ŠĻą”±į>ž’ KMž’’’FGHIJ’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ģ„Į#` ųæ<€bjbjm„m„ 3ŅĻĻźw)(’’’’’’¤n n n x „ „ „ ˜ ’ ’ ’8X’t$˜ ļ€ø¤¤(ĢĢĢĢĢĢn€p€p€p€p€p€p€$§‚h…Œ”€„ @ ĢĢ@ @ ”€„ „ ĢĢ©€^^^@ „ Ģ„ Ģn€^@ n€^^V‚k „ „ NuĢ˜ €”!”·Č ’Z b"ršZ}æ€0ļ€¼r’›…¼2›…Nu›…„ Nu Ģ,ųÖ^Ī¬zĘĢĢĢ”€”€īpĢĢĢļ€@ @ @ @ ˜ ˜ ˜ ³œ½„A˜ ˜ ˜ œ½˜ ˜ ˜ „ „ „ „ „ „ ’’’’  PRINCIPLES OF FINANCE REVIEW PROBLEMS To Accompany Principles of Managerial Finance, Brief, Fifth Edition by Lawrence J. Gitman Published by Pearson Prentice Hall Prepared by Dr. Robert E. Pritchard Professor of Finance William G. Rohrer College of Business Rowan University Glassboro, New Jersey Copyright 2009 by Dr. Robert E. Pritchard PRINCIPLES OF FINANCE REVIEW PROBLEMS Dr. Robert E. Pritchard Professor of Finance The following problems are provided for students taking Principles of Finance. Students should solve these problems in addition to completing their regularly assigned homework problems. Many of the problems were included in prior semesters’ tests at Rowan University. The problems are keyed to chapters in Lawrence J. Gitman’s Principle of Managerial Finance Brief, Fifth Edition. Note that Principles of Finance includes the preparation of linear graphs. Therefore, there are several problems relating to the preparation of graphs for the capital asset pricing model, revenue/cost (breakeven) relationships, and EBIT-EPS relationships. Two grids are provided on page three. Download the grids and use them when you prepare your graphs. Students should not assume that problems on future tests will be the same as those included herein or that the problems included herein cover all the materials in the assigned chapters. None of us is perfect. If you find an error or have comments, please contact Dr. Pritchard. E-mail pritchard@rowan.edu. Thank you. Grids for Drawing Graphs   Chapter 1 The Role and Environment of Managerial Finance Linda Trip purchased 1,000 shares of Waterhouse Inc. stock for $20.00 per share. The company subsequently fell on hard times and declared bankruptcy. The company now owes its creditors $2,000,000. If there are 100,000 shares of common stock outstanding, what is Linda’s liability? Answer: None. As a shareholder, Linda would have no liability. Her loss is limited to the amount she paid for the stock. Refer to problem one and determine the percentage of Waterhouse stock that Linda owns. Answer: 1% Refer to problem one and assume Waterhouse is a partnership and Linda is a 20 percent owner. Determine her liability if the company went bankrupt and owed creditors $2,000,000. Answer: As a partner, Linda is legally responsible for the entire $2,000,00 debt. New Corp. had pretax earnings from operations of $150,000. In addition, it had interest income of $20,000 and received a dividend of $80,000. New Corp. is eligible for the 70 percent intercorporate dividend exclusion. Using the corporate tax tables, determine New Corp.’s total federal tax liability. Answer: $58,910 Old Corp. had earnings before taxes (EBT) of $500,000. This amount includes $100,000 of dividend income from another corporation. Old Corp. is eligible for the 70 percent intercorporate dividend exclusion. Using the corporate tax tables, determine the following: Old Corp.’s federal tax liability. Answer: $146,200 Old Corp.’s earnings after taxes. Answer: $353,800 Old Corp.’s marginal tax rate. Answer: 34% DDD Corp. had earnings before interest and taxes (EBIT) of $200,000. It had interest expense of $40,000 and paid a preferred stock dividend of $30,000. Using the corporate tax tables, determine the following: a. DDD’s federal tax liability. Answer: $45,650 b. DDD’s earnings available to its common shareholders. Answer: $84,350 ABD Corp. had pretax earnings from operations of $200,000. In addition, it had interest income of $50,000 and received a dividend of $80,000. ABD is eligible for the 70 percent intercorporate dividend exclusion. Using the corporate tax tables, determine the following: a. ABD’s total federal tax liability. Answer: $90,110 b. ABD’s marginal tax rate. Answer: 39% At the start of the year XYZ’s common stock was selling at $36.75. By February 27 the price had increased 23 percent. Determine the price on February 27. Answer: $45.20 At the start of the year XYZ’s common stock was selling at $50 a share. By June 30 the price had increased by 15 percent. Then, the market value of the stock decreased from its value on June 30 and, by the end of the year, XYZ’s stock was 25 percent less than its value on June 30. Determine the price of XYZ’s stock at year end. Answer: $43.125 Chapter 2 Financial Statements and Analysis ABC has current assets of $15,000, a current ratio of 1.7, and inventory of $5,000. Determine the following: ABC’s current liabilities. Answer: $8,824 ABC’s quick ratio. Answer: 1.13 ABX has current assets of $10,000, a current ratio of 2.5 and inventory of $5,000. Determine ABX’s quick ratio. Answer: 1.25 ABC has current assets of $5,000, a current ratio of 1.8, and inventory of $2,000. Determine the following. ABC’s current liabilities. Answer: $2,777.78 ABC’s quick ratio. Answer: 1.08 DDD Corp. had sales of $10,000, a gross margin of 40 percent, and average inventory of $2,000. Assume a 365 day year. Determine the following: DDD’s cost of goods sold. Answer: $6,000 b. DDD’s inventory turnover. Answer: 3 times per year c. The average age of DDD’s inventory. Answer: 121.66 days ABC had earnings before taxes of $500,000 for 2006. It has a 40 percent tax rate and paid $70,000 in preferred stock dividends in 2006. At the end of 2005 it had $300,000 of retained earnings. If ABC pays common stock dividends of $150,000 during 2006, determine how much it had in retained earnings at the end of 2006. Answer: $380,000 Use the appropriate information listed below and determine the following: The firm’s gross profit. Answer: $200,000 The firm’s earnings after taxes. Answer: $36,000 The firm’s earnings per share. Answer: $3.60 The firm’s cash flow from operations. Answer: $86,000 The firm’s common stock market price. Answer: $64.80 The firm’s gross profit margin. Answer: 33% The firm’s times interest earned ratio. Answer: 3 times The firm’s return on total assets. Answer: 12% Information Provided Accounts payable $ 50,000 Cost of goods sold 400,000 Depreciation expense 50,000 General and admin expense 60,000 Interest expense 30,000 Sales revenue 600,000 Total assets 300,000 Shareholders equity 120,000 Price/earnings ratio 18 Tax rate 40 % Number of shares of common outstanding: 10,000 Use the appropriate items listed below and determine the following: The firm’s gross profit. Answer: $240,000 The firm’s earnings after taxes. Answer: $60,000 The firm’s earnings per share. Answer: $6.00 The firm’s cash flow from operations. Answer: $115,000 The market price of the common stock Answer: $72.00 Information Provided Accounts payable $200,000 Cost of goods sold 285,000 Depreciation expense 55,000 General and admin expense 60,000 Interest expense 25,000 Sales revenue 525,000 Shareholders’ equity 300,000 Accumulated depreciation 120,000 Tax rate 40 % Number of shares of common outstanding: 10,000 Price to earnings (PE) ratio 12 ABC had earnings before taxes (EBT) of $1,000,000 for 2005. It has a 40 percent tax rate, had depreciation expense of $200,000 during 2005 and paid $100,000 in preferred stock dividends in 2005. At the end of 2004 it had $3,000,000 of retained earnings. At the end of 2005 it had $3,400,000 of retained earnings and there were 100,000 shares of common stock outstanding. Determine the following. The earnings available to common shareholders in 2005. Answer: $500,000 The per share common stock dividend (if any) paid during 2005. Answer: $1.00 The following year-end information financial statement information is provided below for ABC Inc. Sales $14,000 Inventory $3,000 Operating Expenses* 3,000 Cash 1,000 Depreciation expense 1,000 Interest expense 600 Accrued wages 1,000 Accounts payable 2,000 Fixed assets (net) ** 5,000 Long-term debt 4,000 Accounts receivable 2,000 Stockholders’ equity 4,000 Gross profit margin 40 percent Tax rate 40 percent Price to earnings (PE) ratio 14 Shares of common stock outstanding = 500 shares * Operating expenses do not include depreciation. ** Net of accumulated depreciation. Prepare an income statement for ABC. The answer is shown below. Sales $14,000 Cost of goods 8,400 Gross profit $5,600 Operating expense 3,000 Depreciation 1,000 EBIT $1,600 Interest 600 EBT $1,000 Taxes 400 EAT $600 Using the general headings shown below, prepare a balance sheet for ABC. (Note: The amounts shown in bold below are provided. Students are to compute the missing balance sheet amounts.) ABC’s Balance Sheet Assets Liabilities and Stockholders’ Equity Total Current Assets $6,000 Total Current Liabilities $3,000 Total Fixed Assets $ Total Assets $11,000 Total Liab. + Stkholder’s Eq. $ Using the information provided in problem 9, determine the following. Current ratio 2.0 Quick ratio 1.0 Times interest earned 2.67 Total asset turnover 1.27 Debt ratio .64 Average collection period 52.14 days Inventory turnover (assume average inventory equals closing inventory as shown on the firm’s balance sheet) 2.8 Net working capital $3,000 Earnings per share $1.20 Net profit margin 4.28% Market price of the common stock $16.80 DDD Corp. had earnings before interest and taxes (EBIT) of $700,000. It had interest expense of $200,000 and paid a preferred stock dividend of $100,000. Using the corporate tax tables, determine the following: DDD’s federal tax liability. Answer: $170,000 DDD’s earnings available to its common shareholders. Answer: $230,000 c. DDD’s earnings per share (EPS), assuming it has 100,000 share of common stock outstanding. Answer: $2.30 d. The market price of DDD’s common stock assuming DDD has a price/earnings (PE) ratio of 18. Answer: $41.40 Only Corp. has earnings after taxes $50,000. There are 10,000 shares of common stock outstanding and no preferred stock. The price earnings ratio is 13. Determine the market price of the common stock. Answer: $65.00 Use the ratio information provided below and complete the balance sheet and sales information in the table that follows for Besley Industries using the following financial data: Debt ratio: 50 percent Quick ratio: 0.80 times Total assets turnover: 1.5 times Average Collection Period: 36 days Gross profit margin: 40 percent Inventory turnover ratio: 5 times Note that the amounts shown in bold below are provided. Students are to compute the remaining balance sheet amounts as ell as the sales and cost of goods sold. Besley Industries Balance Sheet Assets Liabilities and Stockholders’ Equity Cash ________ Accounts Payable ________ Accounts Receivable ________ Total Current Liab ________ Inventories ________ Long-term Debt $60,000 Total Current Assets ________ Total Debt ________ Fixed Assets ________ Common Stock ________ Retained Earnings $100,000 Total Assets $300,000 Total Liab & Equity ________ Sales ________ Cost of Goods Sold _______ ABC had earnings before taxes of $300,000 for 2005. It has a 40 percent tax rate and paid $40,000 in preferred stock dividends in 2005. At the end of 2001 it had $200,000 of retained earnings. If ABC pays common stock dividends of $50,000 during 2005, determine how much it had in retained earnings at the end of 2005. Answer: $290,000 Chapter 3 Cash flow and Financial Planning A machine cost $200,000. In addition, the following costs were incurred: shipping expense $20,000 and installation expense $30,000. The machine will be depreciated using MACRS 7-year life. Determine the depreciation for the first three years of the asset’s life. Answer: Year 1 $35,000 Year 2 $62,500 Year 3 $45,000 A firm had earnings after taxes in 2005 of $200,000. In addition, it had depreciation charges of $60,000 and amortization charges of $20,000. Determine the firm’s accounting cash flow from its operations during 2005. Answer: $280,000 A firm had earnings after taxes in 2005 of $100,000. In addition, it had depreciation charges of $40,000 and amortization charges of $10,000. Determine the firm’s cash flow from its operations during 2005. Answer: $150,000 XYZ purchased a new printing press during 2003 for $300,000. In addition, the following costs were incurred: shipping expense $20,000 and installation expense $30,000. The press will be depreciated using MACRS 5-year life. Determine the depreciation for the first three years of the asset’s life. Answer: Year 1 $70,000 Year 2 $112,000 Year 3 $66,500 Classify the following transactions as either sources or uses of funds by placing the letter S or U next to the transaction. Accounts receivable +2,000 U Inventory -$3,000 S Depreciation + 500 S Equipment -50,000 S Repurchase of stock + 600 U Cash dividend + 900 U Marketable securities – 900 S Accrued wages +1,000 S Notes payable +20,000 S Long-term debt -5,000 U XYZ purchased a new machine during 2005 for $270,000. In addition, the following costs were incurred: shipping expense $10,000 and installation expense $20,000. The press will be depreciated using MACRS 7-year life. Determine the depreciation for the first three years of the asset’s life. Answer: Year 1 $42,000 Year 2 $75,000 Year 3 $54,000 ABC Corporation’s earnings after taxes for the year were $8,000. During the year it depreciated fixed assets by $4,000. In addition, during the year the following account balances changed as shown below. None of its other account balances changed. Account Change in Balance Inventories Increased $2,000 Land Increased $12,000 Accounts Payable Decreased $3,000 Debt Increased $8,000 Marketable Securities ??? Determine the change in ABC’s marketable securities. Answer __Marketable Securities increased by $3,000_ Classify the following transactions as either sources or uses of funds by placing the letter S or U next to the transaction. Accounts payable +2,000 S Inventory +$4,000 U Depreciation + 500 S Buildings -50,000 S Repurchase of stock + 600 U Cash dividend + 500 U Marketable securities – 600 S Accrued wages -1,000 U Notes payable -20,000 U Long-term debt +5,000 S Last year ABC sold three products. The quantities and sale prices are tabulated below. Next year ABC’s marketing managers expect that both quantities and sale prices will change. The percentage changes are included in the table. Determine the forecast sales revenue for next year. Answer: $814.37 Expected Percentage Changes Product Quantity Sale Price Quantity Price A 100 $3.00 +2% +3% B 200 2.00 +6 -4 C 100 1.00 -5 -3 The Slow Digital Company had sales of $80,000 in March and $90,000 in April. Forecast sales for May, June, and July are $90,000, $100,000, and $100,000, respectively. The firm has a cash balance of $10,000 on May 1 and wishes to maintain a minimum cash balance of $10,000. Given the following data, prepare a cash budget for the months of May, June and July. For each month, be sure to indicate the total amount of excess cash the company will have available to invest or the amount it will need to borrow to maintain the $10,000 cash balance. 1. Twenty percent of the firm's sales are for cash; 40 percent are collected in the next month, and the remaining 40 percent are collected in the second month following the sale. 2. The firm receives other income of $6,000 per month. 3. The firm's actual or expected purchases are sixty percent of the actual or expected sales for the month. They are paid in the month following the purchase. 4. Rent is $5,000 per month. 5. Wages and salaries are 10 percent of the previous month's sales. 6. Cash dividends of $10,000 and interest of $5,000 will be paid in June. Answers May June July Excess Cash $24,000 $39,000 $66,000 To Invest Amount Needed To Borrow ABC sales for March and April were $70,000 and $90,000 respectfully. Forecast sales for May, June, and July are $80,000, $90,000, and $100,000, respectively. Given the following data, prepare a cash budget for the months of May, June and July and determine the company’s net cash flow for each month. 1. Twenty percent of the firm's sales are for cash; 50 percent are collected in the month following the sale, and the remaining 30 percent are collected in the second month following the sale. 2. The firm receives other income of $5,000 per month. 3. The firm's actual or expected purchases are fifty percent of the actual or expected sales for the month. They are paid in the month following the purchase. 4. Rent is $12,000 per month. 5. Wages and salaries are 30 percent of the previous month's sales. 6. Cash dividends of $10,000 will be paid in June and payment of principal and interest totaling $5,000 is due in June. Answer: Net Cash Flow May +$3,000 June -$1,000 July +$10,000 Prepare the cash budget for ABC below. ABC Company Cash Budget March April May June July Sales $70,000 $90,000 $80,000 $90,000 $100,000 New equipment cost $300,000. In addition, the following costs were incurred: shipping expense $30,000 and installation expense $70,000. The machine will be depreciated using MACRS 7-year life. Determine the depreciation for the second year of the machine’s life. Answer: $100,000 Chapter 4 Time of Value of Money Note to Students: You will need a financial calculator (FC) to solve the problems in this and following chapters. In addition to providing your FC answer, you are required to show your work on tests as indicated below. Some of the problems include answers determined using a financial calculator (FC) as well as by using the financial tables located in Appendix A of your textbook. To be certain that you have used your financial calculator correctly, you can check your answer by solving the problem using the financial tables. The solutions obtained when using your financial calculator are more precise than those determined using the financial tables. The reason for the differences between the answers determined using your financial calculator and those determined using the financial tables has to do with rounding errors that occur when the tables are used. Since many problems in this chapter require similar types of calculations, the required work to be shown on tests is provided below for only a limited number of the problems. Note that the following abbreviations are used: FVIF – Future value interest factor FVIFA – Future value interest factor for an annuity PVIF – Present value interest factor PVIFA – Present value interest factor for an annuity You have decided to endow Rowan University with a scholarship. Once the scholarship is completely funded, it will provide $8,000 per year in perpetuity. You expect to fund your Rowan scholarship endowment by making equal annual end-of-year deposits into the scholarship account for 10 years. The rate of interest is expected to be eight percent for all future periods. How large must the endowment be to support the $8,000 scholarship in perpetuity? Answer: $100,000 The following equation/calculations are required to be shown for part a. Endowment = $8,000/.08 = $100,000 How much must you deposit at the end of each year for the next 10 years to accumulate the required amount? Answer: Tables $6,903 FC $6,902.94 The following equation/calculations are required to be shown for part b. Future Value of Annuity = Payment (FVIFA 8%, 10 years) $200,000 = Payment (FVIFA 8%, 10 years) Payment = $6,902.94 Ellen put $5,000 in the bank for 10 years and received eight percent interest. Determine the amount she had at the end of the 10 years based on the following assumptions. The interest compounded annually. Answer: Tables $10,795 FC $10,794.62 The interest compounded semiannually. Answer: Tables $10,955 FC $10,955.62 The interest compounded quarterly. Answer: Tab $11,040 FC $11,040.20 The following equation/calculations are required to be shown for part c. Similar equations/calculations are required for parts a and b. Future Value = Present Value (1 + i/m)mxn = $5,000 (1 + .08/4)4x10 = $5,000 (1.02)40 = $11,040.20 You are saving for your pension. Suppose you can save $5,000 per year at the end of each year for the next 30 years. You already have $20,000 in the fund. Assume you will receive an eight percent return on all your savings during the 30-year period as well as during your retirement. Determine the following: a. The amount you will have at the end of the 30-year period? Answer: Tables $767,650 FC $766,669.19 The following equation/calculations are required to be shown for part a. Accumulation = Present Value (FVIF 8%, 30 years) + Payment (FVIFA 8%, 30 years) = $20,000 (FVIF 8%, 30 years) + $5,000 (FVIFA 8%, 30 years) = $766,669.19 b. Assume the answer to part a is $600,000 (not the correct answer). If you want to have a pension for 20 years, determine how much can you withdraw each year at year's end for the 20 years and have nothing remaining. Answer: Tables $61,112 FC $61,111.32 The following equation/calculations are required to be shown for part b. Present Value of Annuity = Payment (PVIFA 8%, 20 years) $600,000 = Payment (PVIFA 8%, 20 years) Payment = $61,111.32 Suppose you are enrolled in a 401(k) plan and your salary is $30,000 per year and does not increase. Assume you contribute 6% of your salary each year to the plan and your employer contributes an additional 3% each year. All contributions are made at year’s end. Determine your accumulation based on the following: Note: Answers to parts a through d were calculated using a financial calculator. a. Contributing 30 years and obtaining a 6% return. Answer: $213,457.10 Contributing 30 years and obtaining a 10% return. Answer: $444,133.86 Contributing 40 years and obtaining a 6% return. Answer: $417,857.31 Contributing 40 years and obtaining a 10% return. Answer: $1,194,999.90 Assume inflation averages 3% each year for the next 40 years. Determine the purchasing power in today’s dollars of the accumulation you determined in part d. Answer: Tables $366,865 FC $366,335.39 The following equation/calculations are required to be shown for