 11(2), 113-127. Michiels, A., & Molly, V. (2017). Financing decisions in family businesses: A review and suggestions for developing the field. Family Business Review, 30(4), 369-399. Seru, A., & Sufi, A. (2021). Corporate finance (pp. 617-623). University of Chicago Press. Yogasnumurti, R. R., Sadalia, I., & Irawati, N. (2021). The Effect of Financial, Attitude, and Financial Knowledge on the Personal Finance Management of College Collage Students. COST OF CAPITAL CHAPTER 14 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› Determine a firm’s cost of equity capital Determine a firm’s cost of debt Determine a firm’s overall cost of capital and how to use it to value a company Explain how to correctly include flotation costs in capital budgeting projects Describe some of the pitfalls associated with a firm’s overall cost of capital and what to do about them Key Concepts and Skills Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› The Cost of Capital: Some Preliminaries The Cost of Equity The Costs of Debt and Preferred Stock The Weighted Average Cost of Capital Divisional and Project Costs of Capital Company Valuation with the WACC Flotation Costs and the Weighted Average Cost of Capital Chapter Outline Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› We know that the return earned on assets depends on the risk of those assets. The return to an investor is the same as the cost to the company. Our cost of capital provides us with an indication of how the market views the risk of our assets. Knowing our cost of capital can also help us determine our required return for capital budgeting projects. Why Cost of Capital Is Important Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.4 Section 14.1 Lecture Tip: Students often find it easier to grasp the intricacies of cost of capital estimation when they understand why it is important. A good estimate is required for: -good capital budgeting decisions – neither the NPV rule nor the IRR rule can be implemented without knowledge of the appropriate discount rate -financing decisions – the optimal/target capital structure minimizes the cost of capital -operating decisions – cost of capital is used by regulatory agencies in order to determine the “fair” return in some regulated industries (e.g. utilities) The required return is the same as the appropriate discount rate and is based on the risk of the cash flows. We need to know the required return for an investment before we can compute the NPV and make a decision about whether or not to take the investment. We need to earn at least the required return to compensate our investors for the financing they have provided. Required Return Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› Section 14.1 (A) 12.5 The cost of equity is the return required by equity investors given the risk of the cash flows from the firm. Business risk Financial risk There are two major methods for determining the cost of equity. Dividend growth model SML, or CAPM Cost of Equity Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› Section 14.2 12.6 Start with the dividend growth model formula and rearrange to solve for RE. The Dividend Growth Model Approach Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.7 Section 14.2 (A) Remind students that D1 = D0(1+g). You may also want to take this time to remind them that return is comprised of the dividend yield (D1 / P0) and the capital gains yield (g). Suppose that your company is expected to pay a dividend of $1.50 per share next year. There has been a steady growth in dividends of 5.1\% per year and the market expects that to continue. The current price is $25. What is the cost of equity? Example: Dividend Growth Model Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.8 Section 14.2 (A) One method for estimating the growth rate is to use the historical average. Year Dividend Percent Change 2014 1.23 - 2015 1.30 2016 1.36 2017 1.43 2018 1.50 Example: Estimating the Dividend Growth Rate (1.30 – 1.23) / 1.23 = 5.7\% (1.36 – 1.30) / 1.30 = 4.6\% (1.43 – 1.36) / 1.36 = 5.1\% (1.50 – 1.43) / 1.43 = 4.9\% Average = (5.7 + 4.6 + 5.1 + 4.9) / 4 = 5.1\% Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.9 Section 14.2 (A) Our historical growth rates are fairly close, so we could feel reasonably comfortable that the market will expect our dividend to grow at around 5.1\%. Note that when we are computing our cost of equity, it is important to consider what the market expects our growth rate to be, not what we may know it to be internally. The market price is based on market expectations, not our private information. So, another way to estimate the market consensus estimate is to look at analysts’ forecasts and take an average. Lecture Tip: It is noted in the text that there are other ways to compute g. Rather than use the arithmetic mean, as in the example, the geometric mean (which implies a compound growth rate) can be used. OLS regression with the log of the dividends as the dependent variable and time as the independent variable is also an option. Another way to estimate g is to assume that the ROE and retention rate are constant. If this is the case, then g = ROE × retention rate. Advantage – easy to understand and use Disadvantages Only applicable to companies currently paying dividends Not applicable if dividends aren’t growing at a reasonably constant rate Extremely sensitive to the estimated growth rate – an increase in g of 1\% increases the cost of equity by 1\% Does not explicitly consider risk Advantages and Disadvantages of Dividend Growth Model Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.10 Section 14.2 (A) Point out that there is no allowance for the uncertainty about the growth rate. Lecture Tip: Some students may question how you value the stock for a firm that doesn’t pay dividends. In the case of growth-oriented, non-dividend-paying firms, analysts often look at the trend in earnings or use similar firms to project the future date of the first expected dividend and its future growth rate. However, such processes are subject to greater estimation error, and when companies fail to meet (or even exceed) estimates, the stock price can experience a high degree of variability. It should also be pointed out that no firm pays zero dividends forever – at some point, every going concern will pay dividends. Microsoft is a good example. Many people believed that Microsoft would never pay dividends, but even it ran out of investments for all of the cash that it generated and began paying dividends in 2003. Use the following information to compute our cost of equity. Risk-free rate, Rf Market risk premium, E(RM) – Rf Systematic risk of asset,  You can find data on betas and rates at Yahoo! Finance. The SML Approach Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.11 Section 14.2 (B) You will often hear this referred to as the Capital Asset Pricing Model Approach as well. www: Click on the link to go to finance.yahoo.com. Both betas and 3-month T-bills are available on this site. To get betas, enter a ticker symbol to get the stock quote, then choose Key Statistics. To get the T-bill rates, click on “Bonds” under Investing on the home page. Suppose your company has an equity beta of .58, and the current risk-free rate is 6.1\%. If the expected market risk premium is 8.6\%, what is your cost of equity capital? RE = 6.1 + .58(8.6) = 11.1\% Since we came up with similar numbers using both the dividend growth model and the SML approach, we should feel good about our estimate. Example – SML Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.12 Section 14.2 (B) The similarity is completely dependent on estimates of the risk-free rate and market risk premium. Advantages Explicitly adjusts for systematic risk Applicable to all companies, as long as we can estimate beta Disadvantages Have to estimate the expected market risk premium, which does vary over time Have to estimate beta, which also varies over time We are using the past to predict the future, which is not always reliable. Advantages and Disadvantages of SML Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.13 Section 14.2 (B) A good example to illustrate how beta estimates can lag changes in the risk of equity, consider Citigroup (C), which was used in an example in the slides in the previous chapter. In Sept. 2012, (based on calculations on Yahoo) Citigroup had a beta of 2.6. Yet, its capital gains return from Sept 2002 to Sept 2012 was almost -90\%!! On the positive side, in Sept. 2012, APPL had a beta of .88, yet its capital gains return over the past 10 years was over 9,000\%!!!!!. Lecture Tip: Students are often surprised when they find that the two approaches typically result in different estimates. Suggest that it would be more surprising if the results were identical. Why? The underlying assumptions of the two approaches are very different. The constant growth model is a variant of a growing perpetuity model and requires that dividends are expected to grow at a constant rate forever and that the discount rate is greater than the growth rate. The SML approach requires assumptions of normality of returns and/or quadratic utility functions. It also requires the absence of taxes, transaction costs, and other market imperfections. Suppose our company has a beta of 1.5. The market risk premium is expected to be 9\%, and the current risk-free rate is 6\%. We have used analysts’ estimates to determine that the market believes our dividends will grow at 6\% per year and our last dividend was $2. Our stock is currently selling for $15.65. What is our cost of equity? Using SML: RE = 6\% + 1.5(9\%) = 19.5\% Using DGM: RE = [2(1.06) / 15.65] + .06 = 19.55\% Example – Cost of Equity Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.14 Section 14.2 Since the two models are reasonably close, we can assume that our cost of equity is probably around 19.5\%. Again, though, this similarity is a function of the inputs selected and is not indicative of the true similarity that could be expected. The cost of debt is the required return on our company’s debt. We usually focus on the cost of long-term debt or bonds. The required return is best estimated by computing the yield-to-maturity on the existing debt. We may also use estimates of current rates based on the bond rating we expect when we issue new debt. The cost of debt is NOT the coupon rate. Cost of Debt Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.15 Section 14.3 (A) Point out that the coupon rate was the cost of debt for the company when the bond was issued. We are interested in the rate we would have to pay on newly issued debt, which could be very different from past rates. Lecture Tip: Consider what happens to corporate bond rates and mortgage rates as the Federal Reserve board changes the fed funds rate. If the Federal Reserve raises the fed funds rate by a quarter point, virtually all bond rates, from government to municipal to corporate, will increase after this action. Suppose we have a bond issue currently outstanding that has 25 years left to maturity. The coupon rate is 9\%, and coupons are paid semiannually. The bond is currently selling for $908.72 per $1,000 bond. What is the cost of debt? N = 50; PMT = 45; FV = 1000; PV = -908.72; CPT I/Y = 5\%; YTM = 5(2) = 10\% Example: Cost of Debt Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.16 Section 14.3 (A) Remind students that it is a trial and error process to find the YTM if they do not have a financial calculator or spreadsheet application. Reminders Preferred stock generally pays a constant dividend each period. Dividends are expected to be paid every period forever. Preferred stock is a perpetuity, so we take the perpetuity formula, rearrange and solve for RP. RP = D / P0 Cost of Preferred Stock Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› Section 14.3 (B) 12.17 Your company has preferred stock that has an annual dividend of $3. If the current price is $25, what is the cost of preferred stock? RP = 3 / 25 = 12\% Example: Cost of Preferred Stock Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› Section 14.3 (B) 12.18 We can use the individual costs of capital that we have computed to get our “average” cost of capital for the firm. This “average” is the required return on the firm’s assets, based on the market’s perception of the risk of those assets. The weights are determined by how much of each type of financing is used. The Weighted Average Cost of Capital Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› Section 14.4 12.19 Notation E = market value of equity = # of outstanding shares times price per share D = market value of debt = # of outstanding bonds times bond price V = market value of the firm = D + E Weights wE = E/V = percent financed with equity wD = D/V = percent financed with debt Capital Structure Weights Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.20 Section 14.4 (A) Note that for bonds we would find the market value of each bond issue and then add them together. Also note that preferred stock would just become another component of the equation if the firm has issued it. Finally, we generally ignore current liabilities in our computations. However, if a company finances a substantial portion of its assets with current liabilities, it should be included in the process. Lecture Tip: It may be helpful to mention and differentiate between the three types of weightings in the capital structure equation: book, market and target. It is also helpful to mention that the total market value of equity incorporates the market value of all three common equity accounts on the balance sheet (common stock, additional paid-in capital and retained earnings). Lecture Tip: The cost of short-term debt is usually very different from that of long-term debt. Some types of current liabilities are interest-free, such as accruals. However, accounts payable has a cost associated with it if the company forgoes discounts. The cost of notes payable and other current liabilities depends on market rates of interest for short-term loans. Since these loans are often negotiated with banks, you can get estimates of the short-term cost of capital from the company’s bank. The market value and book value of current liabilities are usually very similar, so you can use the book value as an estimate of market value. Suppose you have a market value of equity equal to $500 million and a market value of debt equal to $475 million. What are the capital structure weights? V = 500 million + 475 million = 975 million wE = E/V = 500 / 975 = .5128 = 51.28\% wD = D/V = 475 / 975 = .4872 = 48.72\% Example: Capital Structure Weights Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.21 Section 14.4 (A) We are concerned with aftertax cash flows, so we also need to consider the effect of taxes on the various costs of capital. Interest expense reduces our tax liability (subject to limitation). This reduction in taxes reduces our cost of debt. After-tax cost of debt = RD(1-TC) Dividends are not tax deductible, so there is no tax impact on the cost of equity. WACC = wERE + wDRD(1-TC) Taxes and the WACC Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.22 Section 14.4 (B) Point out that if we have other financing that is a significant part of our capital structure, we would just add additional terms to the equation and consider any tax consequences. The Tax Cuts and Jobs Act of 2017 placed limitations on the amount of interest that can be deducted in certain situations. If there is no deduction, then the pretax and aftertax cost of debt would be equal. If any deduction is allowed, then the aftertax cost would be lower. Lecture Tip: With a lower tax rate and/or less deductibility, the overall WACC would be higher, which would reduce project/firm value. However, the lower tax rate also increases cash flows, which would increase project/firm value. The latter seems to be the dominant impact. Lecture Tip: If the firm utilizes substantial amounts of current liabilities, equation 14.7 from the text should be modified as follows: WACC = (E/V)RE + (D/V)RD(1-TC) + (P/V)RP + (CL/V)RCL(1-TC) where CL/V represents the market value of current liabilities in the firm’s capital structure and V = E + D + P + CL. Equity Information 50 million shares $80 per share Beta = 1.15 Market risk premium = 9\% Risk-free rate = 5\% Debt Information $1 billion in outstanding debt (face value) Current quote = 110 Coupon rate = 9\%, semiannual coupons 15 years to maturity Tax rate = 21\% Extended Example: WACC - I Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.23 Section 14.4 (B) Remind students that bond prices are quoted as a percent of par value. What is the cost of equity? RE = 5 + 1.15(9) = 15.35\% What is the cost of debt? N = 30; PV = -1,100; PMT = 45; FV = 1,000; CPT I/Y = 3.9268 RD = 3.927(2) = 7.854\% What is the after-tax cost of debt? RD(1-TC) = 7.854(1-.21) = 6.205\% Extended Example: WACC - II Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.24 Section 14.4 (B) Point out that students do not have to compute the YTM based on the entire face amount. They can still use a single bond or they could also base everything on 100 (PV = -110; FV = 100; PMT = 4.5). We assume that the interest expense remains fully deductible. What are the capital structure weights? E = 50 million (80) = 4 billion D = 1 billion (1.10) = 1.1 billion V = 4 + 1.1 = 5.1 billion wE = E/V = 4 / 5.1 = .7843 wD = D/V = 1.1 / 5.1 = .2157 What is the WACC? WACC = .7843(15.35\%) + .2157(6.205\%) = 13.38\% Extended Example: WACC - III Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.25 Section 14.4 (B) Go to Yahoo! Finance to get information on Eastman Chemical (EMN). Under Profile and Key Statistics, you can find the following information: # of shares outstanding Book value per share Price per share Beta Under analysts estimates, you can find analysts estimates of earnings growth (use as a proxy for dividend growth). The Bonds section at Yahoo! Finance can provide the T-bill rate. Use this information, along with the CAPM and DGM, to estimate the cost of equity. Eastman Chemical I Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› Section 14.4 (C) 12.26 Go to FINRA to get market information on Eastman Chemical’s bond issues. Enter “Eastman Ch” to find the bond information. Note that you may not be able to find information on all bond issues due to the illiquidity of the bond market. Go to the SEC website to get book value information from the firm’s most recent 10Q. Eastman Chemical II Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› Section 14.4 (C) 12.27 Find the weighted average cost of the debt. Use market values if you were able to get the information. Use the book values if market information was not available. They are often very close. Compute the WACC. Use market value weights if available. Eastman Chemical III Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› Section 14.4 (C) 12.28 Find estimates of WACC at ValuePro. Look at the assumptions. How do the assumptions impact the estimate of WACC? Example: Work the Web Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› Section 14.4 (C) 12.29 Table 14.1 Cost of Equity Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› Section 14.4 (C) 12.30 Table 14.1 Cost of Debt Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› Section 14.4 (C) 12.31 Table 14.1 WACC Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› Section 14.4 (C) 12.32 Using the WACC as our discount rate is only appropriate for projects that have the same risk as the firm’s current operations. If we are looking at a project that does NOT have the same risk as the firm, then we need to determine the appropriate discount rate for that project. Divisions also often require separate discount rates. Does every GE Business Unit have the same cost? Divisional and Project Costs of Capital Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.33 Section 14.5 It is important to point out that a single corporate WACC is not very useful for companies that have several disparate divisions. www: Click on the link and then go to “GE Businesses” to see an index of businesses owned by General Electric. Ask the students if they think that projects proposed by “GE Capital” should have the same discount rate as projects proposed by the “Energy” group. You can go through the list and illustrate why the divisional cost of capital is important for a company like GE. If GE’s WACC was used for every division, then the riskier divisions would get more investment capital and the less risky divisions would lose the opportunity to invest in positive NPV projects. What would happen if we use the WACC for all projects regardless of risk? Assume the WACC = 15\% Project Required Return IRR A 20\% 17\% B 15\% 18\% C 10\% 12\% Example: Using WACC for All Projects Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.34 Section 14.5 (B) Ask students which projects would be accepted if they used the WACC for the discount rate? Compare 15\% to the IRR and accept projects A and B. Now ask students which projects should be accepted if you use the required return based on the risk of the project? Accept B and C. So, what happened when we used the WACC? We accepted a risky project that we shouldn’t have and rejected a less risky project that we should have accepted. What will happen to the overall risk of the firm if the company does this on a consistent basis? Most students will see that the firm will become riskier. What will happen to the firm’s cost of capital as the firm becomes riskier? It will increase (adjusting for changes in market returns in general) as well. Lecture Tip: It may help students to distinguish between the average cost of capital to the firm and the required return on a given investment if the idea is turned around from the firm’s point of view to the investor’s point of view. Consider an investor who is holding a portfolio of T-bills, corporate bonds and common stocks. Suppose there is an equal amount invested in each. The T-bills have paid 5\% on average, the corporate bonds 10\%, and the common stocks 15\%. Thus, the average portfolio return is 10\%. Now suppose that the investor has some additional money to invest and they can choose between T-bills that are currently paying 7\% and common stock that is expected to pay 13\%. What choice will the investor make if he uses the 10\% average portfolio return as his cut-off rate? (Invest in common stock 13\%>10\%, but not in T-bills 7\%<10\%.) What if he uses the average return for each security as the cut-off rate? (Invest in T-bills 7\% > 5\%, but not common stock 13\%<15\%.) Lecture Tip: You may wish to point out here that the divisional concept is no more than a firm-level application of the portfolio concept introduced in the section on risk and return. And, not surprisingly, the overall firm beta is therefore the weighted average of the betas of the firm’s divisions. Find one or more companies that specialize in the product or service that we are considering. Compute the beta for each company. Take an average. Use that beta along with the CAPM to find the appropriate return for a project of that risk. Often difficult to find pure play companies The Pure Play Approach Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.35 Section 14.5 (C) Note that technically you need to unlever the beta for each company before computing the average. Once the average of the unlevered beta has been found, you then relever to match the capital structure of the firm. This is done because the equity beta contains both business risk and financial risk – what we really need is the business risk and then we apply our own financial risk. Consider the project’s risk relative to the firm overall. If the project has more risk than the firm, use a discount rate greater than the WACC. If the project has less risk than the firm, use a discount rate less than the WACC. You may still accept projects that you shouldn’t and reject projects you should accept, but your error rate should be lower than not considering differential risk at all. Subjective Approach Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14-‹#› 12.36 Section 14.5 (D) Lecture Tip: Ask the class to consider a situation in which a company maintains a large portfolio of marketable securities. Now ask them to consider the impact this large security balance would have on a company’s current and quick ratios and how this might impact the company’s ability to meet short-term obligations. The students should easily remember that a larger liquidity ratio implies less risk (and less potential profit). Although the revenue realized from the marketable securities would be less than the interest expense on the … CHAPTER 11 PROJECT ANALYSIS AND EVALUATION Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› Perform and interpret a sensitivity analysis for a proposed investment Perform and interpret a scenario analysis for a proposed investment Determine and interpret cash, accounting, and financial break-even points Explain how the degree of operating leverage can affect the cash flows of a project Discuss how capital rationing affects the ability of a company to accept projects Key Concepts and Skills Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› Evaluating NPV Estimates Scenario and Other What-If Analyses Break-Even Analysis Operating Cash Flow, Sales Volume, and Break-Even Operating Leverage Capital Rationing Chapter Outline Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› NPV estimates are just that – estimates. A positive NPV is a good start – now we need to take a closer look. Forecasting risk – how sensitive is our NPV to changes in the cash flow estimates; the more sensitive, the greater the forecasting risk. Sources of value – why does this project create value? Evaluating NPV Estimates Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› 4 Section 11.1 There are two primary reasons for a positive NPV: (1) we have constructed a good project or (2) we have done a bad job of estimating NPV. Lecture Tip: With the lower flat-tax for corporations, previously unattractive projects may not have positive NPVs. So, there may be a one-time exception to the two reasons for finding positive NPV projects. Lecture Tip: Perhaps the single largest source of positive NPVs is the economic concept of monopoly rents – positive profits that occur from being the only one able or allowed to do something. Monopoly rents are often associated with patent rights and technological edges and they quickly disappear in a competitive market. Introducing this notion in class provides a springboard for discussions of both business and financial strategy, as well as for discussion of the application of economic theory to the real world. According to Alan Shapiro, the following are project characteristics associated with positive NPVs. 1) Economies of scale 2) Product differentiation 3) Cost advantages 4) Access to distribution channels 5) Favorable government policy What happens to the NPV under different cash flow scenarios? At the very least, look at: Best case – high revenues, low costs Worst case – low revenues, high costs Measures of the range of possible outcomes Best case and worst case are not necessarily probable, but they can still be possible. Scenario Analysis Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› 5 Section 11.2 (B) A good example of the worst case actually happening is the sinking of the Titanic. There were a lot of little things that went wrong, none of which were that important by themselves, but in combination they were deadly. A more recent example of the worst case scenario happening is the 2004 hurricane season in Florida. During the months of August and September, 4 hurricanes (Charley, Frances, Ivan, Jeanne) hit the state of Florida (the most previously had been 3 in the state of Texas in the late 1880s). This is ignoring tropical storm Bonnie that hit the panhandle a week before Charley came through. The eyes of 3 of the 4 hurricanes (all but Ivan, who tore through the panhandle) passed over Polk County in central Florida. The probability of 3 hurricanes passing over the same location in the span of 6 weeks is extremely low. The eyes of two of the hurricanes (Frances and Jeanne) made landfall on the east side of Florida within 10 miles of each other. Again, the probability of this happening 3 weeks apart is very, very small. To imagine anything more devastating would have been difficult, making this truly a worst-case scenario…until Katrina paid a visit to New Orleans and the levees failed! Lecture Tip: A major misconception about a project’s estimated NPV at this point is that it depends upon how the cash flows actually turn out. This thinking misses the point that NPV is an ex ante valuation of an uncertain future. The distinction between the valuation of what is expected versus the ex post value of what transpired is often difficult for students to appreciate. A useful analogy for getting this point across is the market value of a new car. The potential to be a “lemon” is in every car, as is the possibility of being a “cream puff.” The greater the likelihood that a car will have problems, the lower the price will be. The point, however, is that a new car doesn’t have many different prices right now – one for each conceivable repair record. Rather, there is one price embodying the different potential outcomes and their expected value. So it is with NPV – the potential for good and bad cash flows is reflected in a single market value. Consider the project discussed in the text in section 11.2. The initial cost is $200,000, and the project has a 5-year life. There is no salvage. Depreciation is straight-line, the required return is 12\%, and the tax rate is 21\%. The base, lower, and upper values are given for unit sales, price per unit, variable costs per unit, and fixed costs. Click on the Excel icon to see base case, best case, and worst case scenarios results. New Project Example Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› 6 Section 11.2 (B) Click on the Excel icon to go to a spreadsheet that includes both the scenario analysis and the sensitivity analysis presented in the book. Scenario Net Income Cash Flow NPV IRR Base case 23,700 63,700 29,624 17.8\% Worst Case -18,565 21,435 -122,732 -17.7\% Best Case 71,495 111,495 201,915 47.9\% Summary of Scenario Analysis Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› 7 Section 11.2 (B) Lecture Tip: You may wish to integrate this discussion of risk with some of the topics to be discussed in forthcoming chapters. The variability between best- and worst-case scenarios is the essence of forecasting risk. Similarly, we link the risk of a security with the variability of its expected return. This point provides another opportunity to link economic theory (investor/manager rationality versus required returns) with real-world decision-making. You might also want to point out that the cases examined in this type of analysis typically aren’t literally the best and worst cases possible. The true worst-case scenario is something absurdly unlikely, such as an earthquake that swallows our production plant. Instead, the worst-case used in scenario analysis is simply a pessimistic (but possible) forecast used to develop expected cash flows. What happens to NPV when we change one variable at a time? This is a subset of scenario analysis where we are looking at the effect of specific variables on NPV. The greater the volatility in NPV in relation to a specific variable, the larger the forecasting risk associated with that variable, and the more attention we want to pay to its estimation. Sensitivity Analysis Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› 8 Section 11.2 (C) Click on the Excel icon to return to the new project spreadsheet. If desired, it may be a good point at which to demonstrate the Solver function in Excel, as you can identify how high/low an input could go before NPV becomes negative. Scenario Unit Sales Cash Flow NPV IRR Base case 6,000 63,700 29,624 17.8\% Worst case 5,500 55,800 1,147 12.2\% Best case 6,500 71,600 58,102 23.2\% Summary of Sensitivity Analysis for New Project Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› Section 11.2 (C) Using an older standard tax rate of 34\%, the worst case scenario gives a negative NPV. This illustrates that the reduction in taxes will make some previously unattractive investments favorable. 9 Simulation is really just an expanded sensitivity and scenario analysis. Monte Carlo simulation can estimate thousands of possible outcomes based on conditional probability distributions and constraints for each of the variables. The output is a probability distribution for NPV with an estimate of the probability of obtaining a positive net present value. The simulation only works as well as the information that is entered, and very bad decisions can be made if care is not taken to analyze the interaction between variables. Simulation Analysis Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› 10 Section 11.2 (D) Lecture Tip: A very useful software is Crystal Ball, which is a simulation package that integrates with Excel. It is relatively inexpensive, yet it is very useful for basic-to-moderate simulation analysis. For example, the software allows you to build models (such as NPV) in Excel, then define the assumptions behind the inputs (such as distribution, possible extreme values, etc.), as well as the interaction (i.e., correlation) between the inputs. Output is then generated based on a simulation of 1,000 runs, providing distribution analysis and numerical summary statistics. Beware “Paralysis of Analysis” At some point you have to make a decision. If the majority of your scenarios have positive NPVs, then you can feel reasonably comfortable about accepting the project. If you have a crucial variable that leads to a negative NPV with a small change in the estimates, then you may want to forego the project. Making a Decision Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› Section 11.2 (D) 11 Common tool for analyzing the relationship between sales volume and profitability There are three common break-even measures: Accounting break-even: sales volume at which NI = 0 Cash break-even: sales volume at which OCF = 0 Financial break-even: sales volume at which NPV = 0 Break-Even Analysis Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› Section 11.3 12 There are two types of costs that are important in breakeven analysis: variable and fixed. Total variable costs = quantity × cost per unit Fixed costs are constant, regardless of output, over some time period. Total costs = fixed + variable = FC + vQ Example: Your firm pays $3,000 per month in fixed costs. You also pay $15 per unit to produce your product. What is your total cost if you produce 1,000 units? What if you produce 5,000 units? Example: Costs Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› 13 Section 11.3 (A) Produce 1000 units: TC = 3000 + 15 × 1000 = 18,000 Produce 5000 units: TC = 3000 + 15 × 5000 = 78,000 Lecture Tip: You may wish to emphasize that, in computing total variable costs, the only relevant costs are those that are directly related to the manufacture and sale of the product. Allocated (or indirect) costs should not enter the analysis. Suggest to the students that when they are uncertain, they should use the “with/without” criterion: will the costs be different if the investment is made? If not, the cost is, by definition, not directly related to the decision and should not be included. Average Cost TC / # of units Will decrease as # of units increases Marginal Cost The cost to produce one more unit Same as variable cost per unit Example: What is the average cost and marginal cost under each situation in the previous example? Produce 1,000 units: Average = 18,000 / 1000 = $18 Produce 5,000 units: Average = 78,000 / 5000 = $15.60 Average vs. Marginal Cost Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› 14 Section 11.3 (A) Lecture Tip: Students should recognize that as quantity increases, total fixed costs remain constant, but on a per unit basis, they decrease with increasing volume. And, as quantity increases, total cost per unit approaches variable cost per unit. If a company expects a high unit sales volume, the company may desire to exploit the possible economies of scale by investing more in fixed costs in an effort to lower variable cost per unit. However, this could create future financial problems if sales expectations fail to materialize. You might mention that this sensitivity to earnings declines will be examined later in this chapter through the discussion of the degree of operating leverage. The quantity that leads to a zero net income NI = (Sales – VC – FC – D)(1 – T) = 0 QP – vQ – FC – D = 0 Q(P – v) = FC + D Q = (FC + D) / (P – v) Accounting Break-Even Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› Section 11.3 (B) 15 Accounting break-even is often used as an early stage screening number. If a project cannot break-even on an accounting basis, then it is not going to be a worthwhile project. Accounting break-even gives managers an indication of how a project will impact accounting profit. Using Accounting Break-Even Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› Section 11.3 (C) 16 We are more interested in cash flow than we are in accounting numbers. As long as a firm has non-cash deductions, there will be a positive cash flow. If a firm just breaks even on an accounting basis, cash flow = depreciation. If a firm just breaks even on an accounting basis, NPV will generally be < 0. Accounting Break-Even and Cash Flow Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› Section 11.4 (A) 17 Consider the following project: A new product requires an initial investment of $5 million and will be depreciated to an expected salvage of zero over 5 years. The price of the new product is expected to be $25,000, and the variable cost per unit is $15,000. The fixed cost is $1 million. What is the accounting break-even point each year? Depreciation = 5,000,000 / 5 = 1,000,000 Q = (1,000,000 + 1,000,000)/(25,000 – 15,000) = 200 units Example Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› 18 Section 11.4 (A) What is the operating cash flow at the