...CSP Problem Set 6.1 How many solutions are there for the map-coloring problem in Figure 6.1? How many solutions if four colors are allowed? Two colors? Answer: we are looking at a map of Australia showing each of its states and territories, as in Figure 6.1, and that we are given the task of coloring each region either red, green, or blue in such a way that no neighboring regions have the same color. To formulate this as a CSP, we define the variables to be the regions: WA, NT, Q, NSW, V , SA, and T. The domain of each variable is the set {red; green; blue}. The constraints require neighboring regions to have distinct colors; for example, the allowable combinations for WA and NT are the pairs {(red; green); (red; blue); (green; red); (green; blue); (blue; red); (blue; green)} . The constraint can also be represented more succinctly as the inequality WA NOT EQUAL TO NT, provided the constraint satisfaction algorithm has some way to evaluate such expressions. There are many possible solutions, such as {WA=red; NT =green; Q=red; NSW =green; V =red; SA=blue; T =red }. 6.2 Consider the problem of placing k knights on an n x n chessboard such that no two knights are attacking each other, where k is given and k≤n^2 a. Choose a CSP formulation. In your formulation, what are the variables? b. What are the possible values of each variable? c. What sets of variables are constrained, and how? d. Now consider the problem of putting as...
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...Problem Set 1 1a. In Excel 1b. In Excel 1c. the excess rate of return on the market is 12-8=4 (Market Premium) The excess rate of return on the firm is: RFR + Alpha + Beta * Market Premium 0.08 + 0.24635305 + 1.475039082 * 0.04 = 0.385354613 2b. In Excel 2c. In Excel Degrees of Freedom is 23 @ 0.025 level of significance the critical t is 2.06866 The month coefficient is the only one that is not statistically significant. The t-stat falls within the critical t value. The coefficients for Price, Advertising, and Interest rate all fall outside the critical t value making them statistically significant. Reject the null hypothesis for Price, Advertising, and Interest rate. Accept the null hypothesis for Month. 2d. In Excel Yes all the independent variables make sense to be positive and negative. Advertising has a positive relationship because more advertising equals more sales. Price and Interest Rate both have a negative relationship because the higher the price and the higher the interest rate the less likely people are going to buy a car so sales will be lower. 2e. In a multiple linear regression model, adjusted R square measures the proportion of the variation in the dependent variable accounted for by the explanatory variables. Unlike R square, adjusted R square allows for the degrees of freedom associated with the sums of the squares. Therefore, even though the residual sum of squares decreases or remains the same as new explanatory variables...
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...Fin 450, Dr. Abraham Problem set 3 1. Suppose you constructed a pro forma balance sheet and the estimate for external funding required was negative. How would you interpret this result? 2. Curly concrete company had the following sales for the last three months. Half its sales are for cash. March SAR 26,000 April SAR 88,000 May SAR 120,000 a) What will be Curly’s cash collection in May if the collection period is 30 days? b) What if the collection period is 45 days? c) What will be balance on the May Accounts receivable account if the collection period is 30 days? if it is 45 days? 3. Cash Budget example Help Dandia’s Treasurer in preparing a cash budget for the period Jan 2009 to March 2009. The primary focus of the analysis is to determine the cash needs for the company. | Sales 20 in cash, rest in 30 days credit terms | | | | | | | 2008 Actual | | | | | | October | | € 360,000 | | | November | | 420,000 | | | December | 1,200,000 | | | | | | | 2009 Projected | | | | | | January | | € 600,000 | | | February | | 240,000 | | | March | | 240,000 | | | | | | | | | | | | Purchases all in 60 day terms | | | | | | | | 2008 Actual | | | | | | October | | € 510,000 | | | November | | 540,000 | | | December | 1,200,000 | | | | | | | 2009 Projected | | ...