part e. Present Value = Future Value (PVIF 3%, 40 years) = $1,194,999.90 (PVIF 3%, 40 years) = $366,335.39 A real estate agent is prequalifying Jack and Jill for a mortgage to determine if they can purchase the house at the top of the hill. At present, Jack and Jill have sufficient funds to cover the property settlement costs and $20,000 for a down payment. Based on their current income and expenses, the realtor has determined that they can afford to pay a $1,500 per month mortgage payment ($18,000 per year at year's end). If the annual mortgage interest rate is seven percent, determine the maximum amount that they can afford to pay for a home. Assume a 30-year fixed rate mortgage and the following: a. The mortgage payments of $18,000 are made at the end of each year. The interest rate is seven percent compounded annually. Answer: Tables $243,362 FC $243,362.74 b. The mortgage payments of $1,500 ($18,000/12 = $1,500) are made at the end of each month. Assume interest is compounded monthly. Answer: FC $245,461.44 The following equations/calculations are required to be shown for part b. Present Value Annuity = Payment (PVIFA 7% compounded monthly, 360 months) = $1,500 (PVIFA 7% compounded monthly, 360 months) = $225,461.44 Maximum House Price = $225,461.44 + $20,000 Down Payment = $245,461.44 Note, for part b, be sure to change the number of payments from the normal default of one per year to 12 per year. When this is done, the number of compoundings per year is automatically changed to equal the number of payments. c. Determine the effective annual rate of seven percent compounded monthly. Answer: 7.229 percent. This is calculated as follows: The following equation/calculations are required to be shown for part c. Effective Annual Rate = (1 + i/m)m – 1 = (1 + .07/12)12 – 1 = .07229 = 7.229% Tom and Joan want to buy a house. They received an inheritance and have $20,000 for a down payment and enough other funds to cover closing costs. If they can pay a maximum of $9,600 per year in mortgage payments and mortgage payments are made at year’s end, determine the following: The maximum price house they can buy if the mortgage rate is 7% based on a 25-year mortgage. Answer: Tables $131,878 FC $131,874.40 The maximum price house they can buy if the mortgage rate is 7% based on a 30-year mortgage. Answer: $139,126 FC $139,126.80 Tom put $1,000 in the bank for 10 years and received 8% interest. Determine the amount he had at the end of the 10 years based on the following assumptions. a. The interest was compounded annually. Answer: Tables $2,159 FC $2,158.92 b. The interest was compounded semiannually. Answer: Tables $2,191 FC $2,191.12 The interest was compounded quarterly. Answer: Tables $2,208 FC $2,208.04 Suppose you are enrolled in a 401(k) plan and your salary is $35,000 per year and does not increase. Assume you contribute 6% of your salary each year to the plan and your employer contributes an additional 3% each year. All contributions are made at year’s end. Determine your accumulation based on the following: Note: Answers to parts a through d were calculated using financial tables. Contributing 30 years and obtaining a 6% return. Answer: Tables $249,029 FC $249,033.29 Contributing 30 years and obtaining a 12% return. Answer: Tables $760,190 FC $760,197.96 Contributing 40 years and obtaining a 6% return. Answer: Tables $487,488 FC $487,500.19 Contributing 40 years and obtaining a 12% return. Answer: Tables $2,416,302 FC $2,416,337.97 Determine the present value of the cash flows shown in the table below based on an opportunity cost of 10%. Answer: Tables $48,004 FC $48,009.07 Year Cash Flow $20,000 8,000/year 12,000 The following equations/calculations are required to be shown. Year 1: Present Value = Future Value (PVIF 10%, 1 year) Years 2-5: Present Value = Annuity Payments [(PVIFA 10%, 5 years) – (PVIF 10%, 1 year)] Year 6: Present Value = Future Value (PVIF 10%, 6 year) Year 1: Present Value = $20,000 (PVIF 10%, 1 year) Year 2-5: Present Value = $8,000 [(PVIFA 10%, 5 years) – (PVIF 10%, 1 year)] Year 6: Present Value = $12,000 (PVIF 10%, 6 year) Year 1: Present Value = $18,181.82 Year 2-5: Present Value = $30,326.29 -$7,272.72 Year 6: Present Value = $6,773.69 Total Present Value = $48,009.08 Note that this problem can also be solved using the Net Present Value (NPV) function of your calculator and entering the initial cash outflow (initial investment) as zero. This methodology is covered in Chapter 9. See Chapter 9, review problem one, for example. If this problem is solved using the Net Present Value function, then the following equations/calculations are required to be shown. NPV = Present Value of Cash Inflows – Initial Investment NPV = [$20,000 (PVIF 10%, year 1) + $8,000 (PVIFA 10%, years 2-5) + $12,000 (PVIF 10%, year 6)] – 0 NPV = $48,009.07 Determine the present value of the cash flows tabulated below based on an opportunity cost of 10 percent. Answer: Tables $27,448 FC $27,450.71 Year Cash Flow 1 $10,000 5,000/year 7,000 Consider the problems shown below. For each, indicate the kind of evaluation that is involved choosing from one of the following: future value, present value, future value of an annuity, present value of an annuity. You place $5,000 in the bank and want to know your accumulation in 10 years when the interest rate is eight percent. Answer: FV You can afford to make mortgage payments of $600 per month ($7,200) per year. Mortgage interest rates are seven percent for a 20-year mortgage. You want to know how much you can borrow. Answer: PVA You plan to put $2,000 in a Roth IRA each year for 40 years and want to know how much you will accumulate if the average return is eight percent. Answer: FVA You just won the lottery and will receive $100,000 per year at year's end for 20 years. Your opportunity cost of money is eight percent and you want to know what the winnings are worth to you today. Answer: PVA You estimate that, as a result of graduating with a business degree from Rowan, you will earn an additional $10,000 per year for the next 40 years. You figured that going to college cost you $30,000 and you have an opportunity cost of money of eight percent. You want to determine if you made a good investment. Answer: PVA Suppose you currently earn $30,000 per year. If inflation averages 3% per year for the next 10 years, how much must you earn 10 years from now to just be even with inflation? Answer: Tables $40,320 FC $40,317.49 Suppose you currently have $20,000 in your individual retirement account and you add $2,000 each year at year’s end for the next 20 years. If you obtain an annual return of 8.5%, determine how much you will have in your IRA at the end of the 20-year period. Answer: FC $198,994.95 Jim wants to purchase a house. He has $30,000 for a down payment and enough other funds to cover closing costs. If he can pay a maximum of $1,000.00 per month in mortgage payments and mortgage payments are made at the end of each month, determine the maximum price house he can buy if the mortgage rate is 8% based on a 25-year mortgage. Answer: FC $159,564.52 Suppose you currently have $30,000 in your individual retirement account and you add $2,000 each year at year’s end for the next 30 years. If you obtain an annual return of 10 percent, determine how much you will have accumulated in your IRA at the end of the 30-year period. Answer: Tables $852,452 FC $852,470.11 Suppose you plan to retire at the end of the 30-year period. The local palm reader has told you that you that you will die exactly 25 years after you retire. Using your financial calculator answer to part a, determine the amount of the equal annual year-end payment you can withdraw from your IRA each year for the 25 years you will live, so that you will have nothing left at the end of the 25-year period. Assume a 10 percent annual rate of return for the entire 25-year period. Answer: FC $93,914.99 Jane wants to buy Bill an engagement ring that will cost $5,000. She plans to wait to be sure that Bill “shapes up” before making the purchase and plans to purchase the ring five years from now. If she has $2,000 now, how much she save each year at year’s end for the five years to accumulate the $5,000. Assume she can obtain an eight percent return on all of her savings during the five-year period. Answer: Tables $351.45 FC $351.37 You just won the lottery and will receive $50,000 per year at year's end for 20 years. Your opportunity cost of money is eight percent. a. Determine the present value of your winnings. Answer: Tables $490,900 FC $490,907.37. b. Suppose the winnings are paid to you at month’s end in the amount of $4,166.67 ($50,000/12 = $4,166.67), and your opportunity cost of money is eight percent. Furthermore, assume the interest is compounded monthly. Determine the present value of your winnings. FC $498,143.28 c. Determine the effective annual rate of eight percent compounded monthly. Answer: 8.24% You estimate that, as a result of graduating with a business degree from Rowan (as opposed to not attending college), you will earn an additional $15,000 per year after taxes for the next 40 years. Assume the $15,000 will be received at the end of each year. You estimate that by the time you graduate, going to college for four years will have cost you $130,000 after taxes (including all tuition, fees, room and board, books, interest on student loans, and the opportunity cost of the additional income you would have earned if you had worked full time for the four years). You have an opportunity cost of money of eight percent. Determine if you made a good investment. Answer: FC The present value of the incremental earnings less the cost of college is $48,869.70. Since it is positive (indicating that the benefit exceeded the cost), you made a good investment. Determine the maximum cost of going to college that you could justify based on your expected incremental earnings. Answer: FC $178,869.70. Three years ago Kate purchased a home with an eight percent $100,000 mortgage with a 30-year amortization. She still owes $97,000 on this mortgage. Since she got her mortgage, mortgage interest rates have fallen to seven percent. Now Kate can refinance her mortgage at seven percent but this will cost her $4,000 in settlement fees and related expenses. If she refinances, she has decided to borrow based on a 20-year mortgage amortization. Assume she refinances $101,000 (the $97,000 she owes on her existing mortgage plus the $4,000 fees and expenses) at seven percent for 20 years. Further assume that her mortgage payments are year end. Determine the increase or decrease in her yearly mortgage payment if she refinances. Answer: Tables $651 more per year or about $54 per month Next, assume her payments are made monthly and compute the amount of Kate’s additional monthly payments. Answer: FC $49.29 A real estate agent is prequalifying John and Jane for a mortgage so they can purchase a home. John and Jane have sufficient funds to