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Chapter 9 Solutions

Course: ACCOUNTING 203, Spring 2011
School: NYU
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9 For Chapter the Investor TO THE NET 1. a. 200 6 Disposal of discontinued operations Net income Diluted income (loss) per share: Continuing operations Discontinued operations Disposal of discontinued operations Net income $ 0.74 (.03 ) $ 0.30 .33 $ 1.04 $ .01 .43 $ 1.48 (.03 ) (.08 ) $ 1.37 Discontinued operations 200 4 $ 1.65 (.03 ) (.10 ) $ 1.52 Earnings per common Basic income (loss) per share:...

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9 For Chapter the Investor TO THE NET 1. a. 200 6 Disposal of discontinued operations Net income Diluted income (loss) per share: Continuing operations Discontinued operations Disposal of discontinued operations Net income $ 0.74 (.03 ) $ 0.30 .33 $ 1.04 $ .01 .43 $ 1.48 (.03 ) (.08 ) $ 1.37 Discontinued operations 200 4 $ 1.65 (.03 ) (.10 ) $ 1.52 Earnings per common Basic income (loss) per share: Continuing operations 200 5 $ $ .31 $ .12 .69 (.02 ) .11 .29 .96 $ b. Price / Earnings Ratio Market Price Per Share Diluted Earnings Per Share Before Nonrecurring Items 2006 $39.09 = 1.48 26.41 2005 $24.43 .69 = 35.41 2004 $23.20 .31 = 74.84 c. Percentage of Earnings Retained Net Income Before Nonrecurring Items All Dividends Net Income Before Nonrecurring Items 2006 2005 $71,563 $8,736 $71,563 $62,827 = $33,568 $9,116 $33,568 = = 87.79% = 72.84% $71,563 $24,452 $33,568 8 .01 .43 2004 $10,700 $7,292 $10,700 $3,408 = = $10,700 9 31.85% d. Dividend Payout Dividends Per Common Share Diluted Earnings Per Share Before Nonrecurring items 2006 $.20 $1.48 2005 $.20 $.69 2004 $.20 $.31 13.51% 28.99 % 64.52 % e. Dividend Yield Dividends per Common Share Market price per Common Share 2006 $.20 $39.09 2005 $.20 $24. 43 2004 $.20 $23. 20 .51% .82% .86% 2. Motorola 2006 2005 $ (404,000,000) $ 1,845,000,000 Other charges (income) $ 2 Gains on sales of investments and businesses, net $4 2004 $ 149,000,000 $ 460,000,000 3. Boeing 2006 $ a. Diluted earnings per common share b. Price/earnings ratio $ $ = 31.2 8 10 2005 $3.19 2004 $2.24 $70.24 $51.90 = 22.02 = 23.17 $3.19 $2.24 c. Percentage of earnings retained Net Income Before Nonrecurring Items All Dividends Net Income Before Nonrecurring Items 2006 $2,206 $956 2005 $2,562 $820 $2,562 $2,206 $1,250 2004 $1,820 $648 $1,820 $1,74 2 $2,56 2 67.99 % $2,206 56.66% $1,17 2 $1,82 0 64.40 % d. Dividend Payout Dividends Per Common Share Diluted Earnings Per Share Before Nonrecurring Items 2006 $1.25 $2.84 $.44 200 5 $1. 05 $3. 19 200 4 $.8 5 $2. 24 $.3 3 $.3 8 e. Dividend Yield Dividends Per Common Share Market Price Per Common Share 2006 $1.25 $88.84 1.41% 2005 $1.0 5 $70. 24 2004 $.85 1.49 1.64 $51. 90 11 % % 12 4. a. Total assets 2006 $215,666,000 2005 $172,759,000 b. Shareholders equity $161,145,000 $81,012,000 c. Common stock shares issued and outstanding 15,734,000 12,789,000 d. Total capitalization Shares issued and outstanding (a) Market price (b) (a) x (b) = 15,734,000 $31.59 $49,703,706 12,789,000 $16.95 $21,677,355 e. Total shareholders equity represents the book amount. Capitalization is equal to shares issued and outstanding multiplied by the market price per share. 13 QUESTIONS 9 - 1. Earnings per share is the amount of income earned on a share of common stock during an accounting period. 9 - 2. The Financial Accounting Standards Board suspended the reporting of earnings per share for nonpublic companies. 9- 3. Keller & Fink is a partnership. Earnings per share is a concept that only applies to corporate income statements. 9 - 4. Earnings per share is a concept that only applies to common stock. The earnings per common share computation only uses earnings available to common stockholders. To arrive at the income that applies to common stock, preferred dividends are subtracted from net income in the numerator of the ratio. 9 - 5. Since earnings pertain to an entire year, they should be related to the common shares outstanding during the year. The year -end common shares outstanding may not be representative of the shares outstanding during the year. 9 - 6. Less preferred dividends will be subtracted from net income in the numerator of the earnings per share computation. This will increase earnings per share. In practice, whether earnings per share will be increased or decreased depends on the after-tax earnings that the firm would have from the funds used to retire the preferred stock in relation to the dividend decrease. 9 - 7. Stock dividends and stock splits do not provide the firm with more funds; they only change the number of outstanding shares. Earnings per share should be related to the outstanding common stock after the stock dividend or stock split. 9- 8. Many firms try to maintain a stable percentage because they have a policy on the percentage of earnings that they want retained for internal growth. 9- 9 . Financial leverage is the use of financing with a fixed charge. Financial leverage will magnify changes in earnings available to the common shareholder. Its use is advantageous when a firm obtains a greater return on the resources obtained than the rate of interest expense. Its use is disadvantageous when a firm obtains a lower return on the resources obtained than the rate of interest expense. 14 9-10. If the interest rate rises, the degree of financial leverage will rise. For example, suppose the firm has the following pattern of earnings with $1,000,000 in long-term debt: Earnings before interest and tax Interest ($1,000,000 at 8%) Earnings before tax Degree of Financial Leverage $ 1,000,000 80,000 $ 920,000 Income Before Interest and Tax Earnings before tax = = $1,000,000 $920,000 = 1.09 If the rate of interest rises to 12%, then the degree of financial leverage will be as follows: Earnings before interest and tax Interest ($1,000,000 at 12%) Earnings before tax $ 1,000,000 120,000 $ 880,000 = $ 1,000,000 880,000 = Degree of financial leverage 1.14 The degree of financial leverage has risen. 9-11. Investors attach a higher price to securities that they feel have higher potential. This gives a higher price/earnings ratio. 