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...Problem 1 a. What do you expect tuition and housing at top private schools to cost during Mary’s first year at college? PV=35,000; r=4%; N=18-5=13 FV=PV*(1+r)n =35,000*1+4%13 =58277.57 b. In nominal dollars, how much must be in the savings account on Mary’s 18th birthday after the last deposit has been made but before the first tuition and housing payment? PV18=58277.57; g=4%; r=10%*(1-τ)=10%*（1-30%）=7%; N=3 Pmt19=PV18*1+g=58277.57*1+4%=60608.67 The present value of year 18-21 at 18th year is: PV18-21=PV18+Pmt19r-g(1-(1+g1+r)N) =58277.57+60608.677%-4%1-1+4%1+7%3 =223488.53 c. What should be the amount of the first deposit to the savings account? FV=223488.53; r=10%*(1-τ)=10%*（1-30%）=7%; g=2%; N=18-5=13 Pmt1=FV1+rN-1+gNr-g =223488.531+7%13-1+2%137%-2% =10010.79 d. Alternatively, Mary’s parents could open a 529 account that allows college savings to grow tax-free. If they saved in this account rather than in a normal investment fund, and still earned the same pre-tax return, how much should be their first deposit? PV18=58277.57; g=4%; r=10%; N=3; Pmt19=PV18*1+g=58277.57*1+4%=60608.67 The present value of year 18-21 at 18th year is: PV18-21=PV18+Pmt19r-g(1-(1+g1+r)N) =58277.57+60608.6710%-4%1-1+4%1+10%3 =214721.71 FV=214721.71; r=10%; g=2%; N=18-5=13 Pmt1=FV1+rN-1+gNr-g =214721.711+10%13-1+2%1310%-2% =7957...
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...1. EP Enterprises has the following income statement. How much net operating profit after taxes (NOPAT) does the firm have? Sales $1,800.00 Costs 1,400.00 Depreciation 250.00 EBIT $ 150.00 Interest expense 70.00 EBT $ 80.00 Taxes (40%) 32.00 Net income $ 48.00 a. $81.23 b. $85.50 c. $90.00 d. $94.50 e. $99.23 2. Tibbs Inc. had the following data for the year ending 12/31/07: Net income = $300; Net operating profit after taxes (NOPAT) = $400; Total assets = $2,500; Short-term investments = $200; Stockholders' equity = $1,800; Total debt = $700; and Total operating capital = $2,300. What was its return on invested capital (ROIC)? a. 14.91% b. 15.70% c. 16.52% d. 17.39% e. 18.26% 3. Aziz Industries has sales of $100,000 and accounts receivable of $11,500, and it gives its customers 30 days to pay. The industry average DSO is 27 days, based on a 365-day year. If the company changes its credit and collection policy sufficiently to cause its DSO to fall to the industry average, and if it earns 8.0% on any cash freed-up by this change, how would that affect its net income, assuming other things are held constant? a. $267.34 b. $281.41 c. $296.22 d. $311.81 e. $328.22 4. Heaton Corp. sells on terms that allow customers 45 days to pay for merchandise...
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...Running head: PROBLEM SET I Problem Set I Problem Set I 4-20 Juan’s Taco Company has restaurants in five college towns. Juan wants to expand into Austin and College Station and needs a bank loan to do this. Mr. Bryan, the banker, will finance construction if Juan can present an acceptable three-month financial plan for January through March. The following are actual and forecasted sales figures: Table 1 Actual November $120,000 December 140,000 Forecast January $190,000 February 210,000 March 230,000 April $230,000 Of Juan’s sales, 30 percent are for cash and the remaining 70 percent are on credit. Of credit sales, 40 percent are paid in the month after sale and 60 percent are paid in the second month after the sale. Materials cost 20 percent of sales and are paid for in cash. Labor expense is 50 percent of sales and it is paid in the month of sales. Selling and administrative expense is 5 percent of sales and is paid in the month of sale. Overhead expense is $12,000 in cash per month; depreciation expense is $25,000 per month. Taxes of $20,000 and dividends of $16,000 will be paid in March. Cash at the beginning of January is $70,000 and the minimum desired cash balance is $65,000.For January, February, and March, prepare a schedule of monthly cash receipts, monthly cash payments, and a complete monthly cash budget with borrowings and repayments. Table 2 Cash Receipts Schedule Sales Credit sales (70%) Cash sales (30%) Collections (month after credit...