cover the property settlement costs. Based on their current income and expenses, the realtor has determined that they can afford to pay a $1,300 per month mortgage payment ($15,600 per year at year's end). At present, mortgage interest rates are seven percent. John and Jane believe they will drop to six percent in the near future. Assume a 30-year mortgage and that the mortgage payments are made at the end of each year (not at the end of each month). Determine how much more expensive a home John and Jane could purchase if the mortgage interest rates drop from seven to six percent. Answer: Tables $21,150.37 ABC Corp borrowed $10,000 with a stated annual interest rate of 10 percent. Interest is paid every 60 days. Assume a 365 day year and determine the effective annual interest rate. Answer: FC 10.43 percent Chapter 5 Risk and Return 1. Determine the following for an investment with estimated returns tabulated below. Probability Return .3 8% .4 10 .2 12 .1 14 The range of the returns. Answer: 6% The expected value of the return for the project. Answer: 10.2% The standard deviation of the returns. Answer: 1.89% Suppose the risk-free rate is 6% and the expected return on the market is 12%. If Merrill Lynch & Company has a beta of 1.6, determine its required return. Answer: 15.6% Using a grid provided on page 3, draw the security market line using the information provided in the above problem. Label the axes. Show the risk-free rate, the market risk premium, the security risk premium, the expected return and beta for the market as well as Merrill’s required return and beta. Determine the following for an investment with estimated returns tabulated below. Probability Return .2 8% .3 10 .3 12 .2 14 The range of the returns. Answer: 6% The expected value of the return for the project. Answer: 11% The standard deviation of the returns. Answer: 2.04% Investment A has an expected return of 12% and standard deviation of 3% while investment B has an expected return of 15% and standard deviation of 4%. Determine the coefficient of variation for each and indicate the project you would select assuming you want to minimize your risk. Coefficient of Variation for Investment A. Answer: .25 Coefficient of variation for Investment B. Answer: .267 c. Answer: As a risk averter, I would select project A because it has the lowest ratio of risk to return. 6. Suppose the risk-free rate is 5% and the expected return on the market is 11%. If ABC Corp. has a beta of 1.8, determine its required return. Answer: 15.8% Using the grid provided on page 3, draw the security market line using the information provided in problem above. Label your graph carefully. Label the axes. Show the risk-free rate, the expected return and beta for the market, ABC’s required return and beta, the market risk premium and ABC’s risk premium. Determine the risk-free rate for a firm with a required return of 15% and a beta of 1.25 when the market return is 14 %. Answer: 10% 9. Determine the standard deviation for an investment with estimated returns tabulated below. Answer: 1.56% Probability Return .2 8% .3 10 .5 12 Suppose there is a stock market (like the S&P 500) that consists of stocks from only four companies: A, B, C, and D. Suppose also that each company’s stock is weighed equally in this very small stock market (i.e., there are equal dollar amounts of each stock in the portfolio). If the betas for stocks A, B, and C are 1.2, 1.3, and 0.7, determine the beta for stock D. Answer: 0.8 Chapter 6 Interest Rates and Bond Valuation ABC Inc. has bonds outstanding that have 20 years to maturity and a par value of $1,000. The bonds have a 10 percent coupon interest rate. Currently, bonds of similar risk are earning eight percent (i.e., they have a yield to maturity of eight percent). Determine the following: The market value of the bonds assuming they pay interest annually at year’s end. Answer: Tables $1,197 FC $1,196.36 b. If the required return on the bonds decreases, what would you expect to happen to the price of the bonds? Answer: The price would increase. The following equation/calculations are required to be shown. Bond Value = Annual Interest Payment (PVIFA 8%, X years) + Maturity Value (PVIF 8%, X years) = $100 (PVIFA 8%, 20 years) + $1,000 (PVIF 8%, 20 years) = $1,196.36 Determine the value of a bond that will mature in 10 years if it has a nine percent coupon interest rate and $1,000 maturity value. Assume that similar risk bonds are currently earning a 10 percent return and this bond pays interest annually at year’s end. Answer: Tables $939 FC $938.55 A bond will mature in 20 years and has a maturity value of $1,000. It has an eight percent coupon interest rate and pays interest annually at year’s end. Currently it is selling for $1,150. Determine its yield to maturity. Answer: FC 6.63% A bond will mature in 20 years and has a maturity value of $1,000. It has a nine percent coupon interest rate. Currently it is selling for $841. Determine its yield to maturity. Answer: Tables 11% FC 11% The following equation/calculations are required to be shown. Bond Value = Annual Interest Payment (PVIFA YTM%, 20 years) + Maturity Value (PVIF YTM%, 20 years) $841 = $90 (PVIFA YTM%, 20 years) + $1,000 (PVIF YTM%, 20 years) YTM = 11% HINT: When using your calculator to calculate yield to maturity remember that most calculators require either the present value ($841 in this problem) or the interest payments and maturity value ($90 per year and $1,000 in this problem) to be entered as a negative number(s). XYZ has outstanding $1,000 par value bonds that were recently listed in the Wall Street Journal as trading at 98 ½. The coupon interest rate is nine percent and interest is paid semiannually. Determine the following. The market price of the bonds. Answer: $985 The dollar amount of the semiannual interest payments. Answer: $45 The bond’s current yield. Answer: 9.14% The following equation/calculations are required to be shown for part c. Current Yield = $90/$985 = 9.14% Quter Corp. bonds will mature in 20 years. They have a maturity value of $1,000, an eight percent coupon interest rate, and pay interest annually at year’s end. Currently, similar quality bonds are yielding a six percent return. a. Determine how much Quter’s bonds should sell for today. Answer: Tables $1,229.60 FC $1,229.39 b. Based on your answer to part a, determine the bond’s current yield, Answer: 6.5% New Corp has outstanding bonds that are convertible to 25 shares of the company’s common stock. The bonds have an eight percent coupon rate of interest and are callable at $1,200. Suppose you own one of these bonds and the company decides to call the bond at a time when the stock is selling for $53 per share. Suppose you had originally purchased the bond for $1,050. If you converted the bond to 25 shares of common when the common stock was selling for $53 per share and then sold the shares for $53 each, determine your total profit or loss. Answer: $275 A bond will mature in 15 years and has a maturity value of $1,000. It has an eight percent coupon interest rate and pays interest annually at year’s end. Currently it is selling for $875. Determine its yield to maturity. Answer: FC 9.61% The following equation/calculations are required to be shown. Bond Value = Annual Interest Payments (PVIFA YTM%, X years) + Maturity Value (PVIF YTM%, X years) $1,147 = $80 ((PVIFA YTM%, 20 years) + $1,000 (PVIF YTM%, 20 years) YTM = 9.61% Chapter 7 Stock Valuation Clunker Cars has paid common stock dividends shown in the following table over the past six years. Year Dividend per share 2000 $ .90 2001 1.05 2002 1.08 2003 1.12 2004 1.14 2005 1.20 Determine the historical compound annual dividend growth rate. Answer: Tables 6% FC 5.92% The following equation/calculations are required to be shown for part a. Future Value = Present Value (FVIF X%, 5 years) $1.20 = $.90 (FVIF X%, 5 years) (FVIF X%, 5 years) = $1.20/$.90 = 1.333 Compound annual growth rate = 5.92% (FC answer) HINT: When using your calculator to calculate the historical compound annual dividend growth rate, remember that most calculators require either the present value ($.90 in this problem) or the future value ($1.20 in this problem) to be entered as a negative number. Assuming Clunker’s dividend next year is $1.25 and that you can earn 14 percent on similar-risk investments, what is the most you would pay per share for this stock? Answer based on 6% dividend growth rate $15.63. Answer based on 5.92% dividend growth rate: $15.47. Clunker’s preferred stock pays an annual dividend of $6.40. It has a par value of $120. Until recently, the required return on similar quality securities had been nine percent. Interest rates fell and now the required return is eight percent. Determine the change in the market value of the preferred resulting from the change in the required return and indicate if the market value increased or decreased. Answer: $8.89 circle one: (increase) decrease Use the capital asset pricing model to determine the required return for Pluto Co. stock that has a beta of 1.3 if the risk-free rate is five percent and the expected return from the stock market is 12 percent. Answer: 14.1% Assume the dividend growth rate for Pluto’s stock has been six percent and that the dividend for next year is expected to be $2.00. Using your answer to the above problem, determine the market price of Pluto’s stock. Answer: $24.69 Moody Boiler has paid dividends shown in the following table over the past seven years. Year Dividend per share 1999 $.90 2000 .96 2001 1.05 2002 1.08 2003 1.13 2004 1.20 2005 1.28 Determine the historical compound annual dividend growth rate. Answer: Tables 6% FC 6.05% Assuming Moody’s dividend next year is $1.36, that you can earn 12 percent on similar-risk investments, and the historical compound annual dividend growth rate is six percent, what is the most you would pay per share for this stock? Answer: $22.67 John’s Cars preferred stock pays an annual dividend of $5.40. It has a par value of $120. Until recently, the required return on similar quality securities had been eight percent. Interest rates increased and now the required return is nine percent. Determine the change in the market value of the preferred resulting from the change in the required return and indicate if the market value increased or decreased. Answer: $7.50 circle one: increase (decrease) ABC Corp. has paid common stock dividends shown in the following table over the past six years. Year Dividend per share 2000 $1.10 2001 1.15 2002 1.23 2003 1.30 2004 1.36 2005 1.47 Determine the historical compound annual dividend growth rate. Answer: Tables 6% FC 5.97% Assuming ABC’s dividend next year is $1.60, and that you can earn 12 percent on similar-risk investments, and the historical compound annual dividend growth rate is six percent, what is the most you would pay per share for this stock? Answer: $26.67 XYZ Company's common stock is expected to pay a dividend