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SAMPLE SOLUTION 2.) PE ratio of WMT Relative PE ratio Average PE ratio 35.2 1.98 17.78 The PE ratio of WMT is about twice as much as the market. WMT is an agressive stock. Investors perceive WMT to be either lower risk or higher growth or both than an average stock. WMT # of shares WMT # of shares 3.) outstanding in actually The difference is due to stock splits. 1988, as reported outstanding in by Valueline (in 1988 (in millions) millions) 4,525 566 4.) Growth rate of Growth rate of Growth rate of dividends in the dividends in the dividends in the past 5 years past 10 years first 5 of the last 10 years 18.00% 21.5% 25.10% The growth rate of dividends during the last five years has been less than the growth rate during the first five years of the last ten years to give an average of 21.5% per year over the last ten years. 11 5.) Price per Share Stock Splits Dividends ($) ($) for WMT as of w/applicable declared per Year 1/1/19XX or 20XX date & ratio share for WMT for (from WSJ) (from Valueline) the year per VL 88 26.00 0.02 89 31.38 0.03 VL reports dividends 90 44.88 2/90 2:1 0.04 per current share, 91 30.25 0.04 and therefore, 92 58.88 0.05 rewrites the historical 93 64.00 2/93 2:1 0.07 information. 94 25.00 0.09 95 21.25 0.10 96 22.25 0.11 97 22.75 0.14 98 39.44 0.16 99 81.44 3/99 2:1 0.20 00 69.13 0.24 01 53.13 0.28 WMT Price Per Share on Jan 1, (1988-2001) as per WSJ 90 2:1 Stock Split, 03/99 80 Price per Share in $ 2:1 Stock Split, 2/90 70 60 50 40 30 20 10 2:1 Stock Split, 2/93 0 88 89 90 91 92 93 94 95 96 97 98 99 00 01 January 1 WMT Dividends per Year (1988-2000) as per VL 0.30 Annual Dividends in $ 2:1 Stock Split, 3/99 0.25 0.20 2:1 Stock Split, 2/90 0.15 2:1 Stock Split, 2/93 0.10 0.05 0.00 88 89 90 91 92 93 94 95 96 97 98 99 00 01 Year 12 6.) The table and graphs below are based on the following assumptions: (1) the value of one share of WMT common stock at the time of purchase (January 1, 1988) is equal to the price of the stock at that point in time; (2) the subsequent value of the one share purchased is equal to the number of shares held (adjusted for splits and stock dividends) times the current market price; (3) the dividends received are assumed to be received entirely at year end, rather than quarterly as usually is the case. 1 2 3 4 5 6 Price per Share Stock Splits Assuming 1 share purchased Value ($) of one Dividends ($) per Dividends ($) received ($) for WMT as w/applicable as of 1/1/88, number of shares share purchased share for WMT on Dec. 31 on 1 share of Jan 1 (from date & ratio held (adjusted for stock splits) 1/1/88 as of Jan for the year (from purchased 1/1/88 Year WSJ) (from Valueline) on Jan 1 1 Valueline) adjusted for splits 88 26.00 1 $26.00 $0.02 0.16 89 31.38 1 31.38 0.03 0.24 90 44.88 2/90 2:1 1 44.88 0.04 0.32 91 30.25 2 60.50 0.04 0.32 92 58.88 2 117.75 0.05 0.40 93 64.00 2/93 2:1 2 128.00 0.07 0.56 94 25.00 4 100.00 0.09 0.72 95 21.25 4 85.00 0.10 0.80 96 22.25 4 89.00 0.11 0.88 97 22.75 4 91.00 0.14 1.12 98 39.44 4 157.75 0.16 1.28 99 81.44 3/96 2:1 4 325.75 0.20 1.60 00 69.13 8 553.00 0.24 1.92 01 53.13 8 425.00 N/A N/A 8 Value of 1 Share of WMT Purchased on 1/1/88 Dividends Received at the Year-End from 1 Share Purchased on 1/1/88 Dividends 2.50 600 Received 500 2.00 Dividends in $ Value in $ 400 1.50 300 1 Share Value 1.00 200 100 0.50 0 0.00 88 90 92 94 96 98 00 88 90 92 94 96 98 00 1/1/XXXX 12/31/XXXX 13 7.) Assuming 1 share Price per Stock Splits with purchased as of 1/1/88, Value ($) of one share ($) as Price per Share applicable date & number of shares held share purchased would have ($) for WMT as of ratio (from (adjusted for stock splits) as 1/1/88 as of been reported Year Jan 1 (from WSJ) Valueline) of 1/1/19XX 1/1/19XX by VL 88 26.00 1 26.00 3.25 89 31.38 1 31.38 3.92 90 44.88 2/90 2:1 1 44.88 5.61 91 30.25 2 60.50 7.56 92 58.88 2 117.75 14.72 93 64.00 2/93 2:1 2 128.00 16.00 94 25.00 4 100.00 12.50 95 21.25 4 85.00 10.63 96 22.25 4 89.00 11.13 97 22.75 4 91.00 11.38 98 39.44 4 157.75 19.72 99 81.44 3/96 2:1 4 325.75 40.72 00 69.13 8 