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...Problem Set 2 International Finance Shrikhande Fall 2006 SUGGESTED SOLUTIONS TO CHAPTER 4 PROBLEMS 1. From base price levels of 100 in 1987, West German and U.S. price levels in 1988 stood at 102 and 106, respectively. If the 1987 $/DM exchange rate was $0.54, what should the exchange rate be in 1988? In fact, the exchange rate in 1988 was DM 1 = $0.56. What might account for the discrepancy? (Price levels were measured using the consumer price index.) Answer. If e1981 is the dollar value of the German mark in 1988, then according to purchasing power parity e1988/.54 = 106/102 or e1988 = $.5612. The discrepancy between the predicted rate of $.5612 and the actual rate of $.56 is insignificant and hence needs no explaining. Historically, however, discrepancies betweenthe PPP rate and the actual rate have frequently occurred. These discrepancies could be due to mismeasurement of the relevant price indices. Estimates based on narrower price indices reflecting only traded goods prices would probably be closer to the mark, so to speak. Alternatively, it could be due to a switch in investors' preferences from dollar to non-dollar assets. 3. In early 1996, the short-term interest rate in France was 3.7%, and forecast French inflation was 1.8%. At the same time, the short-term German interest rate was 2.6% and forecast German inflation was 1.6%. a. Based on these figures, what were the real interest rates in France and Germany? Answer. The French real interest...
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...Problem Set II Problem Set II P2-6A 2013 2014 A. Earnings per share $60,000/30,000 shares= $2.00 $70,000/33,000 shares= $2.12 B. Working capital ($20,000 + $62,000 + $73,000) ($28,000 + $70,000 + $90,000) – -$70,000=$85,000 $75,000 = $113,000 C. Current ratio $155,000/$70,000= 2.2:1 $188,000/$75,000= 2.5:1 D. Debt to total assets ratio $160,000/$685,000= 23.4% $155,000/$760,000= 20.4% E. Free cash flow $56,000 – $38,000 – $15,000= $3,000 $82,000 – $45,000 – $20,000= $17,000 F. The net income and earnings have shown to have increased, in return this shows the company has grown. P13-2A A. Earnings per share $218,000/74,000=$2.95 B. Return on common on stockholders' equity $218,000/[($465,400+$603,400)/2] =$218,000/$534,400 =40.8% C. Return on assets $218,000/[($852,800+$1,026,900)/2]=$218,000/$939,850=23.2% D. Current ratio $377,900/$203,500=1.85:1 E. Receivables turnover $1,890,540/[($102,800+$117,800)/2]=$1,890,540/$110,300=17.1 F. Average collection period 365 days +17.1 =21.3 days G. Inventory turnover $1,058,540/[(115,500+$126,000)/2]=$1,058,540/$120,750=8.8 times H. Days in inventory 365 days +8.8 =41.5 days I. Times interest earned $332,000/$22,000=15.1 J. Asset turnover...
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...Problem Set I Stephen Collum ACC 300 6/17/2013 Paulette Mack P1-3A On June 1, Beardsley Service Co. was started with an initial investment in the company of $22,100 cash. Here are the assets and liabilities of the company at June 30, and the revenues and expenses for the month of June, its first month of operations: |Cash |$ 4,600 |Notes payable |$12,000 | |Accounts receivable |4,000 |Accounts payable |500 | |Service revenue |7,500 |Supplies expense |1,000 | |Supplies |2,400 |Maintenance and repairs expense |600 | |Advertising expense |400 |Utilities expense |300 | |Equipment |26,000 |Salaries and wages expense |1,400 | In June, the company issued no additional stock, but paid dividends of $1,400. Instructions 1. Prepare an income statement and a retained earnings statement for the month of June and a balance sheet at June 30, 2012. 2. Briefly discuss whether the company’s first month of operations was a success. | |Net...
