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W1.1 Equations and InequalitiesSolve the quadratic equation us.docx
- 1. W1.1 Equations and Inequalities Solve the quadratic equation using factoring: 15x2 - x = 2 Calculations Explanations of Calculations Solve the equation by making an appropriate substitution:x4– 16x2 = – 60 Calculations Explanations of Calculations Functions and Their Graphs W2.1
- 2. Use the graph for the following functions to determine domain and range for the function. Express each domain or range in set-builder notation as well as interval notation. a. b. c. Calculations Explanations of Calculations W2.2 Part I. Given the following function, y = f(x), find the indicated values: a. f(3) b. f(-2) c. f(0)
- 3. Part II. Given the function f (x) = – x2 + 7x + 50, find the indicated values: a. f(3) b. f(-3) c. f(0) Calculations Explanations of Calculations W3.3 Transformations and Algebra of Functions Given f (x) = – 3x - 3 and g(x) = 4x2 + 2x- 2, find the following: a. , find the domain b.
- 4. c. d. (don’t forget to factor and simplify if possible) Calculations Explanations of Calculations W3.4 Given f(x) = – x2 -5x + 2 and g(x) = x2 + 9, find the following: a. b. c. Calculations
- 5. Explanations of Calculations d. (-4,2) PLEASE SHOW EXPLANATION OF YOUR WORK IN THE FORMS PROVIDED! THANKS!! Danielle, g f - g f · g f ) ( x g f o ) ( x
- 6. f g o ) 3 ( f g o g f + ProblemYou are a young loan officer working for Goose River Bank in Mayville, ND.Your boss, Mr. Jefferson, has handed you the file of a new customer for the bank, Mayville Motors Inc.They are looking for a loan of $350,000 to expand their business and add a dealership in Hatton, ND.Enclosed you will find the income statement and balance sheet for Mayville Motors for the past 3 years.Conduct the necessary ratio analysis in order to determine whether to grant them a loan.After conducting the analysis, write a memo to Mr. Jefferson detailing your decision.Be sure to backup your decision using your ratios and industry averages. Income Statements200920102011Sales Revenue1,900,0001,700,0001,600,000COGS1,000,0001,100,000 1,150,000Gross Profit900,000600,000450,000Operating Expenses:Selling300,000257,000241,000General & Admin.100,00069,00072,000Leases40,00025,00030,000Depreci ation30,00035,00040,000Total Operating Expenses470,000386,000383,000Earnings Before Interest and Taxes430,000214,00067,000Interest Expense24,00029,00034,000Net Profit Before Taxes406,000185,00033,000Taxes (35%)142,10064,75011,550Net Profit After Taxes263,900120,25021,450
- 7. Balance SheetCurrent Assets:200920102011Cash $135,000$104,365$85,650Accounts Receivable111,250192,005212,410Inventories98,850157,330175 ,830Total Current Assets$345,100$453,700$473,890Property, Plant and Equipment$778,150$930,000$1,054,000Less Accumulated Depreciation170,000205,000245,000Net Property, Plant and Equipment$608,150$725,000$809,000Total Assets$953,250$1,178,700$1,282,890Current Liabilities:Accounts Payable$ 82,350$ 103,550$ 122,390Accrued Expenses37,00054,00064,300Short Term Notes Payable19,00031,00038,100Current Portion On Long-term Debt28,00043,00054,500Total Current Liabilities$ 166,350$ 231,550$ 279,290Long-term Debt:Net Long-term Debt80,000120,000155,000Total Liabilities$ 246,350$ 351,550$ 434,290Stockholders' EquityPaid-in Capital:Common Stock (75,000 shares @ $1 per share)$75,000$75,000$75,000Additional Paid In Excess of Par300,000300,000300,000Total Paid-in Capital$375,000$375,000$375,000Retained Earnings331,900452,150473,600Total Stockholders' Equity$706,900$827,150$848,600Total Liabilities and Stockholders' Equity$ 953,250$ 1,178,700$ 1,282,890 Ratios2,0092,0102,011Industry Avg.Current ratio2.071.961.703Quick Ratio1.481.281.072Average Collection Period21414822 daysInv Turnover107711Debt ratio25.84%29.83%33.85%35%Gross Profit Margin47.37%35.29%28.13%55%Earnings Per Share3.521.600.29$2.25 MemoMemoTo:From:Date:Re: FINANCIAL RATIOS Liquidity Current Ratio Current Assets
- 8. Current Liabilities Quick Ratio Current Assets – Inventory Current Liabilities Average Collection Period 365 / Accounts Receivable Turnover Accounts Receivable Turnover Credit Sales Accounts Receivable Inventory Turnover Cost of Goods Sold Inventory Operating Profitability Profit Margin Net Income Sales Return on Total Assets Net Income Total Assets Fixed Assets Turnover Sales Net Fixed Assets (Property, Plant, & Equipment) Total Asset Turnover Sales Total Assets Return on Equity Net Income Stockholders’ Equity Debt Debt Ratio Total Liabilities Total assets
- 9. Presume all sales are credit sales. Customers are given credit terms of 2/10, n/30. ProjectionsJackson Inc.Complete the project income statement and (NPV & IRR)Projected Income StatementYears12345678910111213SalesCOGSGross profitOperating expensesOperating incomeTax at 35%Net incomeNPVIRR P & LSanders Sales CompanyProfit & Loss StatementFor the Years Ended December 31, 2012, 2011, and 2010201220112010Net Sales$ 3,985,266$ 4,395,877$ 4,657,880Cost of Goods Sold3,228,0653,560,6603,772,883Gross Profit on Sales$757,201$835,217$884,997Operating Expenses:General and Administrative$310,966$299,550$219,815Selling234,550203,24 0156,340Total Operating Expenses$545,516$502,790$376,155Operating Income$211,685$332,427$508,842Other Income (Expense):Interest Income$11,320$13,220$25,610Interest Expense(20,400)(16,800)(12,000)Net Other Income($9,080)($3,580)$13,610Income Before Provision For Income Taxes$202,605$328,847$522,452Provision For Income Taxes70,912115,096182,858Net Income$131,693$213,750$339,594 Balance SheetSanders Sales CompanyBalance SheetAt December 31, 2012, 2011, and 2010Current Assets:201220112010Cash $208,335$228,242$240,362Short- term investments234,455237,700261,000Accounts Receivable391,200324,118268,400Inventories334,400295,60019 0,400Prepaid Expenses88,00064,30036,600Total Current Assets$1,256,390$1,149,960$996,762Property, Plant and Equipment$6,920,000$5,905,087$4,810,750Less Accumulated Depreciation2,300,0002,000,0001,700,000Net Property, Plant and Equipment$4,620,000$3,905,087$3,110,750Total