of $3.00 next year. Its historical compound annual dividend growth rate is four percent. a. If the market requires an 11 percent return on this stock, determine the expected market price using the constant dividend growth model. Answer: $42.85 b. Suppose the consensus of the stock market is that inflation is going to increase. As a result, the market decides to require a 13 percent return on XYZ's stock. XYZ's management does not want the price of its stock to fall from the price determined in part a. Based on expected increases in earning, management decides to increase its common stock dividend. Determine the dividend that is necessary to maintain the existing price of the common stock. Answer: $3.86 Apple Corp. has an outstanding issue of cumulative preferred stock with a par value of $50.00 that pays a 10 percent annual dividend. The board of directors has passed the preferred stock dividend for the last four years. Determine how much must be paid per share to the preferred stockholders before dividends may be paid to common stockholders. Answer: $25.00 per share You want to purchase an increasing perpetuity. You want to receive payments every year at year’s end. The first year you want to receive a payment of $10,000. Then, you want the payments to increase by three percent each year. Determine how much you would pay for this annuity assuming you have an opportunity cost of eight percent. {Hint: Consider Gordon’s constant growth dividend valuation model.) Answer: $200,000 INTEGRATIVE PROBLEM: You want to retire in 30 years and have a pension with a purchasing power of $50,000 per year in today’s dollars. The pension is to be received at the end of each year during your retirement. You expect the inflation rate to be three percent per year from now until you retire. a. Determine the dollar amount of the annual pension you will need in 30 years to provide you with $50,000 of purchasing power in today’s dollars. Answer: Tables $121,350 FC $121,363.12 b. Suppose you want to have your pension last forever and provide you with three percent annual cost of living increases. Suppose further that you expect to earn an average annual return of eight percent on the funds in your pension fund. Using your financial calculator answer to part a, determine how much you must have at retirement to fund your pension. Assume the annual pension fund payments will be made to you at year’s end. [Hint: Use Gordon’s constant growth dividend valuation model.] Answer: $2,427,262.47 c. Suppose you already have $20,000 in your pension fund. Suppose further that you will make annual year-end contributions to your pension fund for the next 30 years and that you will obtain an average return of nine percent annual return on all of your pension fund assets. Using your answer to part b, determine the amount you must contribute to your pension fund at the end of each year for the next 30 years. Answer: Tables $15,859 FC $15,860.52 d. Suppose instead of making end-of-year payments in part c, you make end-of month payments. Using your answer to part b, determine the amount you must contribute to your pension fund at the end of each month for the next 30 years. Continue to assume that you already have $20,000 in your pension fund. [Note: Also continue to assume a nine percent growth rate compounded monthly for both the $20,000 and the monthly payments.] Answer: FC $1,164.91 Chapter 8 Capital Budgeting Cash Flows A machine cost $200,000. It was depreciated using 5-year MACRS for three years. The machine’s owner has a 40 percent tax rate on both ordinary income and capital gains and losses. Determine the following: Its book value. Answer: $58,000 The net after-tax proceeds that will be realized from the sale of the machine for $230,000. Answer: $161,200 The net after-tax proceeds that will be realized from the sale of the machine for $80,000. Answer: $71,200 ABC currently owns a processing system that cost $1,000,000. The company is using MACRS 5-year depreciation. At present, sales are $800,000 and all costs except depreciation are $400,000. ABC’s tax rate is 40 percent. Complete the table shown below. Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 SALES $800,000 $800,000 $800,000 $800,000 $800,000 $800,000 COSTS 400,000 400,000 400,000 400,000 400,000 400,000 DEPN EBT TAX EAT Cash Flow $320,000 $368,000 $316,000 $288,000 $288,000 $260,000 During the second year of the existing processing system’s use, a new system was introduced costing $1,300,000. If purchased, it would replace the existing system and be placed into operation at the start of the third year of the existing system’s life. It would be depreciated using 3-year MACRS. Sales revenue would increase to $1,200,000 and all costs except depreciation would increase to $600,000 a year. Complete the table shown below for the new system. Year 1 Year 2 Year 3 Year 4 SALES $1,200,000 $1,200,000 $1,200,000 $1,200,000 COSTS 600,000 600,000 600,000 600,000 DEPN EBT TAX EAT Cash Flow $531,600 $594,000 $438,000 $396,400 c. Determine the incremental cash inflows for the last four years of the exiting system’s life if the new system is placed into operation. Answer: Year 3 $215,600 Year 4 $306,000 Year 5 $150,000 Year 6 $136,400 ABC is considering the purchase of a new machine for $400,000. The firm has a 40 percent tax rate for ordinary income and capital gains. Suppose the machine will be fully depreciated to a book value of zero and sold 10 years from now for $200,000. ABC has an opportunity cost of 10 percent, determine the present value of the after-tax proceeds resulting from the sale of the machine in 10 years. Answer: $46,320 XYZ purchased a machine tool costing $150,000 two years ago and has depreciated it for two years based on a five-year MACRS life. At the present time, it could be sold for $125,000 and replaced by a new more efficient machine tool costing $200,000. If XYZ has a 40 percent tax rate for both ordinary income and capital gains, determine the after-tax cash outflow required to acquire the new system. Answer: $96,200 ABC is considering the purchase of a new Machine A for $50,000. If purchased, it will be used to replace an older Machine B that has an estimated after-tax salvage value of $20,000. ABC has estimated that the annual after-tax cash inflows that will result from the use of the machines in the table below. If Machine A were actually used to replace Machine B, list the relevant cash flows under the column, “Cash Flows.” (Solution not provided. Fill in the table.) Estimated Annual After-tax Cash Inflows Year Machine A Machine B 1 $18,000 $8,000 2 18,000 8,000 3 18,000 6,000 4 12,000 4,000 5 12,000 4,000 6 18,000 4,000 Time Machine A Machine B Cash Flows Initial Investment $50,000 $20,000* 1 2 3 4 5 6 *After-tax salvage value. A machine cost $100,000. It was depreciated using 5-year MACRS for three years. The machine’s owner has a 40 percent tax rate on both ordinary income and capital gains and losses. Determine the following: Its book value. Answer: $29,000 The net after-tax proceeds that will be realized from the sale of the machine for $130,000. Answer: $89,600 The net after-tax proceeds that will be realized from the sale of the machine for $80,000. Answer: $59,600 The net after-tax proceeds that will be realized from the sale of the machine for $20,000. Answer: $23,600 A firm is planning to upgrade equipment to produce more output at a cost of $900,000 plus installation costs of $100,000. The firm will depreciate the upgrades under MACRS using a 3-year recovery period. The upgrades are expected to be used to produce additional output for the next six years. The added sales are expected to increase annual sales revenue from the current level of $800,000/year to $1,700,000/year. Additional operating costs (not including depreciation) are expected to average 50 percent of the additional sales revenue. The firm’s tax rate is 40 percent. For each of the six years the machine will be used, determine the additional sales revenue (SALES), depreciation (DEPN), earnings before taxes (EBT), earnings after taxes (EAT), and the operating cash inflows (CF). (Complete the table. Totals are provided in each column.) Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 SALES OPER CST DEPN EBT EAT CF $402,000 $450,000 $330,000 $298,000 $270,000 $270,000 ABC is considering the purchase of a new machine for $1,000,000. The firm has a 40 percent tax rate for ordinary income and capital gains. Suppose the machine is fully depreciated to a book value of zero and sold 15 years from now for $400,000. If ABC has an opportunity cost of 10 percent, determine the present value of the after-tax proceeds resulting from the sale of the machine in 15 years. Answer: $57,360 9 PRIVATE Sentry Company is contemplating the purchase of a new high-speed grinder to replace its existing grinder. The existing grinder was purchased two years ago at an installed cost of $70,000. At present, it has been depreciated two years using MACRS with a five-year recovery period. The existing grinder is expected to have a usable life of six more years. The existing grinder can currently be sold for $50,000 without incurring any removal costs. The new grinder will cost $105,000 and require $5,000 in installation costs. It has a six-year usable life and would be depreciated under MACRS using a five-year recovery period. The firm pays 40 percent taxes on both ordinary income and capital gains. The estimated profits before depreciation and taxes for the next five years for both the new and existing grinder are given below. Profits before Depreciation and Taxes Year New grinder Existing grinder 1 $45,000 $26,000 2 45,000 24,000 3 45,000 22,000 4 45,000 20,000 45,000 18,000 6 45,000 16,000 a. Calculate the initial after-tax cost associated with the replacement of the existing grinder with the new one. Answer: $66,560 b. Determine the incremental (additional) operating cash inflows associated with the proposed grinder replacement for the first three years of its life. (Hint: Develop an income statement for each year.) Answers: Year 1 $14,880 Year 2 $23,320 Year 3 $18,800 Chapter 9 Capital Budgeting Techniques: Certainty and Risk A project has expected cash flows as tabulated below. The firm's discount rate is 12 percent. Determine the following: Time Cash Flow Present -$25,000 1-4 + 5,000 5-7 + 4,000 8 + 8,000 9 + 7,000 a. The project's net present value. Answer: Tables $2,053 FC $2,047.71 The following equation/calculations are required to be shown for part a. NPV = Present Value of Cash Inflows – Initial Investment NPV = [$5.000 (PVIFA 12%, years 1-4) + $4,000 (PVIFA 12%, years 5-7) + $8,000 (PVIF 12%, year 8) + $7,000 PVIF 12%, year 9)] – $25,000 NPV = $2,047.71 b. Is the project acceptable? Circle One: (Yes) No c. The project's payback period assuming year-end cash inflows. Answer: 6 years A project has the cash flows tabulated below. Determine its internal rate of return. Answer: FC 8.94% Time Cash