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...FNCE 101 Problem Set #3 Due: 11-5-12 1. A) The private savings would not change, in the long-run, because since consumers tend to be consumption-smoothers, there would be a natural switch from the consumption of foreign goods to the consumption of domestic goods. However, in the short-run, there would be a decrease in savings because the demand for domestic goods would increase thus increasing domestic prices and since consumers are consumption-smoothers, they would dip into private savings, decreasing national private savings. The Domestic Investment would increase because there’s an incentive to invest in domestic assets because of the inevitable increase in production of domestic goods (increase in exports). The gov’t budget deficit would decrease because more domestic production would require less government spending to stimulate the U.S. economy. B) It will not necessarily decrease the current account deficit because other factors, such as net exports, net factor payments and net unilateral payments can outweigh the decrease in imports. Also, if the foreigner who was previously importing the good has a perfectly inelastic demand for American goods, this will not change their demand for American exports and therefore not change the current account deficit of the United States. 2. A) Debit- When the dollars were converted to euros because there is an increased demand for the foreign currency/ Credit- exchanged at a German bank because now the foreign bank is...
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...Problem Set #1 Date 09/22/2015 Sayantani Nandy 1. Sign into Bloomberg and check IBM's page (IBM US Equity). Check Company Overview and then Company Management. Find the composition of the Management Team and the Board and check the backgrounds of the Chair as well as the top 3 longest serving board members. (a) How many of these three board members appear to be independent? (b) What are their compensations? (c) What other board memberships or executive positions do they hold? (d) Do you think having these positions help increase or reduce agency cost and help better align the interest of shareholders with management? Answer: I will start to answer the question with a table of summary: IBM Corp Inc. Sr. No Tenure . (yrs.) 1 2 Independent Board Member CompenCurrent sation shareholding Kenneth Chenault 17.8 "Ken" Other Board/Executive Positions Company Name Title Yes / No Bloomberg Philanthropists Board Member Presidents & Fellows of Harvard Board Member College Proctor & Gamble Company Board Member No American Express Travel related Chairman services Co. American Express Co. Chairman $341,193 $ 1,031,972 BM Corp. Board Member Sidney 14.8 Taurel BioCrossroads IBM McGraw Hill Financial Mc Grawhill, Compensation and Leadership Development IBM, Executive compensation $368,724 $ 2,284,797 and management resources Name Board Member Board Member Board Member No Chairman Chairman Yes 3 Joan E. 11.8...
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...Problem Set 1 MGT-309 – Intro to Logistics Management November 23, 2014 Cosme Lucio Professor Jerry Bilbrey 2a. 2*8*44,000=704,000 .12*.75=.09 704,000/.09= 7,822,222.222222222 = 2796.823595120404 = 2797 2b. Inventory Carrying Costs = (2,797/2)*0.75*12% = $125.87 Order Costs = (44,000/2797) = 15.73 = 16, 16*$8(per order) = $128.00 Transportation Costs = 44,000 units *0.05 per unit = 2,200 (Q=2,797) = 125.87+128+2,200= 2453.87 Inventory Carrying Costs = (4,000/2)*.075*12% = $180 Order Costs = 44,000/4,000 = 11orders, 11orders*$8 per order = $88 Transportation Costs = 44,000*$0.04 per unit = $1760.00 (Q=4,000) = 180+88+1,760 = 2,028 2c. 4,000 CUPS = 11 orders, 33 days between orders 4a. Common days’ supply of chocolate chewies at DC: DS= [(42,000 – 7,000) + 18,500]/4,500 = 11.8888889 = 12(Rounded Up) 4b. Fair Share Allocation Logic: Cincinnati Allocation = (11.8888889 * 2,500) – 12,500 = 17,222.2222 Phoenix Allocation = (11.8888889 * 2,000) – 6,000 = 17,777.7778 6a. Yes. The demand never exceeded what was in stock and causing a stockout. 6b. SD = 1.811 6c. Yes. The frequency wasn’t out of bounds with mean, mode, median. 6d. SD = 1.095445 6e. SD of Combined Probabilities = 6 6g. f(k) = 0.061667 6h. k = 1.1, Required safety stock for the desired 99 percent is 6.42 with an average inventory of 36...