accounting break-even point (ignoring taxes)? OCF = (S – VC – FC - D) + D OCF = (200 × 25,000 – 200 × 15,000 – 1,000,000 -1,000,000) + 1,000,000 = 1,000,000 What is the cash break-even quantity (ignoring taxes)? OCF = [(P-v)Q – FC – D] + D = (P-v)Q – FC Q = (OCF + FC) / (P – v) Q = (0 + 1,000,000) / (25,000 – 15,000) = 100 units Sales Volume and Operating Cash Flow Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› 19 Section 11.4 (B) Cash break-even occurs where operating cash flow = 0. Accounting Break-even Where NI = 0 Q = (FC + D)/(P – v) Cash Break-even Where OCF = 0 Q = (FC + OCF)/(P – v); (ignoring taxes) Financial Break-even Where NPV = 0 Cash BE < Accounting BE < Financial BE Three Types of Break-Even Analysis Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› 20 Section 11.4 (C) Lecture Tip: Inquisitive students may ask how the computations change when you include taxes. The equations change as follows: OCF = [(P − v)Q − FC − D](1 − T) + D Use a tax rate = 21\% and rework the Wettways example from the book: Need 1170 in OCF to break-even on a financial basis OCF = [(40 − 20)(Q) − 500 − 700](1 − .21) + 700 = 1170 Q = 89.75 You end up with a new quantity of 90 units. The firm must sell an additional 16 units to offset the effects of taxes. Although, with the recent tax cuts, this difference is not as large as it previously was. Consider the previous example. Assume a required return of 18\% Accounting break-even = 200 Cash break-even = 100 (ignoring taxes) What is the financial break-even point (ignoring taxes)? What OCF (or payment) makes NPV = 0? N = 5; PV = 5,000,000; I/Y = 18; CPT PMT = 1,598,889 = OCF Q = (1,000,000 + 1,598,889) / (25,000 – 15,000) = 260 units (ignoring taxes) The question now becomes: Can we sell at least 260 units per year? Example: Break-Even Analysis Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› 21 Section 11.4 (C) Assumptions: Cash flows are the same every year, no salvage and no NWC. If there were salvage and NWC, you would net it out to year 0 so that all you have in future years is OCF. Operating leverage is the relationship between sales and operating cash flow. Degree of operating leverage measures this relationship. The higher the DOL, the greater the variability in operating cash flow. The higher the fixed costs, the higher the DOL. DOL depends on the sales level you are starting from. DOL = 1 + (FC / OCF) Operating Leverage Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› Section 11.5 22 Consider the previous example. Suppose sales are 300 units. This meets all three break-even measures. What is the DOL at this sales level? OCF = (25,000 – 15,000) × 300 – 1,000,000 = 2,000,000 DOL = 1 + 1,000,000 / 2,000,000 = 1.5 What will happen to OCF if unit sales increases by 20\%? Percentage change in OCF = DOL × Percentage change in Q Percentage change in OCF = 1.5(.2) = .3 or 30\% OCF would increase to 2,000,000(1.3) = 2,600,000 Example: DOL Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› Section 11.5 (C) 23 Capital rationing occurs when a firm or division has limited resources. Soft rationing – the limited resources are temporary, often self-imposed Hard rationing – capital will never be available for this project The profitability index is a useful tool when a manager is faced with soft rationing. Capital Rationing Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› 24 Section 11.6 If you face hard rationing, you need to reevaluate your analysis. If you truly estimated the required return and expected cash flows appropriately and computed a positive NPV, then capital should be available. Lecture Tip: In 2008, the economy was suffering from a real estate and credit crisis. As a result, lenders essentially withdrew from the market and credit dried up. This is a perfect example of an issue that would create a situation very close to hard rationing for many businesses. Lecture Tip: If lower tax rates result in higher cash flows and more attractive projects, then the issue of capital rationing will become even more pronounced. What is sensitivity analysis, scenario analysis and simulation? Why are these analyses important, and how should they be used? What are the three types of break-even analysis, and how should each be used? What is the degree of operating leverage? What is the difference between hard rationing and soft rationing? Quick Quiz Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› Section 11.7 25 Is it ethical for a medical patient to pay for a portion of R&D costs (since experimental procedures are not covered by insurance) prior to the introduction of the final product? Is it proper for physicians to recommend this procedure when they have a vested interest in its usage? Ethics Issues Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› 26 Case: Researchers associated with South Miami Hospital (SMH) developed a new experimental laser treatment for heart patients. Its development team and the physicians who use the laser consider it to be a lifesaving advance. It should be noted that the physicians who are touting the laser hold a significant stake in the company that produces the laser. To offer a substitute for a balloon angioplasty to treat heart blockages, the experimental laser was developed at a cost of $250,000. SMH estimates that it will cost $20,000 to install the laser. The procedure requires a nurse at $50 per hour, a technician at $30 per hour, and a physician who is paid $750 per hour. Patients are billed $3,000 for the procedure compared to $1,500 for the traditional balloon treatment. Now ask the students to determine the break-even quantity for the new procedure: Fixed cost = 250,000 + 20,000 = 270,000 Variable cost = 50 + 30 + 750 = 830 per hour Cash Break-Even = 250,000 / (3,000 – 830) = 115.2 hours, or approximately 116 patients (assuming a one-hour procedure per patient). A project requires an initial investment of $1,000,000 and is depreciated straight-line to zero salvage over its 10-year life. The project produces items that sell for $1,000 each, with variable costs of $700 per unit. Fixed costs are $350,000 per year. What is the accounting break-even quantity, operating cash flow at accounting break-even (ignoring taxes), and DOL at that output level? Comprehensive Problem Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› 27 Section 11.7 Accounting break-even: Q = (FC + D) / (P – V) = ($350,000 + $100,000) / ($1,000 - $700) = 1,500 units OCF = ( S – VC – FC – D) + D = (1,500 × $1,000 – 1,500 × $700 - $350,000 - $100,000) + $100,000 = $100,000 DOL = 1 + (FC / OCF) = 1 + ($350,000 / 100,000) = 4.5 End of Chapter CHAPTER 11 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11-‹#› 11-‹#› Microsoft Excel 97-2003 Worksheet Scenario Base Lower Upper Unit Sales 6000 5500 6500 Depreciation 40000 Price per unit 80 75 85 VC per unit 60 58 62 No NWC FC per unit 50000 45000 55000 Base Case Analysis Best Case Worst Case Pro Forma Statement Pro Forma Statement Pro Forma Statement Sales 480000 Sales 552500 Sales 412500 VC 360000 VC 377000 VC 341000 FC 50000 FC 45000 FC 55000 Depreciation 40000 Depreciation 40000 Depreciation 40000 EBIT 30000 EBIT 90500 EBIT -23500 Taxes 6300 Taxes 19005 Taxes -4935 NI 23700 NI 71495 NI -18565 Cash Flows Year OCF NCS CFFA Year OCF NCS CFFA Year OCF NCS CFFA 0 -200000 -200000 0 -200000 -200000 0 -200000 -200000 1 63700 63700 1 111495 111495 1 21435 21435 2 63700 63700 2 111495 111495 2 21435 21435 3 63700 63700 3 111495 111495 3 21435 21435 4 63700 63700 4 111495 111495 4 21435 21435 5 63700 63700 5 111495 111495 5 21435 21435 NPV $29,624.24 NPV $201,914.52 NPV -$122,731.62 Sensitivity Analysis For Unit Sales Pro Forma Statement Base Lower Upper Sales 480000 440000 520000 VC 360000 330000 390000 FC 50000 50000 50000 Depreciation 40000 40000 40000 EBIT 30000 20000 40000 Taxes 6300 4200 8400 NI 23700 15800 31600 Cash Flows Year 0 -200,000 -200,000 -200,000 1 63700 55800 71600 2 63700 55800 71600 3 63700 55800 71600 4 63700 55800 71600 5 63700 55800 71600 NPV $29,624.24 $1,146.51 $58,101.98 Numbers in blue were computed in Excel. Sensitivity Base Lower Upper Unit Sales 6000 5500 6500 Depreciation 40000 Price per unit 80 75 85 VC per unit 60 58 62 No NWC FC per unit 50000 45000 55000 Base Case Analysis Best Case Worst Case Pro Forma Statement Pro Forma Statement Pro Forma Statement Sales 480000 Sales 552500 Sales 412500 VC 360000 VC 377000 VC 341000 FC 50000 FC 45000 FC 55000 Depreciation 40000 Depreciation 40000 Depreciation 40000 EBIT 30000 EBIT 90500 EBIT -23500 Taxes 6300 Taxes 19005 Taxes -4935 NI 23700 NI 71495 NI -18565 Cash Flows Year OCF NCS CFFA Year OCF NCS CFFA Year OCF NCS CFFA 0 -200000 -200000 0 -200000 -200000 0 -200000 -200000 1 63700 63700 1 111495 111495 1 21435 21435 2 63700 63700 2 111495 111495 2 21435 21435 3 63700 63700 3 111495 111495 3 21435 21435 4 63700 63700 4 111495 111495 4 21435 21435 5 63700 63700 5 111495 111495 5 21435 21435 NPV $29,624.24 NPV $201,914.52 NPV -$122,731.62 Sensitivity Analysis For Unit Sales Pro Forma Statement Base Lower Upper Sales 480000 440000 520000 VC 360000 330000 390000 FC 50000 50000 50000 Depreciation 40000 40000 40000 EBIT 30000 20000 40000 Taxes 6300 4200 8400 NI 23700 15800 31600 Cash Flows Year 0 -200,000 -200,000 -200,000 1 63700 55800 71600 2 63700 55800 71600 3 63700 55800 71600 4 63700 55800 71600 5 63700 55800 71600 NPV $29,624.24 $1,146.51 $58,101.98 Numbers in blue were computed in Excel. Long-term financial planning and growth Chapter 4 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-‹#› Apply the percentage of sales method Compute the external financing needed to fund a firm’s growth Name the determinants of a firm’s growth Anticipate some of the problems in planning for growth Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Key Concepts and Skills 4-‹#› What Is Financial Planning? Financial Planning Models: A First Look The Percentage of Sales Approach External Financing and Growth Some Caveats Regarding Financial Planning Models Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Chapter Outline 4-‹#› Investment in new assets – determined by capital budgeting decisions Degree of financial leverage – determined by capital structure decisions Cash paid to shareholders – determined by dividend policy decisions Liquidity requirements – determined by net working capital decisions Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Elements of Financial Planning 4-‹#› Section 4.1 4 Planning Horizon – divide decisions into short-run decisions (usually next 12 months) and long-run decisions (usually 2 – 5 years) Aggregation – combine capital budgeting decisions into one large project Assumptions and Scenarios Make realistic assumptions about important variables Run several scenarios where you vary the assumptions by reasonable amounts Determine, at a minimum, worst case, normal case, and best case scenarios Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Financial Planning Process 4-‹#› 5 Section 4.1 (B) The time period used in the financial planning process is called the planning horizon. Lecture Tip: Many students assume that only a single variable need be changed for best- and worst-case scenarios. However, it is often the confluence of several events. For example, consider mid-2008 when commodity prices were increasing dramatically, while at the same time the economy in the U.S. was slowing. This caused many firms to see input prices rise, while demand and pricing power fell on the output side. In addition, many students may suggest aggregation is unrealistic; however, remind them we are not producing a detailed financial plan. Rather, we are highlighting general relationships. In recent times, most large firms have adopted ERP systems to help with this planning process. The discussion of scenario analysis is a good precursor for capital budgeting. Examine interactions – help management see the interactions between decisions Explore options – give management a systematic framework for exploring its opportunities Avoid surprises – help management identify possible outcomes and plan accordingly Ensure feasibility and internal consistency – help management determine if goals can be accomplished and if the various stated (and unstated) goals of the firm are consistent with one another Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Role of Financial Planning 4-‹#› 6 Section 4.1 (C) Committing a plan to paper forces managers to think seriously about the future. Sales Forecast – many cash flows depend directly on the level of sales (often estimated using sales growth rate) Pro Forma Statements – setting up the plan using projected financial statements allows for consistency and ease of interpretation Asset Requirements – the additional assets that will be required to meet sales projections Financial Requirements – the amount of financing needed to pay for the required assets Plug Variable – determined by management deciding what type of financing will be used to make the balance sheet balance Economic Assumptions – explicit assumptions about the coming economic environment Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Financial Planning Model Ingredients 4-‹#› Section 4.2 (A) 7 Gourmet Coffee Inc. Balance Sheet December 31, 2018 Assets 1000 Debt 400 Equity 600 Total 1000 Total 1000 Gourmet Coffee Inc. Income Statement For Year Ended December 31, 2018 Revenues 2000 Less: costs (1600) Net Income 400 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example: Historical Financial Statements 4-‹#› Section 4.3 8 Initial Assumptions Revenues will grow at 15\% (2,000 × 1.15). All items are tied directly to sales, and the current relationships are optimal. Consequently, all other items will also grow at 15\%. Gourmet Coffee Inc. Pro Forma Income Statement For Year Ended 2019 Revenues 2,300 Less: costs (1,840) Net Income 460 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example: Pro Forma Income Statement 4-‹#› Section 4.3 (A) 9 Case I Dividends are the plug variable, so equity increases at 15\%. Dividends = 460 (NI) - 90 (increase in equity) = 370 dividends paid Case II Debt is the plug variable and no dividends are paid. Debt = 1,150 - (600+460) = 90 Repay 400 - 90 = 310 in debt Gourmet Coffee Inc. Pro Forma Balance Sheet Case 1 Assets 1,150 Debt 460 Equity 690 Total 1,150 Total 1,150 Gourmet Coffee Inc. Pro Forma Balance Sheet Case 2 Assets 1,150 Debt 90 Equity 1,060 Total 1,150 Total 1,150 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example: Pro Forma Balance Sheet 4-‹#› Section 4.3 (B) 10 Some items vary directly with sales, while others do not. Income Statement Costs may vary directly with sales – if this is the case, then the profit margin is constant. Depreciation and interest expense may not vary directly with sales – if this is the case, then the profit margin is not constant. Dividends are a management decision and generally do not vary directly with sales – this influences additions to retained earnings. Balance Sheet Initially assume all assets, including fixed, vary directly with sales. Accounts payable will also normally vary directly with sales. Notes payable, long-term debt and equity generally do not vary directly with sales because they depend on management decisions about capital structure. The change in the retained earnings portion of equity will come from the dividend decision. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Percentage of Sales Approach 4-‹#› Section 4.3 (C) 11 Tasha’s Toy Emporium Income Statement, 2018 \% of Sales Sales 5,000 Less: costs (3,500) 70.0\% EBT 1,500 30.0\% Less: taxes (21\% of EBT) (315) 6.3\% Net Income 1,185 23.7\% Dividends 474 Add. To RE 711 Tasha’s Toy Emporium Pro Forma Income Statement, 2019 Sales 5,500 Less: costs (3,850) EBT 1,650 Less: taxes (347) Net Income 1,303 Dividends 521 Add. To RE 782 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example: Income Statement Assume Sales grow at 10\% Dividend Payout Rate = 40\% 4-‹#› Section 4.3 (C) The new “flat tax” imposed by the Tax Cuts and Jobs Act of 2017 simplifies the forecasting of the tax liability. 12 Tasha’s Toy Emporium – Balance Sheet Current \% of Sales Pro Forma Current \% of Sales Pro Forma Assets Liabilities & Owners’ Equity Current Assets Current Liabilities Cash $500 10\% $550 A/P $900 18\% $990 A/R 2,000 40 2,200 N/P 2,500 n/a 2,500 Inventory 4,000 80 4,400 Total 3,400 n/a 3,490 Total 6,500 120 7,150 LT Debt 3,000 n/a 3,000 Fixed Assets Owners’ Equity Net PP&E 5,000 100 5,500 CS & APIC 2,000 n/a 2,000 Total Assets 11,500 220 12,650 RE 3,100 n/a 3,882 Total 5,100 n/a 4,760 Total L & OE 11,500 12,372 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example: Balance Sheet 4-‹#› 13 Section 4.3 (C) There is not a double-ruled line at the bottom of the pro forma columns because the pro forma balance sheet has not yet been made to balance. Since the asset value is larger (12,650 – 12,372 =278), the firm requires external financing. At this point it may be good to note that some assets and liabilities (particularly net working capital) can be considered “spontaneous,” in that they generally change directly with sales. While long-term assets and financing may have a greater impact on the firm, these short-term issues are made continuously and affect daily cash flow. You can also use the same example to illustrate what would happen if the firm is operating at less than full capacity – i.e., the PP&E account would not need to increase as much to capture the increase in sales. The firm needs to come up with an additional $278 in debt or equity to make the balance sheet balance. TA - TL&OE = 12,650 – 12,372 = 278 Choose plug variable ($278 EFN) Borrow more short-term (Notes Payable) Borrow more long-term (LT Debt) Sell more common stock (CS & APIC) Decrease dividend payout, which increases the Additions To Retained Earnings Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example: External Financing Needed 4-‹#› Section 4.3 (C) 14 Suppose that the company is currently operating at 80\% capacity. Full Capacity sales = 5000 / 0.80 = 6,250 Estimated sales = $5,500, so we would still only be operating at 88\%. Therefore, no additional fixed assets would be required. Pro forma Total Assets = 7,150 + 5,000 = 12,150 Total Liabilities and Owners’ Equity = 12,372 Choose plug variable (for $222 EXCESS financing) Repay some short-term debt (decrease Notes Payable) Repay some long-term debt (decrease LT Debt) Buy back stock (decrease CS & APIC) Pay more in dividends (reduce Additions To Retained Earnings) Increase cash account Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example: Operating at Less than Full Capacity 4-‹#› 15 Section 4.3 (D) Capacity at 5500: 5500 / 6250 = .88 Looking for estimates of company growth rates? What do the analysts have to say? Check out Yahoo! Finance – enter a company ticker and follow the “Analyst Estimates” link. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Work the Web Example 4-‹#› Section 4.3 16 At low growth levels, internal financing (retained earnings) may exceed the required investment in assets. As the growth rate increases, the internal financing will not be enough, and the firm will have to go to the capital markets for money. Examining the relationship between growth and external financing required is a useful tool in long-range planning. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Growth and External Financing 4-‹#› 17 Section 4.4 Obviously, for young, high-growth, start-up firms this relationship is imperative, particularly since their access to the capital markets may be limited and internally generated financing has yet to develop. In fact, there are many examples of firms “growing themselves out of business.” These situations are the specialty for “angel” investors and venture capitalists. The internal growth rate tells us how much the firm can grow assets using retained earnings as the only source of financing. The internal growth rate assumes that the dividend payout ratio is constant. Using the information from Tasha’s Toy Emporium ROA = 1,185 / 11,500 = .1030 b = retention ratio = (1 - dividend payout ratio) = .6 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. The Internal Growth Rate (I/S) (B/S) = = .066, or 6.6\% 4-‹#› 18 Section 4.4 (B) This firm could grow assets at 4.3\% without raising additional external capital. Relying solely on internally generated funds will increase equity (retained earnings are part of equity) and assets without an increase in debt. Consequently, the firm’s leverage will decrease over time. If there is an optimal amount of leverage, as we will discuss in later chapters, then the firm may want to borrow to maintain that optimal level of leverage. This idea leads us to the sustainable growth rate. The sustainable growth rate tells us how much the firm can grow by using internally generated funds and issuing debt to maintain a constant debt ratio. Assumptions: The sustainable growth rate also assumes that the dividend payout ratio is constant. No new external equity is issued, but debt increases with growth. Using Tasha’s Toy Emporium ROE = 1185 / 5100 = .2324 b = .4 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. The Sustainable Growth Rate (I/S) (B/S) = = .1025 = 10.25\% 4-‹#› 19 Section 4.4 (B) Note that no new equity is issued. The sustainable growth rate is substantially higher than the internal growth rate. This is because we are allowing the company to issue debt as well as use internal funds. Lecture Tip: Some students will wonder why managers would wish to avoid issuing equity to meet anticipated financing needs. This is a good opportunity to bring in concepts from previous chapters (stockholder/bondholder conflicts of interest and agency costs), as well as to introduce topics to be covered in future chapters (information asymmetry and signaling, flotation costs, high cost of equity and corporate governance). Many texts refer to the sustainable growth rate as b × ROE. This simpler formula assumes that ROE is computed using beginning (rather than ending) equity balances. Profit margin – operating efficiency Total asset turnover – asset use efficiency Financial leverage – choice of optimal debt ratio Dividend policy – choice of how much to pay to shareholders versus reinvesting in the firm Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Determinants of Growth 4-‹#› 20 Section 4.4 (B) The first three components come from the ROE and the DuPont identity. It is important to note at this point that growth is not the goal of a firm in and of itself. Growth is only important so long as it continues to maximize shareholder value. For example, we could grow sales by cutting prices, but this would squeeze margins and possibly reduce overall earnings. It is important to remember that we are working with accounting numbers; therefore, we must ask ourselves some important questions as we go through the planning process: How does our plan affect the timing and risk of our cash flows? Does the plan point out inconsistencies in our goals? If we follow this plan, will we maximize owners’ wealth? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Important Questions 4-‹#› Section 4.5 21 What is the purpose of long-range planning? What are the major decision areas involved in developing a plan? What is the percentage of sales approach? How do you adjust the model when operating at less than full capacity? What is the internal growth rate? What is the sustainable growth rate? What are the major determinants of growth? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Quick Quiz 4-‹#› Section 4.6 22 Should managers overstate budget requests (or growth projections) if they know that central headquarters is going to cut funds across the board? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Ethics Issues 4-‹#› XYZ has the following financial information for 2018: Sales = $2M, Net Inc. = $0.4M, Div. = $0.1M C.A. = $0.4M, F.A. = $3.6M C.L. = $0.2M, LTD = $1M, C.S. = $2M, R.E. = $0.8M What is the sustainable growth rate? If 2019 sales are projected to be $2.4M, what is the amount of external financing needed, assuming XYZ is operating at full capacity, and profit margin and payout ratio remain constant? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Comprehensive Problem 4-‹#› 24 Section 4.6 ROE = net income / shareholders’ equity = $.4M / ($2M + $.8M) = .1429 Payout ratio = dividends/net income = .1M/.4M = .25 Plowback ratio (b) 1 - payout ratio = 1 - .25 = .75 Sustainable growth rate = ROE × b / 1 - ROE × b = .1429 × .75 / (1 - (.1429 × .75)) = .12 Profit margin = net income/sales = .4M/2M = .2 Projected net income = profit margin × projected sales = .2 × $2.4M = $.48M Projected addition to retained earnings = projected net income × (1 - payout ratio) = $.48M × (1-.25) = $.48M × .75 = $.36M \% change in sales = ($2.4M - $2M)/$2M = .2 2018 total assets = $.4M + $3.6M = $4M Projected total assets = $4M × 1.2 = $4.8M Projected C.L. = $.2M × 1.2 = $.24M Projected R.E. = 2012 R.E. + projected addition to R.E. = $.8M + $.36M = $1.16M Projected liabilities and owners’ equity = projected C.L. + LTD + C.S. + projected R.E. = $.24M + $1M + $2M + $1.16M = $4.4M External Financing Needed = projected assets - projected liabilities and OE = $4.8M - $4.4M = $.4M End of Chapter Chapter 4 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4-‹#› 4-‹#› MAKING CAPITAL INVESTMENT DECISIONS CHAPTER 10 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› 9.1 Determine the relevant cash flows for a proposed project Evaluate whether a project is acceptable Explain how to set a bid price for a project Evaluate the equivalent annual cost of a project Key Concepts and Skills Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› 9.2 Project Cash Flows: A First Look Incremental Cash Flows Pro Forma Financial Statements and Project Cash Flows More about Project Cash Flow Alternative Definitions of Operating Cash Flow Some Special Cases of Discounted Cash Flow Analysis Chapter Outline Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› The cash flows that should be included in a capital budgeting analysis are those that will only occur (or not occur) if the project is accepted. These cash flows are called incremental cash flows. The stand-alone principle allows us to analyze each project in isolation from the firm simply by focusing on incremental cash flows. Relevant Cash Flows Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› 9.4 Section 10.1 (A) Lecture Tip: It should be strongly emphasized that a project’s cash flows imply changes in future firm cash flows and, therefore, in the firm’s future financial statements. You should always ask yourself “Will this cash flow occur ONLY if we accept the project?” If the answer is “yes,” it should be included in the analysis because it is incremental. If the answer is “no,” it should not be included in the analysis because it will occur anyway. If the answer is “part of it,” then we should include the part that occurs because of the project. Asking the Right Question Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› 9.5 Section 10.1 (B) Lecture Tip: You might find it useful to clearly delineate the link between the stand-alone principle and the concept of value additivity. By viewing projects as “mini-firms,” we imply that the firm as a whole constitutes a portfolio of mini-firms. As a result, the value of the firm equals the combined value of its components. This is the essence of value additivity, and it is assumed to hold generally whether we are discussing the cash flows in a simple time-value problem, the value of a project, or the value of the firm. Note also that an understanding of this concept paves the way for the analysis of mergers and acquisitions. For a merger to “create value,” the value additivity principle must be violated. (Violations take the form of production efficiencies, economies of scale, etc.) Perhaps a key value of this approach is that it places the burden of proof on those proposing the merger, just as the capital budgeting process places the burden of proof on those proposing investment in the project. Sunk costs – costs that have accrued in the past Opportunity costs – costs of lost options Side effects Positive side effects – benefits to other projects Negative side effects – costs to other projects Changes in net working capital Financing costs Taxes Common Types of Cash Flows Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› 9.6 Section 10.2 With each of these types of cash flows, you should ask the class the question on the previous slide so that they can start to determine if the cash flows are relevant. Personal examples of sunk costs often help students understand the issue. Ask the students to consider a hypothetical situation in which a college student purchased a computer for $1,500 while in high school. A better computer is now available that also costs $1,500. The relevant factors to the decision are what benefits would be provided by the better computer to justify the purchase price. The cost of the original computer is irrelevant. Opportunity costs – the classic example of an opportunity cost is the use of land or plant that is already owned. It is important to point out that this is not “free.” At the very least we could sell the land; consequently, if we choose to use it, we cost ourselves the selling price of the asset. A good example of a positive side effect is when you will establish a new distribution system with this project that can be used for existing or future projects. The benefit provided to those projects needs to be considered. The most common negative side effect is erosion or cannibalism, where the introduction of a new product will reduce the sales of existing, similar products. A good real-world example is McDonald’s introduction of the Arch Deluxe sandwich. Instead of generating all new sales, it primarily reduced sales in the Big Mac and the Quarter Pounder. It is important to consider changes in NWC. We need to remember that operating cash flow derived from the income statement assumes all sales are cash sales and that the COGS was actually paid in cash during that period. By looking at changes in NWC specifically, we can adjust for the difference in cash flow that results from accounting conventions. Most projects will require an increase in NWC initially as we build inventory and receivables. Then, we recover NWC at the end of the project. We do not include financing costs. Students often have difficulty understanding why when it appears that we will only raise capital if we take the project. It is important to point out that because of economies of scale, companies generally do not finance individual projects. Instead, they finance the entire portfolio of projects at one time. The other reason has to do with maintaining a target capital structure over time, but not necessarily each year. Finally, financing cost is included in the required return, thus including the financing-related cash flows would be double counting. Taxes will change as the firm’s taxable income changes. Consequently, we have to consider cash flows on an after-tax basis. The lower tax rate just approved by the Tax Cuts and Jobs Act of 2017, all else equal, will increase after-tax incremental cash flows from a project and potentially lead to an increase in overall investment spending Capital budgeting relies heavily on pro forma accounting statements, particularly income statements. Computing cash flows – refresher Operating Cash Flow (OCF) = EBIT + depreciation – taxes OCF = Net income + depreciation (when there is no interest expense) Cash Flow From Assets (CFFA) = OCF – net capital spending (NCS) – changes in NWC Pro Forma Statements and Cash Flow Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› 9.7 Section 10.3 Operating cash flow – students often have to go back to the income statement to see that the two definitions of operating cash flow are equivalent when there is no interest expense. Lecture Tip: Students sometimes become disheartened at what they perceive as complexities in the various capital budgeting calculations. You may find it useful to remind them that, in reality, setting up timelines and performing calculations are typically the least burdensome portion of the task. Rather, the difficulties arise principally in two areas: (1) generating good investment projects and (2) developing reliable cash flow estimates for these projects. Lecture Tip: Some students may still question why we are ignoring interest, since it is clearly a cash outflow. It should be strongly emphasized that we do not ignore interest expense (or any other financing expense, for that matter); rather, we are only evaluating asset related cash flows. It should be stressed that interest expense is a financing cost, not an operating cost. Sales (50,000 units at $4.00/unit) $200,000 Variable Costs ($2.50/unit) 125,000 Gross profit $ 75,000 Fixed costs 17,430 Depreciation ($90,000 / 3) 30,000 EBIT $ 27,570 Taxes (21\%) 5,790 Net Income $ 21,780 Table 10.1 Pro Forma Income Statement Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› Section 10.3 (A) 9.8 Year 0 1 2 3 NWC $20,000 $20,000 $20,000 $20,000 NFA 90,000 60,000 30,000 0 Total $110,000 $80,000 $50,000 $20,000 Table 10.2 Projected Capital Requirements Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› 9.9 Section 10.3 (A) Ask the students why net fixed assets is decreasing each year. It is important that they understand why this is happening when they go to compute the net capital spending in the next slide. Year 0 1 2 3 OCF $51,780 $51,780 $51,780 Change in NWC -$20,000 20,000 NCS -$90,000 CFFA -$110,00 $51,780 $51,780 $71,780 Table 10.5 Projected Total Cash Flows Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› 9.10 Section 10.3 (B) OCF = EBIT + depreciation – taxes = 27,570 + 30,000 – 5,790 = 51,780; or OCF = NI + depreciation = 21,780 + 30,000 = 51,780 Note that in the Table in the book, the negative signs have already been carried throughout the table so that the columns can just be added. Ultimately, students seem to do better with this format even though the CFFA equation says to subtract the changes in NWC and net capital spending. Change in NWC: We have a net investment in NWC in year 0 of 20,000; we get the investment back at the end of the project when we sell our inventory, collect on our receivables and pay off our payables. Students often forget that we get the investment back at the end. Capital Spending: Remember that Net capital spending = change in net fixed assets + depreciation. So in year one NCS = (60,000 – 90,000) + 30,000 = 0; The same is true for the other years. Lecture Tip: Capital spending at the time of project inception (i.e., the “initial outlay”) includes the following items: + purchase price of the new asset - selling price of the asset replaced (if applicable) + costs of site preparation, setup, and startup +/- increase (decrease) in tax liability due to sale of old asset at other than book value = net capital spending Now that we have the cash flows, we can apply the techniques that we learned in Chapter 9. Enter the cash flows into the calculator and compute NPV and IRR. CF0 = -110,000; C01 = 51,780; F01 = 2; C02 = 71,780; F02 = 1 NPV; I = 20; CPT NPV = 10,648 CPT IRR = 25.8\% Should we accept or reject the project? Making The Decision Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› 9.11 Section 10.3 (C) You can also use the formulas to compute NPV and IRR; just remember that the IRR computation is trial and error. Click on the excel icon to go to an embedded spreadsheet that illustrates how the pro formas and cash flows can be set-up. It also computes the NPV and IRR. Why do we have to consider changes in NWC separately? GAAP requires that sales be recorded on the income statement when made, not when cash is received. GAAP also requires that we record cost of goods sold when the corresponding sales are made, whether we have actually paid our suppliers yet. Finally, we have to buy inventory to support sales, although we haven’t collected cash yet. More on NWC Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› 9.12 Section 10.4 (A) The first two items mean that our operating cash flow does not include the impact of accounts receivable and accounts payable on cash flow. The third item is very much like the purchase of fixed assets. We have to buy the assets (have the cash outflow) before we can generate sales. By looking at changes in NWC, we can incorporate the increased investment in receivables and inventory that are necessary to support additional sales. Because we look at changes in NWC, and not just current assets, we also incorporate the increase in our payable accounts that partially pays for the investment in inventory and receivables. The NWC discussion is very important and should not be overlooked by students. It may be helpful to reemphasize the point of NWC and operating cash flow through accounting entries. The depreciation expense used for capital budgeting should be the depreciation schedule required by the IRS for tax purposes. Depreciation itself is a non-cash expense; consequently, it is only relevant because it affects taxes. Depreciation tax shield = D × T D = depreciation expense T = marginal tax rate Depreciation Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› Section 10.4 (B) Lecture Tip: With the lower tax rate of 21\%, the benefit of the tax-deductibility of depreciation will be reduced. 