553.00 69.13 01 53.13 8 425.00 53.13 8 8.) Value ($) of one Capital Gains Yield Dividends ($) received for Dividend Yield for share purchased for the assuming 1 the year assuming 1 share the year assuming WMT Total 1/1/88 as of Jan 1 share purchase as purchased 1/1/88 1 share Yield for the Year of 1/1/88 purchased as of Year 88 26.00 0.2067 $0.16 0.0062 0.2129 89 31.38 0.4303 0.24 0.0076 0.4379 90 44.88 0.3482 0.32 0.0071 0.3553 91 60.50 0.9463 0.32 0.0053 0.9516 92 117.75 0.0870 0.40 0.0034 0.0904 93 128.00 -0.2188 0.56 0.0044 -0.2144 94 100.00 -0.1500 0.72 0.0072 -0.1428 95 85.00 0.0471 0.80 0.0094 0.0565 96 89.00 0.0225 0.88 0.0099 0.0324 97 91.00 0.7335 1.12 0.0123 0.7458 98 157.75 1.0650 1.28 0.0081 1.0731 99 325.75 0.6976 1.60 0.0049 0.7025 00 553.00 -0.2315 1.92 0.0035 -0.2280 01 425.00 N/A N/A N/A N/A Dividend Yield,Capital Gain Yield, and Total Yield 1.2000 1.0000 0.8000 0.6000 Total Yield 0.4000 Dividend Yield 0.2000 Capital Gain Yield 0.0000 -0.2000 88 89 90 91 92 93 94 95 96 97 98 99 00 -0.4000 Year 14 9.) Total Annual Total Yields Yields for for the Market Year WMT Portfolio 88 0.2129 0.1681 89 0.4379 0.3149 90 0.3553 -0.0317 91 0.9516 0.3055 92 0.0904 0.0767 93 -0.2144 0.0999 94 -0.1428 0.0131 95 0.0565 0.3743 96 0.0324 0.2307 97 0.7458 0.3336 98 1.0731 0.2858 99 0.7025 0.2104 The market portfolio used is the Large Cap 00 -0.2280 -0.0911 portfolio of SBBI. Yearly Market & WMT Total Returns Compared 1.20 1.00 0.80 Total Annual Yields for Total Return 0.60 WMT 0.40 Total Yields for the Market Portfolio 0.20 0.00 88 89 90 91 92 93 94 95 96 97 98 99 00 -0.20 -0.40 Year 10.) Total Risk Correlation Average Coefficient (Standard Coefficient Returns of Item Deviation) (r) (Arith.) Variation WMT 0.4401 0.5921 0.3133 1.4047 Market 0.1509 0.1762 0.8565 Because the correlation coefficient between the market and WMT is less than 1, WMT does not move perfectly with the market. However, because the value is positive it can be said that in general WMT moves in the same direction as the market. In absolute terms, WMT is more risky than is the market (WMT S.D. > Market S.D.) over the period covered. The coefficient of variation shows that WMT has more risk per unit of return. 15 11.) The total risk of a security, or a portfolio, is composed of two types of risk--systematic (nondiversifiable) and unsystematic (diversifiable) risk. Total RiskWMT (s2) = Systematic Risk + Unsystematic Risk = 0.1937 Systematic Risk = 0.0679 Unsystematic Risk = 0.1258 By not including WMT in a well-diversified portfolio, the holder of this stock is giving up the opportunity to eliminate 0.1258, WMT's unsystematic risk, measured as variance. 12.) Dividends Total Cash Date as of Initial & Final Received Flows on 12/31 Cashflows 12/31 12/31 87 -$26.00 $0.00 -$26.00 88 0.16 0.16 89 0.24 0.24 90 0.32 0.32 91 0.32 0.32 92 0.40 0.40 93 0.56 0.56 94 0.72 0.72 95 0.80 0.80 96 0.88 0.88 97 1.12 1.12 98 1.28 1.28 99 1.60 1.60 00 425.00 1.92 426.92 Internal Rate of Return (IRR) = 0.2464 The first date, 12/31/1987 is actually 1/1/1988, the date of purchase This analysis assumes that one share of WMT was purchased on 1/1/1988 and held until 12/31/2000 (or 1/1/2001). The amounts received, and subsequently the IRR obtained, fully reflect all stock splits. All taxes and transaction costs are ignored. In addition, the above computations assume that all dividends were received at year end, rather than quarterly. Finally, it is assumed that all dividends received were reinvested at 0.2464, the internal rate of return. WMT's IRR is the discount rate that equates the present value of the future cash flows (dividends and selling price) to the purchase price. 