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...Problem Set 4 Complete all questions listed below. Clearly label your answers. 1. What determines whether a financial asset is included in the M1 money supply? Why are interest-earning checkable deposits included in M1, whereas interest-earning savings accounts and Treasury bills are not? A financial assest is included in the M1 money supply when it can be quickly converted into the physical form of money, such as dollars and coins. Interested-earning checkable deposits are included because it can be quickly accessible without limitations, such as a checking account. Interest earning savings accounts and Treasury bills are short term investments and may have a time limit. 2. Why are banks able to maintain reserves that are only a fraction of the demand and savings deposits of their customers? Is your money safe in a bank? Why or why not? Savings cannot always be withdrawn and are more stable than checking accounts, as a result banks need to maintain reserves against their checking accounts (Gwartney, et al. 2013). Yes, money is safe in banks because the Federal Deposit Insurance Corporation (FDIC) was established in 1934 as a result of the 1922 to 1933 bank runs. This insurance insures me up to $250,000 per account if the bank fails. 3. What is the Federal Funds Interest rate? if the Fed wants to use open market operations to lower the federal funds rate, what action should it take? Federal Funds Interest rate is the interest rate at which the borrowing bank...
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...Problem set 1 (*optional items) Questions and problems on global firms and governance, international monetary systems, forex markets, and parities. Global firms and governance: 1. How would you define and measure multinational corporations? A firm is called a MNC if it has controlling real assets or operating facilities in multiple countries. Operationally, it can be measured by the extent of “foreign content,” proxied by foreign sales ratios, foreign asset ratios, and foreign employee ratios, or their averages, augmented by the number of countries in which the firm has operations. 2. Define greenfield investment versus foreign direct investment. FDI involves corporate investments in real assets located aboard and includes both greenfield investment and international mergers and acquisitions. The greenfield investment involves construction of plants and equipment or R&D facilities from the scratch. 3. ESM13, chapter 2, question 8. Labor Unions. In Germany and Scandinavia, among others, labor unions have representation on boards of directors or supervisory boards. How might such union representation be viewed under the shareholder wealth maximization model compared to the corporate wealth maximization model? Labor union representation that may be required by statute is an example of governmental direction toward the corporate stakeholder model (or corporate wealth maximization model), in that such a requirement is...
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...Problem Set 1 Problem 1 Which project should the firm select? Why? Project B: Managers should try to maximize their stock’s intrinsic value while also bringing in revenue. The P/E ratio shows the dollar amount investors will pay for $1 of current earnings. Problem 2 If most investors expect the same cash flows from Companies A and B but are more confident that A’s cash flows will be closer to their expected value, which company should have the higher stock price? Explain. The primary goal of a corporation should be to maximize its owner’s value. If a manager is to maximize shareholder wealth, he/she must know how that wealth is determined. Fundamentally, shareholder wealth is the number of shares outstanding at times the market price per share. A stock’s price at any given time depends on the cash flows a “marginal” investor expects to receive after buying the stock. With that being said, Company A’s cash flow would increase the stock price and the risk would be minimal. Management’s goal should be to make decisions designed to maximize the stock’s price. Problem 3 The president of Southern Semiconductor Corporation (SSC) made this statement in the company’s annual report: “SSC’s primary goal is to increase the value of our common stock holders’ equity.” Later in the report, the following announcements were made: a. The company contributed $1.5 million to the symphony orchestra in Birmingham, Alabama, its headquarters city b. The company is spending $500 million...
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