- 10. Assets$5,876,390$5,055,047$4,107,512Current Liabilities:Accounts Payable$ 304,900$ 203,322$ 188,335Accrued Expenses218,102189,265179,477Short Term Notes Payable265,000225,000165,000Current Portion On Long- term Debt75,00055,00035,000Total Current Liabilities$ 863,002$ 672,587$ 567,812Long-term Debt:Net Long-term Debt635,245556,010567,000Total Liabilities$ 1,498,247$ 1,228,597$ 1,134,812Stockholders' EquityPaid-in Capital:Common Stock$2,350,000$2,150,000$1,800,000Additional Paid In Excess of Par1,340,0001,120,000830,000Total Paid-in Capital$3,690,000$3,270,000$2,630,000Retained Earnings688,143556,450342,700Total Stockholders' Equity$4,378,143$3,826,450$2,972,700Total Liabilities and Stockholders' Equity$ 5,876,390$ 5,055,047$ 4,107,512 RatiosCOMPLETE The Financial Ratios for 2012, 2011, & 2010:Financial Ratios - Sanders Sales201220112010Current ratioQuick RatioAccounts Receivable TurnoverInv TurnoverDebt ratioProfit MarginReturn on AssetsReturn on EquityFixed Asset TurnoverAverage Collection Period Industry RatiosIndustry Averages - Compare w/ Sanders calculations201220112010Current ratio1.921.901.83Quick Ratio1.221.191.15A/R Turnover24.023.023.0Inv Turnover23.523.022.0Debt ratio28%27%26%Profit Margin24%24%24%Return on Assets9.00%9.00%9.00%Return on Equity12.00%12.00%12.00%Fixed Asset Turnover2.502.252.00Avg Collection Period15.2115.8715.87 Credit Decision Problem You are called to the office of David West, the senior commercial lender for your employer, Western Bank & Trust. Mr. West informs you that due to an emergency, he will be away for several days. Mr. Stevens asks that that you review the loan application of Sanders Sales Company and make a recommendation to him, in memo form, to approve or reject the
- 11. loan request. The recommendation should have attachments with appropriate financial ratio information on Sanders Sales existing financial statements, should include NPV–style evaluation of the future cash flows resulting from investment in Jackson Inc. (see below), and other financial data you deem necessary to support your recommendation. Sanders Sales Company is requesting a $450,000 loan to help them buy the stock of Jackson Inc., a competitor in the same line of business as Sanders Sales. Sanders Sales Company will use $150,000 of its own cash and investments, in addition to the loan proceeds, to pay the purchase price of $600,000. The loan would be repaid with ten annual payments including principal and interest at an 8% APR. The loan would be collateralized by the stock purchased. Sanders Sales would be a new account for Western Bank & Trust. Sanders Sales is looking for a new banker as they have outgrown the resources of their current banker. Credit reports indicate that Sanders Sales has a good credit history. Mr. West provides you the file containing the loan request, financial statements for Sanders Sales Company for the three preceding years, and financial information regarding investment cash flow information for Jackson Inc. Prospective Financial Information – Jackson Inc. Jackson’s sales in the first year following acquisition are expected to be $625,000. Sales are expected to increase by 12% per year for years 2 & 3, by 9% per year for years 4 & 5, and then decrease by 13% per year for years 6-10. Sales for years 11-13 are expected to decrease by 17% each year. (All increases and decreases are based on the previous year’s sales). It is anticipated that there will be no further sales or other cash flows after 13 years. Cost of goods sold is expected to be 62% of sales each year and
- 12. operating expenses are expected to be 12% of sales. Future cash flows are expected to be materially the same as sales, cost of goods sold and expenses. Income tax is expected to be 35% of income for all years. Presume that net income approximates annual cash inflows. Complete the projected income statement and use the net present value method to support the investment decision. The company uses an 8% cost of capital to evaluate investment decisions, using NPV as the tool to evaluate investments. Expected Outcomes 1) Compute the appropriate financial ratio information for the financial statements of Sanders Sales Company. 2) Perform the Financial Statement Projections, Net Present Value, & IRR computations for Jackson Inc. 3) Compose a memo to Mr. West, making a recommendation to approve or reject the loan request. Use the outcomes from your NPV, IRR and ratio analysis and any other pertinent financial information to support your decision. (Complete the memo in Microsoft Word and upload all parts to Moodle).