16 13.) Geometric Average Rates of Returns Geometric Geometric Average Average ReturnWMT Returnmarket 0.2467 0.1668 SUMMARY OUTPUT Regression Statistics Multiple R 0.5921369 R Square 0.3506261 Adjusted R Square 0.2915921 Standard Error 0.3704502 Observations 13 ANOVA df SS MS F Significance F Regression 1 0.815082717 0.8150827 5.9393929 0.03299266 Residual 11 1.509566718 0.1372333 Total 12 2.324649436 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 0.0090286 0.161699948 0.0558355 0.9564741 -0.34687077 0.364927966 X Variable 1 1.7273107 0.708760398 2.437087 0.0329927 0.167338828 3.287282641 14.) Difference from Possible Reasons for the Differences Between Betas Source for Beta Beta My Calculation Our Calculation 1.7273 N/A 1.) Different market portfolio used for comparison (ex. NYSE Composite, Valueline 1.1500 -0.5773 DJIA, Nasdaq Composite, Wilshire Index, etc) 2.) Different time period used for measurement (different starting / ending dates used, longer / shorter periods of observation, etc). 3.) Frequency of observations (daily, quarterly, yearly, etc). 4.) Precision of measurements taken. Based on our calculation of beta, WMT's risk is more than that of the average stock. This means that WMT would, in general, be classified aggressive. Valueline's beta for WMT suggests that WMT's risk is slightly above that of the market. ` 15.) WMT's Alpha = 0.0090 Alpha is the point where the regression line between the market's returns and a company's (or portfolio's) returns crosses the Y-axis. Based on WMT's regression line, when the market earns 0% return, WMT will earn 0.90%. 16.) The coefficient of determination, R-square, for the regression model is = 0.3506 The R-square indicates that the regression model is fairly robust. 35% of the variability in WMT returns can be explained by the market returns. 17.) The characteristic line for WMT is WMT return = 0.0090 + 1.73 x Return on the market portfolio 18.) Historical Growth Rate of Dividends = 0.2301 17 19.) Required Rate of Return for WMT (rWMT) RF = Risk Free Rate (T-Bill rate with 30 day maturity from WSJ, Jan 2, 2001) = 0.025 rm = Market Return (arithmetic average ) = 0.1762 Because we do not have much faith in our calculated beta, we will use the beta reported by VL to estimate the required rate of return. rWMT = 0.1988 20.) Intrinsic Value of WMT as of January 1, 2001 using Valueline projected cash flows g (2001-2006) = 0.1230 D1 (2001) D2 (2002 D3 (2003) D4 (2004) D5 (2005) D6 (2006) Selling Price $0.28 $0.31 0.35 0.40 0.45 0.50 77.50 V0 = 27.30 The above analysis assumes that the dividends from 2001 to 2006 will grow at a constant rate (computed as "g (2001-2006)" above.) The expected dividend at time 1 (D1) is given in the Valueline chart, as are D2 and D6. As before, all dividends are assumed to be collected at year end. The selling price used is the average selling price projected by Valueline for 2006 year end. 21.) Market Price as of January 2, 2001 is $41.44 From the analysis above, it can be said that WMT is over-priced. Ideally, a holder of any shares of WMT should sell immediately. This assumes, however, that the above analyses are correct in assessing the value of WMT. This more than likely is not the case, because of the assumptions and estimates that were necessarily made in calculating WMT's intrinsic value. The cash flows used are merely estimates created by either Valueline or myself (explained in detail in #14). A problem related to this is that even though dividend streams tend to be relatively stable, actual future dividend disbursements are independent of those in the past. They are completely at the discretion of the board of directors and therefore could vary largely from the estimated values. Another weakness evident in our intrinsic evaluation is that the test period (13 years) used to calculate beta, and subsequently the discount rate, is too long. Similarly, the sample frequency (yearly) is too large. The sample has only 13 data points. More reliable results could be obtained if the data used consisted of monthly or daily returns and over a shorter period of time, say 5 years. 22.) Wealth as of December 31, 2000 assuming a $100 investment in WMT on January 1, 1988 = $1,757.55 Wealth as of December 31, 2000 assuming a $100 investment in the market on January 1, 1988 = $743.25 We assumed that all dividends received from WMT are reinvested in WMT and market dividends are reinvested in the market portfolio. Also, that there are no taxes and transaction costs associated with these investments. 18