Chapter 9
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You invest $2,500 a year for three years at 8 percent. What is the value of your investment after one year? Multiply $2,500 × 1.08. What is the value of your investment after two years? Multiply your answer to part a by 1.08. What is the value of your investment after three years? Multiply your answer to part b by 1.08. This gives your final answer. Confirm that your final answer is correct by going to Appendix A (future value of $1), and looking up the future value for n = 3, and i = 8 percent. Multiply this tabular value by $2,500 and compare your answer to the answer in part c. There may be a slight difference due to rounding.  Future value 
What is the present value of: $8,000 in 10 years at 6 percent? $16,000 in 5 years at 12 percent? $25,000 in 15 years at 8 percent? $1,000 in 40 periods at 20 percent?  Present value 
You will receive $4,000, three years from now. The discount rate is 10 percent. What is the value of your investment two years from now? Multiply $4,000 × .909 (one year’s discount rate at 10 percent). What is the value of your investment one year from now? Multiply your answer to part a by .909 (one year’s discount rate at 10 percent). What is the value of your investment today? Multiply your answer to part b by .909 (one year’s discount rate at 10 percent). Confirm that your answer to part c is correct by going to Appendix B (present value of $1) for n = 3 and i = 10%. Multiply this tabular value by $4,000 and compare your answer to the answer in part c. There may be a slight difference due to rounding.  Present value 
If you invest $12,000 today, how much will you have: In 6 years at 7 percent? In 15 years at 12 percent? In 25 years at 10 percent? In 25 years at 10 percent (compounded semiannually)?  Future value 
Your aunt offers you a choice of $20,000 in 50 years or $45 today. If money is discounted at 13 percent, which should you choose?  Present value 
How much would you have to invest today to receive: $12,000 in 6 years at 12 percent? $15,000 in 15 years at 8 percent? $5,000 each year for 10 years at 8 percent? $40,000 each year for 40 years at 5 percent?  Present value 
If you invest $8,000 per period for the following number of periods, how much would you have? 7 years at 9 percent. 40 years at 11 percent.  Future value 
You invest a single amount of $12,000 for 5 years at 10 percent. At the end of 5 years you take the proceeds and invest them for 12 years at 15 percent. How much will you have after 17 years?  Future value 
Mrs. Crawford will receive $6,500 a year for the next 14 years from her trust. If an 8 percent interest rate is applied, what is the current value of the future payments?  Present value 
John Longwaite will receive $100,000 in 50 years. His friends are very jealous of him. If the funds are discounted back at a rate of 14 percent, what is the present value of his future “pot of gold”?  Present value 
Carrie Tune will receive $19,500 a year for the next 20 years as a result of the new song she has written. If a 10 percent rate is applied, should she be willing to sell out her future rights now for $160,000?  Present value 
General Mills will receive $27,500 per year for the next 10 years as a payment for a weapon he invented. If a 12 percent rate is applied, should he be willing to sell out his future rights now for $160,000?  Present value 
The Western Sweepstakes has just informed you that you have won $1 million. The amount is to be paid out at the rate of $50,000 a year for the next 20 years. With a discount rate of 12 percent, what is the present value of your winnings?  Present value 
Rita Gonzales won the $60 million lottery. She is to receive $1 million a year for the next 50 years plus an additional lump sum payment of $10 million after 50 years. The discount rate is 10 percent. What is the current value of her winnings?  Present value 
Bruce Sutter invests $2,000 in a mint condition Nolan Ryan baseball card. He expects the card to increase in value by 20 percent a year for the next five years. After that, he anticipates a 15 percent annual increase for the next three years. What is the projected value of the card after eight years?  Future value 
Martha Reed has been depositing $1,500 in her savings account every December since 1998. Her account earns 6 percent compounded annually. How much will she have in December of 2007? (Assume that a deposit is made in 2007. Make sure to count the years carefully.)  Future value 
At a growth (interest) rate of 8 percent annually, how long will it take for a sum to double? To triple? Select the year that is closest to the correct answer.  Future value 
If you owe $30,000 payable at the end of five years, what amount should your creditor accept in payment immediately if she could earn 11 percent on her money?  Present value 
Barney Smith invests in a stock that will pay dividends of $3.00 at the end of the first year, $3.30 at the end of the second year, and $3.60 at the end of the third year. Also, he believes that at the end of the third year he will be able to sell the stock for $50. What is the present value of all future benefits if a discount rate of 11 percent is applied? (Round all values to two places to the right of the decimal point.)  Present value 
Mr. Flint retired as president of the Color Tile Company but is currently on a consulting contract for $45,000 per year for the next 10 years. If Mr. Flint’s opportunity cost (potential return) is 10 percent, what is the present value of his consulting contract? Assuming that Mr. Flint will not retire for two more years and will not start to receive his 10 payments until the end of the third year, what would be the value of his deferred annuity?  Present value 
Cousin Bertha invested $100,000 10 years ago at 12 percent, compounded quarterly. How much has she accumulated?  Quarterly compounding