9.13 Straight-line depreciation D = (Initial cost – salvage) / number of years Very few assets are depreciated straight-line for tax purposes. MACRS Need to know which asset class is appropriate for tax purposes Multiply percentage given in table by the initial cost. Depreciate to zero Mid-year convention Computing Depreciation Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› 9.14 Section 10.4 (B) The MACRS percentages are given in Table 10.7. Lecture Tip: Ask the students why a company might prefer accelerated depreciation for tax purposes to the simpler straight-line depreciation. If the salvage value is different from the book value of the asset, then there is a tax effect. Book value = initial cost – accumulated depreciation After-tax salvage = salvage – T × (salvage – book value) After-tax Salvage Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› Section 10.4 (B) 9.15 You purchase equipment for $100,000, and it costs $10,000 to have it delivered and installed. Based on past information, you believe that you can sell the equipment for $17,000 when you are done with it in 6 years. The company’s marginal tax rate is 21\%. What is the depreciation expense each year and the after-tax salvage in year 6 for each of the following situations? Example: Depreciation and After-tax Salvage Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› Section 10.4 (B) 9.16 Suppose the appropriate depreciation schedule is straight-line. D = (110,000 – 17,000) / 6 = 15,500 every year for 6 years BV in year 6 = 110,000 – 6(15,500) = 17,000 After-tax salvage = 17,000 - .21(17,000 – 17,000) = 17,000 Example: Straight-line Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› Section 10.4 (B) 9.17 Year MACRS percent D 1 .3333 .3333(110,000) = 36,663 2 .4445 .4445(110,000) = 48,895 3 .1481 .1481(110,000) = 16,291 4 .0741 .0741(110,000) = 8,151 Example: Three-year MACRS BV in year 6 = 110,000 – 36,663 – 48,895 – 16,291 – 8,151 = 0 After-tax salvage = 17,000 - .21(17,000 – 0) = $13,430 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› 9.18 Section 10.4 (B) Note that with MACRS you do not subtract the expected salvage from the initial cost. Also note that the MACRS \% is multiplied by the initial cost every year. For some reason, students want to multiply by the book value. Year MACRS Percent D 1 .1429 .1429(110,000) = 15,719 2 .2449 .2449(110,000) = 26,939 3 .1749 .1749(110,000) = 19,239 4 .1249 .1249(110,000) = 13,739 5 .0893 .0893(110,000) = 9,823 6 .0892 .0892(110,000) = 9,812 Example: Seven-Year MACRS BV in year 6 = 110,000 – 15,719 – 26,939 – 19,239 – 13,739 – 9,823 – 9,812 = 14,729 After-tax salvage = 17,000 – .21(17,000 – 14,729) = 16,523.09 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› Section 10.4 (B) 9.19 Original Machine Initial cost = 100,000 Annual depreciation = 9,000 Purchased 5 years ago Book Value = 55,000 Salvage today = 65,000 Salvage in 5 years = 10,000 New Machine Initial cost = 150,000 5-year life Salvage in 5 years = 0 Cost savings = 50,000 per year 3-year MACRS depreciation Required return = 10\% Tax rate = 21\% Example: Replacement Problem Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› Section 10.4 (C) (Note, this problem is an additional one to that included in this section in the textbook. Here we focus specifically on replacement.) 9.20 Remember that we are interested in incremental cash flows. If we buy the new machine, then we will sell the old machine. What are the cash flow consequences of selling the old machine today instead of in 5 years? Replacement Problem – Computing Cash Flows Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› Section 10.4 (C) (Note, this problem is an additional one to that included in this section in the textbook. Here we focus specifically on replacement.) 9.21 Year 1 2 3 4 5 Cost Savings 50,000 50,000 50,000 50,000 50,000 Depr. New 49,995 66,675 22,215 11,115 0 Old 9,000 9,000 9,000 9,000 9,000 Increm. 40,995 57,675 13,215 2,115 (9,000) EBIT 9,005 (7,675) 36,785 47,885 59,000 Taxes 1,891 (1,612) 7,725 10,056 12,390 NI 7,114 (6,063) 29,060 37,829 46,610 Replacement Problem – Pro Forma Income Statements Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› Section 10.4 (C) (Note, this problem is an additional one to that included in this section in the textbook. Here we focus specifically on replacement.) 9.22 Year 0 Cost of new machine = 150,000 (outflow) After-tax salvage on old machine = 65,000 - .21(65,000 – 55,000) = 62,900 (inflow) Incremental net capital spending = 150,000 – 62,900 = 87,100 (outflow) Year 5 After-tax salvage on old machine = 10,000 - .21(10,000 – 10,000) = 10,000 (outflow because we no longer receive this) Replacement Problem – Incremental Net Capital Spending Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› 9.23 Section 10.4 (C) (Note, this problem is an additional one to that included in this section in the textbook. Here we focus specifically on replacement.) The year 5 cash flow is the most difficult for students to grasp. It is important to point out that we are looking for ALL changes in cash flow associated with selling the machine today instead of in 5 years. If we do not sell the machine today, then we will have after-tax salvage of 10,000 in 5 years. Since we do sell the machine today, we LOSE the 10,000 cash flow in 5 years. Year 0 1 2 3 4 5 OCF 48,109 51,612 42,275 39,944 37,610 NCS -87,100 -10,000  In NWC 0 0 CFFA -87,100 48,109 51,612 42,275 39,944 27,610 Replacement Problem – Cash Flow From Assets Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› 9.24 Section 10.4 (C) (Note, this problem is an additional one to that included in this section in the textbook. Here we focus specifically on replacement.) OCF = EBIT – T + Depr For Yr 1: 9,005 – 1,891 + 40,995 = 48,109 The negative signs in the CFFA equation were once again carried through the table. That way outflows are in the table as negative and inflows are positive. Now that we have the cash flows, we can compute the NPV and IRR. Enter the cash flows. Compute NPV = $75,478 Compute IRR = 43.31\% Should the company replace the equipment? Replacement Problem – Analyzing the Cash Flows Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› 9.25 Section 10.4 (C) (Note, this problem is an additional one to that included in this section in the textbook. Here we focus specifically on replacement.) Replace the equipment: NPV>0 and IRR>required return. Bottom-Up Approach OCF = NI + depreciation Works only when there is no interest expense Top-Down Approach OCF = Sales – Costs – Taxes Do not subtract non-cash deductions. Tax Shield Approach OCF = (Sales – Costs)(1 – T) + Depreciation × T Other Methods for Computing OCF Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› Section 10.5 9.26 Your company is considering a new computer system that will initially cost $1 million. It will save $300,000 per year in inventory and receivables management costs. The system is expected to last for five years and will be depreciated using 3-year MACRS. The system is expected to have a salvage value of $50,000 at the end of year 5. There is no impact on net working capital. The marginal tax rate is 21\%. The required return is 8\%. Click on the Excel icon to work through the example. Example: Cost Cutting Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› 9.27 Section 10.6 (A) There are two worksheets. The first allows you to enter the information and work the example during class. The second provides the solutions. You may go directly to this one if you do not wish to show the students how to set up the spreadsheet during class time. The example is an additional one to that provided in the textbook. Burnout Batteries Initial Cost = $36 each 3-year life $100 per year to keep charged Expected salvage = $5 Straight-line depreciation Long-lasting Batteries Initial Cost = $60 each 5-year life $88 per year to keep charged Expected salvage = $5 Straight-line depreciation Example: Equivalent Annual Cost Analysis The machine chosen will be replaced indefinitely and neither machine will have a differential impact on revenue. No change in NWC is required. The required return is 15\%, and the tax rate is 21\%. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› Section 10.6 (C) 9.28 How do we determine if cash flows are relevant to the capital budgeting decision? What are the different methods for computing operating cash flow and when are they important? What is equivalent annual cost and when should it be used? Quick Quiz Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› In an L.A. Law episode, an automobile manufacturer knowingly built cars that had a significant safety flaw. Rather than redesigning the cars (at substantial additional cost), the manufacturer calculated the expected costs of future lawsuits and determined that it would be cheaper to sell an unsafe car and defend itself against lawsuits than to redesign the car. What issues does the financial analysis overlook? Ethics Issues Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› A $1,000,000 investment is depreciated using a seven-year MACRS class life. It requires $150,000 in additional inventory and will increase accounts payable by $50,000. It will generate $400,000 in revenue and $150,000 in cash expenses annually, and the tax rate is 21\%. What is the incremental cash flow in years 0, 1, 7, and 8? Comprehensive Problem Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› 9.31 Annual depreciation expense: Year 1: .1429 × $1million = $142,900 Year 7: .0893 × $1million = $89,300 Year 8: .0446 × $1million = $44,600 Time 0 cash flow = -$1million investment – ($150,000 - $50,000) = -$1,100,000 Time 1 cash flow = ($400,000 - $150,000) × (1 - .21) + (.21 × $89,300) = $227,509 Time 7 cash flow = ($400,000 - $150,000) × (1 - .21) + (.21 × $142,900) = $216,253 Time 8 cash flow = ($400,000 - $150,000) x (1 - .21) + (.21 × $44,600) + $100,000 NWC = $306,866 (assumes zero salvage value) End of Chapter CHAPTER 10 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10-‹#› 10-‹#› Sheet1 Pro Forma Income Statements Year 0 1 2 3 Sales 200000 200000 200000 Variable Costs 125000 125000 125000 Gross Profit 75000 75000 75000 Fixed Costs 17430 17430 17430 Depreciation 30000 30000 30000 EBIT 27570 27570 27570 Taxes 5789.7 5789.7 5789.7 Net Income 21780.3 21780.3 21780.3 Cash Flows Operating Cash Flow 51780.3 51780.3 51780.3 Changes in NWC -20000 20000 Net Capital Spending -90000 Cash Flow From Assets -110000 51780.3 51780.3 71780.3 Net Present Value $10,648.32 IRR 25.76\% Sheet2 Sheet3 Unworked Initial Cost Savings Tax Rate Expected Salvage Discount Rate MACRS Depreciation Schedule Year 1 2 3 4 Book value year 5 Percentage 33.33\% 44.45\% 14.81\% 7.41\% Depreciation Expense Year 1 2 3 4 Operating Cash Flow Net Capital Spending Changes in NWC Cash Flow from Assets Net Present Value Internal Rate of Return Depreciation Expense = initial cost * percentage Operating Cash Flow =(sales - costs)*(1 - tax rate) + depreciation*tax rate note that sales = 0 and a cost savings is -costs After-tax Salvage =salvage - tax rate(salvage - book value) Solutions Initial Cost 1,000,000 Savings 300,000 Tax Rate 21\% Expected Salvage 50,000 Discount Rate 8\% MACRS Depreciation Schedule Year 1 2 3 4 Book Value year 5 Percentage 33.33\% 44.45\% 14.81\% 7.41\% Depreciation Expense 333,300 444,500 148,100 74,100 0 Year 0 1 2 3 4 5 Operating Cash Flow 306,993 330,345 268,101 252,561 237,000 Net Capital Spending -1,000,000 39,500 Changes in NWC 0 0 Cash Flow from Assets -1,000,000 306,993 330,345 268,101 252,561 276,500 Net Present Value $154,118.72 Internal Rate of Return 13.90\% Depreciation Expense = initial cost * percentage Operating Cash Flow =(sales - costs)*(1 - tax rate) + depreciation*tax rate note that sales = 0 and a cost savings is -costs Burnout Burnout Initial Cost 36 Tax Rate 21\% Operating Cost 100 Required Return 15\% Depreciation 10 Expected Salvage 5 After-tax salvage 5 Year 0 1 2 3 OCF -76.83 -76.83 -76.83 NCS -36.00 5.00 NWC 0.00 0.00 CFFA -36.00 -76.83 -76.83 -71.83 NPV -$208.13 EAC -$91.16 Long Lasting Long-lasting Initial Cost 60 Tax Rate 21\% Operating Cost 88 Required Return 15\% Depreciation 11 Expected Salvage 5 After-tax salvage 5 STOCK VALUATION CHAPTER 8 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.1 Explain how stock prices depend on future dividends and dividend growth Show how to value stocks using multiples Lay out the different ways corporate directors are elected to office Define how the stock markets work Key Concepts and Skills Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› Common Stock Valuation Some Features of Common and Preferred Stocks The Stock Markets Chapter Outline Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› If you buy a share of stock, you can receive cash in two ways: The company pays dividends. You sell your shares, either to another investor in the market or back to the company. As with bonds, the price of the stock is the present value of these expected cash flows. Cash Flows for Stockholders Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.4 Section 8.1 (A) As the text points out, a stock that currently pays no dividends may or may not have value; a stock that will NEVER pay a dividend cannot have any value as long as investors are rational. For a stock that currently pays no dividend, market value derives from (a) the hope of future dividends and/or (b) the expectation of a liquidating dividend. Suppose you are thinking of purchasing the stock of Moore Oil, Inc. You expect it to pay a $2 dividend in one year, and you believe that you can sell the stock for $14 at that time. If you require a return of 20\% on investments of this risk, what is the maximum you would be willing to pay? Compute the PV of the expected cash flows. Price = (14 + 2) / (1.2) = $13.33 Or FV = 16; I/Y = 20; N = 1; CPT PV = -13.33 One-Period Example Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.5 Section 8.1 (A) Note, the calculation can also be done as: FV = 14; PMT = 2; I/Y = 20; N = 1; CPT PV = -13.33 Now, what if you decide to hold the stock for two years? In addition to the dividend in one year, you expect a dividend of $2.10 in two years and a stock price of $14.70 at the end of year 2. Now how much would you be willing to pay? PV = 2 / (1.2) + (2.10 + 14.70) / (1.2)2 = 13.33 Two-Period Example Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.6 Section 8.1 (A) If you have taught students how to use uneven cash flow keys, then you can show them how to do this on the calculator. The notation below is for the TI BA-II+. Calculator: CF0 = 0; C01 = 2; F01 = 1; C02 = 16.80; F02 = 1; NPV; I = 20; CPT NPV = 13.33 Finally, what if you decide to hold the stock for three years? In addition to the dividends at the end of years 1 and 2, you expect to receive a dividend of $2.205 at the end of year 3 and the stock price is expected to be $15.435. Now how much would you be willing to pay? PV = 2 / 1.2 + 2.10 / (1.2)2 + (2.205 + 15.435) / (1.2)3 = 13.33 Three-Period Example Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.7 Section 8.1 (A) Calculator: CF0 = 0; C01 = 2; F01 = 1; C02 = 2.10; F02 = 1; C03 = 17.64; F03 = 1; NPV; I = 20; CPT NPV = 13.33 You could continue to push back the year in which you will sell the stock. You would find that the price of the stock is really just the present value of all expected future dividends. So, how can we estimate all future dividend payments? Developing The Model Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.8 Section 8.1 (A) In equilibrium, the required return, R, is the same as the “expected return.” Constant dividend (i.e., zero growth) The firm will pay a constant dividend forever. This is like preferred stock. The price is computed using the perpetuity formula. Constant dividend growth The firm will increase the dividend by a constant percent every period. The price is computed using the growing perpetuity model. Supernormal growth Dividend growth is not consistent initially, but settles down to constant growth eventually. The price is computed using a multistage model. Estimating Dividends: Special Cases Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› Section 8.1 (B) 7.9 If dividends are expected at regular intervals forever, then this is a perpetuity, and the present value of expected future dividends can be found using the perpetuity formula. P0 = D / R Suppose a stock is expected to pay a $0.50 dividend every quarter and the required return is 10\% with quarterly compounding. What is the price? P0 = .50 / (.1 / 4) = $20 Zero Growth Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.10 Section 8.1 (B) Remind the students that if dividends are paid quarterly, then the discount rate must be a quarterly rate. Also, if students have been using a financial calculator for most of their calculations, they often forget to convert the interest rate and they leave it as a percent, i.e., P = .5 / (10/4) = .2. Ask them if this is a reasonable answer – “Would you only be willing to pay $0.20 for an asset that will pay you $0.50 every quarter forever?” Dividends are expected to grow at a constant percent per period. P0 = D1 /(1+R) + D2 /(1+R)2 + D3 /(1+R)3 + … P0 = D0(1+g)/(1+R) + D0(1+g)2/(1+R)2 + D0(1+g)3/(1+R)3 + … With a little algebra and some series work, this reduces to: Dividend Growth Model Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.11 Section 8.1 (B) g is the growth rate in dividends; the subscripts denote the period in which the dividend is paid. This is the formula for a growing perpetuity that was developed in chapter 6. Lecture Tip: The newly instituted tax cuts, all else equal, should increase margins and cash flow. Companies can increase dividends or reinvest more in the firm, which would increase the growth rate. In either case, stock values should increase, which is what has happened to the market – beginning even before the cuts were officially announced. Suppose Big D, Inc., just paid a dividend of $0.50 per share. It is expected to increase its dividend by 2\% per year. If the market requires a return of 15\% on assets of this risk, how much should the stock be selling for? P0 = .50(1+.02) / (.15 - .02) = $3.92 DGM – Example 1 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.12 Section 8.1 (B) The biggest mistake that students make with the DGM is using the wrong dividend. Be sure to emphasize that we are finding a present value, so the dividend needed is the one that will be paid NEXT period, not the one that has already been paid. Suppose TB Pirates, Inc., is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5\% per year and the required return is 20\%, what is the price? P0 = 2 / (.2 - .05) = $13.33 Why isn’t the $2 in the numerator multiplied by (1.05) in this example? DGM – Example 2 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.13 Section 8.1 (B) Does this result look familiar? The examples used to develop the earlier model were based on a 5\% growth rate in dividends. Stock Price Sensitivity to Dividend Growth, g D1 = $2; R = 20\% Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.14 Section 8.1 (B) As the growth rate approaches the required return, the stock price increases dramatically. Price 0.01 0.02 0.03 0.04 0.05 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 10.53 11.11 11.76 12.5 13.33 14.29 15.38 16.670000000000002 18.18 20 22.22 25 28.57 33.33 40 50 66.67 100 200 0.01 0.02 0.03 0.04 0.05 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 0.01 0.02 0.03 0.04 0.05 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 0.01 0.02 0.03 0.04 0.05 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 Growth Rate Stock Price Stock Price Sensitivity to Required Return, R D1 = $2; g = 5\% Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.15 Section 8.1 (B) As the required return approaches the growth rate, the price increases dramatically. This graph is a mirror image of the previous one. Lecture Tip: The newly instituted tax cuts, all else equal, should increase margins and cash flow. Companies can increase dividends or reinvest more in the firm, which would increase the growth rate. In either case, stock values should increase, which is what has happened to the market – beginning even before the cuts were officially announced. Price 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 200 100 66.67 50 40 33.33 28.57 25 22.22 20 18.18 16.670000000000002 15.38 14.29 13.33 12.5 11.76 11.11 10.53 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 Growth Rate Stock Price Gordon Growth Company is expected to pay a dividend of $4 next period, and dividends are expected to grow at 6\% per year. The required return is 16\%. What is the current price? P0 = 4 / (.16 - .06) = $40 Remember that we already have the dividend expected next year, so we don’t multiply the dividend by 1+g. Example 8.3: Gordon Growth Company - I Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.16 Section 8.1 (B) What is the price expected to be in year 4? P4 = D4(1 + g) / (R – g) = D5 / (R – g) P4 = 4(1+.06)4 / (.16 - .06) = 50.50 What is the implied return given the change in price during the four year period? 50.50 = 40(1+return)4; return = 6\% PV = -40; FV = 50.50; N = 4; CPT I/Y = 6\% The price is assumed to grow at the same rate as the dividends. Example 8.3: Gordon Growth Company - II Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.17 Section 8.1 (B) Point out that the formula is completely general. The dividend in the numerator is always for one period later than the price we are computing. This is because we are computing a Present Value, so we have to start with a future cash flow. This is very important when discussing supernormal growth. We know the dividend in one year is expected to be $4 and it will grow at 6\% per year for four more years. So, D5 = 4(1.06)(1.06)(1.06)(1.06) = 4(1.06)4 Lecture Tip: In his book, A Random Walk Down Wall Street, pp. 82 – 89, (1985, W.W. Norton & Company, New York), Burton Malkiel gives four “fundamental” rules of stock prices. Loosely paraphrased, the rules are as follows. Other things equal: -Investors pay a higher price, the larger the dividend growth rate -Investors pay a higher price, the larger the proportion of earnings paid out as dividends -Investors pay a higher price, the less risky the company’s stock -Investors pay a higher price, the lower the level of interest rates Suppose a firm is expected to increase dividends by 20\% in one year and by 15\% in two years. After that, dividends will increase at a rate of 5\% per year indefinitely. If the last dividend was $1 and the required return is 20\%, what is the price of the stock? Remember that we have to find the PV of all expected future dividends. Nonconstant Growth Example - I Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› Section 8.1 (B) 7.18 Compute the dividends until growth levels off. D1 = 1(1.2) = $1.20 D2 = 1.20(1.15) = $1.38 D3 = 1.38(1.05) = $1.449 Find the expected future price. P2 = D3 / (R – g) = 1.449 / (.2 - .05) = 9.66 Find the present value of the expected future cash flows. P0 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)2 = 8.67 Nonconstant Growth Example - II Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.19 Section 8.1 (B) Point out that P2 is the value, at year 2, of all expected dividends year 3 on. The final step is exactly the same as the 2-period example at the beginning of the chapter. We can look at it as if we buy the stock today and receive the $1.20 dividend in 1 year, receive the $1.38 dividend in 2 years and then immediately sell it for $9.66. Calculator: CF0 = 0; C01 = 1.20; F01 = 1; C02 = 11.04; F02 = 1; NPV; I = 20; CPT NPV = 8.67 What is the value of a stock that is expected to pay a constant dividend of $2 per year if the required return is 15\%? What if the company starts increasing dividends by 3\% per year, beginning with the next dividend? The required return stays at 15\%. Quick Quiz – Part I Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.20 Section 8.1 (B) Zero growth: 2 / .15 = 13.33 Constant growth: 2(1.03) / (.15 - .03) = $17.17 Start with the DGM: Using the DGM to Find R Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.21 Section 8.1 (C) Point out that D1 / P0 is the dividend yield and g is the capital gains yield. Suppose a firm’s stock is selling for $10.50. It just paid a $1 dividend, and dividends are expected to grow at 5\% per year. What is the required return? R = [1(1.05)/10.50] + .05 = 15\% What is the dividend yield? 1(1.05) / 10.50 = 10\% What is the capital gains yield? g = 5\% Example: Finding the Required Return Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› Section 8.1 (C) 7.22 Another common valuation approach is to multiply a benchmark PE ratio by earnings per share (EPS) to come up with a stock price. Pt = Benchmark PE ratio × EPSt The benchmark PE ratio is often an industry average or based on a company’s own historical values. The price-sales ratio can also be used. Stock Valuation Using Multiples Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› Section 8.1 (D) The price-sales ratio is often used to value newer companies that do not pay dividends and are not yet profitable (meaning that earnings are negative). 7.23 Suppose a company had earnings per share of $3 over the past year. The industry average PE ratio is 12. Use this information to value this company’s stock price. Pt = 12 × $3 = $36 per share Example: Stock Valuation Using Multiples Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› Section 8.1 (D) 7.24 Table 8.1 – Stock Valuation Summary (1) Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› Section 8.1 7.25 Table 8.1 – Stock Valuation Summary (2) Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› Section 8.1 7.26 Voting Rights Proxy voting Classes of stock Other Rights Share proportionally in declared dividends Share proportionally in remaining assets during liquidation Preemptive right – first shot at new stock issue to maintain proportional ownership if desired Features of Common Stock Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.27 Section 8.2 (A) Shareholders have the right to vote for the board of directors and other important issues. Cumulative voting increases the likelihood of minority shareholders getting a seat on the board. Proxy votes are similar to absentee ballots. Proxy fights occur when minority owners are trying to get enough votes to obtain seats on the Board or affect other important issues that are coming up for a vote. Different classes of stock can have different rights. Owners may want to issue a nonvoting class of stock if they want to make sure that they maintain control of the firm. Lecture Tip: Large institutions, such as mutual funds and pension funds, used to remain on the sidelines when it came to corporate control. However, several institutions have become much more active in recent years and have worked to force companies to operate in the shareholders’ best interests. CalPERS, the pension plan for California public employees, has been at the forefront of the corporate governance movement. For more information, see http://www.calpers-governance.org/principles/home. Dividends are not a liability of the firm until a dividend has been declared by the Board. Consequently, a firm cannot go bankrupt for not declaring dividends. Dividends and Taxes Dividend payments are not considered a business expense; therefore, they are not tax deductible. The taxation of dividends received by individuals depends on the holding period. Dividends received by corporations have a minimum 70\% exclusion from taxable income. Dividend Characteristics Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.28 Slide 8.2 (A) Dividend exclusion: If corporation A owns less than 20\% of corporation B stock, then 30\% of the dividends received from corporation B are taxable. If A owns between 20\% and 80\% of B, then 20\% of the dividends received are taxable. If A owns more than 80\%, a consolidated statement can be filed and dividends received from B are essentially untaxed. Dividends Stated dividend that must be paid before dividends can be paid to common stockholders Dividends are not a liability of the firm, and preferred dividends can be deferred indefinitely. Most preferred dividends are cumulative – any missed preferred dividends have to be paid before common dividends can be paid. Preferred stock generally does not carry voting rights. Features of Preferred Stock Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.29 Section 8.2 (B) Point out that there are a lot of features of preferred stock that are similar to debt. In fact, many new issues have sinking funds that effectively convert what was a perpetual security into an equity security with a definite maturity. However, for tax purposes, preferred stock is equity and dividends are not a tax deductible expense, unless they meet specific characteristics as discussed in the text. Corporations that own stock in other corporations are permitted to exclude 50 percent of the dividend amounts they receive and are taxed on only the remaining 50 percent (the 50 percent exclusion was reduced from 70 percent by the Tax Cuts and Jobs Act of 2017). Real-World Tip: Here’s a gruesome-sounding security – the “death spiral.” Actually, the name refers to convertible preferred shares that have a floating conversion ratio. That is, the conversion ratio varies with the price of the firm’s common stock. Also known as “toxic convertibles,” The Wall Street Journal reports that, when the issuer’s common stock falls, more shares must be issued to redeem the convertible securities, so this dilution pushes the common stock price down further. Hence, the “death spiral” appellation. Dealers vs. Brokers New York Stock Exchange (NYSE) Largest stock market in the world License holders (1,366) Designated market makers (DMMs) Floor brokers Supplemental liquidity providers (SLPs) Operations Floor activity Stock Market Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.30 Section 8.3 (A) and (B) DMMs, formerly known as “specialists,” act as dealers in particular stocks. A DMM maintains an inventory and stands ready to trade at quoted bid (DMM posts the price at which they will buy) and ask (DMM posts the price at which they will sell) prices. They make their profit from the difference between the bid and ask prices, called the bid-ask spread. The smaller the spread, the more competition and the more liquid the stock. The move to decimalization allows for a smaller bid-ask spread. There will be more discussion of this later. Floor broker: a broker matches buyers and sellers. They perform the search function for a fee (commission). They do not hold an inventory of securities. SLPs: investment firms that agree to be active participants in stocks assigned to them. They trade purely for their own accounts. Unlike DMMs and floor brokers, SLPs do not operate on the floor of the stock exchange. Lecture Tip: Some students find it hard to grasp the relative importance of primary and secondary market transactions. Suggest that they consider automobile sales rather than stocks. New automobiles are sold through a network of dealers and salesman (brokers) to the public. In any given year, however, the majority of transactions are between people buying and selling existing automobiles, i.e., the secondary (used) car market. As with secondary market transactions in stocks, used car purchases do not directly benefit the issuer/manufacturer. You can also introduce the notion of information asymmetry and signaling at this point, see the classic article by George Akerlof titled “Market for Lemons.” www: Check out the NYSE by clicking on the embedded link. Students are often amazed at all of the information that is available. Not a physical exchange – computer-based quotation system Multiple market makers Electronic Communications Networks Three levels of information Level 1 – median quotes, registered representatives Level 2 – view quotes, brokers, and dealers Level 3 – view and update quotes, dealers only Large portion of technology stocks NASDAQ Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.31 Section 8.3 (C) Point out that the NASDAQ market site in Times Square is NOT an exchange. It is just offices and basically a place for reporters to report on what is happening with Nasdaq stocks. Electronic Communications Networks provide trading in NASDAQ securities. To see more detail, visit Instinet. Work the Web Example Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› Section 8.3 (C) 7.32 Reading Stock Quotes What information is provided in the stock quote? You can go to Bloomberg for current stock quotes. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.33 Section 8.3 (D) This quote is the Costco quote from the text. 52 week high = 169.59 52 week low = 138.57 Company is Costco Wholesale Annual dividend = $1.80 per share Dividend yield = 1.12\% P/E ratio = 29.31 Most recent price = 160.63 Lecture Tip: A useful assignment is to require students to obtain a recent Wall Street Journal and examine the financial section. Have the students examine the dividend column for various stocks and point out the number of non-dividend paying stocks. Also have them identify the information available in each quote. This allows them to see more information at once than they would normally see with online quotes. You observe a stock price of $18.75. You expect a dividend growth rate of 5\%, and the most recent dividend was $1.50. What is the required return? What are some of the major characteristics of common stock? What are some of the major characteristics of preferred stock? Quick Quiz – Part II Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.34 Section 8.4 r = [1.5(1.05)/18.75] + .05 = 13.4\% The status of pension funding (i.e., over- vs. under-funded) depends heavily on the choice of a discount rate. When actuaries are choosing the appropriate rate, should they give greater priority to future pension recipients, management, or shareholders? How has the increasing availability and use of the internet impacted the ability of stock traders to act unethically? Ethics Issues Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.35 XYZ stock currently sells for $50 per share. The next expected annual dividend is $2, and the growth rate is 6\%. What is the expected rate of return on this stock? If the required rate of return on this stock were 12\%, what would the stock price be, and what would the dividend yield be? Comprehensive Problem Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.36 Section 8.4 Expected return = 2/50 + .06 = .10 Price = 2/ (.12 - .06) = $33.33 Dividend yield = 2 / 33.33 = 6\% End of Chapter Chapter 8 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 8-‹#› g-R D g-R g)1(D P 1 0 0    g P D g P g)1(D R g-R D g - R g)1(D P 0 1 0 0 1 0 0       Introduction to Corporate Finance Chapter 1 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 1-‹#› 1.1 Define the basic types of financial management decisions and the role of the financial manager Explain the goal of financial management Articulate the financial implications of the different forms of business organization Explain the conflicts of interest that can arise between managers and owners Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Key Concepts and Skills 1-‹#› Corporate Finance and the Financial Manager Forms of Business Organization The Goal of Financial Management The Agency Problem and Control of the Corporation Financial Markets and the Corporation Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Chapter Outline 1-‹#› 1.3 Some important questions that are answered using finance: What long-term investments should the firm take on? Where will we get the long-term financing to pay for the investment? How will we manage the everyday financial activities of the firm? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Corporate Finance 1-‹#› 1.4 Section 1.1 (A) Emphasize that “business finance” is just another name for “corporate finance” mentioned under the four basic types. Students often get confused by the terminology, especially when different terms are used to refer to the same thing. Financial managers try to answer some or all of these questions. The top financial manager within a firm is usually the Chief Financial Officer (CFO). Other financial managers include: Treasurer – oversees cash management, credit management, capital expenditures, and financial planning Controller – oversees taxes, cost accounting, financial accounting and data processing Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Financial Manager 1-‹#› 1.5 Section 1.1 (B) Capital budgeting What long-term investments or projects should the business take on? Capital structure How should we pay for our assets? Should we use debt or equity? Working capital management How do we manage the day-to-day finances of the firm? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Financial Management Decisions 1-‹#› 1.6 Provide some examples of capital budgeting decisions: what product or service will the firm sell, should we replace old equipment with newer, more advanced equipment, etc. Be sure to define debt and equity. Provide some examples of working capital management: who should we sell to on credit, how much inventory should we carry, when should we pay our suppliers, etc. Three major forms in the United States (See: Nolo) Sole Proprietorship Partnership General Limited Corporation Limited Liability Company Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Forms of Business Organization 1-‹#› 1.7 Section 1.2 www.nolo.com provides a discussion about which form of business may be appropriate for an entrepreneur. Advantages Easiest to start Least regulated Single owner keeps all the profits Taxed once as personal income Disadvantages Limited to life of owner Equity capital limited to owner’s personal wealth Unlimited liability Difficult to sell ownership interest Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Sole Proprietorship 1-‹#› 1.8 Section 1.2 (A) With the new Tax Cuts and Jobs Act, up to 20 percent of business income may be exempt from taxation. Advantages Two or more owners More capital available Relatively easy to start Income taxed once as personal income Disadvantages Unlimited liability General partnership Limited partnership Partnership dissolves when one partner dies or wishes to sell Difficult to transfer ownership Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Partnership 1-‹#› 1.9 Section 1.2 (B) Note that unlimited liability applies to all partners in a general partnership but only to the general partners in a limited partnership. Written agreements are essential due to the unlimited liability. Limited partners cannot be involved in the business or else they may be deemed as general partners. Like sole proprietorships, with the new Tax Cuts and Jobs Act, up to 20 percent of business income may be exempt from taxation. Advantages Limited liability Unlimited life Separation of ownership and management Transfer of ownership is easy Easier to raise capital Disadvantages Double taxation (income taxed at the corporate rate and then dividends taxed at the personal rate) Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Corporation 1-‹#› 1.10 Section 1.2 (C) Discuss how separation of ownership and management can be both an advantage and a disadvantage: Advantages You can benefit from ownership in several different businesses (diversification) You can take advantage of the expertise of others (comparative advantage) Easier to transfer ownership Disadvantage Agency problems if management goals and owner goals are not aligned A pertinent discussion is the implementation of Sarbanes-Oxley and the effect it has had. Although increased information flow is good for shareholders, it has come at a cost. In fact, some firms have chosen to “go dark,” while others have avoided going public altogether. What should be the goal of a corporation? Maximize profit? Minimize costs? Maximize market share? Maximize the current value of the company’s stock? Does this mean we should do anything and everything to maximize owner wealth? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Goal of Financial Management 1-‹#› 1.11 Section 1.3 Try to have the students discuss each of the goals above and the inherent problems of the first three goals: Maximize profit – Are we talking about long-run or short-run profits? Do we mean accounting profits or some measure of cash flow? Minimize costs – We can minimize costs today by not purchasing new equipment or delaying maintenance, but this may not be in the best interest of the firm or its owners. Maximize market share – This was a strategy of many of the “dot.com” companies. They issued stock and then used it primarily for advertising to increase the number of “hits” to their web sites. Even though many of the companies had a huge market share, they still did not have positive earnings and their owners were not happy. Maximize the current value of the company’s stock There is no short run vs. long run here. The stock price should incorporate expectations about the future of the company and consider the trade-off between short-run profits and long-run profits. The purpose of a for-profit business should be to make money for its owners. Maximizing the current stock price increases the wealth of the owners of the firm. This is analogous to maximizing owners’ equity for firms that do not have publicly traded stock. Non-profits can also follow the same principle, but their “owners” are the constituencies that they were created to help. Also be sure to note that this goal is not specific to corporations, but is generally applied to any form of business, including not-for-profits. Agency relationship Principal hires an agent to represent his/her interests Stockholders (principals) hire managers (agents) to run the company Agency problem Conflict of interest between principal and agent Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. The Agency Problem 1-‹#› 1.12 Section 1.4 A common example of an agency relationship is a real estate broker – in particular if you break it down between a buyer’s agent and a seller’s agent. A classic conflict of interest is when the agent is paid on commission, so they may be less willing to let the buyer know that a lower price might be accepted or they may elect to only show the buyer homes that are listed at the high end of the buyer’s price range. Direct agency costs – the purchase of something by management that can’t be justified from a risk-return standpoint, and monitoring costs. Indirect agency costs – management’s tendency to forgo risky or expensive projects that could be justified from a risk-return standpoint. Managerial compensation Incentives can be used to align management and stockholder interests. The incentives need to be structured carefully to make sure that they achieve their goal. Corporate control The threat of a takeover may result in better management. Other stakeholders Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Managing Managers 1-‹#› 1.13 Section 1.4 Incentives – discuss how incentives must be carefully structured. For example, tying bonuses to profits might encourage management to pursue short-run profits and forego projects that require a large initial outlay. Stock options may work, but there may be an optimal level of insider ownership. Beyond that level, management may be in too much control and may not act in the best interest of all stockholders. The type of stock can also influence the effectiveness of the incentive. A relatively recent issue with the backdating of options also seems to run counter to the purpose of aligning incentives. Corporate control – ask the students why the threat of a takeover might make managers work toward the goals of stockholders. Other groups also have a financial stake in the firm. They can provide a valuable monitoring tool, but they can also try to force the firm to do things that are not in the owners’ best interests. The Internet provides a wealth of information about individual companies. One excellent site is Yahoo! Finance. Go to the site, choose a company and see what information you can find! Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Work the Web Example 1-‹#› Section 1.5 1.14 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Firm Cash Flows 1-‹#› Section 1.5 (A) Discuss the cash flows to and from the firm. The main point is that cash comes into the firm from the sale of debt and equity. The money is used to purchase assets. Those assets generate cash that is used to pay stakeholders, reinvest in additional assets, repay debtholders, and pay dividends to stockholders. 1.15 Cash flows to and from the firm Primary vs. secondary markets Dealer vs. auction markets Listed vs. over-the-counter securities NYSE NASDAQ Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Financial Markets 1-‹#› 1.16 Section 1.5 (B) Students are often confused by the fact that the NASDAQ is an OTC market. Explain that the NASDAQ market site is just a convenient place for reporters to show how stocks are moving, but that trading does not actually take place there. You may wish to note the evolution of these particular markets, e.g., moving to publicly traded firms, emergence of electronic trading, and increased industry consolidation. www: Click on the NYSE and NASDAQ hyperlinks to go to their respective web sites What are the three types of financial management decisions and what questions are they designed to answer? What are the three major forms of business organization? What is the goal of financial management? What are agency problems and why do they exist within a corporation? What is the difference between a primary market and a secondary market? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Quick Quiz 1-‹#› Is it ethical for tobacco companies to sell a product that is known to be addictive and a danger to the health of the user? Is it relevant that the product is legal? Should boards of directors consider only price when faced with a buyout offer? Is it ethical to concentrate only on shareholder wealth, or should stakeholders as a whole be considered? Should firms be penalized for attempting to improve returns by stifling competition (e.g., Microsoft)? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Ethics Issues 1-‹#› 1.18 These Ethics Issues can be addressed throughout the chapter or as a dedicated discussion as given here. The second issue relates to the buyout offer for Gillette that was rejected due to information regarding the launch of the highly successful “Sensor” razor. End of chapter Chapter 1 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 1-‹#› 1-‹#› Financial Statements, Taxes, and Cash Flow Chapter 2 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› 2.1 Describe the difference between accounting value (or “book” value) and market value Describe the difference between accounting income and cash flow Describe the difference between average and marginal tax rates Determine a firm’s cash flow from its financial statements Key Concepts and Skills Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› The Balance Sheet The Income Statement Taxes Cash Flow Chapter Outline Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› The balance sheet is a snapshot of the firm’s assets and liabilities at a given point in time. Assets are listed in order of decreasing liquidity. Ease of conversion to cash Without significant loss of value Balance Sheet Identity Assets = Liabilities + Stockholders’ Equity Balance Sheet Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› 2.4 Section 2.1 Liquidity is a very important concept. Students tend to remember the “convert to cash quickly” component of liquidity, but often forget the part about “without loss of value.” Remind them that we can convert anything to cash quickly if we are willing to lower the price enough, but that doesn’t mean it is liquid. Also, point out that a firm can be TOO liquid. Excess cash holdings lead to overall lower returns. The Balance Sheet Figure 2.1 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› 2.5 Section 2.1 The left-hand side lists the assets of the firm. Current assets are listed first because they are the most liquid. Fixed assets can include both tangible and intangible assets, and they are listed at the bottom because they generally are not very liquid. These are a direct result of management’s investment decisions. (Please emphasize that “investment decisions” are not limited to investments in financial assets.) Note that the balance sheet does not list some very valuable assets, such as the people who work for the firm. The liabilities and equity (or ownership) components of the firm are listed on the right-hand side. This indicates how the assets are paid for. Since the balance sheet has to balance, total equity = total assets - total liabilities. The portion of equity that can most easily fluctuate to create this balance is retained earnings. The right-hand side of the balance sheet is a direct result of management’s financing decisions. Remember that shareholders’ equity consists of several components and that total equity includes all of these components, not just the “common stock” item. In particular, remind students that retained earnings belong to the shareholders. Net Working Capital = Current Assets - Current Liabilities Positive when the cash that will be received over the next 12 months exceeds the cash that will be paid out Usually positive in a healthy firm Liquidity Ability to convert to cash quickly without a significant loss in value Liquid firms are less likely to experience financial distress. But liquid assets typically earn a lower return. Trade-off to find balance between liquid and illiquid assets Net Working Capital and Liquidity Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› 2.6 Section 2.1 (C) After a basic accounting class, students may believe a higher current ratio (or, similarly, more cash on hand) is always better. So, it is good to remind students that a cash balance is a use of funds and has an opportunity cost. U.S. Corporation Balance Sheet Table 2.1 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. To I/S Back to Example 2-‹#› 2.7 Section 2.1 (E) The first example computing cash flows has a link to the information in this table. The arrow in the corner is used to return you to the example. Here is an example of a simplified balance sheet. Many students make it through business school without ever seeing an actual balance sheet, particularly those who are not majoring in finance or accounting. I encourage you to bring in some annual reports and let the students see the differences between the simplified statements they see in textbooks and the real thing. This is a good place to talk about some of the specific types of items that show up on a balance sheet and remind the students what accounts receivable, accounts payable, notes payable, etc. are. The embedded links are used to navigate through a later example. The balance sheet provides the book value of the assets, liabilities, and equity. Market value is the price at which the assets, liabilities, or equity can actually be bought or sold. Market value and book value are often very different. Why? Which is more important to the decision-making process? Market Value vs. Book Value Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› 2.8 Section 2.1 (F) Current assets and liabilities generally have book values and market values that are very close. This is not necessarily the case with the other assets, liabilities, and equity of the firm. Assets are listed at historical costs less accumulated depreciation – this may bear little resemblance to what they could actually be sold for today. The balance sheet also does not include the value of many important assets, such as human capital. Consequently, the “Total Assets” line on the balance sheet is generally not a very good estimate of what the assets of the firm are actually worth. Liabilities are listed at face value. When interest rates change or the risk of the firm changes, the value of those liabilities change in the market as well. This is especially true for longer-term liabilities. Equity is the ownership interest in the firm. The market value of equity (stock price times number of shares) depends on the future growth prospects of the firm and on the market’s estimation of the current value of ALL of the assets of the firm. The best estimate of the market value of the firm’s assets is market value of liabilities + market value of equity. Market values are generally more important for the decision making process because they are more reflective of the cash flows that would occur today. Example 2.2 Klingon Corporation Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› 2.9 Section 2.1 (F) Shareholders are the ones that benefit from increases in the market value of a firm’s assets. They are also the ones that bear the losses of a decrease in market value. Consequently, managers need to consider the impact of their decisions on the market value of assets, not on their book value. Here is a good illustration: Suppose that the MV of assets declined to $700 and the market value of long-term debt remained unchanged. What would happen to the market value of equity? It would decrease to 700 - 500 = 200. The market-to-book ratio, which compares the market value of equity to the book value of equity, is often used by analysts as a measure of valuation for a stock. It is generally a bad sign if a company’s market-to-book ratio approaches 1.00 (meaning market value = book value) because of the GAAP employed in creating a balance sheet. It is definitely a bad sign if the ratio is less than 1.00. GAAP does provide for some assets to be marked-to-market, primarily those assets for which current market values are readily available due to trading in liquid markets. However, it does not generally apply to long-term assets, where market values and book values are likely to differ the most. The income statement is more like a video of the firm’s operations for a specified period of time. You generally report revenues first and then deduct any expenses for the period. Matching principle – GAAP says to show revenue when it accrues and match the expenses required to generate the revenue Income Statement Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› 2.10 Section 2.2 Matching principle – this principle leads to non-cash deductions like depreciation. This is why net income is NOT a measure of the cash flow during the period. Consider discussing that the top half of the income statement addresses investment decisions, whereas the bottom half deals with financing. U.S. Corporation Income Statement – Table 2.2 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. To B/S Back to Example 2-‹#› 2.11 Section 2.2 The first example computing cash flows has a link to the information in this table. The arrow in the corner is used to return you to the example. Remember that these are simplified income statements for illustrative purposes. Earnings before interest and taxes is often called operating income. COGS would include both the fixed costs and the variable costs needed to generate the revenues. Analysts often look at EBITDA (earnings before interest, taxes, depreciation, and amortization) as a measure of the operating cash flow of the firm. It is not true in the strictest sense because taxes are an operating cash flow as well, but it does provide a reasonable estimate for analysis purposes. It is important to point out that depreciation expense is often figured two different ways, depending on the purpose of the financial statements. If we are computing the taxes that we will owe, we use the depreciation schedule provided by the IRS. In this instance, the “life” of the asset for depreciation purposes may be very different from the useful life of the asset. Statements that are prepared for investors often use straight-line depreciation because it will tend to have a lower depreciation charge than MACRS early in the asset’s life. This reduces the “expense,” and thus increases the firm’s reported EPS. This is a good illustration of why it is important to look at a firm’s cash flow and not just its EPS. The embedded links are used to navigate through a later example. Publicly traded companies must file regular reports with the Securities and Exchange Commission. These reports are usually filed electronically and can be searched at the SEC public site called EDGAR. Visit EDGAR to search for company filings. Work the Web Example Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› Section 2.2 2.12 The one thing we can rely on with taxes is that they are always changing. In fact, the Tax Cuts and Jobs Act of 2017 will drop the corporate tax rate to a flat 21 percent beginning in 2018. Marginal vs. average tax rates Marginal tax rate – the percentage paid on the next dollar earned Average tax rate – the tax bill / taxable income Average tax rates vary widely across different companies and industries Check out the IRS website for up-to-date information. Taxes Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› 2.13 Section 2.3 Point out that taxes can be a very important component of the decision making process, but what students learn about tax specifics now could change tomorrow. Consequently, it is important to keep up with the changing tax laws and to utilize specialists in the tax area when making decisions where taxes are involved. Click on the embedded link to go to the IRS web site for the most up-to-date tax information. It is important to point out that we are concerned with the taxes that we will pay if a decision is made. Consequently, the marginal tax rate is what we should use in our analysis. Students can view the average tax rates for various industries in Table 2.5. Point out that the tax rates discussed in the book are just federal taxes. Many states and cities have income taxes as well, and those taxes should figure into any analysis that we conduct. The new Tax Cuts and Jobs Act reduces the U.S. corporate tax rate from among the highest in the developed world, to a “middle of the road” rate. Suppose your firm earns $4 million in taxable income. What is the firm’s tax liability? What is the average tax rate? What is the marginal tax rate? If you are considering a project that will increase the firm’s taxable income by $1 million, what tax rate should you use in your analysis? Example: Marginal vs. Average Rates Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› 2.14 Section 2.3 (B) Tax liability: Using 2017 rates: .15(50,000) + .25(75,000 - 50,000) + .34(100,000 - 75,000) + .39(335,000 - 100,000) + .34(4,000,000 - 335,000) = $1,360,000 Average rate: 1,360,000 / 4,000,000 = .34 or 34\% Marginal rate comes from the table and it is 34\% also, but they are not always the same. Using 2018 rates: .21*4,000,000 = $840,000 (notice the large drop vs. 2017!) Average = marginal = flat = .21 or 21\% In either case, the marginal rate is appropriate for analysis of a proposed project. Cash flow is one of the most important pieces of information that a financial manager can derive from financial statements. The statement of cash flows does not provide us with the same information that we are looking at here. We will look at how cash is generated from utilizing assets and how it is paid to those that finance the purchase of the assets. The Concept of Cash Flow Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› Section 2.4 2.15 Cash Flow From Assets (CFFA) = Cash Flow to Creditors + Cash Flow to Stockholders Cash Flow From Assets = Operating Cash Flow - Net Capital Spending - Changes in NWC Cash Flow From Assets Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› 2.16 Section 2.4 (A) The first equation is how the cash flow from the firm is divided among the investors who financed the assets. The second equation is the cash flow that the firm receives from its assets. This is an important equation to remember. We will come back to it and use it again when we do our capital budgeting analysis. We want to base our decisions on the timing and risk of the cash flows we expect to receive from a project. OCF (I/S) = EBIT + depreciation - taxes = $628 NCS (B/S and I/S) = ending net fixed assets - beginning net fixed assets + depreciation = $130 Changes in NWC (B/S) = ending NWC - beginning NWC = $391 CFFA = 628 - 130 - 391 = $107 Example: U.S. Corporation – Part I Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› 2.17 Section 2.4 (A) Use the information from the balance sheet and income statement presented previously to work through this example. There is a hyperlink on “I/S” that will take you to that slide. Another one exists on “B/S.” There are links on each statement to bring you back here. OCF = 694 + 65 - 131 = 628 NCS = 1709 - 1644 + 65 = 130 Students often have a difficult time understanding why a cash outflow has a positive sign and a cash inflow has a negative sign. Emphasize that we are talking about spending in the net capital spending formula and investment in NWC. The formula for CFFA takes care of reducing cash flow when NCS is positive and increasing CF when it is negative. Ending NWC = 1464 - 389 = 1075 Beginning NWC = 1112 - 428 = 684 Changes in NWC = 1075 - 684 = 391 CF to Creditors (B/S and I/S) = interest paid - net new borrowing = $24 CF to Stockholders (B/S and I/S) = dividends paid - net new equity raised = $83 CFFA = 24 + 83 = $107 Example: U.S. Corporation – Part II Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› 2.18 Section 2.4 (A) Use the information from the balance sheet and income statement presented previously to work through this example. There is a hyperlink on “I/S” that will take you to that slide. Another one exists on “B/S.” There are links on each statement to bring you back here. Net New Borrowing = ending LT debt - beginning LT debt = 454 - 408 = 46 CF to creditors = 70 - 46 = 24 Net New Equity = 640 - 600 = 40 (Be sure to point out that we want equity raised in the capital markets, not retained earnings). CF to Stockholders = 123 - 40 = 83 Cash Flow Summary - Table 2.6 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› 2.19 Section 2.4 (C) This provides a summary for the various cash flow calculations. It is a good place to refer back when working on cash flows in the capital budgeting section. Current Accounts 2018: CA = 3,625; CL = 1,787 2017: CA = 3,596; CL = 2,140 Fixed Assets and Depreciation 2018: NFA = 2,194; 2014: NFA = 2,261 Depreciation Expense = 500 Long-term Debt and Equity 2018: LTD = 538; Common stock & APIC = 462 2017: LTD = 581; Common stock & APIC = 372 Income Statement EBIT = 1,014; Taxes = 193 Interest Expense = 93; Dividends = 460 Example: Balance Sheet and Income Statement Info Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› 2.20 Section 2.5 OCF = 1,014 + 500 - 193 = 1,321 NCS = 2,194 - 2,261 + 500 = 433 Changes in NWC = (3,625 - 1,787) - (3,596 - 2,140) = 382 CFFA = 1,321 - 433 - 382 = 506 CF to Creditors = 93 - (538 - 581) = 136 CF to Stockholders = 460 - (462 - 372) = 370 CFFA = 136 + 370 = 506 The CF identity holds. Example: Cash Flows Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› 2.21 Section 2.5 What is the difference between book value and market value? Which should we use for decision-making purposes? What is the difference between accounting income and cash flow? Which do we need to use when making decisions? What is the difference between average and marginal tax rates? Which should we use when making financial decisions? How do we determine a firm’s cash flows? What are the equations, and where do we find the information? Quick Quiz Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› Section 2.5 2.22 Why is manipulation of financial statements not only unethical and illegal, but also bad for stockholders? Ethics Issues Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› 2.23 Current Accounts 2018: CA = 4,400; CL = 1,500 2017: CA = 3,500; CL = 1,200 Fixed Assets and Depreciation 2018: NFA = 3,400; 2014: NFA = 3,100 Depreciation Expense = 400 Long-term Debt and Equity (R.E. not given) 2018: LTD = 4,000; Common stock & APIC = 400 2017: LTD = 3,950; Common stock & APIC = 400 Income Statement EBIT = 2,000; Taxes = 300 Interest Expense = 350; Dividends = 500 Compute the CFFA Comprehensive Problem Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› 2.24 OCF = $2,000 + $400 - $300 = $2,100 NCS = $ 3,400 - $3,100 + $400 = $700 Changes in NWC = ($4,400 - $1,500) - ($3,500 - $1,200) = $600 CFFA = $2,100 - $700 - $600 = $800 CF to Creditors = $350 - ($4,000 - $3,950) = $300 CF to Stockholders = $500 CFFA = $300 + $500 = $800 END OF CHAPTER CHAPTER 2 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2-‹#› 2-‹#› 2.25 CHAPTER 7 INTEREST RATES AND BOND VALUATION Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.1 Define important bond features and types of bond Explain bond values and yields and why they fluctuate Describe bond ratings and what they mean Outline the impact of inflation on interest rates Illustrate the term structure of interest rates and the determinants of bond yields Key Concepts and Skills Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.2 Remember, as with any asset, the value of a bond is simply the present value of its future cash flows. Bonds and Bond Valuation More about Bond Features Bond Ratings Some Different Types of Bonds Bond Markets Inflation and Interest Rates Determinants of Bond Yields Chapter Outline Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› Par value (face value) = principal amount, repaid at maturity Coupon = stated interest payment Coupon rate = annual coupon divided by face value Maturity date Yield or Yield to maturity = rate of return required in the market for the bond Bond Definitions Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.4 Section 7.1 (A) Although the coupon is typically paid in cash, examples exist of firms paying investors with product. Yield to maturity, required return, and market rate are used interchangeably. Bond Value = PV of coupons + PV of par Bond Value = PV of annuity + PV of lump sum As interest rates increase, present values decrease. So, as interest rates increase, bond prices decrease and vice versa. Present Value of Cash Flows as Rates Change Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› Section 7.1 (B) 6.5 Consider a bond with a coupon rate of 10\% and annual coupons. The par value is $1,000, and the bond has 5 years to maturity. The yield to maturity is 11\%. What is the value of the bond? Using the formula: B = PV of annuity + PV of lump sum B = 100[1 – 1/(1.11)5] / .11 + 1,000 / (1.11)5 B = 369.59 + 593.45 = 963.04 Using the calculator: N = 5; I/Y = 11; PMT = 100; FV = 1,000 CPT PV = -963.04 Valuing a Discount Bond with Annual Coupons Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.6 Section 7.1 (B) Remember the sign convention on the calculator. The easy way to remember it with bonds is we pay the PV (-) so that we can receive the PMT (+) and the FV(+). Slide 7.9 discusses why this bond sells at less than par Lecture Tip: You may wish to stress the issue that the coupon rate and the face value are fixed by the bond indenture when the bond is issued (except for floating-rate bonds). Therefore, the expected cash flows don’t change during the life of the bond. However, the bond price will change as interest rates change and as the bond approaches maturity. Lecture Tip: You may wish to further explore the loss in value of $115 in the example in the book. You should remind the class that when the 8\% bond was issued, bonds of similar risk and maturity were yielding 8\%. The coupon rate was set so that the bond would sell at par value; therefore, the coupons were set at $80 per year. One year later, the ten-year bond has nine years remaining to maturity. However, bonds of similar risk and nine years to maturity are being issued to yield 10\%, so they have coupons of $100 per year. The bond we are looking at only pays $80 per year. Consequently, the old bond will sell for less than $1,000. The mathematical reason for that is discussed in the text. However, many students can intuitively grasp that you wouldn’t be willing to pay as much for a bond that only pays $80 per year for 9 years as you would for a bond that pays $100 per year for 9 years. Suppose you are reviewing a bond that has a 10\% annual coupon and a face value of $1000. There are 20 years to maturity, and the yield to maturity is 8\%. What is the price of this bond? Using the formula: B = PV of annuity + PV of lump sum B = 100[1 – 1/(1.08)20] / .08 + 1000 / (1.08)20 B = 981.81 + 214.55 = 1196.36 Using the calculator: N = 20; I/Y = 8; PMT = 100; FV = 1000 CPT PV = -1,196.36 Valuing a Premium Bond with Annual Coupons Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› Section 7.1 (B) 6.7 Graphical Relationship Between Price and Yield-to-maturity (YTM) Yield-to-maturity (YTM) Bond characteristics: 10 year maturity, 8\% coupon rate, $1,000 par value Yield-to-Maturity (YTM) Bond Price, in dollars Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.8 Section 7.1 (B) Bond characteristics: Coupon rate = 8\% with annual coupons; Par value = $1,000; Maturity = 10 years Bond Value 0.03 0.04 0.05 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 1426.51 1324.44 1231.6500000000001 1147.2 1070.24 1000 935.82 877.11 823.32 773.99 0.03 0.04 0.05 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.03 0.04 0.05 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.03 0.04 0.05 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 If YTM = coupon rate, then par value = bond price If YTM > coupon rate, then par value > bond price Why? The discount provides yield above coupon rate. Price below par value, called a discount bond If YTM < coupon rate, then par value < bond price Why? Higher coupon rate causes value above par. Price above par value, called a premium bond Bond Prices: Relationship Between Coupon and Yield Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.9 Section 7.1 (B) There are the purely mechanical reasons for these results. We know that present values decrease as rates increase. Therefore, if we increase our yield above the coupon, the present value (price) must decrease below par. On the other hand, if we decrease our yield below the coupon, the present value (price) must increase above par. There are also more intuitive ways to explain this relationship. Explain that the yield to maturity is the interest rate on newly issued debt of the same risk and that debt would be issued so that the coupon = yield. Then, suppose that the coupon rate is 8\% and the yield is 9\%. Ask the students which bond they would be willing to pay more for. Most will say that they would pay more for the new bond. Since it is priced to sell at $1,000, the 8\% bond must sell for less than $1,000. The same logic works if the new bond has a yield and coupon less than 8\%. Another way to look at it is that return = “dividend yield” + capital gains yield. The “dividend yield” in this case is just the coupon rate. The capital gains yield has to make up the difference to reach the yield to maturity. Therefore, if the coupon rate is 8\% and the YTM is 9\%, the capital gains yield must equal approximately 1\%. The only way to have a capital gains yield of 1\% is if the bond is selling for less than par value. (If price = par, there is no capital gain.) Technically, it is the current yield, not the coupon rate + capital gains yield, but from an intuitive standpoint, this helps some students remember the relationship and current yields and coupon rates are normally reasonably close. The Bond Pricing Equation Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.10 Section 7.1 (B) This formalizes the calculations we have been doing. If an ordinary bond has a coupon rate of 14 percent, then the owner will get a total of $140 per year, but this $140 will come in two payments of $70 each. The yield to maturity is quoted at 16 percent. The bond matures in seven years. Note: Bond yields are quoted like APRs; the quoted rate is equal to the actual rate per period multiplied by the number of periods. Example 7.1 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› Section 7.1 (B) 6.11 How many coupon payments are there? What is the semiannual coupon payment? What is the semiannual yield? What is the bond price? B = 70[1 – 1/(1.08)14] / .08 + 1,000 / (1.08)14 = 917.56 Or PMT = 70; N = 14; I/Y = 8; FV = 1,000; CPT PV = -917.56 Example 7.1 (ctd.) Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.12 Section 7.1 (B) The students can read the example in the book. The basic information is as follows: Coupon rate = 14\%, semiannual coupons YTM = 16\% Maturity = 7 years Par value = $1,000 Price Risk Change in price due to changes in interest rates Long-term bonds have more price risk than short-term bonds. Low coupon rate bonds have more price risk than high coupon rate bonds. Reinvestment Rate Risk Uncertainty concerning rates at which cash flows can be reinvested Short-term bonds have more reinvestment rate risk than long-term bonds. High coupon rate bonds have more reinvestment rate risk than low coupon rate bonds. Interest Rate Risk Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.13 Section 7.1 (C) Real-World Tip: Upon learning the concept of interest rate risk, students sometimes conclude that bonds with low interest-rate risk (i.e. high coupon bonds) are necessarily “safer” than otherwise identical bonds with lower coupons. In reality, the contrary may be true: increasing interest rate volatility over the last two decades has greatly increased the importance of interest rate risk in bond valuation. The days when bonds represented a “widows and orphans” investment are long gone. You may wish to point out that one potentially undesirable feature of high-coupon bonds is the required reinvestment of coupons at the computed yield-to-maturity if one is to actually earn that yield. Those who purchased bonds in the early 1980s (when even high-grade corporate bonds had coupons over 11\%) found, to their dismay, that interest payments could not be reinvested at similar rates a few years later without taking greater risk. A good example of the trade-off between interest rate risk and reinvestment risk is the purchase of a zero-coupon bond – one eliminates reinvestment risk but maximizes interest-rate risk. Figure 7.2 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.14 Section 7.1 (C) Yield to Maturity (YTM) is the rate implied by the current bond price. Finding the YTM requires trial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity. If you have a financial calculator, enter N, PV, PMT, and FV, remembering the sign convention (PMT and FV need to have the same sign, PV the opposite sign.) Computing Yield to Maturity Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› Section 7.1 (D) 6.15 Consider a bond with a 10\% annual coupon rate, 15 years to maturity, and a par value of $1,000. The current price is $928.09. Will the yield be more or less than 10\%? N = 15; PV = -928.09; FV = 1,000; PMT = 100; CPT I/Y = 11\% YTM with Annual Coupons Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.16 Section 7.1 (D) The students should be able to recognize that the YTM is more than the coupon since the price is less than par. Suppose a bond with a 10\% coupon rate and semiannual coupons, has a face value of $1,000, 20 years to maturity and is selling for $1,197.93. Is the YTM more or less than 10\%? What is the semiannual coupon payment? How many periods are there? N = 40; PV = -1,197.93; PMT = 50; FV = 1,000; CPT I/Y = 4\% (Is this the YTM?) YTM = 4\% × 2 = 8\% YTM with Semiannual Coupons Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› Section 7.1 (D) The 4\% value is the 6-month interest rate. YTM is an annual rate. 6.17 Table 7.1 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› Section 7.1 (D) 6.18 Current Yield = annual coupon / price Yield to maturity = current yield + capital gains yield Example: 10\% coupon bond, with semiannual coupons, face value of 1,000, 20 years to maturity, $1,197.93 price Current yield = 100 / 1,197.93 = .0835 = 8.35\% Price in one year, assuming no change in YTM = 1,193.68 Capital gain yield = (1,193.68 – 1,197.93) / 1,197.93 = -.0035 = -.35\% YTM = 8.35 - .35 = 8\%, which is the same YTM computed earlier Current Yield vs. Yield to Maturity Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.19 Section 7.1 (D) This is the same information as the YTM calculation on slide 7.17. The YTM computed on that slide was 8\% Lecture Tip: You may wish to discuss the components of required returns for bonds in a fashion analogous to the stock return discussion in the next chapter. As with common stocks, the required return on a bond can be decomposed into current income and capital gains components. The yield-to-maturity (YTM) equals the current yield plus the capital gains yield. Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate. If you know the price of one bond, you can estimate its YTM and use that to find the price of the second bond. This is a useful concept that can be transferred to valuing assets other than bonds. Bond Pricing Theorems Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› Section 7.1 (D) 6.20 There is a specific formula for finding bond prices on a spreadsheet. PRICE(Settlement,Maturity,Rate,Yld,Redemption, Frequency,Basis) YIELD(Settlement,Maturity,Rate,Pr,Redemption, Frequency,Basis) Settlement and maturity need to be actual dates. The redemption and Pr need to be input as \% of par value. Click on the Excel icon for an example. Bond Prices with a Spreadsheet Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.21 Section 7.1 (D) Please note that you must have the analysis tool pack add-ins installed to access the PRICE and YIELD functions. If you do not have these installed on your computer, you can use the PV and the RATE functions to compute price and yield as well. Click on the TVM tab to find these calculations. Debt Not an ownership interest Creditors do not have voting rights Interest is considered a cost of doing business and is tax deductible Creditors have legal recourse if interest or principal payments are missed Excess debt can lead to financial distress and bankruptcy Equity Ownership interest Common stockholders vote for the board of directors and other issues Dividends are not considered a cost of doing business and are not tax deductible Dividends are not a liability of the firm, and stockholders have no legal recourse if dividends are not paid An all equity firm can not go bankrupt merely due to debt since it has no debt Differences Between Debt and Equity Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.22 Section 7.2 Contract between the company and the bondholders that includes: The basic terms of the bonds The total amount of bonds issued A description of property used as security, if applicable Sinking fund provisions Call provisions Details of protective covenants The Bond Indenture Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› Section 7.2 (C) 6.23 Registered vs. Bearer Forms Security Collateral – secured by financial securities Mortgage – secured by real property, normally land or buildings Debentures – unsecured Notes – unsecured debt with original maturity less than 10 years Seniority Bond Classifications Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.24 Section 7.2 (C) This is standard terminology in the US – but it may not transfer to other countries. For example, debentures are secured debt in the United Kingdom. Lecture Tip: Domestically issued bearer bonds will become obsolete in the near future. Since bearer bonds are not registered with the corporation, it is easier for bondholders to receive interest payments without reporting them on their income tax returns. In an attempt to eliminate this potential for tax evasion, all bonds issued in the US after July 1983 must be in registered form. It is still legal to offer bearer bonds in some other nations, however. Some foreign bonds are popular among international investors particularly due to their bearer status. Lecture Tip: Although the majority of corporate bonds have a $1,000 face value, there are an increasing number of “baby bonds” outstanding, i.e., bonds with face values less than $1,000. The use of the term “baby bond” goes back at least as far as 1970, when it was used in connection with AT&T’s announcement of the intent to issue bonds with low face values. It was also used in describing Merrill Lynch’s 1983 program to issue bonds with $25 face values. More recently, the term has come to mean bonds issued in lieu of interest payments by firms unable to make the payments in cash. Baby bonds issued under these circumstances are also called “PIK” (payment-in-kind) bonds, or “bunny” bonds, because they tend to proliferate in LBO circumstances. The coupon rate depends on the risk characteristics of the bond when issued. Which bonds will have the higher coupon, all else equal? Secured debt versus a debenture Subordinated debenture versus senior debt A bond with a sinking fund versus one without A callable bond versus a non-callable bond Bond Characteristics and Required Returns Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.25 Section 7.2 (C) Debenture: secured debt is less risky because the income from the security is used to pay it off first Subordinated debenture: will be paid after the senior debt Bond without sinking fund: company has to come up with substantial cash at maturity to retire debt, and this is riskier than systematic retirement of debt through time Callable – bondholders bear the risk of the bond being called early, usually when rates are lower. They don’t receive all of the expected coupons and they have to reinvest at lower rates. High Grade Moody’s Aaa and S&P AAA – capacity to pay is extremely strong Moody’s Aa and S&P AA – capacity to pay is very strong Medium Grade Moody’s A and S&P A – capacity to pay is strong, but more susceptible to changes in circumstances Moody’s Baa and S&P BBB – capacity to pay is adequate, adverse conditions will have more impact on the firm’s ability to pay Bond Ratings – Investment Quality Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.26 Section 7.3 Lecture Tip: The question sometimes arises as to why a potential issuer would be willing to pay rating agencies tens of thousands of dollars in order to receive a rating, especially given the possibility that the resulting rating could be less favorable than expected. This is a good place to remind students about the pervasive nature of agency costs and point out a real-world example of their effects on firm value. You may also wish to use this issue to discuss some of the consequences of information asymmetries in financial markets. Low Grade Moody’s Ba and B S&P BB and B Considered possible that the capacity to pay will degenerate. Very Low Grade Moody’s C (and below) and S&P C (and below) income bonds with no interest being paid, or in default with principal and interest in arrears Bond Ratings – Speculative Grade Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.27 Section 7.3 It is a good exercise to ask students which bonds will have the highest yield to maturity (lowest price) all else equal. Treasury Securities Federal government debt T-bills – pure discount bonds with original maturity of one year or less T-notes – coupon debt with original maturity between one and ten years T-bonds – coupon debt with original maturity greater than ten years Municipal Securities Debt of state and local governments Varying degrees of default risk, rated similar to corporate debt Interest received is tax-exempt at the federal level. Government Bonds Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› Section 7.4 (A) 6.28 A taxable bond has a yield of 8\%, and a municipal bond has a yield of 6\%. If you are in a 30\% tax bracket, which bond do you prefer? 8\%(1 - .3) = 5.6\% The after-tax return on the corporate bond is 5.6\%, compared to a 6\% return on the municipal At what tax rate would you be indifferent between the two bonds? 8\%(1 – T) = 6\% T = 25\% Example 7.4 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.29 Section 7.4 (A) You should be willing to accept a lower stated yield on municipals because you do not have to pay taxes on the interest received. You will want to make sure the students understand why you are willing to accept a lower rate of interest. It may be helpful to take the example and illustrate the indifference point using dollars instead of just percentages. The discount you are willing to accept depends on your tax bracket. However, The new tax cuts will make municipal bonds relatively less attractive, potentially reducing values across this asset class. Consider a taxable bond with a yield of 8\% and a tax-exempt municipal bond with a yield of 6\%. Suppose you own one $1,000 bond in each and both bonds are selling at par. You receive $80 per year from the corporate and $60 per year from the municipal. How much do you have after taxes if you are in the 30\% tax bracket? Corporate: 80 – 80(.3) = 56; Municipal = 60 Why should the federal government exempt munis from taxation? It provides an incentive for local governments to raise capital on their own. Make no periodic interest payments (coupon rate = 0\%) The entire yield-to-maturity comes from the difference between the purchase price and the par value. Cannot sell for more than par value Sometimes called zeroes, deep discount bonds, or original issue discount bonds (OIDs) Treasury Bills and principal-only Treasury strips are good examples of zeroes. Zero Coupon Bonds Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.30 Section 7.4 (B) Most students are familiar with Series EE savings bonds. Point out that these are actually zero coupon bonds. The investor pays one-half of the face value and must hold the bond for a given number of years before the face value is realized. As with any other zero-coupon bond, reinvestment risk is eliminated, but an additional benefit of EE bonds is that, unlike corporate zeroes, the investor need not pay taxes on the accrued interest until the bond is redeemed. Further, it should be noted that interest on these bonds is exempt from state income taxes. And, savings bonds yields are indexed to Treasury rates. Coupon rate floats depending on some index value Examples – adjustable rate mortgages and inflation-linked Treasuries There is less price risk with floating rate bonds. The coupon floats, so it is less likely to differ substantially from the yield-to-maturity. Coupons may have a “collar” – the rate cannot go above a specified “ceiling” or below a specified “floor”. Floating-Rate Bonds Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.31 Section 7.4 (C) Lecture Tip: Imagine this scenario: General Motors receives cash from a lender in return for the promise to make periodic interest payments that “float” with the general level of market rates. Sounds like a floating-rate bond, doesn’t it? Well, it is, except that if you replace “General Motors” with “Joe Smith,” you have just described an adjustable-rate mortgage. Whereas there is less price risk, there is greater reinvestment (or refinancing) risk. Catastrophe bonds Income bonds Convertible bonds Put bonds There are many other types of provisions that can be added to a bond and many bonds have several provisions – it is important to recognize how these provisions affect required returns Other Bond Types Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.32 Section 7.4 (D) It is a useful exercise to ask the students if these bonds will tend to have higher or lower required returns compared to bonds without these specific provisions. Catastrophe bonds – issued by property and casualty companies. Pay interest and principal as usual unless claims reach a certain threshold for a single disaster. At that point, bondholders may lose all remaining payments. Higher required return Income bonds – coupon payments depend on level of corporate income. If earnings are not enough to cover the interest payment, it is not owed. Higher required return Convertible bonds – bonds can be converted into shares of common stock at the bondholders discretion. Lower required return Put bond – bondholder can force the company to buy the bond back prior to maturity. Lower required return Sukuk are bonds that have been created to meet a demand for assets that comply with Shariah, or Islamic law. Shariah does not permit the charging or paying of interest. Sukuk are typically bought and held to maturity, and they are extremely illiquid. Sukuk Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› Section 7.4 (E) 6.33 Primarily over-the-counter transactions with dealers connected electronically Extremely large number of bond issues, but generally low daily volume in single issues Makes getting up-to-date prices difficult, particularly on small company or municipal issues Treasury securities are an exception. Bond Markets Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7-‹#› 6.34 Section 7.5 … RETURN, RISK, AND THE SECURITY MARKET LINE CHAPTER 13 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 1-‹#› Show how to calculate expected returns, variance, and standard deviation Discuss the impact of diversification Summarize the systematic risk principle Describe the security market line and the risk-return trade-off Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Key Concepts and Skills 1-‹#› Expected Returns and Variances Portfolios Announcements, Surprises, and Expected Returns Risk: Systematic and Unsystematic Diversification and Portfolio Risk Systematic Risk and Beta The Security Market Line The SML and the Cost of Capital: A Preview Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Chapter Outline 1-‹#› 11.3 Lecture Tip: You may find it useful to emphasize the economic foundations of the material in this chapter. Specifically, we assume: -Investor rationality: Investors are assumed to prefer more money to less and less risk to more, all else equal. The result of this assumption is that the ex ante risk-return trade-off will be upward sloping. -As risk-averse return-seekers, investors will take actions consistent with the rationality assumptions. They will require higher returns to invest in riskier assets and are willing to accept lower returns on less risky assets. -Similarly, they will seek to reduce risk while attaining the desired level of return, or increase return without exceeding the maximum acceptable level of risk. Expected returns are based on the probabilities of possible outcomes. In this context, “expected” means average if the process is repeated many times. The “expected” return does not even have to be a possible return. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Expected Returns 1-‹#› 11.4 Section 13.1 (A) Use the following example to illustrate the mathematical nature of expected returns: Consider a game where you toss a fair coin: If it is Heads, then student A pays student B $1. If it is Tails, then student B pays student A $1. Most students will remember from their statistics that the expected value is $0 (=.5(1) + .5(-1)). That means that if the game is played over and over then each student should expect to break-even. However, if the game is only played once, then one student will win $1 and one will lose $1. Suppose you have predicted the following returns for stocks C and T in three possible states of the economy. What are the expected returns? State Probability C T___ Boom 0.3 0.15 0.25 Normal 0.5 0.10 0.20 Recession ??? 0.02 0.01 RC = .3(15) + .5(10) + .2(2) = 9.9\% RT = .3(25) + .5(20) + .2(1) = 17.7\% Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example: Expected Returns 1-‹#› 11.5 Section 13.1 (A) What is the probability of a recession? 1- 0.3 - 0.5 = 0.2 If the risk-free rate is 4.15\%, what is the risk premium? Stock C: 9.9 – 4.15 = 5.75\% Stock T: 17.7 – 4.15 = 13.55\% Variance and standard deviation measure the volatility of returns. Using unequal probabilities for the entire range of possibilities Weighted average of squared deviations Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Variance and Standard Deviation 1-‹#› 11.6 Section 13.1 (B) It’s important to point out that these formulas are for populations, unlike the formulas in chapter 12 that were for samples (dividing by n-1 instead of n). Further, the probabilities that are used account for the division. Remind the students that standard deviation is the square root of the variance. Consider the previous example. What are the variance and standard deviation for each stock? Stock C 2 = .3(0.15-0.099)2 + .5(0.10-0.099)2 + .2(0.02-0.099)2 = 0.002029  = 4.50\% Stock T 2 = .3(0.25-0.177)2 + .5(0.20-0.177)2 + .2(0.01-0.177)2 = 0.007441  = 8.63\% Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example: Variance and Standard Deviation 1-‹#› 11.7 Section 13.1 (B) It is helpful to remind students that the standard deviation (but not the variance) is expressed in the same units as the original data, which is a percentage return in our example. Consider the following information: State Probability ABC, Inc. Return Boom .25 0.15 Normal .50 0.08 Slowdown .15 0.04 Recession .10 -0.03 What is the expected return? What is the variance? What is the standard deviation? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Another Example 1-‹#› 11.8 Section 13.1 (B) E(R) = .25(0.15) + .5(0.08) + .15(0.04) + .1(-0.03) = 8.05\% Variance = .25(.15-0.0805)2 + .5(0.08-0.0805)2 + .15(0.04-0.0805)2 + .1(-0.03-0.0805)2 = 0.00267475 Standard Deviation = 5.17\% A portfolio is a collection of assets. An asset’s risk and return are important in how they affect the risk and return of the portfolio. The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Portfolios 1-‹#› 11.9 Section 13.2 Lecture Tip: Each individual has their own level of risk tolerance. Some people are just naturally more inclined to take risk, and they will not require the same level of compensation as others for doing so. Our risk preferences also change through time. We may be willing to take more risk when we are young and without a spouse or kids. But, once we start a family, our risk tolerance may drop. Suppose you have $15,000 to invest and you have purchased securities in the following amounts. What are your portfolio weights in each security? $2000 of C $3000 of KO $4000 of INTC $6000 of BP Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example: Portfolio Weights C: 2/15 = .133 KO: 3/15 = .2 INTC: 4/15 = .267 BP: 6/15 = .4 1-‹#› 11.10 Section 13.2 (A) C – Citigroup KO – Coca-Cola INTC – Intel BP – BP Show the students that the sum of the weights = 1 The expected return of a portfolio is the weighted average of the expected returns of the respective assets in the portfolio. You can also find the expected return by finding the portfolio return in each possible state and computing the expected value as we did with individual securities. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Portfolio Expected Returns 1-‹#› Section 13.2 (B) 11.11 Consider the portfolio weights computed previously. If the individual stocks have the following expected returns, what is the expected return for the portfolio? C: 19.69\% KO: 5.25\% INTC: 16.65\% BP: 18.24\% E(RP) = .133(19.69\%) + .2(5.25\%) + .267(16.65\%) + .4(18.24\%) = 15.41\% Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example: Expected Portfolio Returns 1-‹#› Section 13.2 (B) 11.12 Compute the portfolio return for each state: RP = w1R1 + w2R2 + … + wmRm Compute the expected portfolio return using the same formula as for an individual asset. Compute the portfolio variance and standard deviation using the same formulas as for an individual asset. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Portfolio Variance 1-‹#› 11.13 Section 13.2 (C) Consider the following information on returns and probabilities: Invest 50\% of your money in Asset A. State Probability A B Portfolio Boom .4 30\% -5\% 12.5\% Bust .6 -10\% 25\% 7.5\% What are the expected return and standard deviation for each asset? What are the expected return and standard deviation for the portfolio? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example: Portfolio Variance 1-‹#› 11.14 Section 13.2 (C) If A and B are your only choices, what percent are you investing in Asset B? 50\% Asset A: E(RA) = .4(30) + .6(-10) = 6\% Variance(A) = .4(30-6)2 + .6(-10-6)2 = 384 Std. Dev.(A) = 19.6\% Asset B: E(RB) = .4(-5) + .6(25) = 13\% Variance(B) = .4(-5-13)2 + .6(25-13)2 = 216 Std. Dev.(B) = 14.7\% Portfolio (solutions to portfolio return in each state appear with mouse click after last question) Portfolio return in boom = .5(30) + .5(-5) = 12.5 Portfolio return in bust = .5(-10) + .5(25) = 7.5 Expected return = .4(12.5) + .6(7.5) = 9.5 or Expected return = .5(6) + .5(13) = 9.5 Variance of portfolio = .4(12.5-9.5)2 + .6(7.5-9.5)2 = 6 Standard deviation = 2.45\% Note that the variance is NOT equal to .5(384) + .5(216) = 300 and Standard deviation is NOT equal to .5(19.6) + .5(14.7) = 17.17\% What would the expected return and standard deviation for the portfolio be if we invested 3/7 of our money in A and 4/7 in B? Portfolio return = 10\% and standard deviation = 0 Portfolio variance using covariances: COV(A,B) = .4(30-6)(-5-13) + .6(-10-6)(25-13) = -288 Variance of portfolio = (.5)2(384) + (.5)2(216) + 2(.5)(.5)(-288) = 6 Standard deviation = 2.45\% Consider the following information on returns and probabilities: State Probability X Z Boom .25 15\% 10\% Normal .60 10\% 9\% Recession .15 5\% 10\% What are the expected return and standard deviation for a portfolio with an investment of $6,000 in asset X and $4,000 in asset Z? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Another Example: Portfolio Variance 1-‹#› 11.15 Section 13.2 (C) Portfolio return in Boom: .6(15) + .4(10) = 13\% Portfolio return in Normal: .6(10) + .4(9) = 9.6\% Portfolio return in Recession: .6(5) + .4(10) = 7\% Expected return = .25(13) + .6(9.6) + .15(7) = 10.06\% Variance = .25(13-10.06)2 + .6(9.6-10.06)2 + .15(7-10.06)2 = 3.6924 Standard deviation = 1.92\% Compare to return on X of 10.5\% and standard deviation of 3.12\% And return on Z of 9.4\% and standard deviation of .49\% Using covariances: COV(X,Z) = .25(15-10.5)(10-9.4) + .6(10-10.5)(9-9.4) + .15(5-10.5)(10-9.4) = .3 Portfolio variance = (.6 × 3.12)2 + (.4 × .49)2 + 2(.6)(.4)(.3) = 3.6868 Portfolio standard deviation = 1.92\% (difference in variance due to rounding) Lecture Tip: Here are a few tips to pass along to students suffering from “statistics overload”: -The distribution is just the picture of all possible outcomes. -The mean return is the central point of the distribution. -The standard deviation is the average deviation from the mean. -Assuming investor rationality (two-parameter utility functions), the mean is a proxy for expected return and the standard deviation is a proxy for total risk. Realized returns are generally not equal to expected returns. There is the expected component and the unexpected component. At any point in time, the unexpected return can be either positive or negative. Over time, the average of the unexpected component is zero. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Expected vs. Unexpected Returns 1-‹#› Section 13.3 (A) 11.16 Announcements and news contain both an expected component and a surprise component. It is the surprise component that affects a stock’s price and therefore its return. This is very obvious when we watch how stock prices move when an unexpected announcement is made or earnings are different than anticipated. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Announcements and News 1-‹#› 11.17 Section 13.3 (B) Lecture Tip: It is easy to see the effect of unexpected news on stock prices and returns. Consider the following two cases: (1) On November 17, 2004 it was announced that K-Mart would acquire Sears in an $11 billion deal. Sears’ stock price jumped from a closing price of $45.20 on November 16 to a closing price of $52.99 (a 7.79\% increase) and K-Mart’s stock price jumped from $101.22 on November 16 to a closing price of $109.00 on November 17 (a 7.69\% increase). Both stocks traded even higher during the day. Why the jump in price? Unexpected news, of course. (2) On November 18, 2004, Williams-Sonoma cut its sales and earnings estimates for the fourth quarter of 2004 and its share price dropped by 6\%. There are plenty of other examples where unexpected news causes a change in price and expected returns. Efficient markets are a result of investors trading on the unexpected portion of announcements. The easier it is to trade on surprises, the more efficient markets should be. Efficient markets involve random price changes because we cannot predict surprises. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Efficient Markets 1-‹#› Section 13.3 (B) 11.18 Risk factors that affect a large number of assets Also known as non-diversifiable risk or market risk Includes such things as changes in GDP, inflation, interest rates, etc. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Systematic Risk 1-‹#› 11.19 Section 13.4 (A) Risk factors that affect a limited number of assets Also known as unique risk and asset-specific risk Includes such things as labor strikes, part shortages, etc. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Unsystematic Risk 1-‹#› 11.20 Section 13.4 (A) Lecture Tip: You can expand the discussion of the difference between systematic and unsystematic risk by using the example of a strike by employees. Students will generally agree that this is unique or unsystematic risk for one company. However, what if the UAW stages the strike against the entire auto industry. Will this action impact other industries or the entire economy? If the answer to this question is yes, then this becomes a systematic risk factor. The important point is that it is not the event that determines whether it is systematic or unsystematic risk; it is the impact of the event. Total Return = expected return + unexpected return Unexpected return = systematic portion + unsystematic portion Therefore, total return can be expressed as follows: Total Return = expected return + systematic portion + unsystematic portion Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Returns 1-‹#› Section 13.4 (B) 11.21 Portfolio diversification is the investment in several different asset classes or sectors. Diversification is not just holding a lot of assets. For example, if you own 50 Internet stocks, you are not diversified. However, if you own 50 stocks that span 20 different industries, then you are diversified. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Diversification 1-‹#› 11.22 Section 13.5 Video Note: “Portfolio Management” looks at the value of diversification. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Table 13.7 1-‹#› Section 13.5 (A) 11.23 Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns. This reduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from another. However, there is a minimum level of risk that cannot be diversified away and that is the systematic portion. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. The Principle of Diversification 1-‹#› 11.24 Section 13.5 (B) A discussion of the potential benefits of international investing may be helpful at this point. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Figure 13.1 1-‹#› Section 13.5 (B) 11.25 The risk that can be eliminated by combining assets into a portfolio. Often considered the same as unsystematic, unique or asset-specific risk If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify away. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Diversifiable Risk 1-‹#› Section 13.5 (C) 11.26 Total risk = systematic risk + unsystematic risk The standard deviation of returns is a measure of total risk. For well-diversified portfolios, unsystematic risk is very small. Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Total Risk 1-‹#› Section 13.5 (D) 11.27 There is a reward for bearing risk. There is not a reward for bearing risk unnecessarily. The expected return on a risky asset depends only on that asset’s systematic risk since unsystematic risk can be diversified away. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Systematic Risk Principle 1-‹#› 11.28 Section 13.6 (A) A discussion of diversification via mutual funds and ETFs may add to the students’ understanding. How do we measure systematic risk? We use the beta coefficient. What does beta tell us? A beta of 1 implies the asset has the same systematic risk as the overall market. A beta < 1 implies the asset has less systematic risk than the overall market. A beta > 1 implies the asset has more systematic risk than the overall market. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Measuring Systematic Risk 1-‹#› 11.29 Section 13.6 (B) Lecture Tip: Remember that the cost of equity depends on both the firm’s business risk and its financial risk. So, all else equal, borrowing money will increase a firm’s equity beta because it increases the volatility of earnings. Robert Hamada derived the following equation to reflect the relationship between levered and unlevered betas (excluding tax effects): L = U(1 + D/E) where: L = equity beta of a levered firm; U = equity beta of an unlevered firm; D/E = debt-to-equity ratio Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Table 13.8 – Selected Betas 1-‹#› 11.30 Section 13.6 (B) Lecture Tip: Students sometimes wonder just how high a stock’s beta can get. In earlier years, one would say that, while the average beta for all stocks must be 1.0, the range of possible values for any given beta is from - to +. Today, the Internet provides another way of addressing the question. Go to the Yahoo! Finance stock screener site. This site allows you to search many financial markets by fundamental criteria. Consider the following information: Standard Deviation Beta Security C 20\% 1.25 Security K 30\% 0.95 Which security has more total risk? Which security has more systematic risk? Which security should have the higher expected return? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Total vs. Systematic Risk 1-‹#› 11.31 Section 13.6 (B) Security K has the higher total risk. Security C has the higher systematic risk. Security C should have the higher expected return. Many sites provide betas for companies. Yahoo! Finance provides beta, plus a lot of other information under its Key Statistics section. Enter a ticker symbol and get a basic quote. Click on Key Statistics. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Work the Web Example 1-‹#› Section 13.6 (B) 11.32 Consider the previous example with the following four securities. Security Weight Beta C .133 1.685 KO .2 0.195 INTC .267 1.161 BP .4 1.434 What is the portfolio beta? .133(1.685) + .2(.195) + .267(1.161) + .4(1.434) = 1.147 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example: Portfolio Betas 1-‹#› 11.33 Section 13.6 (C) Which security has the highest systematic risk? C Which security has the lowest systematic risk? KO Is the systematic risk of the portfolio more or less than the market? more Remember that the risk premium = expected return – risk-free rate. The higher the beta, the greater the risk premium should be. Can we define the relationship between the risk premium and beta so that we can estimate the expected return? YES! Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Beta and the Risk Premium 1-‹#› Section 13.7 (A) 11.34 Example: Portfolio Expected Returns and Betas Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Rf E(RA) A 1-‹#› 11.35 Section 13.7 (A) Based on the example in the book: Point out that there is a linear relationship between beta and expected return. Ask if the students remember the form of the equation for a line. Y = mx + b E(R) = slope (Beta) + y-intercept The y-intercept is = the risk-free rate, so all we need is the slope Lecture Tip: The example in the book illustrates a greater than 100\% investment in asset A. This means that the investor has borrowed money on margin (technically at the risk-free rate) and used that money to purchase additional shares of asset A. This can increase the potential returns, but it also increases the risk. Expected Return 0 0.4 0.8 1.2 1.6 2 2.4 0.08 0.11 0.14000000000000001 0.17 0.2 0.23 0.26 0 0.4 0.8 1.2 1.6 2 2.4 0 0.4 0.8 1.2 1.6 2 2.4 0 0.4 0.8 1.2 1.6 2 2.4 Beta Expected Return The reward-to-risk ratio is the slope of the line illustrated in the previous example. Slope = (E(RA) – Rf) / (A – 0) Reward-to-risk ratio for previous example = (20 – 8) / (1.6 – 0) = 7.5 What if an asset has a reward-to-risk ratio of 8 (implying that the asset plots above the line)? What if an asset has a reward-to-risk ratio of 7 (implying that the asset plots below the line)? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Reward-to-Risk Ratio: Definition and Example 1-‹#› 11.36 Section 13.7 (A) Ask students if they remember how to compute the slope of a line: rise / run. If the reward-to-risk ratio = 8, then investors will want to buy the asset. This will drive the price up and the expected return down (remember time value of money and valuation). When will the flurry of trading stop? When the reward-to-risk ratio reaches 7.5. If the reward-to-risk ratio = 7, then investors will want to sell the asset. This will drive the price down and the expected return up. When will the flurry of trading stop? When the reward-to-risk ratio reaches 7.5. In equilibrium, all assets and portfolios must have the same reward-to-risk ratio, and they all must equal the reward-to-risk ratio for the market. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Market Equilibrium 1-‹#› Section 13.7 (A) 11.37 The security market line (SML) is the representation of market equilibrium. The slope of the SML is the reward-to-risk ratio: (E(RM) – Rf) / M But since the beta for the market is always equal to one, the slope can be rewritten. Slope = E(RM) – Rf = market risk premium Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Security Market Line 1-‹#› 11.38 Section 13.7 (B) Based on the discussion earlier, we now have all the components of the line: E(R) = [E(RM) – Rf] + Rf Lecture Tip: Although the realized market risk premium has on average been approximately 8.5\%, the historical average should not be confused with the anticipated risk premium for any particular future period. There is abundant evidence that the realized market return has varied greatly over time. The historical average value should be treated accordingly. On the other hand, there is currently no universally accepted means of coming up with a good ex ante estimate of the market risk premium, so the historical average might be as good a guess as any. In the late 1990’s, there was evidence that the risk premium had been shrinking. In fact, Alan Greenspan was concerned with the reduction in the risk premium because he was afraid that investors had lost sight of how risky stocks actually are. Investors had a wake-up call in late 2000 and 2001 (and again in 2008 and 2009). The capital asset pricing model defines the relationship between risk and return. E(RA) = Rf + A(E(RM) – Rf) If we know an asset’s systematic risk, we can use the CAPM to determine its expected return. This is true whether we are talking about financial assets or physical assets. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. The Capital Asset Pricing Model (CAPM) 1-‹#› Section 13.7 (B) 11.39 Pure time value of money: measured by the risk-free rate Reward for bearing systematic risk: measured by the market risk premium Amount of systematic risk: measured by beta Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Factors Affecting Expected Return 1-‹#› Section 13.7 (B) 11.40 Consider the betas for each of the assets given earlier. If the risk-free rate is 4.15\% and the market risk premium is 7.5\%, what is the expected return for each? Security Beta Expected Return C 2.685 3.15 + 1.685(7.5) = 15.79\% KO 0.195 3.15 + 0.195(7.5) = 4.61\% INTC 2.161 3.15 + 1.161(7.5) = 11.86\% BP 2.434 3.15 + 1.434(7.5) = 13.93\% Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example - CAPM 1-‹#› 11.41 Section 13.7 (B) Lecture Tip: Students should remember … CHAPTER 12 SOME LESSONS FROM CAPITAL MARKET HISTORY Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› Calculate the return on an investment Discuss the historical returns on various types of investments Discuss the historical risks on various important types of investments Explain the implications of market efficiency Key Concepts and Skills Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› Returns The Historical Record Average Returns: The First Lesson The Variability of Returns: The Second Lesson More about Average Returns Capital Market Efficiency Chapter Outline Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› We can examine returns in the financial markets to help us determine the appropriate returns on non-financial assets. Lessons from capital market history There is a reward for bearing risk. The greater the potential reward, the greater the risk. Risk, Return, and Financial Markets Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› Section 12.1 10.4 Total dollar return = income from investment + capital gain (loss) due to change in price Example: You bought a bond for $950 one year ago. You have received two coupons of $30 each. You can sell the bond for $975 today. What is your total dollar return? Income = 30 + 30 = 60 Capital gain = 975 – 950 = 25 Total dollar return = 60 + 25 = $85 Dollar Returns Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› 10.5 Section 12.1 (A) Lecture Tip: The issues discussed in this section need to be stressed. Many students feel that if you don’t sell a security, you won’t have to consider the capital gain or loss involved. (This is a common investor’s mistake – holding a loser too long because of reluctance to admit a bad decision was made.) Point out that non-recognition is relevant for tax purposes – only realized income must be reported. However, whether or not you have liquidated the asset is irrelevant when measuring a security’s pre-tax performance. Also, we need to annualize total returns so that we can compare the performance of different securities available in the market. It is generally more intuitive to think in terms of percentage rather than dollar returns. Dividend yield = income / beginning price Capital gains yield = (ending price – beginning price)/ beginning price Total percentage return = dividend yield + capital gains yield Percentage Returns Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› 10.6 Section 12.1 (B) Note that the “dividend” yield is really just the yield on cash flows received from the security (other than the selling price). You bought a stock for $35, and you received dividends of $1.25. The stock is now selling for $40. What is your dollar return? Dollar return = 1.25 + (40 – 35) = $6.25 What is your percentage return? Dividend yield = 1.25 / 35 = 3.57\% Capital gains yield = (40 – 35) / 35 = 14.29\% Total percentage return = 3.57 + 14.29 = 17.86\% Example: Calculating Returns Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› 10.7 Section 12.1 (B) You might want to point out that total percentage return is also equal to total dollar return / beginning price. Total percentage return = 6.25 / 35 = 17.86\% Financial markets allow companies, governments and individuals to increase their utility. Savers have the ability to invest in financial assets so that they can defer consumption and earn a return to compensate them for doing so. Borrowers have better access to the capital that is available so that they can invest in productive assets. Financial markets also provide us with information about the returns that are required for various levels of risk. The Importance of Financial Markets Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› Section 12.2 10.8 Figure 12.4 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› Section 12.2 (A) 10.9 Large-Company Stock Returns Long-Term Government Bond Returns U.S. Treasury Bill Returns Year-to-Year Total Returns Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› 10.10 Click on each of the excel icons to see a chart of year-to-year returns similar to the charts in the text. The charts were created using the data in Table 12.1. The annual total return for stocks has been quite volatile. Investment Average Return Large Stocks 12.0\% Small Stocks 16.6\% Long-term Corporate Bonds 6.3\% Long-term Government Bonds 6.0\% U.S. Treasury Bills 3.4\% Inflation 3.0\% Average Returns Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› 10.11 A brief review of statistical properties may be in order at this point, particularly as it relates to the normal distribution. The “extra” return earned for taking on risk Treasury bills are considered to be risk-free. The risk premium is the return over and above the risk-free rate. Risk Premiums Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› 10.12 Investment Average Return Risk Premium Large Stocks 12.0\% 8.6\% Small Stocks 16.6\% 13.2\% Long-term Corporate Bonds 6.3\% 2.9\% Long-term Government Bonds 6.0\% 2.6\% U.S. Treasury Bills 3.4\% 0.0\% Table 12.3: Average Annual Returns and Risk Premiums Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› 10.13 Ask the students to think about why the different investments have different risk premiums. Large stocks: 12.0 – 3.4 = 8.6 Small stocks: 16.6 – 3.4 = 13.2 LT Corp. bonds: 6.3 – 3.4 = 2.9 LT Gov’t. bonds: 6.0 – 3.4 = 2.6 Figure 12.9 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› Section 12.4 (A) 10.14 Variance and standard deviation measure the volatility of asset returns. The greater the volatility, the greater the uncertainty. Historical variance = sum of squared deviations from the mean / (number of observations – 1) Standard deviation = square root of the variance Variance and Standard Deviation Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› 10.15 Lecture Tip: Occasionally, students ask why we include the above-mean returns in measuring dispersion, since these are desirable from the investor’s viewpoint. This question provides a natural springboard for a discussion of alternative variability measures. Here we discuss semivariance as an alternative to variance. In Portfolio Selection (1959), Harry Markowitz states: “Analyses based on [semivariance] tend to produce better portfolios than those based on [variance]. Variance considers extremely high and extremely low returns equally undesirable. An analysis based on [variance] seeks to eliminate extremes. An analysis based on [semivariance] on the other hand, concentrates on reducing losses.” Semivariance is computed in a manner similar to the traditional variance, except that if the deviation is positive, its value is replaced by zero. We still tend to use variance instead of semivariance because semivariance tends to complicate the risk-return issue, and besides, if returns are symmetrically distributed, then variance is two times semivariance. Year Actual Return Average Return Deviation from the Mean Squared Deviation 1 .15 .105 .045 .002025 2 .09 .105 -.015 .000225 3 .06 .105 -.045 .002025 4 .12 .105 .015 .000225 Totals .42 .00 .0045 Example: Variance and Standard Deviation Variance = .0045 / (4-1) = .0015 Standard Deviation = .03873 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› 10.16 Remind students that the variance for a sample is computed by dividing the sum of the squared deviations by the number of observations – 1. The standard deviation is just the square root. Lecture Tip: It is sometimes difficult to get students to appreciate the risk involved in investing in common stocks. They see the large average returns and miss the variance. A simple exercise illustrating the risk of the different securities can be performed using Table 12.1. Each student (or the entire class) is given an initial investment. They are then allowed to choose a security class. Use a random number generator and the last two digits of the year to sample the distribution. The initial investment is then increased or decreased based on the return. This works best if the trials are limited to between one and five. How volatile are mutual funds? Morningstar provides information on mutual funds, including volatility. Go to the Morningstar site. Pick a fund, such as the American Funds EuroPacific Growth Fund (AEPGX). Enter the ticker, press go, and then click “Ratings & Risk”. Work the Web Example Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› Section 12.4 (B) 10.17 Figure 12.10 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› Section 12.4 (C) 10.18 The normal distribution is a symmetric, bell-shaped frequency distribution. It is completely defined by its mean and standard deviation. As seen in Figure 12.10, the returns appear to be at least roughly normally distributed. Normal distribution Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› Section 12.4 (D) 10.19 Figure 12.11 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› 10.20 2008 was one of the worst years for stock market investors in history. The S&P 500 plunged 37 percent. The index lost 17 percent in October alone. From March ‘09 to Feb ‘11, the S&P 500 doubled in value. Long-term Treasury bonds gained over 40 percent in 2008. They lost almost 26 percent in 2009. Recent market volatility Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› Two lessons for investors from this recent volatility: Stocks have significant risk Diversification matters 10.21 Arithmetic average – return earned in an average period over multiple periods Geometric average – average compound return per period over multiple periods The geometric average will be less than the arithmetic average unless all the returns are equal. Which is better? The arithmetic average is overly optimistic for long horizons. The geometric average is overly pessimistic for short horizons. So, the answer depends on the planning period under consideration. 15 – 20 years or less: use the arithmetic 20 – 40 years or so: split the difference between them 40 + years: use the geometric Arithmetic vs. Geometric Mean Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› 10.22 The calculation of an appropriate average can be extended using Blume’s formula as described in the text. What is the arithmetic and geometric average for the following returns? Year 1 5\% Year 2 -3\% Year 3 12\% Arithmetic average = (5 + (–3) + 12)/3 = 4.67\% Geometric average = [(1+.05) × (1-.03) × (1+.12)]1/3 – 1 = .0449 = 4.49\% Example: Computing Averages Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› Section 12.5 (B) 10.23 Stock prices are in equilibrium or are “fairly” priced. If this is true, then you should not be able to earn “abnormal” or “excess” returns. Efficient markets DO NOT imply that investors cannot earn a positive return in the stock market. Efficient Capital Markets Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› 10.24 Consider asking the students if market efficiency has increased over time. Figure 12.14 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› Section 12.6 (A) 10.25 There are many investors out there doing research. As new information comes to market, this information is analyzed and trades are made based on this information. Therefore, prices should reflect all available public information. If investors stop researching stocks, then the market will not be efficient. What Makes Markets Efficient? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› 10.26 Point out that one consequence of the wider availability of information and lower transaction costs is that the market will be more volatile. It is easier to trade on “small” news instead of just big events. It is also important to remember that not all available information is reliable information. It’s important to still do the research and not just jump on everything that crosses the news wire. The case of Emulex, discussed earlier, is an excellent example. Daniel Tully, Chairman Emeritus of Merrill Lynch: “I’m not smart enough to know the top or the bottom of a market.” Efficient markets do not mean that you can’t make money. They do mean that, on average, you will earn a return that is appropriate for the risk undertaken and there is not a bias in prices that can be exploited to earn excess returns. Market efficiency will not protect you from wrong choices if you do not diversify – you still don’t want to “put all your eggs in one basket.” Common Misconceptions about EMH Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› 10.27 Lecture tip: Claims of superior performance in stock picking are very common and often hard to verify. However, if markets are semistrong form efficient, the ability to consistently earn excess returns is unlikely. Lecture Tip: Even the experts get confused about the meaning of capital market efficiency. Consider the following quote from a column in Forbes magazine: “Popular delusion three: Markets are efficient. The efficient market [sic] hypothesis, or EMH, would do credit to medieval alchemists and is about as scientific as their efforts to turn base metals into gold.” The writer is definitely not a proponent of EMH. Now consider this quote: “The truth is nobody can consistently predict the ups and downs of the market.” This statement is clearly consistent with the EMH. Ironically, the same person wrote both statements in the same column with exactly nine lines of type separating them. Prices reflect all information, including public and private. If the market is strong form efficient, then investors could not earn abnormal returns regardless of the information they possessed. Empirical evidence indicates that markets are NOT strong form efficient and that insiders could earn abnormal returns. Strong Form Efficiency Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› 10.28 Students are often very interested in insider trading. The case of Martha Stewart is one with which most students tend to be familiar. Prices reflect all publicly available information including trading information, annual reports, press releases, etc. If the market is semistrong form efficient, then investors cannot earn abnormal returns by trading on public information. Implies that fundamental analysis will not lead to abnormal returns Semistrong Form Efficiency Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› 10.29 Empirical evidence suggests that some stocks are semistrong form efficient, but not all. Larger, more closely followed stocks are more likely to be semistrong form efficient. Small, more thinly traded stocks may not be semistrong form efficient, but liquidity costs may wipe out any abnormal returns that are available. Prices reflect all past market information such as price and volume. If the market is weak form efficient, then investors cannot earn abnormal returns by trading on market information. Implies that technical analysis will not lead to abnormal returns Empirical evidence indicates that markets are generally weak form efficient. Weak Form Efficiency Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› 10.30 Emphasize that just because technical analysis shouldn’t lead to abnormal returns, that doesn’t mean that you won’t earn fair returns using it – efficient markets imply that you will. You might also want to point out that there are many technical trading rules that have never been empirically tested; so it is possible that one of them might lead to abnormal returns. But if it is well publicized, then any abnormal returns that were available will soon evaporate. Which of the investments discussed has had the highest average return and risk premium? Which of the investments discussed has had the highest standard deviation? What is capital market efficiency? What are the three forms of market efficiency? Quick Quiz Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› Section 12.7 10.31 Program trading is defined as automated trading generated by computer algorithms designed to react rapidly to changes in market prices. Is it ethical for investment banking houses to operate such systems when they may generate trade activity ahead of their brokerage customers, to which they owe a fiduciary duty? Suppose that you are an employee of a printing firm that was hired to proofread proxies that contained unannounced tender offers (and unnamed targets). Should you trade on this information, and would it be considered illegal? Ethics Issues Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› 10.32 Case 2: The court decided in Chiarella v. United States that an employee of a printing firm, who was requested to proofread proxies that contained unannounced tender offers (and unnamed targets) was not guilty of insider trading because the employee determined the identity of the target through his own expertise. Your stock investments return 8\%, 12\%, and -4\% in consecutive years. What is the geometric return? What is the sample standard deviation of the above returns? Using the standard deviation and mean that you just calculated, and assuming a normal probability distribution, what is the probability of losing 3\% or more? Comprehensive Problem Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› 10.33 Section 12.7 (1.08 × 1.12 × .96)^.3333 – 1 = .0511 Mean = ( .08 + .12 + -.04) / 3 = .0533 Variance = (.08 - .0533)^2 + (.12 - .0533)^2 = (-.04 - .0533)^2 / (3 - 1)= .00693 Standard deviation = .00693 ^ .5 = .0833 Probability: a 3\% loss (return of -3\%) lies one standard deviation below the mean. There is 16\% of the probability falling below that point (68\% falls between -3\% and 13.66\%, so 16\% lies below -3\% and 16\% lies above 13.66\%). End of Chapter Chapter 12 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12-‹#› 12-‹#› Large Companies Long-Term Government Bonds U.S. Treasury Bills Large Company 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 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 2014 2015 2016 Year Total Return Large Company Stocks 0.1375 0.357 0.4508 -0.088 -0.2513 -0.436 -0.0875 0.5295 -0.0231 0.4679 0.3249 -0.3545 0.3163 -0.0143 -0.1036 -0.1202 0.2075 0.2538 0.1949 0.3621 -0.0842 0.0505 0.0499 0.1781 0.3005 0.2379 0.1839 -0.0107 0.5223 0.3162 0.0691 -0.105 0.4357 0.1201 0.0047 0.2684 -0.0875 0.227 0.1643 0.1238 -0.1006 0.2398 0.1103 -0.0843 0.0394 0.143 0.1899 -0.1469 -0.2647 0.3723 0.2393 -0.0716 0.0657 0.1861 0.325 -0.0492 0.2155 0.2256 0.0627 0.3173 0.1867 0.0525 0.1661 0.3169 -0.031 0.3046 0.0762 0.1008 0.0132 0.3758 0.2296 0.3336 0.2858 0.2104 -0.091 -0.1189 -0.221 0.2889 0.1088 0.0491 0.1579 0.0549 -0.37 0.2646 0.1506 0.0211 0.16 0.3239 0.1369 0.0141 0.1198 Long-Term Bonds 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 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 2014 2015 2016 Long-Term Government Bonds Year Total Return 0.0569 0.0658 0.0115 0.0439 0.0447 -0.0215 0.0851 0.0192 0.0759 0.042 0.0513 0.0144 0.0421 0.0384 0.057 0.0047 0.018 0.0201 0.0227 0.0529 0.0054 -0.0102 0.0266 0.0458 -0.0098 -0.002 0.0243 0.0228 0.0308 -0.0073 -0.0172 0.0682 -0.0172 -0.0202 0.1121 0.022 0.0572 0.0179 0.0371 0.0093 0.0512 -0.0286 0.0225 -0.0563 0.1892 0.1124 0.0239 0.033 0.04 0.0552 0.1556 0.0038 -0.0126 0.0126 -0.0248 0.0404 0.4428 0.0129 0.1529 0.3227 0.2239 -0.0303 0.0684 0.1854 0.0774 0.1936 0.0734 0.1306 -0.0732 0.2594 0.0013 0.1202 0.1445 -0.0751 0.1722 0.0551 0.1515 0.0201 0.0812 0.0689 0.0028 0.1085 0.4178 -0.2561 0.0773 0.3575 0.018 -0.1469 0.2474 -0.0064 0.0176 T-bills 1926 1927 1928 0.0447 0.0227 0.0115 0.0088 0.0052 0.0027 0.0017 0.0017 0.0027 0.0006 0.0004 0.0004 0.0014 0.0034 0.0038 0.0038 0.0038 0.0038 0.0062 0.0106 0.0112 0.0122 0.0156 0.0175 0.0187 0.0093 0.018 0.0266 0.0328 0.0171 0.0348 0.0281 0.024 0.0282 0.0323 0.0362 0.0406 0.0494 0.0439 0.0549 0.069 0.065 0.0436 0.0423 0.0729 0.0799 0.0587 0.0507 0.0545 0.0764 0.1056 0.121 0.146 0.1094 0.0899 0.099 0.0771 0.0609 0.0588 0.0694 0.0844 0.0769 0.0543 0.0348 0.0303 0.0439 0.0561 0.0514 0.0519 0.0486 0.048 0.0598 0.0333 0.0161 0.0094 0.0114 0.0279 0.0497 0.0452 0.0124 0.0015 0.0014 0.0006 0.0008 0.0005 0.0003 0.0004 0.0021 T-Bills Year Total Return 0.033 0.0315 0.0405 Sheet1 Year Large-Company Stocks Long-Term Government Bonds U.S. Treasury Bills Consumer Price Index 1926 0.1375 0.0569 0.033 -0.0112 1927 0.357 0.0658 0.0315 -0.0226 1928 0.4508 0.0115 0.0405 -0.0116 1929 -0.088 0.0439 0.0447 0.0058 1930 -0.2513 0.0447 0.0227 -0.064 1931 -0.436 -0.0215 0.0115 -0.0932 1932 -0.0875 0.0851 0.0088 -0.1027 1933 0.5295 0.0192 0.0052 0.0076 1934 -0.0231 0.0759 0.0027 0.0152 1935 0.4679 0.042 0.0017 0.0299 1936 0.3249 0.0513 0.0017 0.0145 1937 -0.3545 0.0144 0.0027 0.0286 1938 0.3163 0.0421 0.0006 -0.0278 1939 -0.0143 0.0384 0.0004 0 1940 -0.1036 0.057 0.0004 0.0071 1941 -0.1202 0.0047 0.0014 0.0993 1942 0.2075 0.018 0.0034 0.0903 1943 0.2538 0.0201 0.0038 0.0296 1944 0.1949 0.0227 0.0038 0.023 1945 0.3621 0.0529 0.0038 0.0225 1946 -0.0842 0.0054 0.0038 0.1813 1947 0.0505 -0.0102 0.0062 0.0884 1948 0.0499 0.0266 0.0106 0.0299 1949 0.1781 0.0458 0.0112 -0.0207 1950 0.3005 -0.0098 0.0122 0.0593 1951 0.2379 -0.002 0.0156 0.06 1952 0.1839 0.0243 0.0175 0.0075 1953 -0.0107 0.0228 0.0187 0.0074 1954 0.5223 0.0308 0.0093 -0.0074 1955 0.3162 -0.0073 0.018 0.0037 1956 0.0691 -0.0172 0.0266 0.0299 1957 -0.105 0.0682 0.0328 0.029 1958 0.4357 -0.0172 0.0171 0.0176 1959 0.1201 -0.0202 0.0348 0.0173 1960 0.0047 0.1121 0.0281 0.0136 1961 0.2684 0.022 0.024 0.0067 1962 -0.0875 0.0572 0.0282 0.0133 1963 0.227 0.0179 0.0323 0.0164 1964 0.1643 0.0371 0.0362 0.0097 1965 0.1238 0.0093 0.0406 0.0192 1966 -0.1006 0.0512 0.0494 0.0346 1967 0.2398 -0.0286 0.0439 0.0304 1968 0.1103 0.0225 0.0549 0.0472 1969 -0.0843 -0.0563 0.069 0.062 1970 0.0394 0.1892 0.065 0.0557 1971 0.143 0.1124 0.0436 0.0327 1972 0.1899 0.0239 0.0423 0.0341 1973 -0.1469 0.033 0.0729 0.0871 1974 -0.2647 0.04 0.0799 0.1234 1975 0.3723 0.0552 0.0587 0.0694 1976 0.2393 0.1556 0.0507 0.0486 1977 -0.0716 0.0038 0.0545 0.067 1978 0.0657 -0.0126 0.0764 0.0902 1979 0.1861 0.0126 0.1056 0.1329 1980 0.325 -0.0248 0.121 0.1252 1981 -0.0492 0.0404 0.146 0.0892 1982 0.2155 0.4428 0.1094 0.0383 1983 0.2256 0.0129 0.0899 0.0379 1984 0.0627 0.1529 0.099 0.0395 1985 0.3173 0.3227 0.0771 0.038 1986 0.1867 0.2239 0.0609 0.011 1987 0.0525 -0.0303 0.0588 0.0443 1988 0.1661 0.0684 0.0694 0.0442 1989 0.3169 0.1854 0.0844 0.0465 1990 -0.031 0.0774 0.0769 0.0611 1991 0.3046 0.1936 0.0543 0.0306 1992 0.0762 0.0734 0.0348 0.029 1993 0.1008 0.1306 0.0303 0.0275 1994 0.0132 -0.0732 0.0439 0.0267 1995 0.3758 0.2594 0.0561 0.0254 1996 0.2296 0.0013 0.0514 0.0332 1997 0.3336 0.1202 0.0519 0.017 1998 0.2858 0.1445 0.0486 0.0161 1999 0.2104 -0.0751 0.048 0.0268 2000 -0.091 0.1722 0.0598 0.0339 2001 -0.1189 0.0551 0.0333 0.0155 2002 -0.221 0.1515 0.0161 0.024 2003 0.2889 0.0201 0.0094 0.019 2004 0.1088 0.0812 0.0114 0.033 2005 0.0491 0.0689 0.0279 0.034 2006 0.1579 0.0028 0.0497 0.0254 2007 0.0549 0.1085 0.0452 0.0408 2008 -0.37 0.4178 0.0124 0.0009 2009 0.2646 -0.2561 0.0015 0.0272 2010 0.1506 0.0773 0.0014 0.015 2011 0.0211 0.3575 0.0006 0.0296 2012 0.16 0.018 0.0008 0.0174 2013 0.3239 -0.1469 0.0005 0.015 2014 0.1369 0.2474 0.0003 0.0075 2015 0.0141 -0.0064 0.0004 0.0074 2016 0.1198 0.0176 0.0021 0.0211 0.117628 0.057509 0.037589 0.030752 Sheet2 Sheet3 Large … WORKING WITH FINANCIAL STATEMENTS Chapter 3 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.1 Standardize financial statements for comparison purposes Compute, and more importantly, interpret some common ratios Name the determinants of a firm’s profitability Explain some of the problems and pitfalls in financial statement analysis Key Concepts and Skills Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.2 Digital Equipment’s CEO stated: “Make your numbers or I’m sure your successor will.” Cash Flow and Financial Statements: A Closer Look Standardized Financial Statements Ratio Analysis The DuPont Identity Using Financial Statement Information Chapter Outline Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 2018 2017 2018 2017 Cash 108 58 A/P 307 303 A/R 1,156 992 N/P 26 119 Inventory 501 361 Other CL 1,662 1,353 Other CA 403 264 Total CL 1,995 1,775 Total CA 2,168 1,675 LT Debt 843 1,091 Net FA 3,438 3,358 C/S 2,768 2,167 Total Assets 5,606 5,033 Total Liab. & Equity 5,606 5,033 Sample Balance Sheet Numbers in millions of dollars Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.4 Section 3.1 The following slides provide an additional example to help reinforce the concepts. For future calculations, it may be helpful to print copies of the sample balance sheet and income statement so that you do not need to keep referring back to these slides. Sample Income Statement Revenues 5,000 Cost of Goods Sold (2,006) Expenses (1,740) Depreciation (116) EBIT 1,138 Interest Expense (7) Taxable Income 1,131 Taxes (238) Net Income 893 EPS 4.68 Dividends per share 1.53 Numbers in millions of dollars, except EPS & DPS Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.5 Section 3.1 The income statement is for 2018. The net income figure and EPS are based on income from continuing operations. There are 190.9 million shares outstanding. Sources Cash inflow – occurs when we “sell” something Decrease in asset account (Sample B/S) Accounts receivable, inventory, and net fixed assets Increase in liability or equity account Accounts payable, other current liabilities, and common stock Uses Cash outflow – occurs when we “buy” something Increase in asset account Cash and other current assets Decrease in liability or equity account Notes payable and long-term debt Sources and Uses of Cash Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.6 Section 3.1 (A) Click on Sample B/S to go to the Balance Sheet to illustrate the accounts that are sources and uses, On the B/S Click on the small green arrow to return to this slide. Cash inflow – occurs when we sell assets, sell debt instruments (take on more debt), or sell stock shares Cash outflow – occurs when we buy assets, buy back debt instruments (pay off some debt), or buy back stock shares Statement that summarizes the sources and uses of cash Changes divided into three major categories Operating Activity – includes net income and changes in most current accounts Investment Activity – includes changes in fixed assets Financing Activity – includes changes in notes payable, long-term debt, and equity accounts, as well as dividends Statement of Cash Flows Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› Section 3.1 (B) The new tax law will generally result in higher operating cash flow, as, all else equal, net income will be higher. This will result in a larger increase in equity as well. 3.7 Cash, beginning of year 58 Financing Activity Operating Activity Decrease in Notes Payable -93 Net Income 893 Decrease in LT Debt -248 Plus: Depreciation 116 Change in C/S (less RE) 0 Increase in A/P 4 Dividends Paid -292 Increase in Other CL 309 Net Cash from Financing -633 Less: Increase in other CA -139 Increase in A/R -164 Net Increase in Cash 50 Increase in Inventory -140 Net Cash from Operations 879 Cash End of Year 108 Investment Activity Purchase of Fixed Assets -196 Net Cash from Investments -196 Sample Statement of Cash Flows Numbers in millions of dollars Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.8 Section 3.1 (B) Investment activity: change in net fixed assets + depreciation (have to add back depreciation because it was deducted from the fixed asset account to get the net fixed asset figure). If the number is positive, then we acquired fixed assets; if it’s negative, then we sold fixed assets. 3438 - 3358 + 116 = 196 so we bought 196 million worth of fixed assets Remind students that part of the increase in the C/S account shown on the balance sheet is the increase in Retained Earnings. That is already incorporated in the net income under operating activity. Dividends paid = 190.9*1.53 = 292 million Additions to RE = 893 - 292 = 601 Change in C/S = 2768 - 2167 - 601 = 0 Common-Size Balance Sheets Compute all accounts as a percent of total assets Common-Size Income Statements Compute all line items as a percent of sales Standardized statements make it easier to compare financial information, particularly as the company grows. They are also useful for comparing companies of different sizes, particularly within the same industry. Standardized Financial Statements Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› Section 3.2 The tax law change may result in a one-time (favorable) jump in ratios that are impacted by the reduced tax liability. 3.9 Ratios allow for better comparison through time or between companies. As we look at each ratio, ask yourself what the ratio is trying to measure and why that information is important. Ratios are used both internally and externally. Ratio Analysis Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.10 Section 3.3 Lecture Tip: Be sure that your students understand that “real-world” financial statements are not as straightforward as the simplified ones presented in the textbook. Actually reviewing some financial statements of companies with which they are familiar may help. Short-term solvency, or liquidity, ratios Long-term solvency, or financial leverage, ratios Asset management, or turnover, ratios Profitability ratios Market value ratios Categories of Financial Ratios Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.11 Section 3.3 The ratios in the following slides will be computed using the 2018 information from the Sample Balance Sheet and Income Statement. Lecture Tip: Remind students that the point of the analysis is not simply the ability to compute the ratios, but rather the ability to interpret them. Current Ratio = CA / CL 2,168 / 1,995 = 1.09 times Quick Ratio = (CA - Inventory) / CL (2,168 - 501) / 1,995 = .84 times Cash Ratio = Cash / CL 108 / 1,995 = .05 times NWC to Total Assets = NWC / TA (2,168 - 1,995) / 5,606 = .03 Interval Measure = CA / average daily operating costs 2,168 / ((2,006 + 1,740)/365) = 211.2 days Computing Liquidity Ratios B/S I/S Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.12 Section 3.3 (A) The firm is just barely able to cover current liabilities with its current assets. A short-term creditor might find this a bit disconcerting and may reduce the likelihood that they would lend money to the company. The ratio should be compared to the industry – it’s possible that this industry has a substantial amount of cash flow and that they can meet their current liabilities out of cash flow instead of relying solely on the liquidation of current assets that are on the books. Also, the CR for 2017 was .94, so the company has improved from the previous year. The quick ratio is quite a bit lower than the current ratio, so inventory seems to be an important component of current assets. This company carries a low cash balance, although the cash ratio has increased from the previous year (.03 in 2017). This may be an indication that they are aggressively investing in assets that will provide higher returns. We need to make sure that we have enough cash to meet our obligations, but too much cash reduces the return earned by the company. The NWC to TA measure seems relatively low, but is consistent with the current ratio. The Interval Measure indicates that the company can meet average daily expenses with current assets for about 211 days. Lecture Tip: Remind students that a high current ratio may actually be a negative, as current assets generally produce a lower return than fixed assets. To build on this understanding, make students evaluate the interaction among ratios. For example, suggest a scenario in which the current ratio exhibits no change over a two- or three-year period, while the quick ratio experiences a steady decline. How could this occur? Total Debt Ratio = (TA - TE) / TA (5,606 - 2,768) / 5,606 = 50.62\% Debt/Equity = TD / TE (5,606 - 2,768) / 2,768 = 1.03 times Equity Multiplier = TA / TE = 1 + D/E 1 + 1.03 = 2.03 Long-term debt ratio = LTD / (LTD + TE) 843 / (843 + 2,768) = 23.35\% Computing Long-term Solvency Ratios B/S I/S Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.13 Section 3.3 (B) Note that these are often called leverage ratios and that this group of ratios measures two aspects of leverage: level of indebtedness and the ability to service this debt. TE = total equity, and TA = total assets. The numerator in the total debt ratio could also be found by adding all of the current and long-term liabilities. The firm finances about 50\% of its assets with debt. This is down from about 57\% from the previous year. Another way to compute the D/E ratio if you already have the total debt ratio: D/E = Total debt ratio / (1 - total debt ratio) = .5062 / (1 - .5062) = 1.03 The EM is one of the ratios that is used in the DuPont Identity as a measure of the firm’s financial leverage. The Long-term debt ratio is down from 33.49\% in 2011. Times Interest Earned = EBIT / Interest 1,138 / 7 = 162.57 times Cash Coverage = (EBIT + Depreciation) / Interest (1,138 + 116) / 7 = 179.14 times Computing Coverage Ratios B/S I/S Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.14 Section 3.3 (B) Even though the company is financed with over 52\% debt, they have a substantial amount of operating income available to cover the required interest payments. Remember that depreciation is a non-cash deduction. A better indication of a firm’s ability to meet interest payments may be to add back the depreciation to get an estimate of cash flow before taxes. Lecture Tip: The importance of coverage ratios is sometimes overlooked, particularly when one considers their importance to all types of creditors. Inventory Turnover = Cost of Goods Sold / Inventory 2,006 / 501 = 4.00 times Days’ Sales in Inventory = 365 / Inventory Turnover 365 / 4.00 = 91 days Computing Inventory Ratios B/S I/S Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.15 Section 3.3 (C) Inventory turnover can be computed using either ending inventory or average inventory when you have both beginning and ending figures. It is important to be consistent with whatever benchmark you are using to analyze the company’s strengths or weaknesses. It is also important to consider seasonality in sales. If the balance sheet is prepared at a time when there is a large inventory build-up to meet seasonal demand, then the inventory turnover will be understated and you might believe that the company is not performing as well as it is. On the other hand, if the balance sheet is prepared when inventory has been drawn down due to seasonal sales, then the inventory turnover would be overstated and the company may appear to be doing better than it really is. Averages using annual data may not fix this problem. If a company has seasonal sales, you may want to look at quarterly averages to get a better indication of turnover. Lecture Tip: You may wish to mention that there may be significant inconsistencies in the methods used to compute ratios by financial advisory firms. When using ratios supplied by others, it is important to be aware of the exact financial items used. A manufacturer would typically consider inventory at cost, and thus, relate inventory to cost of goods sold. However, a retailer might maintain its inventory level based on retail price. In the latter case, inventory should be related to sales to compute inventory turnover. The markup would cancel in the numerator and denominator and give an accurate indication of turnover based on cost. Furthermore, some analysts use average inventory over some period instead of ending inventory. The same is true for the other assets used in the various turnover ratios. Receivables Turnover = Sales / Accounts Receivable 5,000 / 1,156 = 4.33 times Days’ Sales in Receivables = 365 / Receivables Turnover 365 / 4.33 = 84 days Computing Receivables Ratios B/S I/S Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.16 Section 3.3 (C) Technically, the sales figure should be credit sales. This is often difficult to determine from the income statements provided in annual reports. If you use total sales instead of credit sales, you will overstate your turnover level. You need to recognize this bias when credit sales are unavailable, particularly if a large portion of the sales are cash sales. As with inventory turnover, you can use either ending receivables or an average of beginning and ending. You also run into the same seasonal issues as discussed with inventory. Probably the best benchmark for days’ sales in receivables is the company’s credit terms. If the company offers a discount (1/10 net 30), then you would like to see days’ sales in receivables less than 30. If the company does not offer a discount (net 30), then you would like to see days’ sales in receivables close to the net terms. If days’ sales in receivables is substantially larger than the net terms, then you first need to look for biases, such as seasonality in sales. If this does not provide an explanation for the difference, then the company may need to take another look at its credit policy (who it grants credit to and its collection procedures). Lecture Tip: Be sure to remind students that ratio analysis is a means to an end, not an end in itself. The results of the analysis provide us with red flags or items for additional investigation. Lecture Tip: Students also need to realize that comparisons across industries can be problematic. Total Asset Turnover = Sales / Total Assets 5,000 / 5,606 = .89 It is not unusual for TAT < 1, especially if a firm has a large amount of fixed assets NWC Turnover = Sales / NWC 5,000 / (2,168 - 1,995) = 28.90 times Fixed Asset Turnover = Sales / NFA 5,000 / 3,438 = 1.45 times Computing Total Asset Turnover B/S I/S Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.17 Section 3.3 (C) Having a TAT of less than one is not a problem for most firms. Fixed assets are expensive and are meant to provide sales over a long period of time. This is why the matching principle indicates that they should be depreciated instead of immediately expensed. This is one of the ratios that will be used in the DuPont identity. Profit Margin = Net Income / Sales 893 / 5,000 = 17.86\% Return on Assets (ROA) = Net Income / Total Assets 893 / 5,606 = 15.93\% Return on Equity (ROE) = Net Income / Total Equity 893 / 2,768 = 32.26\% Computing Profitability Measures B/S I/S Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.18 Section 3.3 (D) You can also compute the gross profit margin and the operating profit margin. GPM = (Sales - COGS) / Sales = (5,000 - 2,006) / 5,000 = 59.88\% OPM = EBIT / Sales = 1,138 / 5,000 = 22.76\% Profit margin is one of the components of the DuPont identity and is a measure of operating efficiency. It measures how well the firm controls the costs required to generate the revenues. It tells how much the firm earns for every dollar in sales. In the example, the firm earns almost $0.18 for each dollar in sales. Note that the ROA and ROE are returns on accounting numbers. As such, they are not directly comparable with returns found in the marketplace. ROA is sometimes referred to as ROI (return on investment). As with many of the ratios, there are variations in how they can be computed. The most important thing is to make sure that you are computing them the same way as the benchmark you are using. ROE will always be higher (in absolute terms) than ROA as long as the firm has debt. The greater the leverage the larger the difference will be. ROE is often used as a measure of how well management is attaining the goal of owner wealth maximization. The DuPont identity is used to identify factors that affect the ROE. Market Price = $87.65 per share Shares outstanding = 190.9 million PE Ratio = Price per share / Earnings per share 87.65 / 4.68 = 18.73 times Market-to-book ratio = Market value per share / Book value per share 87.65 / (2,768 / 190.9) = 6.04 times Computing Market Value Measures – I Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.19 Section 3.3 (D) Lecture Tip: It is good for students to understand that average is not always best. Further, average levels may vary through time with the economy, and this is particularly relevant for market value measures. Further, comparisons across countries may be difficult due to differences in accounting and reporting standards. A good discussion may be asking the question: “does a market-to-book ratio below one indicate a good investment?” It may be an indication of undervaluation; however, such a ratio may also indicate negative consensus regarding the future viability of the firm. Enterprise value = market value of stock + book value of liabilities - cash 16,732 + 2,838 - 108 = $19,462 EBITDA ratio = Enterprise value / EBITDA 19,462 / (1,138 + 116) = 15.52 times Computing Market Value Measures – II Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.20 Section 3.3 (D) We use the book value for liabilities because we typically can’t get market values, at least not for all of them. However, book value is usually a reasonable approximation for market value when it comes to liabilities, particularly short-term debts. The EBITDA ratio is similar in spirit to the PE ratio, but it relates the value of all of the operating assets (the enterprise value) to a measure of the operating cash flow generated by those assets (EBITDA). ROE = NI / TE Multiply by 1 (TA/TA) and then rearrange ROE = (NI / TE) (TA / TA) ROE = (NI / TA) (TA / TE) = ROA × EM Multiply by 1 (Sales/Sales) again and then rearrange ROE = (NI / TA) (TA / TE) (Sales / Sales) ROE = (NI / Sales) (Sales / TA) (TA / TE) ROE = PM × TAT × EM Deriving the DuPont Identity Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› Section 3.4 (A) 3.21 ROE = PM × TAT × EM Profit margin is a measure of the firm’s operating efficiency – how well it controls costs. Total asset turnover is a measure of the firm’s asset use efficiency – how well does it manage its assets. Equity multiplier is a measure of the firm’s financial leverage. Using the DuPont Identity Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.22 Section 3.4 (A) Improving our operating efficiency or our asset use efficiency will improve our return on equity. If the TAT is low compared to our benchmark, then we can break it down into more detail by looking at inventory turnover and receivables turnover. If those areas are strong, then we can look at fixed asset turnover and cash management. We can also improve our ROE by increasing our leverage – up to a point. Debt affects a lot of other factors, including profit margin, so we have to be a little careful here. We want to make sure we have enough debt to utilize our interest tax credit effectively, but we don’t want to overdo it. The choice of leverage is discussed in more detail in chapter 16. Expanded DuPont Analysis – DuPont Data Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.23 Section 3.4 (B) Extended DuPont Chart Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.24 Section 3.4 (B) Internal uses Performance evaluation – compensation and comparison between divisions Planning for the future – guide in estimating future cash flows External uses Creditors Suppliers Customers Stockholders Why Evaluate Financial Statements? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.25 Section 3.5 (A) Lecture Tip: Discuss with students that the ratios that are most important to a firm are those that best represent their business. So, whereas inventory turnover may be relevant for a retailer or manufacturer, it is less important for a service firm. The best ratios may be those that are uniquely developed for the business under review. Ratios are not very helpful by themselves; they need to be compared to something. Time-Trend Analysis Used to see how the firm’s performance is changing through time Internal and external uses Peer Group Analysis Compare to similar companies or within industries SIC and NAICS codes Benchmarking Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.26 Section 3.5 (B) SIC codes have been used many years to identify industries and allow for comparison with industry average ratios. The SIC codes are limited, however, and have not kept pace with a rapidly changing environment. Consequently, the North American Industry Classification System was introduced in 1997 to alleviate some of the problems with SIC codes. Click on the link to go to the NAICS home page. It provides information on the change to the NAICS and conversion between SIC and NAICS codes. There is no underlying theory, so there is no way to know which ratios are most relevant. Benchmarking is difficult for diversified firms. Globalization and international competition makes comparison more difficult because of differences in accounting regulations. Varying accounting procedures, i.e. FIFO vs. LIFO Different fiscal years Extraordinary events Potential Problems Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› Section 3.5 (C) 3.27 The Internet makes ratio analysis much easier than it has been in the past. Go to Reuters website. Click on Markets, then Stocks, then choose a company and enter its ticker symbol. Click on Financials to see what information is available. Work the Web Example Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.28 Section 3.5 (C) Lecture Tip: An interesting discussion revolves around the benefits and disadvantages of the easy availability of information. The advantages are apparent, but the downside includes an ability for traders to take advantage of efficiency by quickly and widely disseminating false information. What is the Statement of Cash Flows, and how do you determine sources and uses of cash? How do you standardize balance sheets and income statements and why is standardization useful? What are the major categories of ratios and how do you compute specific ratios within each category? What are some of the problems associated with financial statement analysis? Quick Quiz Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› Section 3.6 3.29 Should financial analysts be held liable for their opinions regarding the financial health of firms? How closely should ratings agencies work with the firms they are reviewing? I.e., what level of independence is appropriate? Ethics Issues Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› XYZ Corporation has the following financial information for the previous year: Sales: $8M, PM = 8\%, CA = $2M, FA = $6M, NWC = $1M, LTD = $3M Compute the ROE using the DuPont Analysis. Comprehensive Problem Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3.31 Total assets = CA + FA = $2M + $6M = $8M TAT = Sales / TA = $8M / $8M = 1 NWC = CA - CL; CL = CA - NWC = $2M - $1M = $1M Total liabilities = CL + LTD = $1M + $3M = $4M Total equity = total assets - total liabilities = $8M - $4M = $4M EM = assets / equity = $8M / $4M = 2 ROE = PM × TAT × EM = 8\% × 1 × 2 = 16\% Without using DuPont, ROE = NI / total equity = PM × sales / total equity = 8\% × $8M / 4M = 16\% End of Chapter Chapter 3 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3-‹#› 3-‹#› CHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› Show the reasons why the net present value criterion is the best way to evaluate proposed investments Discuss the payback rule and some of its shortcomings Discuss the discounted payback rule and some of its shortcomings Explain accounting rates of return and some of the problems with them Present the internal rate of return criterion and its strengths and weaknesses Calculate the modified internal rate of return Illustrate the profitability index and its relation to net present value Key Concepts and Skills Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› Net Present Value The Payback Rule The Discounted Payback The Average Accounting Return The Internal Rate of Return The Profitability Index The Practice of Capital Budgeting Chapter Outline Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.3 Lecture Tip: A logical prerequisite to the analysis of investment opportunities is the creation of investment opportunities. Unlike the field of investments, where the analyst more or less takes the investment opportunity set as a given, the field of capital budgeting relies on the work of people in the areas of engineering, research and development, information technology and others for the creation of investment opportunities. As such, it is important to remind students of the importance of creativity in this area, as well as the importance of analytical techniques. We need to ask ourselves the following questions when evaluating capital budgeting decision rules: Does the decision rule adjust for the time value of money? Does the decision rule adjust for risk? Does the decision rule provide information on whether we are creating value for the firm? Good Decision Criteria Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.4 Section 9.1 Economics students will recognize that the practice of capital budgeting defines the firm’s investment opportunity schedule. The difference between the market value of a project and its cost How much value is created from undertaking an investment? The first step is to estimate the expected future cash flows. The second step is to estimate the required return for projects of this risk level. The third step is to find the present value of the cash flows and subtract the initial investment. Net Present Value Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.5 Section 9.1 (A) We learn how to estimate the cash flows and the required return in subsequent chapters. The NPV measures the increase in firm value, which is also the increase in the value of what the shareholders own. Thus, making decisions with the NPV rule facilitates the achievement of our goal in Chapter 1 – making decisions that will maximize shareholder wealth. Lecture Tip: Although this point may seem obvious, it is often helpful to stress the word “net” in net present value. It is not uncommon for some students to carelessly calculate the PV of a project’s future cash flows and fail to subtract out its cost (after all, this is what the programmers of Lotus and Excel did when they programmed the NPV function). The PV of future cash flows is not NPV; rather, NPV is the amount remaining after offsetting the PV of future cash flows with the initial cost. Thus, the NPV amount determines the incremental value created by undertaking the investment. You are reviewing a new project and have estimated the following cash flows: Year 0: CF = -165,000 Year 1: CF = 63,120; NI = 13,620 Year 2: CF = 70,800; NI = 3,300 Year 3: CF = 91,080; NI = 29,100 Average Book Value = 72,000 Your required return for assets of this risk level is 12\%. Project Example Information Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.6 Section 9.1 (B) This example will be used for each of the decision rules so that the students can compare the different rules and see that conflicts can arise. This illustrates the importance of recognizing which decision rules provide the best information for making decisions that will increase owner wealth. If the NPV is positive, accept the project. A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners. Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal. NPV – Decision Rule Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.7 Section 9.1 (B) Lecture Tip: Here’s another perspective on the meaning of NPV. If we accept a project with a negative NPV of -$2,422, this is financially equivalent to investing $2,422 today and receiving nothing in return. Therefore, the total value of the firm would decrease by $2,422. This assumes that the various components (cash flow estimates, discount rate, etc.) used in the computation are correct. Lecture Tip: In practice, financial managers are rarely presented with zero NPV projects for at least two reasons. First, in an abstract sense, zero is just another of the infinite number of values the NPV can take; as such, the likelihood of obtaining any particular number is small. Second, and more pragmatically, in most large firms, capital investment proposals are submitted to the finance group from other areas for analysis. Those submitting proposals recognize the ambivalence associated with zero NPVs and are less likely to send them to the finance group in the first place. Using the formulas: NPV = -165,000 + 63,120/(1.12) + 70,800/(1.12)2 + 91,080/(1.12)3 = 12,627.41 Using the calculator: CF0 = -165,000; C01 = 63,120; F01 = 1; C02 = 70,800; F02 = 1; C03 = 91,080; F03 = 1; NPV; I = 12; CPT NPV = 12,627.41 Do we accept or reject the project? Computing NPV for the Project Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.8 Section 9.1 (B) Again, the calculator used for the illustration is the TI BA-II plus. The basic procedure is the same; you start with the year 0 cash flow and then enter the cash flows in order. F01, F02, etc. are used to set the frequency of a cash flow occurrence. Many calculators only require you to use this function if the frequency is something other than 1. Since we have a positive NPV, we should accept the project. Does the NPV rule account for the time value of money? Does the NPV rule account for the risk of the cash flows? Does the NPV rule provide an indication about the increase in value? Should we consider the NPV rule for our primary decision rule? Decision Criteria Test – NPV Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.9 Section 9.1 (B) The answer to all of these questions is yes. The risk of the cash flows is accounted for through the choice of the discount rate. Lecture Tip: The new tax law contains a provision that allows firms, in some cases, to take bonus depreciation in year one up to 100 percent of the cost of the asset. This will, all else equal, increase the NPV of proposed projects. Spreadsheets are an excellent way to compute NPVs, especially when you have to compute the cash flows as well. Using the NPV function The first component is the required return entered as a decimal. The second component is the range of cash flows beginning with year 1. Subtract the initial investment after computing the NPV. Calculating NPVs with a Spreadsheet Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.10 Section 9.1 (B) Click on the Excel icon to go to an embedded Excel worksheet that has the cash flows along with the right and wrong way to compute NPV. Click on the cell with the solution to show the students the difference in the formulas. How long does it take to get the initial cost back in a nominal sense? Computation Estimate the cash flows. Subtract the future cash flows from the initial cost until the initial investment has been recovered. Decision Rule – Accept if the payback period is less than some preset limit. Payback Period Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› Section 9.2 (A) 8.11 Assume we will accept the project if it pays back within two years. Year 1: 165,000 – 63,120 = 101,880 still to recover Year 2: 101,880 – 70,800 = 31,080 still to recover Year 3: 31,080 – 91,080 = -60,000 project pays back in year 3 Do we accept or reject the project? Computing Payback Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.12 Section 9.2 (A) The payback period is year 3 if you assume that the cash flows occur at the end of the year, as we do with all of the other decision rules. If we assume that the cash flows occur evenly throughout the year, then the project pays back in 2.34 years. Either way, the payback rule would say to reject the project. Does the payback rule account for the time value of money? Does the payback rule account for the risk of the cash flows? Does the payback rule provide an indication about the increase in value? Should we consider the payback rule for our primary decision rule? Decision Criteria Test – Payback Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.13 Section 9.2 (B) The answer to all of these questions is no. Lecture Tip: The payback period can be interpreted as a naïve form of discounting if we consider the class of investments with level cash flows over arbitrarily long lives. Since the present value of a perpetuity is the payment divided by the discount rate, a payback period cutoff can be seen to imply a certain discount rate. That is: cost/annual cash flow = payback period cutoff cost = annual cash flow times payback period cutoff The PV of a perpetuity is: PV = annual cash flow / R. This illustrates the inverse relationship between the payback period cutoff and the discount rate. Advantages Easy to understand Adjusts for uncertainty of later cash flows Biased toward liquidity Disadvantages Ignores the time value of money Requires an arbitrary cutoff point Ignores cash flows beyond the cutoff date Biased against long-term projects, such as research and development, and new projects Advantages and Disadvantages of Payback Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.14 Section 9.2 (D) Teaching the payback rule seems to put one in a delicate situation – as the text indicates, the rule is flawed as an indicator of project desirability. Yet, past surveys suggest that practitioners often use it as a secondary decision measure. How can we explain this apparent discrepancy between theory and practice? While the payback period is widely used in practice, it is rarely the primary decision criterion. As William Baumol pointed out in the early 1960s, the payback rule serves as a crude “risk screening” device – the longer cash is tied up, the greater the likelihood that it will not be returned. The payback period may be helpful when mutually exclusive projects are compared. Given two similar projects with different paybacks, the project with the shorter payback is often, but not always, the better project. Similarly, the bias toward liquidity may be justifiable in such industries as healthcare, where technology changes rapidly, requiring quick payback to make machines justifiable, or in international investments where the possibility of government seizure of assets exists. Compute the present value of each cash flow and then determine how long it takes to pay back on a discounted basis. Compare to a specified required period. Decision Rule: Accept the project if it pays back on a discounted basis within the specified time. Discounted Payback Period Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› Section 9.3 8.15 Assume we will accept the project if it pays back on a discounted basis in 2 years. Compute the PV for each cash flow and determine the payback period using discounted cash flows. Year 1: 165,000 – 63,120/1.121 = 108,643 Year 2: 108,643 – 70,800/1.122 = 52,202 Year 3: 52,202 – 91,080/1.123 = -12,627 project pays back in year 3 Do we accept or reject the project? Computing Discounted Payback Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.16 Section 9.3 No – it doesn’t pay back on a discounted basis within the required 2-year period. Does the discounted payback rule account for the time value of money? Does the discounted payback rule account for the risk of the cash flows? Does the discounted payback rule provide an indication about the increase in value? Should we consider the discounted payback rule for our primary decision rule? Decision Criteria Test – Discounted Payback Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.17 Section 9.3 The answer to the first two questions is yes. The answer to the third question is no because of the arbitrary cut-off date. Since the rule does not indicate whether or not we are creating value for the firm, it should not be the primary decision rule. Advantages Includes time value of money Easy to understand Does not accept negative estimated NPV investments when all future cash flows are positive Biased towards liquidity Disadvantages May reject positive NPV investments Requires an arbitrary cutoff point Ignores cash flows beyond the cutoff point Biased against long-term projects, such as R&D and new products Advantages and Disadvantages of Discounted Payback Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› Section 9.3 8.18 There are many different definitions for average accounting return. The one used in the book is: Average net income / average book value Note that the average book value depends on how the asset is depreciated. Need to have a target cutoff rate Decision Rule: Accept the project if the AAR is greater than a preset rate. Average Accounting Return Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.19 Section 9.4 The example in the book uses straight line depreciation to a zero salvage; that is why you can take the initial investment and divide by 2. If you use MACRS, you need to compute the BV in each period and take the average in the standard way. Assume we require an average accounting return of 25\%. Average Net Income: (13,620 + 3,300 + 29,100) / 3 = 15,340 AAR = 15,340 / 72,000 = .213 = 21.3\% Do we accept or reject the project? Computing AAR Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.20 Section 9.4 Students may ask where you came up with the 25\%. Point out that this is one of the drawbacks of this rule. There is no good theory for determining what the return should be. We generally just use some rule of thumb. This rule would indicate that we reject the project. Does the AAR rule account for the time value of money? Does the AAR rule account for the risk of the cash flows? Does the AAR rule provide an indication about the increase in value? Should we consider the AAR rule for our primary decision rule? Decision Criteria Test – AAR Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.21 Section 9.4 The answer to all of these questions is no. In fact, this rule is even worse than the payback rule in that it doesn’t even use cash flows for the analysis. It uses net income and book value. Thus, it is not surprising that most surveys indicate that few large firms employ the payback and/or AAR methods exclusively. Advantages Easy to calculate Needed information will usually be available Disadvantages Not a true rate of return; time value of money is ignored Uses an arbitrary benchmark cutoff rate Based on accounting net income and book values, not cash flows and market values Advantages and Disadvantages of AAR Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.22 Section 9.4 Lecture Tip: An alternative view of the AAR is that it is the micro-level analogue to the ROA discussed in a previous chapter. As you remember, firm ROA is normally computed as Firm Net Income / Firm Total Assets. And, it is not uncommon to employ values averaged over several quarters or years in order to smooth out this measure. Some analysts ask, “If the ROA is appropriate for the firm, why is it less appropriate for a project?” Perhaps the best answer is that whether you compute the measure for the firm or for a project, you need to recognize the limitations – it doesn’t account for risk or the time value of money and it is based on accounting, rather than market, data. This is the most important alternative to NPV. It is often used in practice and is intuitively appealing. It is based entirely on the estimated cash flows and is independent of interest rates found elsewhere. Internal Rate of Return Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.23 Section 9.5 The IRR rule is very important. Management, and individuals in general, often have a much better feel for percentage returns, and the value that is created, than they do for dollar increases. A dollar increase doesn’t appear to provide as much information if we don’t know what the initial expenditure was. Whether or not the additional information is relevant is another issue. Definition: IRR is the return that makes the NPV = 0 Decision Rule: Accept the project if the IRR is greater than the required return. IRR – Definition and Decision Rule Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› Section 9.5 8.24 If you do not have a financial calculator, then this becomes a trial and error process. Calculator Enter the cash flows as you did with NPV. Press IRR and then CPT. IRR = 16.13\% > 12\% required return Do we accept or reject the project? Computing IRR Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.25 Section 9.5 Many of the financial calculators will compute the IRR as soon as it is pressed; others require that you press compute. NPV Profile for the Project IRR = 16.13\% Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.26 Section 9.5 Note that the NPV profile is also a form of sensitivity analysis. NPV 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14000000000000001 0.16 0.18 0.2 0.22 60000 50760 42121 34031 26446 19324 12627 6323 381 -5227 -10525 -15536 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14000000000000001 0.16 0.18 0.2 0.22 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14000000000000001 0.16 0.18 0.2 0.22 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14000000000000001 0.16 0.18 0.2 0.22 Discount Rate NPV Does the IRR rule account for the time value of money? Does the IRR rule account for the risk of the cash flows? Does the IRR rule provide an indication about the increase in value? Should we consider the IRR rule for our primary decision criteria? Decision Criteria Test - IRR Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.27 Section 9.5 The answer to all of these questions is yes, although it is not always as obvious. The IRR rule accounts for time value because it is finding the rate of return that equates all of the cash flows on a time value basis. The IRR rule accounts for the risk of the cash flows because you compare it to the required return, which is determined by the risk of the project. The IRR rule provides an indication of value because we will always increase value if we can earn a return greater than our required return. We could consider the IRR rule as our primary decision criteria, but as we will see, it has some problems that the NPV does not have. That is why we end up choosing the NPV as our ultimate decision rule. Knowing a return is intuitively appealing It is a simple way to communicate the value of a project to someone who doesn’t know all the estimation details. If the IRR is high enough, you may not need to estimate a required return, which is often a difficult task. Advantages of IRR Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.28 Section 9.5 You should point out, however, that if you get a very large IRR then you should go back and look at your cash flow estimates again. In competitive markets, extremely high IRRs should be rare. Also, since the IRR calculation assumes that you can reinvest future cash flows at the IRR, a high IRR may be unrealistic. You start with the cash flows the same as you did for the NPV. You use the IRR function. You first enter your range of cash flows, beginning with the initial cash flow. You can enter a guess, but it is not necessary. The default format is a whole percent – you will normally want to increase the decimal places to at least two. Calculating IRRs With A Spreadsheet Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.29 Section 9.5 Click on the Excel icon to go to an embedded spreadsheet so that you can illustrate how to compute IRR on the spreadsheet. Summary Net Present Value Accept Payback Period Reject Discounted Payback Period Reject Average Accounting Return Reject Internal Rate of Return Accept Summary of Decisions for the Project Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.30 Section 9.5 So, what should we do? We have two rules that indicate to accept and three that indicate to reject. NPV and IRR will generally give us the same decision. Exceptions: Nonconventional cash flows – cash flow signs change more than once Mutually exclusive projects Initial investments are substantially different (issue of scale). Timing of cash flows is substantially different. NPV vs. IRR Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› Section 9.5 (A) 8.31 When the cash flows change sign more than once, there is more than one IRR. When you solve for IRR you are solving for the root of an equation, and when you cross the x-axis more than once, there will be more than one return that solves the equation. If you have more than one IRR, which one do you use to make your decision? IRR and Nonconventional Cash Flows Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.32 Section 9.5 (A) Lecture Tip: A good introduction to mutually exclusive projects and non-conventional cash flows is to provide examples that students can relate to. An excellent example of mutually exclusive projects is the choice of which college or university to attend. Many students apply and are accepted to more than one college, yet they cannot attend more than one at a time. Consequently, they have to decide between mutually exclusive projects. Nonconventional cash flows and multiple IRRs occur when there is a net cost to shutting down a project. The most common examples deal with collecting natural resources. After the resource has been harvested, there is generally a cost associated with restoring the environment. Suppose an investment will cost $90,000 initially and will generate the following cash flows: Year 1: 132,000 Year 2: 100,000 Year 3: -150,000 The required return is 15\%. Should we accept or reject the project? Another Example: Nonconventional Cash Flows Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.33 Section 9.5 (A) NPV = – 90,000 + 132,000 / 1.15 + 100,000 / (1.15)2 – 150,000 / (1.15)3 = 1,769.54 Calculator: CF0 = -90,000; C01 = 132,000; F01 = 1; C02 = 100,000; F02 = 1; C03 = -150,000; F03 = 1; I = 15; CPT NPV = 1769.54 If you compute the IRR on the calculator, you get 10.11\% because it is the first one that you come to. So, if you just blindly use the calculator without recognizing the uneven cash flows, NPV would say to accept and IRR would say to reject. Another type of nonconventional cash flow involves a “financing” project, where there is a positive cash flow followed by a series of negative cash flows. This is the opposite of an “investing” project. In this case, our decision rule reverses, and we accept a project if the IRR is less than the cost of capital, since we are borrowing at a lower rate. NPV Profile IRR = 10.11\% and 42.66\% Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› 8.34 Section 9.5 (A) You should accept the project if the required return is between 10.11\% and 42.66\%. NPV 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55000000000000004 -8000 -3158.41 -52.59 1769.54 2638.89 2800 2435.14 1681.15 641.4 -605.6 -2000 -3496.02 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55000000000000004 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55000000000000004 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55000000000000004 Discount Rate NPV The NPV is positive at a required return of 15\%, so you should Accept. If you use the financial calculator, you would get an IRR of 10.11\% which would tell you to Reject. You need to recognize that there are non-conventional cash flows and look at the NPV profile. Summary of Decision Rules Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9-‹#› Section 9.5 (A) 8.35 Mutually exclusive projects If you choose one, you can’t choose the other. Example: You can choose to attend graduate school at either Harvard or Stanford, but not both. Intuitively, you would use the following decision rules: NPV – choose the project with the higher NPV IRR – choose the project with the higher IRR IRR and Mutually … CHAPTER 6 DISCOUNTED CASH FLOW VALUATION (CALCULATOR) Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.1 This version relies primarily on the financial calculator with a brief presentation of formulas. The calculator discussed is the TI-BA-II+. The slides are easy to modify for whatever calculator you prefer. Determine the future and present value of investments with multiple cash flows Explain how loan payments are calculated and how to find the interest rate on a loan Describe how loans are amortized or paid off Show how interest rates are quoted (and misquoted) Key Concepts and Skills Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› Future and Present Values of Multiple Cash Flows Valuing Level Cash Flows: Annuities and Perpetuities Comparing Rates: The Effect of Compounding Loan Types and Loan Amortization Chapter Outline Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› You think you will be able to deposit $4,000 at the end of each of the next three years in a bank account paying 8 percent interest. You currently have $7,000 in the account. How much will you have in three years? How much will you have in four years? Multiple Cash Flows – FV (Example 6.1) Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› Section 6.1 (A) 5.4 Find the value at year 3 of each cash flow and add them together. Today’s (year 0) CF: 3 N; 8 I/Y; -7,000 PV; CPT FV = 8817.98 Year 1 CF: 2 N; 8 I/Y; -4,000 PV; CPT FV = 4,665.60 Year 2 CF: 1 N; 8 I/Y; -4,000 PV; CPT FV = 4,320 Year 3 CF: value = 4,000 Total value in 3 years = 8,817.98 + 4,665.60 + 4,320 + 4,000 = 21,803.58 Value at year 4: 1 N; 8 I/Y; -21,803.58 PV; CPT FV = 23,547.87 Multiple Cash Flows – FV (Example 6.1, CTD.) Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.5 Section 6.1 (A) The students can read the example in the book. It is also provided here. You think you will be able to deposit $4,000 at the end of each of the next three years in a bank account paying 8 percent interest. You currently have $7,000 in the account. How much will you have in three years? In four years? Point out that there are several ways that this can be worked. The book works this example by rolling the value forward each year. The presentation will show the second way to work the problem, finding the future value at the end for each cash flow and then adding. Point out that you can find the value of a set of cash flows at any point in time, all you have to do is get the value of each cash flow at that point in time and then add them together. I entered the PV as negative for two reasons. (1) It is a cash outflow since it is an investment. (2) The FV is computed as positive, and the students can then just store each calculation and then add from the memory registers, instead of writing down all of the numbers and taking the risk of keying something back into the calculator incorrectly. Formula: Today (year 0): FV = 7000(1.08)3 = 8,817.98 Year 1: FV = 4,000(1.08)2 = 4,665.60 Year 2: FV = 4,000(1.08) = 4,320 Year 3: value = 4,000 Total value in 3 years = 8817.98 + 4665.60 + 4320 + 4000 = 21,803.58 Value at year 4 = 21,803.58(1.08) = 23,547.87 Suppose you invest $500 in a mutual fund today and $600 in one year. If the fund pays 9\% annually, how much will you have in two years? Year 0 CF: 2 N; -500 PV; 9 I/Y; CPT FV = 594.05 Year 1 CF: 1 N; -600 PV; 9 I/Y; CPT FV = 654.00 Total FV = 594.05 + 654.00 = 1,248.05 Multiple Cash Flows – FV Example 2 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.6 Section 6.1 (A) Formula: FV = 500(1.09)2 + 600(1.09) = 1,248.05 How much will you have in 5 years if you make no further deposits? First way: Year 0 CF: 5 N; -500 PV; 9 I/Y; CPT FV = 769.31 Year 1 CF: 4 N; -600 PV; 9 I/Y; CPT FV = 846.95 Total FV = 769.31 + 846.95 = 1,616.26 Second way – use value at year 2: 3 N; -1,248.05 PV; 9 I/Y; CPT FV = 1,616.26 Multiple Cash Flows – FV Example 2 (ctd.) Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.7 Section 6.1 (A) Formula: First way: FV = 500(1.09)5 + 600(1.09)4 = 1,616.26 Second way: FV = 1248.05(1.09)3 = 1,616.26 Suppose you plan to deposit $100 into an account in one year and $300 into the account in three years. How much will be in the account in five years if the interest rate is 8\%? Year 1 CF: 4 N; -100 PV; 8 I/Y; CPT FV = 136.05 Year 3 CF: 2 N; -300 PV; 8 I/Y; CPT FV = 349.92 Total FV = 136.05 + 349.92 = 485.97 Multiple Cash Flows – FV Example 3 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.8 Section 6.1 (A) Formula: FV = 100(1.08)4 + 300(1.08)2 = 136.05 + 349.92 = 485.97 Find the PV of each cash flow and add them Year 1 CF: N = 1; I/Y = 12; FV = 200; CPT PV = -178.57 Year 2 CF: N = 2; I/Y = 12; FV = 400; CPT PV = -318.88 Year 3 CF: N = 3; I/Y = 12; FV = 600; CPT PV = -427.07 Year 4 CF: N = 4; I/Y = 12; FV = 800; CPT PV = -508.41 Total PV = 178.57 + 318.88 + 427.07 + 508.41 = 1,432.93 Multiple Cash Flows – pv (Example 6.3) Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.9 Section 6.1 (B) The students can read the example in the book. You are offered an investment that will pay you $200 in one year, $400 the next year, $600 the next year and $800 at the end of the fourth year. You can earn 12 percent on very similar investments. What is the most you should pay for this one? Point out that the question could also be phrased as “How much is this investment worth?” Remember the sign convention. The negative numbers imply that we would have to pay 1,432.93 today to receive the cash flows in the future. Formula: Year 1 CF: 200 / (1.12)1 = 178.57 Year 2 CF: 400 / (1.12)2 = 318.88 Year 3 CF: 600 / (1.12)3 = 427.07 Year 4 CF: 800 / (1.12)4 = 508.41 Example 6.3 Timeline 0 1 2 3 4 200 400 600 800 178.57 318.88 427.07 508.41 1,432.93 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› Section 6.1 (B) 5.10 You can use the PV or FV functions in Excel to find the present value or future value of a set of cash flows. Setting the data up is half the battle – if it is set up properly, then you can just copy the formulas. Click on the Excel icon for an example. Multiple Cash Flows Using a Spreadsheet Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.11 Section 6.1 (B) Click on the tabs at the bottom of the worksheet to move from a future value example to a present value example. Lecture Tip: The present value of a series of cash flows depends heavily on the choice of discount rate. You can easily illustrate this dependence in the spreadsheet on Slide 6.10 by changing the cell that contains the discount rate. A separate worksheet on the slide provides a graph of the relationship between PV and the discount rate. You are considering an investment that will pay you $1,000 in one year, $2,000 in two years, and $3,000 in three years. If you want to earn 10\% on your money, how much would you be willing to pay? N = 1; I/Y = 10; FV = 1,000; CPT PV = -909.09 N = 2; I/Y = 10; FV = 2,000; CPT PV = -1,652.89 N = 3; I/Y = 10; FV = 3,000; CPT PV = -2,253.94 PV = 909.09 + 1,652.89 + 2,253.94 = 4,815.93 Multiple Cash Flows – PV Another Example Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.12 Section 6.1 (B) Formula: PV = 1000 / (1.1)1 = 909.09 PV = 2000 / (1.1)2 = 1,652.89 PV = 3000 / (1.1)3 = 2,253.94 PV = 909.09 + 1,652.89 + 2,253.94 = 4,815.92 Another way to use the financial calculator for uneven cash flows is to use the cash flow keys. Press CF and enter the cash flows beginning with year 0. You have to press the “Enter” key for each cash flow. Use the down arrow key to move to the next cash flow. The “F” is the number of times a given cash flow occurs in consecutive periods. Use the NPV key to compute the present value by entering the interest rate for I, pressing the down arrow, and then computing the answer. Clear the cash flow worksheet by pressing CF and then 2nd CLR Work. Multiple Uneven Cash Flows – Using the Calculator Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.13 Section 6.1 (B) The next example will be worked using the cash flow keys. Note that with the BA-II Plus, the students can double check the numbers they have entered by pressing the up and down arrows. It is similar to entering the cash flows into spreadsheet cells. Other calculators also have cash flow keys. You enter the information by putting in the cash flow and then pressing CF. You have to always start with the year 0 cash flow, even if it is zero. Remind the students that the cash flows have to occur at even intervals, so if you skip a year, you still have to enter a 0 cash flow for that year. Your broker calls you and tells you that he has this great investment opportunity. If you invest $100 today, you will receive $40 in one year and $75 in two years. If you require a 15\% return on investments of this risk, should you take the investment? Use the CF keys to compute the value of the investment. CF; CF0 = 0; C01 = 40; F01 = 1; C02 = 75; F02 = 1 NPV; I = 15; CPT NPV = 91.49 No – the broker is charging more than you would be willing to pay. Decisions, Decisions Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.14 Section 6.1 (B) You can also use this as an introduction to NPV by having the students put –100 in for CF0. When they compute the NPV, they will get –8.51. You can then discuss the NPV rule and point out that a negative NPV means that you do not earn your required return. You should also remind them that the sign convention on the regular TVM keys is NOT the same as getting a negative NPV. You are offered the opportunity to put some money away for retirement. You will receive five annual payments of $25,000 each beginning in 40 years. How much would you be willing to invest today if you desire an interest rate of 12\%? Use cash flow keys: CF; CF0 = 0; C01 = 0; F01 = 39; C02 = 25,000; F02 = 5; NPV; I = 12; CPT NPV = 1,084.71 Saving For Retirement Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› Section 6.1 (B) 5.15 Saving For Retirement Timeline 0 1 2 … 39 40 41 42 43 44 0 0 0 … 0 25K 25K 25K 25K 25K Notice that the year 0 cash flow = 0 (CF0 = 0) The cash flows in years 1 – 39 are 0 (C01 = 0; F01 = 39) The cash flows in years 40 – 44 are 25,000 (C02 = 25,000; F02 = 5) Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› Section 6.1 (B) 5.16 Suppose you are looking at the following possible cash flows: Year 1 CF = $100; Years 2 and 3 CFs = $200; Years 4 and 5 CFs = $300. The required discount rate is 7\%. What is the value of the cash flows at year 5? What is the value of the cash flows today? What is the value of the cash flows at year 3? Quick Quiz – Part I Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.17 Section 6.1 The easiest way to work this problem is to use the uneven cash flow keys and find the present value first and then compute the others based on that. CF0 = 0; C01 = 100; F01 = 1; C02 = 200; F02 = 2; C03 = 300; F03 = 2; I = 7; CPT NPV = 874.17 Value in year 5: PV = 874.17; N = 5; I/Y = 7; CPT FV = 1,226.07 Value in year 3: PV = 874.17; N = 3; I/Y = 7; CPT FV = 1,070.90 Using formulas and one CF at a time: Year 1 CF: FV5 = 100(1.07)4 = 131.08; PV0 = 100 / 1.07 = 93.46; FV3 = 100(1.07)2 = 114.49 Year 2 CF: FV5 = 200(1.07)3 = 245.01; PV0 = 200 / (1.07)2 = 174.69; FV3 = 200(1.07) = 214 Year 3 CF: FV5 = 200(1.07)2 = 228.98; PV0 = 200 / (1.07)3 = 163.26; FV3 = 200 Year 4 CF: FV5 = 300(1.07) = 321; PV0 = 300 / (1.07)4 = 228.87; PV3 = 300 / 1.07 = 280.37 Year 5 CF: FV5 = 300; PV0 = 300 / (1.07)5 = 213.90; PV3 = 300 / (1.07)2 = 262.03 Value at year 5 = 131.08 + 245.01 + 228.98 + 321 + 300 = 1,226.07 Present value today = 93.46 + 174.69 + 163.26 + 228.87 + 213.90 = 874.18 (difference due to rounding) Value at year 3 = 114.49 + 214 + 200 + 280.37 + 262.03 = 1,070.89 (difference due to rounding) Annuity – finite series of equal payments that occur at regular intervals If the first payment occurs at the end of the period, it is called an ordinary annuity. If the first payment occurs at the beginning of the period, it is called an annuity due. Perpetuity – infinite series of equal payments Annuities and Perpetuities Defined Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› Section 6.2 5.18 Perpetuity: PV = C / r Annuities: Annuities and Perpetuities – Basic Formulas Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.19 Section 6.2 Lecture Tip: The annuity factor approach is a short-cut approach in the process of calculating the present value of multiple cash flows and it is only applicable to a finite series of level cash flows. Financial calculators have reduced the need for annuity factors, but it may still be useful from a conceptual standpoint to show that the PVIFA is just the sum of the PVIFs across the same time period. You can use the PMT key on the calculator for the equal payment. The sign convention still holds. Ordinary annuity versus annuity due You can switch your calculator between the two types by using the 2nd BGN 2nd Set on the TI BA-II Plus. If you see “BGN” or “Begin” in the display of your calculator, you have it set for an annuity due. Most problems are ordinary annuities. Annuities and the Calculator Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.20 Section 6.2 Other calculators also have a key that allows you to switch between Beg/End. After carefully going over your budget, you have determined you can afford to pay $632 per month toward a new sports car. You call up your local bank and find out that the going rate is 1 percent per month for 48 months. How much can you borrow? To determine how much you can borrow, we need to calculate the present value of $632 per month for 48 months at 1 percent per month. Annuity – Example 6.5 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› Section 6.2 (A) 5.21 You borrow money TODAY so you need to compute the present value. 48 N; 1 I/Y; -632 PMT; CPT PV = 23,999.54 ($24,000) Formula: Annuity – Example 6.5 (ctd.) Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.22 Section 6.2 (A) The students can read the example in the book. After carefully going over your budget, you have determined you can afford to pay $632 per month towards a new sports car. You call up your local bank and find out that the going rate is 1 percent per month for 48 months. How much can you borrow? Note that the difference between the answer here and the one in the book is due to the rounding of the Annuity PV factor in the book. Suppose you win the Publishers Clearinghouse $10 million sweepstakes. The money is paid in equal annual end-of-year installments of $333,333.33 over 30 years. If the appropriate discount rate is 5\%, how much is the sweepstakes actually worth today? 30 N; 5 I/Y; 333,333.33 PMT; CPT PV = 5,124,150.29 Annuity – Sweepstakes Example Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.23 Section 6.2 (A) Formula: PV = 333,333.33[1 – 1/1.0530] / .05 = 5,124,150.29 You are ready to buy a house, and you have $20,000 for a down payment and closing costs. Closing costs are estimated to be 4\% of the loan value. You have an annual salary of $36,000, and the bank is willing to allow your monthly mortgage payment to be equal to 28\% of your monthly income. The interest rate on the loan is 6\% per year with monthly compounding (.5\% per month) for a 30-year fixed rate loan. How much money will the bank loan you? How much can you offer for the house? Buying a House Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.24 Section 6.2 (A) It might be good to note that the outstanding balance on the loan at any point in time is simply the present value of the remaining payments. Bank loan Monthly income = 36,000 / 12 = 3,000 Maximum payment = .28(3,000) = 840 30×12 = 360 N .5 I/Y -840 PMT CPT PV = 140,105 Total Price Closing costs = .04(140,105) = 5,604 Down payment = 20,000 – 5,604 = 14,396 Total Price = 140,105 + 14,396 = 154,501 Buying a House (ctd.) Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.25 Section 6.2 (A) You might point out that you would probably not offer 154,501. The more likely scenario would be 154,500 , or less if you assumed negotiations would occur. Formula PV = 840[1 – 1/1.005360] / .005 = 140,105 The present value and future value formulas in a spreadsheet include a place for annuity payments. Click on the Excel icon to see an example. Annuities on the Spreadsheet – Example Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› Section 6.2 (A) 5.26 You know the payment amount for a loan, and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive 5,000 per month in retirement. If you can earn 0.75\% per month and you expect to need the income for 25 years, how much do you need to have in your account at retirement? Quick Quiz – Part II Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.27 Section 6.2 (A) Calculator PMT = 5,000; N = 25×12 = 300; I/Y = .75; CPT PV = 595,808 Formula PV = 5000[1 – 1 / 1.0075300] / .0075 = 595,808 Suppose you want to borrow $20,000 for a new car. You can borrow at 8\% per year, compounded monthly (8/12 = .66667\% per month). If you take a 4-year loan, what is your monthly payment? 4(12) = 48 N; 20,000 PV; .66667 I/Y; CPT PMT = 488.26 Finding the Payment Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.28 Section 6.2 (A) Formula 20,000 = PMT[1 – 1 / 1.006666748] / .0066667 PMT = 488.26 Another TVM formula that can be found in a spreadsheet is the payment formula. PMT(rate, nper, pv, fv) The same sign convention holds as for the PV and FV formulas. Click on the Excel icon for an example. Finding the Payment on a Spreadsheet Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› Section 6.2 (A) 5.29 You ran a little short on your spring break vacation, so you put $1,000 on your credit card. You can afford only the minimum payment of $20 per month. The interest rate on the credit card is 1.5 percent per month. How long will you need to pay off the $1,000? Finding the Number of Payments – Example 6.6 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› Section 6.2 (A) 5.30 The sign convention matters! 1.5 I/Y 1,000 PV -20 PMT CPT N = 93.111 months = 7.75 years And this is only if you don’t charge anything more on the card! Finding the Number of Payments – Example 6.6 (ctd.) Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.31 Section 6.2 (A) You ran a little short on your spring break vacation, so you put $1,000 on your credit card. You can only afford to make the minimum payment of $20 per month. The interest rate on the credit card is 1.5 percent per month. How long will you need to pay off the $1,000? This is an excellent opportunity to talk about credit card debt and the problems that can develop if it is not handled properly. Many students don’t understand how it works, and it is rarely discussed. This is something that students can take away from the class, even if they aren’t finance majors. 1000 = 20(1 – 1/1.015t) / .015 .75 = 1 – 1 / 1.015t 1 / 1.015t = .25 1 / .25 = 1.015t t = ln(1/.25) / ln(1.015) = 93.111 months = 7.75 years Suppose you borrow $2,000 at 5\%, and you are going to make annual payments of $734.42. How long before you pay off the loan? Sign convention matters!!! 5 I/Y 2,000 PV -734.42 PMT CPT N = 3 years Finding the Number of Payments – Another Example Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.32 Section 6.2 (A) 2000 = 734.42(1 – 1/1.05t) / .05 .136161869 = 1 – 1/1.05t 1/1.05t = .863838131 1.157624287 = 1.05t t = ln(1.157624287) / ln(1.05) = 3 years Suppose you borrow $10,000 from your parents to buy a car. You agree to pay $207.58 per month for 60 months. What is the monthly interest rate? Sign convention matters!!! 60 N 10,000 PV -207.58 PMT CPT I/Y = .75\% Finding the Rate Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› Section 6.2 (A) 5.33 Trial and Error Process Choose an interest rate and compute the PV of the payments based on this rate. Compare the computed PV with the actual loan amount. If the computed PV > loan amount, then the interest rate is too low. If the computed PV < loan amount, then the interest rate is too high. Adjust the rate and repeat the process until the computed PV and the loan amount are equal. Annuity – Finding the Rate Without a Financial Calculator Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› Section 6.2 (A) 5.34 You want to receive $5,000 per month for the next 5 years. How much would you need to deposit today if you can earn 0.75\% per month? What monthly rate would you need to earn if you only have $200,000 to deposit? Suppose you have $200,000 to deposit and can earn 0.75\% per month. How many months could you receive the $5,000 payment? How much could you receive every month for 5 years? Quick Quiz – Part III Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.35 Section 6.2 (A) Q1: 5(12) = 60 N; .75 I/Y; 5000 PMT; CPT PV = -240,867 PV = 5000(1 – 1 / 1.007560) / .0075 = 240,867 Q2: -200,000 PV; 60 N; 5000 PMT; CPT I/Y = 1.439\% Trial and error without calculator Q3: -200,000 PV; .75 I/Y; 5000 PMT; CPT N = 47.73 (47 months plus partial payment in month 48) 200,000 = 5000(1 – 1 / 1.0075t) / .0075 .3 = 1 – 1/1.0075t 1.0075t = 1.428571429 t = ln(1.428571429) / ln(1.0075) = 47.73 months Q4: -200,000 PV; 60 N; .75 I/Y; CPT PMT = 4,151.67 200,000 = C(1 – 1/1.007560) / .0075 C = 4,151.67 Suppose you begin saving for your retirement by depositing $2,000 per year in an IRA. If the interest rate is 7.5\%, how much will you have in 40 years? Remember the sign convention! 40 N 7.5 I/Y -2,000 PMT CPT FV = 454,513.04 Future Values for Annuities Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.36 Section 6.2 (B) FV = 2000(1.07540 – 1)/.075 = 454,513.04 Lecture Tip: It should be emphasized that annuity factor tables (and the annuity factors in the formulas) assumes that the first payment occurs one period from the present, with the final payment at the end of the annuity’s life. If the first payment occurs at the beginning of the period, then FV’s have one additional period for compounding and PV’s have one less period to be discounted. Consequently, you can multiply both the future value and the present value by (1 + r) to account for the change in timing. You are saving for a new house and you put $10,000 per year in an account paying 8\%. The first payment is made today. How much will you have at the end of 3 years? 2nd BGN 2nd Set (you should see BGN in the display) 3 N -10,000 PMT 8 I/Y CPT FV = 35,061.12 2nd BGN 2nd Set (be sure to change it back to an ordinary annuity) Annuity Due Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.37 Section 6.2 (C) Note that the procedure for changing the calculator to an annuity due is similar on other calculators. Formula: FV = 10,000[(1.083 – 1) / .08](1.08) = 35,061.12 What if it were an ordinary annuity? FV = 32,464 (so you receive an additional 2,597.12 by starting to save today.) Annuity Due Timeline 0 1 2 3 10000 10000 10000 32,464 35,016.12 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.38 Section 6.2 (C) If you use the regular annuity formula, the FV will occur at the same time as the last payment. To get the value at the end of the third period, you have to take it forward one more period. Suppose the Fellini Co. wants to sell preferred stock at $100 per share. A similar issue of preferred stock already outstanding has a price of $40 per share and offers a dividend of $1 every quarter. What dividend will Fellini have to offer if the preferred stock is going to sell? Perpetuity – Example 6.7 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› Section 6.2 (D) 5.39 Perpetuity formula: PV = C / r Current required return: 40 = 1 / r r = .025 or 2.5\% per quarter Dividend for new preferred: 100 = C / .025 C = 2.50 per quarter Perpetuity – Example 6.7 (ctd.) Copyright … CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY (CALCULATOR) Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.1 This version relies primarily on the financial calculator with a brief presentation of formulas. The calculator discussed is the TI BA-II+. The slides are easy to modify for whatever calculator you prefer. Determine the future value of an investment made today Determine the present value of cash to be received at a future date Find the return on an investment Calculate how long it takes for an investment to reach a desired value Key Concepts and Skills Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› Future Value and Compounding Present Value and Discounting More about Present and Future Values Chapter Outline Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› Present Value – earlier money on a time line Future Value – later money on a time line Interest rate – “exchange rate” between earlier money and later money Discount rate Cost of capital Opportunity cost of capital Required return Basic Definitions Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.4 Section 5.1 It’s important to point out that there are many different ways to refer to the interest rate that we use in time value of money calculations. Students often get confused with the terminology, especially since they tend to think of an “interest rate” only in terms of loans and savings accounts. Suppose you invest $1,000 for one year at 5\% per year. What is the future value in one year? Interest = 1,000(.05) = 50 Value in one year = principal + interest = 1,000 + 50 = 1,050 Future Value (FV) = 1,000(1 + .05) = 1,050 Suppose you leave the money in for another year. How much will you have two years from now? FV = 1,000(1.05)(1.05) = 1,000(1.05)2 = 1,102.50 Future Value – Example 1 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.5 Section 5.1 (A) Point out that we are just using algebra when deriving the FV formula. We have 1,000(1) + 1,000(.05) = 1,000(1+.05) FV = PV(1 + r)t FV = future value PV = present value r = period interest rate, expressed as a decimal t = number of periods Future value interest factor = (1 + r)t Future Value: General Formula Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› Section 5.1 (A) 4.6 Simple interest vs. Compound interest Consider the previous example FV with simple interest = 1,000 + 50 + 50 = 1,100 FV with compound interest = 1,102.50 The extra 2.50 comes from the interest of .05(50) = 2.50 earned on the first interest payment Effects of Compounding Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.7 Section 5.1 (B) Lecture Tip: Slide 5.7 distinguishes between simple interest and compound interest and can be used to emphasize the effects of compounding and earning interest on interest. It is important that students understand the impact of compounding now, or they will have more difficulty distinguishing when it is appropriate to use the APR and when it is appropriate to use the effective annual rate. Texas Instruments BA-II Plus FV = future value PV = present value I/Y = period interest rate P/Y must equal 1 for the I/Y to be the period rate Interest is entered as a percent, not a decimal N = number of periods Remember to clear the registers (CLR TVM) after each problem. Other calculators are similar in format. Calculator Keys Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.8 Section 5.1 (B) We are providing information on the Texas Instruments BA-II Plus – other calculators are similar. If you recommend or require a specific calculator other than this one, you may want to make the appropriate changes. Note: the more information students have to remember to enter, the more likely they are to make a mistake. For this reason, I normally tell my students to set P/Y = 1 and leave it that way. Then I teach them to work on a period basis, which is consistent with using the formulas. If you want them to use the P/Y function, remind them that they will need to set it every time they work a new problem and that CLR TVM does not affect P/Y. If students are having difficulty getting the correct answer, make sure they have done the following: Set decimal places to floating point (2nd Format, Dec = 9 enter) or show 4 to 5 decimal places if using an HP Double check and make sure P/Y = 1 Make sure to clear the TVM registers after finishing a problem (or before starting a problem) It is important to point out that CLR TVM clears the FV, PV, N, I/Y and PMT registers. C/CE and CLR Work DO NOT affect the TVM keys The remaining slides will work the problems using the notation provided above for calculator keys. The formulas are presented in the notes section. Suppose you invest the $1,000 from the previous example for 5 years. How much would you have? 5 N; 5 I/Y; 1,000 PV CPT FV = -1,276.28 The effect of compounding is small for a small number of periods, but increases as the number of periods increases. (Simple interest would have a future value of $1,250, for a difference of $26.28.) Future Value – Example 2 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.9 Section 5.1 (B) It is important at this point to discuss the sign convention in the calculator. The calculator is programmed so that cash outflows are entered as negative and inflows are entered as positive. If you enter the PV as positive, the calculator assumes that you have received a loan that you will have to repay at some point. The negative sign on the future value indicates that you would have to repay $1,276.28 in 5 years. Show the students that if they enter the 1,000 as negative, the FV will compute as a positive number. Also, you may want to point out the change sign key on the calculator. There seems to be a few students each semester that have never had to use it before. Formula: FV = 1,000(1.05)5 = 1,000(1.27628) = 1,276.28 Suppose you had a relative deposit $10 at 5.5\% interest 200 years ago. How much would the investment be worth today? 200 N; 5.5 I/Y; 10 PV CPT FV = -447,189.84 What is the effect of compounding? Simple interest = 10 + 200(10)(.055) = 120.00 Compounding added $447,069.84 to the value of the investment Future Value – Example 3 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.10 Section 5.1 (B) You might also want to point out that it doesn’t matter what order you enter the information into the calculator. Formula: FV = 10(1.055)200 = 10(44,718.9838) = 447,189.84 Suppose your company expects to increase unit sales of widgets by 15\% per year for the next 5 years. If you sell 3 million widgets in the current year, how many widgets do you expect to sell in the fifth year? 5 N;15 I/Y; 3,000,000 PV CPT FV = -6,034,072 units (remember the sign convention) Future Value as a General Growth Formula Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.11 Section 5.1 (C) Formula: FV = 3,000,000(1.15)5 = 3,000,000(2.011357187) = 6,034,072 This example also presents a good illustration of the Rule of 72, which approximates the number of years it will take to double an initial amount at a given rate. In this example, 72/15 = 4.8, or approximately 5 years. What is the difference between simple interest and compound interest? Suppose you have $500 to invest and you believe that you can earn 8\% per year over the next 15 years. How much would you have at the end of 15 years using compound interest? How much would you have using simple interest? Quick Quiz – Part I Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.12 Section 5.1 N = 15; I/Y = 8; PV = 500; CPT FV = -1,586.08 Formula: 500(1.08)15 = 500(3.172169) = 1,586.08 500 + 15(500)(.08) = 1,100 Lecture Tip: You may wish to take this opportunity to remind students that, since compound growth rates are found using only the beginning and ending values of a series, they convey nothing about the values in between. For example, a firm may state that “EPS has grown at a 10\% annually compounded rate over the last decade” in an attempt to impress investors of the quality of earnings. However, this just depends on EPS in year 1 and year 11. For example, if EPS in year 1 = $1, then a “10\% annually compounded rate” implies that EPS in year 11 is (1.10)10 = 2.5937. So, the firm could have earned $1 per share 10 years ago, suffered a string of losses, and then earned $2.59 per share this year. Clearly, this is not what is implied by management’s statement above. How much do I have to invest today to have some amount in the future? FV = PV(1 + r)t Rearrange to solve for PV = FV / (1 + r)t When we talk about discounting, we mean finding the present value of some future amount. When we talk about the “value” of something, we are talking about the present value unless we specifically indicate that we want the future value. Present Value Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.13 Section 5.2 Point out that the PV interest factor = 1 / (1 + r)t Suppose you need $10,000 in one year for the down payment on a new car. If you can earn 7\% annually, how much do you need to invest today? PV = 10,000 / (1.07)1 = 9,345.79 Calculator 1 N 7 I/Y 10,000 FV CPT PV = -9,345.79 Present Value –Example 1 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.14 Section 5.2 (A) The remaining examples will just use the calculator keys. Lecture Tip: It may be helpful to utilize the example of $100 compounded at 10 percent to emphasize the present value concept. Start with the basic formula: FV = PV(1 + r)t and rearrange to find PV = FV / (1 + r)t. Students should recognize that the discount factor is the inverse of the compounding factor. Ask the class to determine the present value of $110 and $121 if the amounts are received in one year and two years, respectively, and the interest rate is 10\%. Then demonstrate the mechanics: $100 = $110 (1 / 1.1) = 110 (.9091) $100 = $121 (1 / 1.12) = 121(.8264) The students should recognize that it was an initial investment of $100 invested at 10\% that created these two future values. You want to begin saving for your daughter’s college education and you estimate that she will need $150,000 in 17 years. If you feel confident that you can earn 8\% per year, how much do you need to invest today? N = 17; I/Y = 8; FV = 150,000 CPT PV = -40,540.34 (remember the sign convention) Present Value – Example 2 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.15 Section 5.2 (B) Formula: 150,000 / (1.08)17 = 150,000(.270268951) = 40,540.34 Your parents set up a trust fund for you 10 years ago that is now worth $19,671.51. If the fund earned 7\% per year, how much did your parents invest? N = 10; I/Y = 7; FV = 19,671.51 CPT PV = -10,000 Present Value – Example 3 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.16 Section 5.2 (B) The actual number computes to –9999.998. This is a good place to remind the students to pay attention to what the question asked, and to be reasonable in their answers. A little common sense should tell them that the original amount was 10,000 and that the calculation doesn’t come out exactly because the future value is rounded to the nearest cent. Formula: 19,671.51 / (1.07)10 = 19,671.51(.508349292) = 9999.998 = 10,000 For a given interest rate – the longer the time period, the lower the present value What is the present value of $500 to be received in 5 years? 10 years? The discount rate is 10\% 5 years: N = 5; I/Y = 10; FV = 500 CPT PV = -310.46 10 years: N = 10; I/Y = 10; FV = 500 CPT PV = -192.77 Present Value – Important Relationship I Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.17 Section 5.2 (B) Remember the sign convention. Formulas: PV = 500 / (1.1)5 = 500(.620921323) = 310.46 PV = 500 / (1.1)10 = 500(.385543289) = 192.77 For a given time period – the higher the interest rate, the smaller the present value What is the present value of $500 received in 5 years if the interest rate is 10\%? 15\%? Rate = 10\%: N = 5; I/Y = 10; FV = 500 CPT PV = -310.46 Rate = 15\%; N = 5; I/Y = 15; FV = 500 CPT PV = -248.59 Present Value – Important Relationship II Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.18 Section 5.2 (B) Formulas: PV = 500 / (1.1)5 = 500(.620921323) = 310.46 PV = 500 / (1.15)5 = 500(.497176735) = 248.59 Since there is a reciprocal relationship between PVIFs and FVIFs, you should also point out that future values increase as the interest rate increases. What is the relationship between present value and future value? Suppose you need $15,000 in 3 years. If you can earn 6\% annually, how much do you need to invest today? If you could invest the money at 8\%, would you have to invest more or less than at 6\%? How much? Quick Quiz – Part II Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.19 Section 5.2 Relationship: The mathematical relationship is PV = FV / (1 + r)t. One of the important things for them to take away from this discussion is that the present value is always less than the future value when we have positive rates of interest. N = 3; I/Y = 6; FV = 15,000; CPT PV = -12,594.29 PV = 15,000 / (1.06)3 = 15,000(.839619283) = 12,594.29 N = 3; I/Y = 8; FV = 15,000; CPT PV = -11,907.48 (Difference = 686.81) PV = 15,000 / (1.08)3 = 15,000(.793832241) = 11,907.48 PV = FV / (1 + r)t There are four parts to this equation: PV, FV, r and t If we know any three, we can solve for the fourth. If you are using a financial calculator, be sure to remember the sign convention or you will receive an error (or a nonsense answer) when solving for r or t. The Basic PV Equation - Refresher Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.20 Section 5.3 Lecture Tip: Students who fail to grasp the concept of time value often do so because it is never really clear to them that given a 10\% opportunity rate, $110 to be received in one year is equivalent to having $100 today (or $90.90 one year ago, or $82.64 two years ago, etc.). At its most fundamental level, compounding and discounting are nothing more than using a set of formulas to find equivalent values at any two points in time. In economic terms, one might stress that equivalence just means that a rational person will be indifferent between $100 today and $110 in one year, given a 10\% opportunity. This is true because she could (a) take the $100 today and invest it to have $110 in one year or (b) she could borrow $100 today and repay the loan with $110 in one year. A corollary to this concept is that one can’t (or shouldn’t) add, subtract, multiply or divide money values in different time periods unless those values are expressed in equivalent terms, i.e., at a single point in time. Often we will want to know what the implied interest rate is on an investment Rearrange the basic PV equation and solve for r FV = PV(1 + r)t r = (FV / PV)1/t – 1 If you are using formulas, you will want to make use of both the yx and the 1/x keys Discount Rate Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› Section 5.3 (B) 4.21 You are looking at an investment that will pay $1,200 in 5 years if you invest $1,000 today. What is the implied rate of interest? r = (1,200 / 1,000)1/5 – 1 = .03714 = 3.714\% Calculator – the sign convention matters!!! N = 5 PV = -1,000 (you pay 1,000 today) FV = 1,200 (you receive 1,200 in 5 years) CPT I/Y = 3.714\% Discount Rate – Example 1 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.22 Section 5.3 (B) It is very important at this point to make sure that the students have more than 2 decimal places visible on their calculator. Efficient key strokes for formula: 1,200 / 1,000 = yx 5 1/x = - 1 = .03714 If they receive an error when they try to use the financial keys, they probably forgot to enter one of the numbers as a negative. Suppose you are offered an investment that will allow you to double your money in 6 years. You have $10,000 to invest. What is the implied rate of interest? N = 6 PV = -10,000 FV = 20,000 CPT I/Y = 12.25\% Discount Rate – Example 2 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.23 Section 5.3 (B) Formula: r = (20,000 / 10,000)1/6 – 1 = .122462 = 12.25\% Suppose you have a 1-year old son and you want to provide $75,000 in 17 years towards his college education. You currently have $5,000 to invest. What interest rate must you earn to have the $75,000 when you need it? N = 17; PV = -5,000; FV = 75,000 CPT I/Y = 17.27\% Discount Rate – Example 3 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.24 Section 5.3 (B) Formula: r = (75,000 / 5,000)1/17 – 1 = .172686 = 17.27\% This is a great problem to illustrate how TVM can help you set realistic financial goals and possibly adjust your expectations based on what you can currently afford to save. What are some situations in which you might want to know the implied interest rate? You are offered the following investments: You can invest $500 today and receive $600 in 5 years. The investment is considered low risk. You can invest the $500 in a bank account paying 4\%. What is the implied interest rate for the first choice and which investment should you choose? Quick Quiz – Part III Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.25 Section 5.3 Implied rate: N = 5; PV = -500; FV = 600; CPT I/Y = 3.714\% r = (600 / 500)1/5 – 1 = 3.714\% Choose the bank account because it pays a higher rate of interest (assuming tax rates and other issues are consistent across both investments). How would the decision be different if you were looking at borrowing $500 today and either repaying at 4\%, or repaying $600? In this case, you would choose to repay $600 because you would be paying a lower rate. Start with the basic equation and solve for t (remember your logs). FV = PV(1 + r)t t = ln(FV / PV) / ln(1 + r) You can use the financial keys on the calculator as well; just remember the sign convention. Finding the Number of Periods Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.26 Section 5.3 (C) Remind the students that ln is the natural logarithm and can be found on the calculator. The rule of 72 is a quick way to estimate how long it will take to double your money: # years to double = 72 / r, where r is number of percent. You want to purchase a new car, and you are willing to pay $20,000. If you can invest at 10\% per year and you currently have $15,000, how long will it be before you have enough money to pay cash for the car? I/Y = 10; PV = -15,000; FV = 20,000 CPT N = 3.02 years Number of Periods – Example 1 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.27 Section 5.3 (C) Formula: t = ln(20,000 / 15,000) / ln(1.1) = 3.02 years Suppose you want to buy a new house. You currently have $15,000, and you figure you need to have a 10\% down payment plus an additional 5\% of the loan amount for closing costs. Assume the type of house you want will cost about $150,000 and you can earn 7.5\% per year. How long will it be before you have enough money for the down payment and closing costs? Number of Periods – Example 2 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› Section 5.3 (C) 4.28 How much do you need to have in the future? Down payment = .1(150,000) = 15,000 Closing costs = .05(150,000 – 15,000) = 6,750 Total needed = 15,000 + 6,750 = 21,750 Compute the number of periods. Using a financial calculator: PV = -15,000; FV = 21,750; I/Y = 7.5 CPT N = 5.14 years Using the formula: t = ln(21,750 / 15,000) / ln(1.075) = 5.14 years Number of Periods – Example 2 (ctd.) Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.29 Section 5.3 (C) Loan amount = 150,000 – down payment = 150,000 – 15,000 = 135,000 When might you want to compute the number of periods? Suppose you want to buy some new furniture for your family room. You currently have $500, and the furniture you want costs $600. If you can earn 6\%, how long will you have to wait if you don’t add any additional money? Quick Quiz – Part IV Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.30 Section 5.3 Calculator: PV = -500; FV = 600; I/Y = 6; CPT N = 3.13 years Formula: t = ln(600/500) / ln(1.06) = 3.13 years Use the following formulas for TVM calculations FV(rate,nper,pmt,pv) PV(rate,nper,pmt,fv) RATE(nper,pmt,pv,fv) NPER(rate,pmt,pv,fv) The formula icon is very useful when you can’t remember the exact formula. Click on the Excel icon to open a spreadsheet containing four different examples. Spreadsheet Example Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.31 Section 5.4 Click on the tabs at the bottom of the worksheet to move between examples. Many financial calculators are available online. Go to Investopedia’s website and work the following example: You need $50,000 in 10 years. If you can earn 6\% interest, how much do you need to invest today? You should get $27,919.74 Work the Web Example Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› Section 5.4 4.32 Table 5.4 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› You have $10,000 to invest for five years. How much additional interest will you earn if the investment provides a 5\% annual return, when compared to a 4.5\% annual return? How long will it take your $10,000 to double in value if it earns 5\% annually? What annual rate has been earned if $1,000 grows into $4,000 in 20 years? Comprehensive Problem Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 4.34 Section 5.4 N = 5 PV = -10,000 At I/Y = 5, the FV = 12,762.82 At I/Y = 4.5, the FV = 12,461.82 The difference is attributable to interest. That difference is 12,762.82 – 12,461.82 = 301 To double the 10,000: I/Y = 5 PV = -10,000 FV = 20,000 CPT N = 14.2 years Note, the rule of 72 indicates 72/5 = 14 years, approximately. N = 20 PV = -1,000 FV = 4,000 CPT I/Y = 7.18\% End of Chapter Chapter 5 - Calculator Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5C-‹#› 5C-‹#› 4.35 Future Value You have $10,000 to invest. You will need the money in 5 years and you expect to earn 8\% per year. How much will you have in 5 years. What are you looking for? PV = 10,000 NPER = 5 Use the FV formula: RATE = 8\% (Same as .08) FV(rate,nper,pmt,pv) Compute FV = $14,693.28 (Notice that the spreadsheet has the same sign convention as the calculators with positive inflows and negative outflows. A negative sign was placed before the FV formula to make the result positive.) Note that this problem does not include a payment, so it was entered as 0. Present Value You need $150,000 in 18 years for your daughters eductation. If you can earn 6\% per year, how much do you need to invest today? What are you looking for? FV = 150,000 NPER = 18 Use the PV formula: RATE = 6\% (Same as .06) PV(rate,nper,pmt,fv) Compute PV = $52,551.57 Rate You have $30,000 to invest and you need $45,000 for a down payment and closing costs on a house. If you want to buy the house in 2 years, what rate of interest do you need to earn? What are you looking for? PV = 30,000 FV = 45,000 Use the RATE formula: RATE(nper,pmt,pv,fv) NPER = 2 Compute RATE = 22.47\% (Note that the rate will display as a whole percent, you need to format the cell to see the decimal places.) Note a negative sign was entered before the cell reference for the FV to maintain the sign convention. Number of Periods You have $15,000 to invest right now and you figure you will need $25,000 to buy a new car. If you can earn 9\% per year, how long before you can buy the car? What are you looking for? PV = 15,000 FV = 25,000 Use the NPER formula: RATE = 9\% (Same as .09) NPER(rate,pmt,pv,fv) Compute NPER = 5.9275850487 years

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CLA 2 PAPER &AMP; PPT - FINANCIAL MANAGEMENT

CLA 2 Paper & PPT - Financial Management - Business & Finance

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