9-12. A relatively new firm often has a low dividend payout ratio because it needs funds to establish itself (i.e. increase inventory, increase accounts receivable, etc.). A firm with a substantial growth record and/or substantial growth prospects needs funds for expansion. They utilize them in this manner rather than paying them out to the owners. 9-13. A low dividend yield may indicate that the firm is retaining its earnings for growth. The investor might expect to get his/her returns in the form of market price appreciation. 15 9-14. Book value is based on a mixture of valuation basis, such as historical costs. Current value accounting should make book value closer to market. 9-15. Stock options are a form of potential dilution of earnings. With the requirement that stock option expense be recorded in the income statement, the dilution will reduce earnings each year. 9-16. A relatively small number of stock appreciation rights can prove to be a material drain on future earnings and cash of a company because stock appreciation rights are tied to the future market price of the stock. 9-17. If the stock price decreases in relation to the prior year, then the estimate of total compensation expense related to the stock appreciation rights will decrease. The decrease in the estimate of total compensation expense will be added to income for the current year. 16 PROBLEMS PROBLEM 9-1 Degree of Financial Leverage Earnings Before Interest and Tax Earnings Before Tax = $975,000 + $70,000 $975,000 = $1,045,000 $975,000 = 1.07 PROBLEM 9-2 a. Degree of Financial Leverage Earnings Before Interest and Tax Earnings Before Tax = = $1,000,000 $800,000 = 1.25 b. Prior earnings before interest and tax 10% increase Adjusted income before interest and tax Interest Income before tax Tax (50% rate) Net income Earnings will increase by 12.5% to $450,000 ($400,000 x 112.5% = $450,000) $ 1,000,000 100,000 $ 1,100,000 200,000 $ 900,000 450,000 450,000 c. $800,000 200,000 600,000 300,000 $300,000 This is a decline in profit of 25%, with a decline in earnings before interest and tax of 20%. 17 PROBLEM 9-3 a. 1. Percentage of Earnings Retained = Net Income before nonrecurring items All Dividends Net Income before nonrecurring items 2007 $ 31,200,000 2. Price/Earnings Ratio 2005 $ 29,800,000 21,700,000 910,000 $ 22,610,000 8,590,000 27.53% Net income (A) Less: Common dividend Preferred dividend (B) (A) (B) = (C) (C) (A) 2006 $ 30,600,000 19,500,000 910,000 $ 20,410,000 10,190,000 33.30% 18,360,000 910,000 $ 19,270,000 10,530,000 35.34% = Market Price Per Share Fully Diluted Earnings Per Share 2007 $12.80 $1.12 = 2005 $16.30 $1.27 = 11.43 3. Dividend Payout 2006 $14.00 $1.20 = 11.67 = 12.83 Dividends Per Common Share Fully Diluted Earnings Per Share 2007 $0.90 $1.12 = 80.36% 4. Dividend Yield = 2006 $0.85 $1.20 2005 $0.82 $1.27 = 70.83% = 64.57% Dividends Per Common Share Market Price Per Common Share 2007 $0.90 $12.80 2006 $0.85 $14.00 2005 $0.82 $16.30 = 7.03% = 6.07% = 5.03% 18 5. Book Value Per Share = Total Stockholders' Equity Preferred Stock Equity Number of Common Shares Outstanding 2007 Total assets: $1,280,100,000 Less: Liabilities (800,400,000) Stockholders Equity 479,700,000 Less: Nonredeemable preferred stock (15,300,000) (A) Common stock equity $ $464,400,000 (B) Shares outstanding end of year 24,280,000 2006 $ 1,267,200,000 (A) (B) $ $ $19.13 2005 $ 1,260,400,000 (808,500,000) 458,700,000 (799,200,000) 461,200,000 (15,300,000) (15,300,000) $ $443,400,000 $ $445,900,000 23,100,000 22,500,000 $19.19 $ $19.82 b. The percentage of earnings retained is decreasing. The related ratio, dividend payout, is therefore increasing. The price/earnings ratio has been relatively stable. The dividend yield has increased and is relatively high. The market price per share is substantially below the book value. It appears that this stock is being purchased for the relatively high dividend and not for growth potential. 19 PROBLEM 9-4 a. 1. Percentage of Earnings Retained = Net Income before nonrecurring items All Dividends Net Income before nonrecurring items 2007 $ 9,100,000 2005 $ 16,500,000 (6,080,000) $ 3,020,000 Net income (B) Less: Cash dividends (A) 2006 $ 13,300,000 (5,900,000) $ 7,400,000 (6,050,000) $ 10,450,000 (A) (B) 33.19% 2. Price/Earnings Ratio = 55.64% 63.33% Market Price Per Share Fully Diluted Earnings Per Share 2007 $41.25 $2.30 = 2005 $29.00 $4.54 = 17.93 3. Dividend Payout 2006 $35.00 $3.40 = 10.29 = 6.39 Dividends Per Common Share Fully Diluted Earnings Per Share 2007 200 6 $1. 90 $3. 40 $1.90 $2.30 = 82.61% 4. Dividend Yield = 200 5 $1. 90 $4. 54 = 55.88% = 41.85% Dividends Per Common Share Market Price Per Common Share 2007 $1.90 2006 $1.9 0 20 2005 $1.9 0 $41.25 $35. 00 $29. 00 = 4.61% = 5.43% = 6.55% 21 5. Book Value Per Share = Market Price Value Ratio of Market Price to Book Value 2007 $41.25 120.5% = $34.23 2006 $35.0 0 108.0 % 2005 $29.0 0 105.0 % = $32.41 = $27.62 b. The percentage of earnings retained materially declined. The related ratio, dividend payout, materially increased. The price earnings ratio materially increased, which is difficult to explain, considering the decline in earnings and the other ratios computed. The dividend yield has declined each year, while the book value per share increased each year. The increase in market price and the increase in price earnings ratio appears to be explained by the increase in order backlog at year -end and the increase in net contracts awarded. 