Flow Present -$115,000 1 - 5 +18,000 6 – 9 +14,000 10 +36,000 A project is expected to cost $100,000 and produce year-end after-tax cash inflows of $30,000 per year for 6 years. Determine the project's internal rate of return. Answer: Tables Approximately 20% FC 19.91% A machine costs $68,140 and is expected to produce cash inflows of $14,000 per year. How many years must the machine be used to produce an internal rate of return of 10 percent? Answer: Tables 7 years FC 7 years Note: The IRR function on some financial calculators is “compute only.” That is, it is not possible to enter a value for IRR and then solve for the number of years. Consequently, this problem should be solved using the same type of calculations used to determine bond yield to maturity with one exception. Whereas bonds have a maturity value (usually $1,000), there is no maturity value in this problem. This solution process is demonstrated below. Remember to enter zero for the future value. The following equation/calculations are required to be shown. Cash Outflow = Annual Cash Inflow (PVIFA IRR%, X years) -$68,140 = $14,000 (PVIFA 10%, X years) X = 7 years A machine costs $75,000 and is expected to produce cash inflows of $12,000 per year. How many years must the machine be used to produce an internal rate of return of 12 percent? Answer: FC 12.23 years A project is expected to cost $200,000 and produce year-end after-tax cash inflows of $30,000 per year for six years and then $15,000 for the following five years. Determine the project's internal rate of return. Answer: Calculator 5.08% Determine the project’ net present value assuming a 10 percent discount rate. Answer: FC -$37,245.17 A project has expected cash flows as tabulated below. The firm's discount rate is 14 percent. Determine the following: Time Cash Flow Present -$22,000 1 + 6,000 2 + 7,000 3 + 8,000 4 + 7,000 a. The project's net present value. Answer: Tables -$1,811 FC -$1,806.24 b. Is the project acceptable? Circle One: Yes (No) c. The project's payback period assuming continuous cash inflows. Answer: 3.14 years The project’s payback period assuming year-end cash inflows. Answer: 4 years 8. A project has the cash flows tabulated below. Determine its internal rate of return. Answer: FC 12.70% Time Cash Flow Present -$110,825 1 - 5 +20,000 6 – 10 +15,000 11 +40,000 New equipment costs $91,272. The owner expects to use the equipment for 15 years. Assume that the use of the equipment will result in the same cash inflow each year for each of the next 15 years. Determine how much cash inflow the equipment must produce each year to provide a 10 percent internal rate of return. Answer: Tables $12,000 FC $11,999.87 Chapter 10 The Cost of Capital XYZ Corp. is selling a new issue of $100 par value preferred stock. It has an annual dividend of nine percent. XYZ received $98 per share less floatation costs. The floatation costs were $6.00 per share. Determine the after-tax cost of the preferred stock. Express your answer as a percent. Answer: 9.78% ABC Corp. issued $1,000 par value bonds having a 30-year life with a 10 percent coupon interest rate. The floatation cost was $40 per bond and the bonds were sold at a $20 discount. The firm has a 40 percent tax rate and the bonds pay interest annually. Determine the after-tax cost to maturity using the approximation formula and financial calculator. Express your answer as a percent. Answer: Approximation Formula 6.28% FC 6.40% Discussion of solution: There are two ways to solve for the pretax cost of the bonds to ABC Corp: Either 1) use the approximation formula or 2) use the same methodology used to calculate the yield to maturity. The latter procedure results in the more precise answer. The calculations shown below employ the second procedure. First, recall that YTM was used as the unknown in Chapter 6 to solve for a bond’s yield to maturity. The yield to maturity is the total rate of return a bondholder will receive when purchasing a bond (including the discounted value of both the annuity stream of interest payments and the bond’s maturity value). The YTM is not the same as the pretax cost of the bond debt to ABC Corp. Therefore, YTM is not the unknown. The internal rate of return (IRR) of the bond is the pretax cost of the bond to the issuing company, ABC Corp. However, unlike capital budgeting problems where a cash outflow (the initial cost) is usually followed by a series of cash inflows, the reverse sequence takes place when bonds are issued. An initial inflow (the net proceeds from the sale of the bond – $940 in this problem) is received by the issuing company, ABC Corp. This cash inflow is followed by 1) an annuity stream of interest payments (cash outflows) paid by ABC Corp. to the bondholders ($100 per year for 30 years in this problem) and 2) the maturity value of the bond (cash outflow) paid to the bondholders ($1,000 in this problem). The following equation/calculations are required to be shown. First, the net proceeds from the sale of the bond are calculated: $1,000 – ($40 + $20) = $940. The net proceeds from the sale of each bond by ABC Corp is $940. Second, the bond’s IRR (pretax cost of interest) is determined as shown below: Bond Value = Annual Interest Payments (PVIFA IRR%, X years) + Maturity Value (PVIF IRR%, X years) $940 = $100 (PVIFA IRR%, 30 years) + $1,000 (PVIF IRR%, 30 years) IRR = 10.67% Note that the calculated IRR is the pretax cost of debt to ABC Corp. Third, calculate the after-tax cost. After-tax cost = 10.67% (1 – .4) = 6.40% ABC Inc. has outstanding common stock selling for $42.50 per share. Its annual dividend growth rate has been six percent and the projected dividend per share for next year is $2.40. If new shares are sold they will be under priced at $1.00 per share and the floatation cost will be $3.00 per share. Using the constant growth valuation model, determine the following: Express your answers as a percent. The after-tax cost of retained earnings. Answer: 11.65% The after-tax cost of new common stock. Answer: 12.23% New Corp has 1,000,000 shares of common outstanding selling for $30.00 per share and 100,000 shares of preferred outstanding selling for $50.00 per share. New also has $15,000,000 in debt. The after-tax costs of each source of financing are given in the table. Using this information determine the firm’s weighted after-tax cost of capital. Express your answer as a percent. Answer: 11.3% Source of Financing Amount After-Tax Cost Common Stock 14 % Preferred Stock 11 Long-Term Debt 6 ABC Corp. issued $1,000 par value bonds having a 20-year life with a 10 percent coupon interest rate. The floatation cost was $30 per bond and the bonds were sold at a $10 discount. The firm has a 40 percent tax rate and the bonds pay interest annually. Determine the after-tax cost to maturity using the approximation formula and financial calculator. Express your answer as a percent. Answer: Approximation Formula 6.2% FC 6.29% XYZ Corp. is selling a new issue of $100 par value preferred stock. It has an annual dividend of 11 percent and was sold for $104 per share. The floatation costs were $6.00 per share. Determine the cost of the preferred stock. Express your answer as a percent. Answer: 11.22% Firm C has outstanding common stock selling for $42.50 per share. Its annual dividend growth rate has been eight percent and the projected dividend per share for next year is $2.00. If new shares are sold they will be underpriced by $1.00 per share and the floatation cost will be $2.00 per share. Using the constant growth valuation model determine the following. Express your answers as a percent. The cost of retained earnings. Answer: 12.7% The cost of new common stock. Answer: 13.06% New Corp has determined the market values of its sources of capital and their after tax costs. Using this information determine the firm’s weighted after-tax cost of capital. Express your answer as a percent. Answer: 10.63% Source of Financing Amount Cost Common Stock $20,000,000 14 % Preferred Stock 5,000,000 11 Long-Term Debt 15,000,000 6 9. New Company Incorporated plans to raise capital as shown below: Common stock: $200,000,000. The floatation cost is five percent of the stock’s sale price. The dividend next period will be $4.00, the stock will be sold at $100.00 per share, and the dividend growth rate is six percent. Preferred stock: $50,000,000. The floatation cost is five percent of the stock's $100 par value. The dividend is $9.00. The stock will be sold at $96.00 per share. Long-term debt (bonds): $150,000,000. The floatation cost is $40.00 per bond. The bonds have a 20 year maturity, a $1,000 maturity value and will sell at $1,010. The coupon interest rate is 10 percent. Determine the pre-tax cost of the bonds using your financial calculator. New Company's tax rate is 40 percent. Determine the following. Express your answers as a percent. a. The after-tax cost of the common stock. Answer: 10.2% b. The after-tax cost of the preferred stock. Answer: 9.9% c. The after-tax cost of the long-term debt. Answer: FC 6.22% d. The weighted average after-tax cost of capital. Answer: 8.67% 10. ZEN Corp. is selling a new issue of $100 par value preferred stock. It has an annual dividend of eight percent and was sold for $102 per share. The floatation costs were $5.00 per share. Determine the after-tax cost of the preferred stock. Express your answer as a percent. Answer: 8.25% 11. ABC Corp. issued $1,000 par value bonds having a 20-year life with a nine percent coupon interest rate. They were sold at a $15 discount. The firm has a 40 percent tax rate and the bonds pay interest annually. The floatation cost was $22 per bond. Determine the after-tax cost to maturity using your financial calculator formula. Express your answer as a percent. Answer: FC 5.65% Chapter 11 Leverage and Capital Structure 1. ABC produces one product and sells it for $12.00 per unit. The variable operating cost is $8.00 per unit. Furthermore, ABC has fixed operating costs of $200,000, fixed interest expense of $100,000 and a 40 percent tax rate. Determine the following: The breakeven point for operating costs in units and dollars of sales (i.e., EBIT = 0). Answer: 50,000 units $600,000 $ sales The breakeven point for total costs in units and dollars of sales (i.e., EBT=EAT=EPS=0). Answer: 75,000 units $900,000 $ sales The degree of operating leverage at an output of 100,000 units. Answer: 2.0 The degree of financial leverage at an output of 100,000 units. Answer: 2.0 The degree of total leverage at an output of 100,000 units. Answer: 4.0 The earnings after taxes at an output of 100,000 units. Answer: $60,000: Suppose output is increased by 10 percent to 110,000 units. Determine the new earnings after taxes. Answer: $84,000 Using your answer to part f, determine the price of ABC’s stock. Assume 60,000 shares of common stock are outstanding and a PE ratio of 12. Answer: $12.00 ABC produces one product and sells it for $12.00 per unit. The variable cost