22 PROBLEM 9-5 Simple Earnings Per Share = Net Income Preferred Dividends Weighted Average Number of Common Shares Outstanding Year 1 $40,000 $22,500 38,000 Year 2 $42,000 $27,500 38,00 $0.46 $0.38 The decline in earnings per share is caused by the issuance of preferred stock. PROBLEM 9-6 January 1, shares outstanding July 1, two-for-one stock split Adjusted shares outstanding for the year 50,000 shares 2 (A) 100,000 October 1 stock issue 10,000 shares Proportion of year that the new shares were outstanding 0.25 Weighted average for the new shares on an annual basis (B) 2,500 Denominator of the earnings per share computation for the current year (A) + (B) 102,500 PROBLEM 9-7 Revision of 2006 earnings per share: 2006 reported earnings per share July 1, 2007 stock split Adjusted 2006 earnings per share December 31, 2007 stock split Adjusted 2006 earnings per share $ 2.00 x 0.5 $ 1.00 x 0.5 $ 0.50 Comparative Earnings Per Share 2007 2006 Earnings Per Share $1.50 $.50 PROBLEM 9-8 a. Net income Preferred dividends January 1, 2007 shares of common stock outstanding July 1, 2007 common stock issue, 1,000 shares x Numerator $ 35,000 (3,000) 20,000 $ 32,000 Earnings per share b. From (a) Less extraordinary gain Recurring earnings per share Denominator 500 20,500 $1.56 $ 32,000 5,000 $ 27,000 $1.32 20,500 shares 20,500 PROBLEM 9-9 a. Numerator $ 200,000 (10,000) Net income Preferred dividends Common shares outstanding on January 1 Common stock issue on July 1, 5,000 shares Weighted average Two-for-one stock split on December 31 Denominator 20,000 shares 2,500 (5,000 x ) 22,500 $ 190,000 2 45,000 shares $190,000/45,000 shares = $4.22 per share b. Current Year Earnings per share reported for the prior year Two-for-one stock split on December 31 of the current year ($8.00 x 0.5) = $4.00 Prior Year $8.00 $4.00 Earnings per share computed in (a) for the current year $4.22 PROBLEM 9-10 a. 1. Percentage of Earnings Retained Cash dividends Preferred dividends Total dividends Net income (B) Net income dividends (A) Percentage of earnings retained (A) (B) = Net Income before nonrecurring items All Dividends Net Income before nonrecurring items 2007 $0.80 x 25,380,000 $20,304,000 4,567,000 24,871,000 32,094,000 7,223,000 2006 $0.76 x 25,316,000 $19,240,160 930,000 20,170,160 31,049,000 10,878,840 22.51% 35.04% 2. Price/Earnings Ratio Market Price Per Share Fully Diluted Earnings Per Share = 2007 2006 $12.94 $1.08 $15.19 $1.14 = 11.98% 3. Dividend Payout = = 13.32% Dividends Per Common Share Fully Diluted Earnings Per Share 2007 2006 $0.80 $1.08 = 74.07% 4. Dividend Yield $0.76 $1.14 = 66.67% Dividends Per Common Share Market Price Per Common Share = 2007 $0.80 $12.94 $0.76 $15.19 = 6.18% 5. Book Value Per Share 2006 = 5.00% = Common Equity Common Shares Outstanding Total assets Less: total liabilities Less: nonredeemable preferred stock Common equity (A) Shares outstanding (B) 2007 $ 1,264,086,000 (823,758,000) (16,600,000) $ 423,728,000 + 25,380,000 2006 $ 1,173,924,000 (742,499,000) (16,600,000) $ 414,825,000 + 25,316,000 Book value per share (A) (B) $16.70 $16.39 b. Having the percentage of earnings retained decline provides mixed feelings. It implies that more is going to shareholders, but at the same time, earnings retained for growth have diminished. The rise in the dividend payout ratio supports this position. The price/earnings ratio has declined as a result of the drop in price. This decline indicates lower shareholder expectations but might also indicate a good time to buy. Dividend yield is up, caused by the rise in dividends and more so by the drop in price. Book value per share is up. However, book value is above market, which shows that the investors do not view the assets as worth their book value. This is not a good sign. Overall the signals are mixed. There is not enough information to determine if this is a good investment. PROBLEM 9-11 a. The major advantage of receiving stock appreciation rights instead of stock options is that the executive does not to have make a big cash outlay at the date of exercise, but rather receives a payment for the share appreciation. This helps the executives cash flow. b. The related credit is to a liability under the stock appreciation plan that would probably be classified as long-term, since exercise cannot occur until 2010. c. In 2010, the company must pay off the liability related to the appreciation in cash. For this problem, it is $30,000. In doing financial statement analysis, this future cash flow, if material, must be considered. As in this case, the full impact may not be apparent until the last year, if the market price rises sharply. PROBLEM 9-12 a. b. 3 2 Common shareholders equity divided by the number of common chares outstanding gives book value per share. Book Value Per Share = Total Stockholders Equity Preferred Stock (At Liquidation) Number of Common Shares Outstanding $1,000,000 + $1,500,000 + $500,000 - $1,100,000 150,000 Shares = $12.67 PROBLEM 9-13 a. 1. Degree of Financial Leverage = Earnings Before Interest and Tax Earnings Before Tax 2007: $110,500 + $9,500 $110,500 = 1.09 2006: $107,700 + $6,600 $107,700 = 1.06 2005: $100,450 + $6,800 $100,450 = 1.07 2004: $124,100 + $6,900 $124,100 = 1.06 2003: $119,000 + $7,000 $119,000 = 1.06 2. Earnings Per Common Share 2007: Continuing operations Extraordinary gain * Should be used in primary analysis. 2006: $2.57 2005: $2.36 2004: $3.23 2. * 67 . 69 3. $ 36 $ 2003: $2.81 3. Price/Earnings Ratio = Market Price Per Share Fully Diluted Earnings Per Share 2007: $24. 00 $2.6 7 = 8.99 2006: $22. 00 $2.5 7 = 8.56 2005: $21. 00 $2.3 6 = 8.90 2004: $37. 00 $3.2 3 = 11.46 2003: $29. 00 $2.8 1 = 10.32 4. Percentage of Earnings Retained = Net Income before nonrecurring items All Dividends Net Income before nonrecurring items 2007: $77,500 $3,920 $91,640 $77,500 = (23.30%) 2006: $74,400 $6,100 $66,410 $74,400 = 2.54% 2005: $68,350 $6,400 $60,900 $68,350 = 1.54% 2004: $93,700 $6,600 $84,970 $93,700 = 2.27% 2003: $81,600 $6,000 $81,200 $81,600 = (6.86%) 5. Dividend Payout = Dividends Per Common Share Fully Diluted Earnings Per Share 2007: $3. 16 $2. 67 = 118.35% 2006: $2. 29 $2. 57 = 89.11% 2005: $2. 10 $2. 36 = 88.98% 2004: $2. 93 $3. 23 = 90.71% 2003: $2. 80 $2. 81 = 99.64% 6. Dividend Yield = Dividends Per Common Share Market Price Per Common Share 2007: $3.1 6 $24. 00 = 13.17% 2006: $2.2 9 $22. 00 = 10.41% 2005: $2.1 0 = 10.00% $21. 00 2004: $2.9 3 $37. 00 = 7.92% 2003: $2.8 0 $29. 00 = 9.66% 7. Book Value Per Share = Total Stockholders Equity Preferred Stock Equity Number of Common Shares Outstanding 2007: $489,000 $49,000 29,000 = $15.17 2006: $514,000 $76,000 29,000 = $15.10 2005: $516,000 $80,000 29,000 = $15.03 2004: $517,000 $82,000 29,000 = $15.00 2003: $508,000 $75,000 29,000 = $14.93 8. Materiality of Options 2003 - 2007: = Stock Options Outstanding Number of Shares of Common Stock Outstanding $1,000,0 00 29,000,0 00 = 3.45% b. This firm has a very low degree of financial leverage. Earnings from continuing operations and the price/earnings ratio have been relatively stable. Practically all of the earnings have been paid out in dividends, thus, book value per share has only increased slightly. The dividend yield is very high. The market price has declined substantially. Options outstanding appear to be immaterial. In general, the investor analysis is positive if the investor wants high dividends. Growth prospects do not appear to be good. PROBLEM 9-14 a. 3 2007 ---- EPS previously reported 2007 declared a 4-for-1 stock split 2007 reported .30 EPS b. .20 .20 4 New EBIT Prior EBIT $ $ (a) Financial leverage (b) (a) x (b) c. 2005 $.80 .25 .25 .30 2006 $100 4 2,000,000 1,000,000 1,000,000 1.5 $ 1,500,000 Adjust the shares in 2007 by adding 10% additional shares. Divide the previous number of shares for 2007 by the new number of shares. This is the percentage of the previous reported earnings per share that should be reported as the adjusted earnings per share. For illustration, assume the following; (A) Previous shares 10% stock dividend (B) New number of shares (A) (B) 100,000/110,000 100,0 00 10,00 0 110,0 00 = .909 d. 3 The price/earnings ratio usually reflects investors opinions of the future prospects for the firm. e. 4 Degree of financial leverage gives a perspective on risk in the capital structure. f. 3 The earnings per share ratio is computed for common stock. g. 2 Increasing financial leverage can be a risky strategy from the viewpoint of stockholders of companies having low and falling profits. h. 1 10% x 1.3 = 13% i. 2 Dividend yield represents dividends per common share in relation to market price per common share. j. 5 Book value per share may not approximate market value per share because of all of the reasons listed. CASES CASE 9-1 CASEYS a. 1. 50,189,812 (Shares of common issued) 2. 50,189,812 (Shares of common stock outstanding) 3. Weighted average shares outstanding is used to compute earnings per share b. Diluted earnings per share c. Net earnings from continuing operations Note: Net earnings should also be considered so that all items are considered. d. Book value 2005 $469,137,000 50,189,812 2004 $439,794,0 00 50,015,862 $9.35 $8.79 e. Dividend payout 2005 $9,771 $42,532 23.0% 2004 $6,47 9 $37,8 97 17.1% 2003 $4,96 3 $41,0 12 12.1% Note: This is computed slightly different than the book formula. CASE 9-2 MET-PRO SPLIT a. 1. $5,888,379 (No change) 2. Earnings per share Basic and diluted were the same earnings per share. 0.95 x 3/4 = 0.71 3. Common stock a. Par value 0.10 b. Shares authorized 18,000,000 (No change) c. Shares issued 7,226,303 x 4/3 = 9,635,071 CASE 9-3 STOCK-BASED COMPENSATION (This case provides the opportunity to review the materiality of employee stock options on three separate companies in two widely different industries.) a. Yes. Industries that are high tech tend to have substantial stock-based compensation. We would expect Boeing and Google to use stock-based compensation more extensively than Kroger. b. Materiality of Options = Net Income Before Nonrecurring Net Income Before Nonrecurring Items Not Including Option Expense Items InIncluding Option Expense Net Income Before Nonrecurring Items Not Including Option Expense Kroger Co. ($1,115 + $72) $1,115 $1,115 + $72 = $72 $1,259 = 5.72 % Boeing Company $2,206 + $743 $2,206 $2,206 + $743 = $743 $2,249 = 25.19 % Google $3,077,446 + $17,629 + $287,485 + $59,389 + $93,597 13,077,446 $3,077,446 = $458,100 $3,077,446 = 14.89 % As expected, Boeing and Google have material stock based compensation. CASE 9-4 BIG BOY (This case provides an opportunity to compute several of the ratios introduced in this chapter.) a. 1. Degree of Financial Leverage 2007 $16,191,584 = Earnings Before Interest and Tax Earnings Before Tax 2006 $16,268,22 7 $13,496,88 5 $13,519,413 = 1.20 = 1.21 2. Price/Earnings Ratio 2007 $31.95 = Market Price Per Share Diluted Earnings Per Share, Before Nonrecurring Items 2006 $25. 70 $1.7 8 $1.78 = 17.95 = 14.4 4 3. Percentage of Earnings Retained = 2007 Net Income Before Nonrecurring Items All Dividends Net Income Before Nonrecurring Items 2006 $9,267,556 $2,239,666 $9,159,765 $2,229,327 $9,159,765 $9,267,556 $7,027,890 = $9,267,556 4. Dividend Yield $6,930,438 = $9,159,765 75.83% = Dividends Per Common Share Market Price Per Common Share 2007 $.44 1.38 = % $31.95 5. Book Value Per Share 2006 $.44 1.71 = % $25.70 = Total Stockholders Equity Preferred Stock Equity Number of Common Shares Outstanding 2007 $107,869,775 7,568,680 2,445,764 $107,869,775 = 5,122,916 75.66% $21.06 2006 $100,681,436 7,521,930 2,447,323 $100,681,436 = 5,074,607 $19.84 b. 1. Degree of financial leverage appears to be high. 2. Price/earnings ratio has increased without an earnings per share increase. This could indicate risk to the stock price. 3. Percentage of earnings retained was steady and would likely be reasonable. 4. Material decline in dividend yield. Dividend yield is relatively low. 5. Book value per share increased moderately. c. 1. Special Items 2007 Gains on sale of assets 2006 Gains on sale of assets 2005 Gains on sale of assets Life insurance benefits in excess of cash surrender value 2. 2007 Net Earnings Estimated tax rate: $4,251,857 = $13,519,413 $ 9,267,556 31.45% Special item, net of tax $250,069 x (1 31.45%) 2006 Net Earnings Estimated tax rate: $4,337,120 = $13,496,885 $ 171,422 $ 9,096,134 $ 9,159,765 32.13% Special item, net of tax $567,987 x (1 32.13%) $ 385,493 $ 8,774,272 3. 