is $8.00 per unit. Furthermore, ABC has fixed operating costs of $200,000, interest expense of $100,000 and a 40 percent tax rate. [Same information as above problem.] Using grids provided on page 3, prepare two graphs. First, graph the breakeven point for EBIT. Show fixed operating costs, variable operating costs, total costs, and total revenue. Label the breakeven point and your axes. Second, graph the breakeven point for EBT. Show fixed operating costs, interest expense, total fixed costs, variable operating costs, total costs, and total revenue. Label the breakeven point and your axes. Your Corp. is just going into business. You believe that if you can raise $2,000,000, you can invest it to produce an EBIT of $300,000. You are considering two financial plans. The first is all common stock equity to be sold at $50.00 per share. The second is 60 percent common stock equity to be sold at $50.00 per share and the remainder debt at 10 percent interest. Your Corp. has a 40 percent tax rate. Determine the expected EPS for each plan. Answer: All equity $4.50 60% equity $5.50 Using a grid provided on page 3, graph the relationship between EPS and EBIT for the two financial plans described in the problem above. Label your graph carefully. ABC produces one product and sells it for $10.00 per unit. The variable cost is $6.00 per unit. Furthermore, ABC has fixed operating costs of $200,000, fixed interest expense of $100,000 and a 40 percent tax rate. Determine the following: The breakeven point for operating costs in units and dollars of sales (i.e., EBIT = 0). Answer: 50,000 units $500,000 $ sales The breakeven point for total costs in units and dollars of sales (i.e., EBT=EAT=EPS=0). Answer: 75,000 units $750,000 $ sales The degree of operating leverage at an output of 150,000 units. Answer: 1.5 The degree of financial leverage at an output of 150,000 units. Answer: 1.333 The degree of total leverage at an output of 150,000 units. Answer: 2.0 The earnings after taxes at an output of 150,000 units. Answer: $180,000 Suppose output is increased by 10 percent from 150,000 to 165,000 units. Determine the new earnings after taxes. Answer: $216,000 Using your answer to part f, determine the price of ABC’s stock. Assume 60,000 shares of common stock are outstanding and a PE ratio of 15. Answer: $45.00 Using the grid provided on page 3, prepare two graphs for problem 5. On the first, plot revenues and costs showing the breakeven point for EBIT. On the second plot revenues and costs showing the breakeven point for EBT, EAT, and EPS. Label your graphs carefully ABC produces one product and sells it for $10.00 per unit. The variable cost is $6.00 per unit. Furthermore, ABC has fixed operating costs of $200,000, interest expense of $100,000 and a 40 percent tax rate. Determine the breakeven point for EBT in units and dollars. Then, using a grid provided on page 3, graph the breakeven point for EBT. Show fixed operating costs, interest expense, total fixed costs, variable costs, total costs, and total revenue. Answer: 75,000 units and $750,000 ABC Corp. is just going into business. Management believes that if it can raise $1,000,000, it can invest it to produce an EBIT of $200,000. Management is considering three financial plans. The first is all common stock equity to be sold at $50.00 per share. The second is 80 percent common stock equity to be sold at $50.00 per share and remainder debt at 10 percent interest. The third is 50 percent stock to be sold at $47.00 per share and the remainder debt at 12 percent interest. Assume a 40 percent tax rate. Determine the earnings per share for each of the three financing plans. Answer: All equity $6.00 80% equity $6.75 50% equity $7.89 Using the grid provided on page 3, graph the relationship between EPS and EBIT for the three financial plans described in problem 8. Label your graph carefully. XYZ Corp. is just going into business. Management believes that if it can raise $2,000,000, it can invest the funds to produce an EBIT of $400,000. It is considering two financial plans. The first is all common stock equity to be sold at $50.00 per share. The second is 60 percent common stock equity to be sold at $50.00 per share and the remainder debt at 12 percent interest. XYZ Corp. has a 40 percent tax rate. Determine the expected EPS for each plan. Answer: All equity $6.00 60% equity $7.60 ZYX Corp. has been in business for several years. To date, management has avoided using any debt and has financed its operations entirely with common stock equity. It currently has $10,000,000 in common stock equity financing. The stock sells for $100 per share. Management is considering repurchasing 30,000 shares of its common stock. It expects to pay an average of $110 per share for a total of $3,300,000. It can borrow the $3,300,000 and pay 10 percent interest on this loan. After the repurchase, its financial structure will consist of 70,000 shares of common selling at $110 and $3,300,000 in debt at 10 percent interest. ZYX has an EBIT of $2,000,000. Assume a 40 percent tax rate. Determine the earnings per share for the original all equity plan and the new financing plan. Answer: All equity $12.00 New plan $14.31 New Corp. is just going into business. Management believes that if it can raise $2,000,000, it can invest it to produce an EBIT of $400,000. Management is considering three financial plans. The first is all common stock equity to be sold at $50.00 per share. The second is 80 percent common stock equity to be sold at $50.00 per share and remainder debt at 10 percent interest. The third is 50 percent stock to be sold at $47.00 per share and the remainder debt at 12 percent interest. Assume a 40 percent tax rate. Determine the earnings per share for each of the three financing plans. Answer: All equity $6.00 80% equity $6.75 50% equity $7.90 Solve algebraically for the value of EBIT that will result in the same EPS for the all equity and the 80 percent equity financing plans. Answer: EBIT $200,000 EPS $3.00 New Corp. is just going into business. Management believes that if it can raise $2,000,000, it can invest it to produce an EBIT of $400,000. Management is considering two financial plans. The first is all common stock equity to be sold at $50.00 per share. The second is 80 percent common stock equity to be sold at $50.00 per share and remainder debt with a 10 percent interest rate. Assume a 40 percent tax rate. Solve algebraically for the value of EBIT that will result in the same EPS for the two financing plans. Answer: $200,000 ABC produces one product and sells it for $25.00 per unit. The variable operating cost is $20.00 per unit. Furthermore, ABC has fixed operating costs of $500,000, fixed interest expense of $200,000 and a 40 percent tax rate. Determine the following: The breakeven point for operating costs in units and dollars of sales (i.e., EBIT = 0). Answer: 100,000 units $2,500,000 sales The breakeven point for total costs in units and dollars of sales (i.e., EBT=EAT=EPS=0). Answer: 140,000 units $3,500,000 sales The degree of operating leverage at an output of 200,000 units. Answer: 2 The degree of financial leverage at an output of 200,000 units. Answer: 1.67 The degree of total leverage at an output of 200,000 units. Answer: 3.34 The earnings after taxes at an output of 200,000 units. Answer: $180,000 g. Suppose output is increased by 10 percent from 200,000 to 220,000 units. Determine the new earnings after taxes. Answer: $240,000 Using the grid provided on page 3, prepare two graphs for problem 14. On the first, plot revenues and costs showing the breakeven point for EBIT. On the second plot revenues and costs showing the breakeven point for EBT, EAT, and EPS. Label your graphs carefully. A recent news article indicated that a company’s sales increased last year by about 20 percent while its earnings after taxes had concurrently increased 80 percent. At the same time, the number of shares of common stock outstanding remained constant. Based on this information, determine the company’s degree of total leverage. Answer: 4 Chapter 12 Dividend Policy 1. The following financial information is available for ABC Corp. Earnings available to common shareholders $1,000,000 Number of shares of common stock outstanding 400,000 Market price per share of common stock $40 Determine the following: The earnings per share (EPS). Answer: $2.50 The price-earnings (PE) ratio. Answer: 16 Assume the firm uses $500,000 of its available earnings to repurchase shares at $40 per share. Determine the following: The expected market price per share of common stock after the repurchase. Assume the PE ratio determined in part b remains constant. Answer: $41.29 Jane owned 20,000 shares of ABC stock before the repurchase. Assuming she does not sell any shares, determine the percentage of ABC stock she owns after the repurchase. Answer: 5.16% ABC has the stockholder’s equity account shown below. The firm’s common stock sells for $50.00 per share. Preferred stock $500,000 Common stock (20,000 shrs @ $1.00 par) 20,000 Paid-in capital in excess of par 380,000 Retained earnings 2,000,000 Total stockholder’s equity $2,900,000 Show the effects of a 10 percent stock dividend. (Complete the table below.) Preferred stock $ Common stock ( shrs @ ) Paid-in capital in excess of par Retained earnings _________ Total stockholder’s equity $2,900,000 b. Determine the price per share of the common stock when it was originally issued. Answer: $20/share ABC has the stockholder’s equity account shown below. The firm’s common stock sells for $50.00 per share. Preferred stock $500,000 Common stock (20,000 shrs @ $1.00 par) 20,000 Paid-in capital in excess of par 380,000 Retained earnings 2,000,000 Total stockholder’s equity $2,900,000 Show the effects of a 2-for-1 stock split. Preferred stock $500,000 Common stock (40,000 shares @ $.50 par) 20,000 Paid-in capital in excess of par 380,000 Retained earnings 2,000,000 Total stockholder’s equity $2,900,000 The following financial information is available for ABC Corp. Earnings available to common shareholders $1,000,000 Number of shares of common stock outstanding 400,000 Market price per share of common stock $40 Determine the following. The earnings per share (EPS). Answer: $2.50 The price-earnings (PE) ratio. Answer: 16 Assume the firm uses $500,000 of its available earnings to repurchase shares at $40 per share. Determine the following. The earnings per share (EPS) after repurchase. Answer: $2.58 The expected market price per share of common stock after the repurchase. Assume the PE ratio determined in part b remains constant. Answer: $41.28 Jane owned 20,000 shares of ABC stock before the repurchase. Assuming she does not sell any shares, determine the percentage of ABC stock she owns after the repurchase. Answer: 5.16% The following financial information is available for XYZ Corp. Earnings available to common shareholders $7,500,000 Number of shares of common stock