2005 Net Earnings Estimated tax rate: $4,913,997 = $19,654,822 $ 14,740,825 25.00% Gains on sale of assets $ 86,921 Life insurance gain $ 4,440,000 $ 4,526,921 Special item, net of tax $4,526,921 x (1 25.00%) $ 3,395,191 $ 11,345,634 d. 1. Frischs Restaurants Consolidated Statement of Earnings (In part) Vertical Common-Size 2007 100.0% Sales Gross profit Operating profit 10.0 5.6 2006 100.0 % 9.8 5.6 2005 100.0 % 10.9 6.5 2. Gross profit declined substantially. Operating profit declined materially. CASE 9-5 NEWS, NEWS, NEWS (This case provides an opportunity to view five-year horizontal and vertical commonsize analysis. There are also three ratios.) a. 1. The Gannett Co. Selected Financial Data Horizontal Common-Size Analysis 2006 200 5 200 4 200 3 200 2 Net operating revenues: Newspaper advertising 132.6 Newspaper circulation 112.5 Broadcasting 110.8 All other 145.1 Total 126.9 127 .4 108 .8 95. 5 126 .5 120 .0 119 .4 104 .9 106 .5 118 .2 115 .1 106 .7 102 .7 93. 3 110 .1 104 .5 100 .0 100 .0 100 .0 100 .0 100 .0 2. Only the all other area had a substantial increase. Newspaper advertising had a moderate increase. Broadcasting and newspaper circulation had minor increases. b. 1. The Gannett Co. Selected Financial Data Vertical Common-Size Analysis* 2006 200 5 200 4 200 3 200 2 Net operating revenues: Newspaper advertising 66.9 Newspaper circulation 16.3 Broadcasting 10.6 67. 9 16. 6 9.7 66. 4 16. 7 11. 3 5.6 100 .0 65. 3 18. 0 10. 9 5.7 100 .0 64. 0 18. 4 12. 2 5.5 100 .0 All other Total 6.2 100.0 5.8 100 .0 * There are some rounding differences. 2. None of the areas had substantial changes considering that the time period was from 2002 2006. Newspaper advertising increase was offset by newspaper circulation decrease. c. 1. The Gannett Co. Selected Financial Data Horizontal Common-Size 2006 200 5 200 4 200 3 200 2 125 .1 118 .3 317 .1 125 .1 116 .8 108 .1 158 .8 116 .5 105 .3 103 .8 112 .9 105 .2 100 .0 100 .0 100 .0 100 .0 Operating expenses: Cost and expenses 136.5 Depreciation Amortization of intangible assets 114.4 Total 136.0 463.9 2. Only amortization of intangible assets increased materially considering the time period. d. 1. The Gannett Co. Selected Financial Data Vertical Common-Size* 2006 2005 200 4 200 3 200 2 95.4 4.0 95. 1 4.5 95. 3 4.4 95. 1 4.7 95. 1 4.8 .4 100 .0 .2 100 .0 .2 100 .0 .2 100 .0 Operating expenses: Cost and expenses Depreciation Amortization of intangible assets Total .6 100.0 * Some rounding differences 2. Cost and expenses make up over 95% of total operating expenses. There were no major changes in this area. e. 1. Degree of Financial Leverage 2006 $1,719,482 + $288,040 $1,719,482 $2,007,522 $1,719,482 116.8 Earnings Before Interest and Tax Earnings Before Tax = 2005 $1,817,855 + $210,625 $1,817,855 $2,028,4 80 $1,817,8 55 111.6 2004 $1,960,183 + $140,647 $1,960,183 $2,100,8 30 $1,960,1 83 107.2 2. Price/Earnings Ratio 2006 $60.46 $4.90 12.34 3. Dividend Yield 2006 $1.20 $60.46 1.98% = Market Price Per Share Diluted Earnings Per Share, Before Nonrecurring Items 2005 $61. 09 $4.9 2 2004 $80. 69 $4.8 4 12.4 2 16.6 7 = Dividends Per Common Share Market Price Per Common Share 2005 $1.1 2 $61. 09 2004 $1.0 4 $80. 69 1.83 % 1.29 % f. Degree of financial leverage increased substantially. The price/earnings ratio decreased materially. The dividend yield increased materially. CASE 9-6 EAT AT MY RESTAURANT INVESTOR VIEW (This case represents an opportunity to review these restaurants from an investor view). a. Yum Brands, Inc. All-inclusive degree of financial leverage This ratio increased slightly; would likely be considered to be moderate. Diluted earnings per share before nonrecurring items 2006 $2.92 2005 $2.55 Material increase in earnings per share Percentage of earnings retained 2006 2005 82.52% 83.86% Substantial amount of earnings retained Dividend yield 2006 2005 1.47% .95% Dividend yield increased materially Price / Earnings Ratio 2006 2005 20.09 18.38 Moderate increase in price / earnings ratio Market price per share 2006 2005 $58.65 $46.88 Material increase in market price per share Panera Bread All-inclusive degree of financial leverage No financial leverage Diluted earnings per share before nonrecurring items 2006 2005 $1.84 $1.65 Material increase in earnings per share Percentage of earnings retained 100% of earnings retained Dividend yield No dividend yield Price / Earnings Ratio Material decrease in price/earnings ratio, but it is still very high. Market price per share Material decrease in market price per share Starbucks All-inclusive degree of financial leverage Very little financial leverage Diluted earnings per share 2006 2005 $.73 $.61 Material increase in diluted earnings per share Percentage of earnings retained 100% of earnings retained Dividend yield No dividend yield Price / Earnings Ratio Material decrease in price/earnings ratio, but it is still very high. Market price per share 2006 2005 $34.05 $50.10 Material decrease in market price per share b. All-inclusive degree of financial leverage Yum Brands, Inc. has a moderate all-inclusive degree of financial leverage. Starbucks has very little and Panera Bread did not have an all-inclusive degree of financial leverage. Diluted Earnings Per Share Before Nonrecurring Items All these companies had a material increase. The most substantial percentage increase was at Starbucks, followed by Yum Brands, Inc. and then Panera Bread. Percentage of Earnings Retained Yum Brands, Inc. had a substantial amount of earnings retained. Panera Bread and Starbucks retained all of their earnings. Dividend Yield Yum Brands, Inc. increased dividend yield materially, but the yield would be considered to be moderate. Panera Bread and Starbucks did not pay a dividend. Price/Earnings Ratio Moderate increase for Yum Brands, Inc. Material decrease for Panera Bread and Starbucks. Yum Brands, Inc. price/earnings ratio is substantially lower than for Panera Bread and Starbucks. Market Price Per Share Material increase for Yum Brands, Inc. Material decrease for Panera Bread and Starbucks. c. Based on the above, which firm would you select? Would select Yum Brands, Inc.; influenced partially by the lower price/earnings ratio along with the dividend. THOMSON ONE 1. This Thomson One exercise, using the Merck & Company, provides for comments on several market factors including price earnings ratio, market capitalization, and cash dividends. 2. This Thomson One exercise uses Apple Computer, Dell Computer, and HewlettPackard. Factors considered are earnings per share, forecasts and price/earnings ratio.
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NYU - ACCOUNTING - 203
Chapter 10Statement of Cash FlowsTO THE NET1. a. SIC 3812 Search, Detection, Navigation, Guidance, Aeronautical Systemsb. Item 1 BusinessNorthrop Grumman Corporation is a integrated enterprise consisting of some25 formerly separate businesses that c
NYU - ACCOUNTING - 203
Chapter 11Expanded AnalysisTO THE NET1. a. Baldor Electric Company is a leading manufacturing company of industrialelectric motors, drives, and generators, currently supplying over 8,000 customersin more than 160 industries.b.Inventory balanceInve
NYU - ACCOUNTING - 203
Chapter 12Special Industries: Banks, Utilities, Oil and Gas,Transportation, Insurance, Real Estate CompaniesTO THE NET1. a. Item 1 BusinessMarket Area CompetitionThe bank contends with considerable competition both in generating loans andattracting
NYU - ACCT - 644
Gibson, Financial Reporting & Analysis, 11eChapter 5Basics of AnalysisTo The Net1.Years Ended December 31In Millions200620052004(In millions)Operating revenue:Ocean transportationLogistics servicesProperty leasingProperty salesAgribusiness
NYU - ACCT - 644
1Chapter 6Liquidity of Short-term Assets:Related Debt-Paying AbilityTO THE NET1. a. 1. 3531 Construction Machinery & Equipment2. Item 1. BusinessFounded in 1969, JLG, Inc is the worlds leading producer of accessequipment based on gross revenues.3.
NYU - ACCT - 644
Chapter 7Long-TermDebt-Paying AbilityCOPYRIGHT 2009 South-Western, a part of Cengage Learning.Times Interest EarnedRecurring Earnings, Excluding InterestExpense, Tax Expense, Equity Earnings,and Minority EarningsInterest Expense, Including Capital
NYU - ACCT - 644
Chapter 7Long-Term Debt-Paying AbilityTO THE NET1. a. SIC 7990 Services Miscellaneous Amusement and Recreationb. Item 1 BusinessThe Walt Disney Company, together with its subsidiaries, is a diversifiedworldwide entertainment company with operations
NYU - ACCT - 644
Chapter 8ProfitabilityCOPYRIGHT 2009 South-Western, a part of Cengage Learning.Profitability Measures Exclude items of income not arising fromnormal operations Discontinued operations Extraordinary itemsCopyright 2009 by South-Western, a part of C
NYU - ACCT - 644
Chapter 8ProfitabilityTO THE NET1. a. SIC 7370 Services Computer Programming, Data Processing, Etc.b. Item 1 businessGoogle is a global technology leader focused on improving the ways peopleconnect with information.c.RevenueIncome from operations
NYU - ACCT - 644
The following are extracted from the financial statements of Frem, Inc., for 2008, 2007, and2006.Fifteen Points.2008Net salesCost of salesSelling and administrative expensesOther income:InterestOtherEarnings before tax and extraordinary creditP
NYU - BUS - 202
Chapter 1Introducing StrategicManagementOBJECTIVES1 Understand what a strategy is and identify thedifference between business-level and corporatelevel strategyUnderstand the relationship between strategy2 formulation and implementation3 Describe t
NYU - BUS - 202
Chapter 2Leading Strategically ThroughEffective Vision and MissionOBJECTIVES1 Explain how strategic leadership is essential tostrategy formulation and implementation2 Understand the relationships among vision, mission,values and strategy3 Understa
NYU - BUS - 202
Chapter 3Examining the InternalEnvironment: Resources,Capabilities, and ActivitiesOBJECTIVES1Explain the internal context of strategy2Identify a firms resources and capabilities and explaintheir role in its performance3Define dynamic capabiliti
NYU - BUS - 202
Chapter 4Exploring the External Environment:Macro and Industry DynamicsOBJECTIVES1 Explain the importance of the external context forstrategy and firm performance2 Use PESTEL to identify the macro characteristics ofthe external context3 Identify t
NYU - BUS - 202
Chapter FiveCrafting Business Strategy1OBJECTIVES1 Define generic strategies and show how theyrelate to a firms strategic position2 Describe the drivers of low-cost, differentiation, andfocus strategic positions3 Identify and explain the risks ass
NYU - BUS - 202
Chapter 7Developing CorporateStrategyOBJECTIVES1 Define corporate strategy2 Understand the roles of economies of scope andrevenue-enhancement synergy in corporatestrategy3 Explain the different forms of diversification4 Understand when it makes s
NYU - BUS - 202
Chapter 8Looking at InternationalStrategiesOBJECTIVES1 Define international strategy and identify itsimplications for the strategy diamond2 Understand why a firm would want to expandinternationally and explain the relationship betweeninternational
NYU - BUS - 202
Chapter 9Understanding Alliances andCooperative StrategiesOBJECTIVES1 Describe why strategic alliances are importantstrategy vehicles 2 Describe the motivations behind alliances andshow how theyve changed over time3 Explain the various forms and s
NYU - BUS - 202
Chapter 10Studying Mergers andAcquisitionsOBJECTIVES1 Explain the motivations behind acquisitions andshow how theyve changed over time2 Explain why mergers and acquisitions are importantvehicles of corporate strategy3 Identify the various types of
NYU - BUS - 202
Chapter 13Corporate Governance in theTwenty-First CenturyOBJECTIVES1 Explain what is meant by corporate governance2 Describe how corporate governance relates tocompetitive advantage and understand its basicprinciples and practices3 Identify the ro
UNAM MX - CHEMISTRY - 101
ESTUDIO DEL SISTEMA IO3-/I3-/IINTRODUCCINExisten diversos tipos de reacciones en la naturaleza, las cuales se dan de forma natural enel medio, ya sea por efectos climatolgicos o efectos que ocurren en los diversosintegrantes del medio. Por ello el homb
UNAM MX - CHEMISTRY - 101
UNIVERSIDAD NACIONAL AUTNOMA DE MXICOFACULTAD DE ESTUDIOS SUPERIORES CUAUTITLANINGENIERA QUMICAASIGNATURA: QUMICA ANALTICA IPROFESORA: Q. MARA EUGENIA CARBAJAL ARENASMENDOZA CAMARENA DANIEL HORACIO. EQUIPO 2CUESTIONARIOClorhdrico.PREVIO2:Determi
UNAM MX - CHEMISTRY - 101
UNIVERSIDAD NACIONAL AUTNOMA DE MXICOFACULTAD DE ESTUDIOS SUPERIORES CUAUTITLANINGENIERA QUMICAASIGNATURA: LABORATORIO MULTIDISCIPLINARIO EXPERIMENTAL IVPROFESOR: MARA DE JESS CRUZ ONOFREBIANNI RIVERA VALDIVIAINFORME EXPERIMENTAL # 6. TORRE DE ENFRI
University of Texas - ECE - EE 381K-11
Wireless Communications (Fall 2010)Iran University of Science and TechnologyInstructor: Dr. B.AbolhassaniHomework- chapter4Due Data: Monday,17 Aban 13891. Find the median path loss under the Hata model assuming fc = 900 MHz, ht = 20m, hr = 5 m andd
University of Texas - ECE - EE 381K-11
)0102 Wireless Communications (FallIran University of Science and TechnologyInstructor: Dr. B.AbolhassaniT.As: Eman MahmoodiPreparation Instruction . MATLAB mfile . simulink . . comment.