outstanding 2,500,000 Market price per share of common stock $60 Determine the following. The earnings per share (EPS). Answer: $3.00 The price-earnings (PE) ratio. Answer: 20 Assume the firm uses $5,000,000 of its available earnings to repurchase shares at $60 per share. Determine the following. The earnings per share (EPS) after repurchase. Answer: $3.10 The expected market price per share of common stock after the repurchase. Assume the PE ratio determined in part b remains constant. Answer: $62.07 Peter owned 10,000 shares of ABC stock before the repurchase. Assuming he does not sell any shares, determine the percentage of ABC stock he owns after the repurchase. Answer: .414% Chapter 13 Working Capital and Current Assets Management ABC has forecast its total funding requirements for next year as shown below: Month Amount Month Amount January $4,000,000 July $10,000,000 February 4,000,000 August 14,000,000 March 5,000,000 September 10,000,000 April 7,000,000 October 7,000,000 May 8,000,000 November 7,000,000 June 8,000,000 December 4,000,000 Assume management has decided to raise $7,000,000 in long-term funds at an annual rate of 10 percent. Management will borrow to meet additional seasonal needs at an eight percent annual rate. Determine the following: a. The annual cost of the long-term borrowing. Answer: $700,000 b. The annual cost of the short-term borrowing. Answer: $100,000 Small appliance currently has credits sales of $10 million per year and an average collection period of 30 days. Assume the price of Small Appliance's products is $70 and the variable costs are $50 per unit. The firm is considering an account receivable change that is expected to result in a five percent increase in sales and an increase in the average collection period to 60 days. No change in bad debt expense is expected. The firm's equal-risk opportunity cost on its investment in accounts receivable is 10 percent. a. Determine the additional profit contribution from the new sales that the firm will realize if it takes the proposal. Answer: $142,857 b. Determine the additional investment in accounts receivable that will result if the firm takes the proposal. Answer: $645,790 c. Determine the annual dollar cost of the additional investment in accounts receivable. Answer: $64,579 d. Determine the net increase (or loss) to pretax profits (EBT) if the firm implements the plan. Answer: $78,278 Suppose that the bad debt expense is expected to increase from one to two percent of sales rather than not changing. e. Determine the additional bad debt expense. Answer: $110,000 f. Determine the net increase (or loss) to pretax profits (EBT) if the firm implements the plan. Answer: ($31,722) ABC Corp. has inventories with an average age of 60 days. Their accounts receivable are collected on average in 45 days and accounts payable are paid in 30 days. The firm spends $10,000,000 on operating cycle investments each year. Determine the following: The firm’s operating cycle. Answer: 105 days The firm’s cash conversion cycle. Answer: 75 days The amount of negotiated financing required to support the firm’s cash conversion cycle. Answer: $2,054,795 ABC managers have forecast its total funding requirements for next year as shown below: Month Amount Month Amount January $2,000,000 July $12,000,000 February 2,000,000 August 14,000,000 March 2,000,000 September 9,000,000 April 4,000,000 October 5,000,000 May 6,000,000 November 4,000,000 June 9,000,000 December 3,000,000 Management has decided to raise $6.0 million using long-term financing at an annual cost of 10 percent. Furthermore, management plans to borrow any additional funds the company will need using short-term debt with an annual interest rate of six percent. Finally, during those months when the company has excess cash, management plans to invest it at an annual rate of four percent. a. Determine the annual dollar cost of the long-term financing. Answer: $600,000 b. Determine the investment income that will result from the investment of excess cash. Answer: $66,667 c. Determine the net cost of the loan. Answer: $633,333 A firm has the balance sheet shown below. The firm annually earns approximately five percent on current assets and 15 percent on its fixed assets. Assets Liabilities + Equity Current assets $10,000 Current liabilities $3,000 Fixed assets 20,000 Long-term debt 10,000 Equity 17,000 Total $30,000 $30,000 To increase its earnings, management is considering shifting some of its current assets to fixed assets. If it must maintain a current ratio of at least 2.0, determine the following: a. The maximum amount it can shift from current to fixed assets. Answer: $4,000 b. The increase in profits resulting from the shift in assets. Answer: $400 ABC sells 10,000 units of a product for $80. This product has a variable cost of $60.00. The average collection period is currently 45 days and the average bad debt expense is four percent of sales. ABC's management believes that if ABC extends credit to a group of somewhat less credit worthy customers it will be able to increase sales by 10 percent. Concurrently, management believes the bad debt expense will increase to five percent and the collection period will increase to 60 days. The firm has a required return on equally-risky investments of 10 percent. Determine the following: a. The expected increase in the cost of funds invested in accounts receivables if the plan is implemented. Answer: $3,452 b. The expected increase in bad debt expense that will result if the plan is implemented. Answer: $12,000 c. The expected increase or decrease in pretax profits that will result if the plan is implemented. Answer: Pretax profits will (circle one) (increase) decrease Amount: $4,548 ABC Industries has daily cash receipts of $200,000. A recent analysis of its collections indicated that customers' payments were in the mail an average of three days. Once received, the payments are processed in 1.5 days. After payments are deposited, it takes an average of three days for these receipts to clear the banking system. a. How many days collection float does the firm currently have? Answer: 7.5 days b. Suppose the firm's opportunity cost is 10 percent and that it could pay an annual fee of $30,000 to reduce the float by two days. Determine the additional pretax profit or loss if ABC pays the fee and reduces its float by two days. Answer: Additional (circle one) (Profit) Loss Amount $10,000 XYZ turns its inventory eight times each year, has an average payment period of 30 days, and has an average collection period of 60 days. The firm's total annual outlays for operating cycle investments are $6.0 million. a. Calculate the firm's operating cycle. Answer 105 days b. Calculate the firm's cash conversion cycle. Answer 76 days Note: the 76 days results from rounding the average inventory age up to 46 days. c. Determine the amount of financing needed to support the firm's cash conversion cycle. Answer $1,249,315 Assume the firm pays 12 percent for its financing. By how much would it increase its annual profits by favorably changing its current cash conversion period by 10 days? Answer $20,000 New Industries has daily cash receipts of $100,000. A recent analysis of its collections indicated that customers' payments were in the mail an average of three days. Once received, the payments are processed in two. After payments are deposited, it takes an average of three days for these receipts to clear the banking system. a. How many days collection float does the firm currently have? Answer 8 days b. Suppose the firm's opportunity cost is 10 percent and that it could pay an annual fee of $20,000 to reduce the float by three days. Determine the additional pretax profit or loss if New pays the fee and reduces its float by three days. Answer $10,000 profit c. Suppose interest rates change. Determine the interest rate at which New will just break even if it decides to pay the $20,000 to reduce the float by three days. Answer 6.67% Chapter 14 Current Liabilities Management 1. XYZ Corp. recently sold 180-day commercial paper with a face value of $2,000,000 and received initial proceeds of $1,920,000. Determine the interest rate on the paper for the 180 days. Answer: 4.17% The following equation/calculations are required to be shown. Solution: $80,000/$1,920,000 = .041666 = 4.17% Assume the paper is rolled over every 180 days and that there are 365 days in the year. Determine the effective annual rate of the loan. Answer: 8.63% The following equation/calculations are required to be shown. Solution: Interest is compounded 365/180 = 2.027777 times per year EAR = (1 + .041666)2.02777 – 1 = 1.08629 – 1 = .0863 = 8.63% A vendor selling material to ABC. Corporation offers terms of 2/15 net 45. If ABC’s managers decide to pay in 45 days and forgo the discount, determine the effective annual interest rate the company will pay the vendor. Answer: 24.83% Bank lent Company $100,000 for one year on a discount basis. The stated interest rate is 10 percent. Bank will require a 15 percent compensating balance. Determine the effective interest rate on the loan. Answer: 13.33% National Bank requires borrowers to maintain a six percent compensating balance on all of their loans. It charges 10 percent interest on its loans. Almost Broke Company plans to borrow $100,000 for one year. a. Determine the dollar amount of interest and the effective rate of interest on the loan. Answer: $ Amount $10,000 Effective Interest Rate 10.64% b. Suppose National Bank lends Almost Broke the $100,000 on a discount basis, determine the dollar amount of interest and the effective rate of interest on the loan. Answer: $ Amount $10,000 Effective Interest Rate 11.9% Company sold commercial paper having a face value of $2,000,000 for $1,940,000. The paper has a 120-day maturity. Assuming the paper is rolled over every 120 days, determine the effective annual interest rate that Company will pay on its commercial paper. Answer: 9.71% The following equation/calculations are required to be shown. Interest is compounded 365/120 = 3.041666 times per year Interest for 120 days = $60,000/$1,940,000 = .0309278 EAR = (1 + .0309278)3.041666 – 1 = 1.09707 – 1 = .09707 = 9.71% A firm needs $10,000. When the owner went to apply for a loan, the bank offered a discount loan at eight percent interest. Since the company needs the entire $10,000, determine how much it must borrow assuming it accepts the bank’s offer. Answer $10,870 Solution: let X = amount of the loan Then, X – .08X = $10,000 X = $10,870 Bank lent Company $2,000,000 for one year on a discount basis. The stated interest rate for the loan was the prime interest rate plus two percent. The prime interest rate was five percent for the entire period of the loan. Bank requires an eight percent compensating balance. Determine the effective interest rate on the loan. Answer 8.24%  Year 3 of the existing system’s life.     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