University of Texas - ECE - EE 381K-11
)0102 Wireless Communications (FallIran University of Science and Technology1 MATLAB simulation projects- projectInstructor: Dr. B.Abolhassani9831 Due data: Saturday, 15 Aban) C A . ) (function MATLAB A C ( GOS ) .( ) B) C ( GOS ) ( ).
University of Texas - ECE - EE 381K-11
)0102 Wireless Communications (FallIran University of Science and Technology2 MATLAB simulation projects- projectInstructor: Dr. B.Abolhassani9831 Due data: Tuesday, 2 Azar . two-ray .) (10log10Pr) dB ) (log10d GLOS=1 hr=2m ht=50m =-1 f=900MHz 1
University of Texas - ECE - EE 381K-11
)0102 Wireless Communications (FallIran University of Science and Technology3 MATLAB simulation projects- projectInstructor: Dr. B.Abolhassani9831 Due data: Friday, 26 Azar) MATLAB AWGN BPSK . ( SNR 0dB 12dB . )) Gray BPSK
University of Texas - ECE - EE 381K-11
)0102 Wireless Communications (FallIran University of Science and Technology4 MATLAB simulation projects- projectInstructor: Dr. B.Abolhassani9831 Due date: Saturday, 25 Day) BPSK 01msec . 0 KHz 011Hz .) . ()
University of Texas - ECE - EE 381K-11
Wireless Communications (Fall 2010)Iran University of Science and TechnologyInstructor: Dr. B.AbolhassaniQuiz 11- Assume each user of a single base station mobile radio system averagesthree calls per hour, each call lasting an average of two minutes.
Stanford - EEAP - ee359
Chapter 11. In case of an accident, there is a high chance of getting lost. The transportation cost is very high each time. However, if the infrastructure is set once, it will be very easy to use it repeatedly. Time for wireless transmission is negligibl
Stanford - EEAP - ee359
Chapter 21. Pr = Pt 103 = Pt 103 = Pt Gl 4d 4 10 4 1002 = c/fc = 0.062 Pt = 4.39KW2 Pt = 438.65KWAttenuation is very high for high frequencies 2. d= 100m ht = 10m hr = 2m delay spread = = 3. =2 (x +xl) x+x l c= 1.33x +xl =(ht + hr )2 + d2 (ht
Stanford - EEAP - ee359
Chapter 31. d = vt2r + r = d + 2hdEquivalent low-pass channel impulse response is given byc(, t) = 0 (t)ej0 (t) ( 0 (t) + 1 (t)ej1 (t) ( 1 (t)G0 (t) = 4d l with d = vt0 (t) = 2fc 0 (t) D00 (t) = d/cD0 = t 2fD0 (t)dtvfD0 (t) = cos 0 (t)0 (t)
Stanford - EEAP - ee359
Chapter 41. C = B log2 1 +C=SN0 Blog2 1+ NSB1B0As B by LHospitals ruleC=S1N0 ln 22. B = 50 MHzP = 10 mWN0 = 2 109 W/HzN = N0 BC = 6.87 Mbps.Pnew = 20 mW, C = 13.15 Mbps (for x1, log(1 + x) x)B = 100 MHz, Notice that both the bandwidth
Stanford - EEAP - ee359
Chapter 61. (a) For sinc pulse, B =12Ts Ts =12B= 5 105 sP(b) SN R = N0bB = 10Since 4-QAM is multilevel signallingPEs2sSN R = N0bB = N0 BTs = NEBB Ts = 120E SNR per symbol = Ns = 50ESNR per bit = Nb = 2.5 (a symbol has 2 bits in 4QAM)
Stanford - EEAP - ee359
Chapter 71. Ps = 103QPSK, Ps = 2Q( s ) 103 , s 0 = 10.8276.MPout (0 ) =1e 0ii=1 1 = 10, 2 = 31.6228, 3 = 100.M =10Pout = 1 e 1= 0.6613M =20Pout = 1 e 11e 0M =30Pout = 1 e 11e 0= 0.191721e2 03= 0.0197M 1e/2. p ( ) = M 1 e/
Stanford - EEAP - ee359
Chapter 101. (a)(AAH )T= (AH )T .ATT= (AT ) AT= AAH (AAH )HFor AAH ,= AAH = , i.e. eigen-values are realAAH = QQH(b) X H AAH X = (X H A)(X H A)H = X H A 0 AAH is positive semidenite.(c) IM + AAH = IM + QQH = Q(I + )QHAH positive semidenite
Stanford - EEAP - ee359
Chapter 111. See Fig 12B = 100 KHzfc-Bfc+Bfc = 100 MHzFigure 1: Band of interest.B = 50 KHz, fc = 100 MHzHeq (f ) =1=fH (f )Noise PSD = N0 W/Hz. Using this we getfc +BNoise Power ==N0 |Heq (f )|2 dffc Bfc +BN0f 2 dffc B3 (fc +B )= N
Stanford - EEAP - ee359
Chapter 151. City has 10 macro-cellseach cell has 100 users total number of users = 1000Cells are of size 1 sqkmmaximumdistance traveled to traverse = 2km2 time = 30 = 169.7sIn the new setupnumber of cells = 105 microcellstotal number of users =
Polytechnic University of Puerto Rico - EE - el630
TABLE OF CONTENTSPROBABILITY THEORYLecture 1 Lecture 2 Lecture 3 Lecture 4 Lecture 5 Lecture 6 Lecture 7 Lecture 8 Lecture 9 Lecture 10 Lecture 11 Lecture 12 Lecture 13 Basics Independence and Bernoulli Trials Random Variables Binomial Random Variable A
Polytechnic University of Puerto Rico - EE - el630
2. Independence and Bernoulli Trials (Euler, Ramanujan and Bernoulli Numbers)Independence: Events A and B are independent ifP ( AB ) = P ( A) P ( B ).(2-1) It is easy to show that A, B independent implies A, B; A, B ; A, B are all independent pairs. F
Polytechnic University of Puerto Rico - EE - el630
3. Random VariablesLet (, F, P) be a probability model for an experiment, and X a function that maps every , to a unique point x R, the set of real numbers. Since the outcome is not certain, so is the value X ( ) = x . Thus if B is some subset of R, we m
Polytechnic University of Puerto Rico - EE - el630
4. Binomial Random Variable Approximations, Conditional Probability Density Functions and Stirlings FormulaLet X represent a Binomial r.v as in (3-42). Then from (2-30) n k nk P (k1 X k 2 ) = Pn ( k ) = p q . k = k1 k = k1 k k2 k2(4-1)Since the binom
Polytechnic University of Puerto Rico - EE - el630
5. Functions of a Random VariableLet X be a r.v defined on the model (, F , P ), and suppose g(x) is a function of the variable x. DefineY = g ( X ).(5-1)Is Y necessarily a r.v? If so what is its PDF FY ( y ), pdf fY ( y ) ? Clearly if Y is a r.v, the
Polytechnic University of Puerto Rico - EE - el630
6. Mean, Variance, Moments and Characteristic FunctionsFor a r.v X, its p.d.f f X ( x) represents complete information about it, and for any Borel set B on the x-axisP ( X ( ) B ) =Bf X ( x ) dx .(6-1)Note that f X ( x) represents very detailed info
Polytechnic University of Puerto Rico - EE - el630
7. Two Random VariablesIn many experiments, the observations are expressible not as a single quantity, but as a family of quantities. For example to record the height and weight of each person in a community or the number of people and the total income i
Polytechnic University of Puerto Rico - EE - el630
8. One Function of Two Random VariablesGiven two random variables X and Y and a function g(x,y), we form a new random variable Z asZ = g ( X , Y ).(8-1)Given the joint p.d.f f XY ( x , y ), how does one obtain f Z ( z ), the p.d.f of Z ? Problems of t
Polytechnic University of Puerto Rico - EE - el630
9. Two Functions of Two Random VariablesIn the spirit of the previous lecture, let us look at an immediate generalization: Suppose X and Y are two random variables with joint p.d.f f XY ( x, y). Given two functions g ( x, y ) and h( x, y ), define the ne
Polytechnic University of Puerto Rico - EE - el630
10. Joint Moments and Joint Characteristic FunctionsFollowing section 6, in this section we shall introduce various parameters to compactly represent the information contained in the joint p.d.f of two r.vs. Given two r.vs X and Y and a function g ( x, y
Polytechnic University of Puerto Rico - EE - el630
11. Conditional Density Functions and Conditional Expected ValuesAs we have seen in section 4 conditional probability density functions are useful to update the information about an event based on the knowledge about some other related event (refer to ex
Polytechnic University of Puerto Rico - EE - el630
12. Principles of Parameter EstimationThe purpose of this lecture is to illustrate the usefulness of the various concepts introduced and studied in earlier lectures to practical problems of interest. In this context, consider the problem of estimating an
Polytechnic University of Puerto Rico - EE - el630
13. The Weak Law and the StrongLaw of Large NumbersJames Bernoulli proved the weak law of large numbers (WLLN)around 1700 which was published posthumously in 1713 in histreatise Ars Conjectandi. Poisson generalized Bernoullis theoremaround 1800, and
Polytechnic University of Puerto Rico - EE - el630
14. Stochastic ProcessesIntroduction Let denote the random outcome of an experiment. To every such outcome suppose a waveform X (t, ) X (t , ) is assigned. The collection of such X (t, ) waveforms form a X (t, ) stochastic process. The set of cfw_ k and
Polytechnic University of Puerto Rico - EE - el630
15. Poisson ProcessesIn Lecture 4, we introduced Poisson arrivals as the limiting behavior of Binomial random variables. (Refer to Poisson approximation of Binomial random variables.) From the discussion there (see (4-6)-(4-8) Lecture 4) " k arrivals occ
Polytechnic University of Puerto Rico - EE - el630
16. Mean Square EstimationGiven some information that is related to an unknown quantity of interest, the problem is to obtain a good estimate for the unknown in terms of the observed data. Suppose X 1 , X 2 , , X n represent a sequence of random variable
Polytechnic University of Puerto Rico - EE - el630
17. Long Term Trends and Hurst PhenomenaFrom ancient times the Nile river region has been known for its peculiar long-term behavior: long periods of dryness followed by long periods of yearly floods. It seems historical records that go back as far as 622
Polytechnic University of Puerto Rico - EE - el630
18. Power SpectrumFor a deterministic signal x(t), the spectrum is well defined: If X ( ) represents its Fourier transform, i.e., if X ( ) = x(t )e j t dt ,+(18-1)then | X ( ) |2 represents its energy spectrum. This follows from Parsevals theorem sinc
Polytechnic University of Puerto Rico - EE - el630
20. Extinction Probability for Queues and Martingales(Refer to section 15.6 in text (Branching processes) fordiscussion on the extinction probability). 20.1 Extinction Probability for Queues: A customer arrives at an empty server and immediately goes fo
MIT - EE - 6.432
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.432 Stochastic Processes, Detection and Estimation Problem Set 1 Spring 2004 Issued: Tuesday, February 3, 2004 Due: Tuesday, February 10, 2004Reading: For t
MIT - EE - 6.432
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.432 Stochastic Processes, Detection and Estimation Problem Set 2 Spring 2004 Issued: Tuesday, February 10, 2004 Due: Thursday, February 19, 2004Reading: For
MIT - EE - 6.432
Massachusetts Institute of TechnologyDepartment of Electrical Engineering and Computer Science6.432 Stochastic Processes, Detection and EstimationProblem Set 3Spring 2004Issued: Thursday, February 19, 2004Due: Thursday, February 26, 2004Reading: Th