Determine the amount of money in a savings account at the end of five years, given an initial deposit of $3,000 and an 8 percent annual interest rate when interest is compounded (a) annually, (b) semiannually, and (c) quarterly.  Special compounding 
As stated in the chapter, annuity payments are assumed to come at the end of each payment period (termed an ordinary annuity). However, an exception occurs when the annuity payments come at the beginning of each period (termed an annuity due). To find the present value of an annuity due, subtract 1 from n an add 1 to the tabular value. To find the future value of an annuity, add 1 to n and subtract 1 from the tabular value. For example, to find the future value of a $100 payment at the beginning of each period for five periods at 10 percent, go to Appendix C for n = 6 and i = 10 percent. Look up the value of 7.716 and subtract 1 from it for an answer of 6.716 or $671.60 ($100 × 6.716). What is the future value of a 10year annuity of $2,000 per period where payments come at the beginning of each period? The interest rate is 8 percent.  Annuity due 
Related to the discussion in problem 23, what is the present value of a 10year annuity of $3,000 per period in which payments come at the beginning of each period? The interest rate is 12 percent.  Annuity due 
Your grandfather has offered you a choice of one of the three following alternatives: $5,000 now; $1,000 a year for eight years; or $12,000 at the end of eight years. Assuming you could earn 11 percent annually, which alternative should you choose? If you could earn 12 percent annually, would you still choose the same alternative?  Present value alternative

You need $23,956 at the end of nine years, and your only investment outlet is a 7 percent longterm certificate of deposit (compounded annually). With the certificate of deposit, you make an initial investment at the beginning of the first year. What single payment could be made at the beginning of the first year to achieve this objective? What amount could you pay at the end of each year annually for nine years to achieve this same objective?  Payments Required

Beverly Hills started a paper route on January 1, 2001. Every three months, she deposits $300 in her bank account, which earns 8 percent annually but is compounded quarterly. On December 31, 2004, she used the entire balance in her bank account to invest in an investment at 12 percent annually. How much will she have on December 31, 2007?  Quarterly compounding 
Tom Phillips has just invested $8,760 for his son (age one). This money will be used for his son’s education 17 years from now. He calculates that he will need $60,000 by the time the boy goes to school. What rate of return will Mr. Phillips need in order to achieve this goal?  Yield 
On January 1, 2005, Mr. Dow bought 100 shares of stock at $12 per share. On December 31, 2008, he sold the stock for $18 per share. What is his annual rate of return? Interpolate to find the answer.  Yield with interpolation 
C. D. Rom has just given an insurance company $30,000. In return, he will receive an annuity of $3,200 for 20 years. At what rate of return must the insurance company invest this $30,000 in order to make the annual payments? Interpolate.  Yield with interpolation 
Frank Bell has just retired from the telephone company. His total pension funds have an accumulated value of $200,000, and his life expectancy is 16 more years. His pension fund manager assumes he can earn a 12 percent return on his assets. What will be his yearly annuity for the next 16 years?  Solving for an annuity 
Dr. Oats, a nutrition professor, invests $80,000 in a piece of land that is expected to increase in value by 14 percent per year for the next five years. She will then take the proceeds and provide herself with a 10year annuity. Assuming a 14 percent interest rate for the annuity, how much will this annuity be?  Solving for an annuity 
You wish to retire in 20 years, at which time you want to have accumulated enough money to receive an annual annuity of $12,000 for 25 years after retirement. During the period before retirement you can earn 8 percent annually, while after retirement you can earn 10 percent on your money. What annual contributions to the retirement fund will allow you to receive the $12,000 annuity?  Solving for an annuity 
Rusty Steele will receive the following payments at the end of the next three years: $4,000, $7,000, and $9,000. Then from the end of the fourth year through the end of the tenth year, he will receive an annuity of $10,000. At a discount rate of 10 percent, what is the present value of all future benefits?  Deferred annuity 
Kelly Greene has a contract in which she will receive the following payments for the next five years: $3,000, $4,000, $5,000, $6,000 and $7,000. She will then receive an annuity of $9,000 a year from the end of the sixth through the end of the 15th year. The appropriate discount rate is 13 percent. If she is offered $40,000 to cancel the contract, should she do it?  Present value 
Kay Mart has purchased an annuity to begin payment at the end of 2009 (the date of the first payment). Assume it is now the beginning of 2007. The annuity is for $12,000 per year and is designed to last eight years. If the discount rate for the calculation is 11 percent, what is the most she should have paid for the annuity?  Deferred annuity 
If you borrow $9,725 and are required to pay back the loan in five equal annual installments of $2,500, what is the interest rate associated with the loan?  Yield 
Tom Busby owes $20,000 now. A lender will carry the debt for four more years at 8 percent interest. That is, in this particular case, the amount owed will go up 8 percent per year for four years. The lender then will require Busby to pay off the loan over 12 years at 11 percent interest. What will his annual payments be?  Loan repayment 
If your aunt borrows $50,000 from the bank at 10 percent interest over the eightyear life of the loan, what equal annual payments must be made to discharge the loan, plus pay the bank its required rate of interest (round to the nearest dollar)? How much of her first payment will be applied to interest? To principal? How much of her second payment will be applied to each?  Loan repayment 
Jim Thomas borrows $70,000 toward the purchase of a home at 12 percent interest. His mortgage is for 30 years. How much will his annual payments be? (Although home payments are usually on a monthly basis, we shall do our analysis on an annual basis for ease of computation. We will get a reasonably accurate answer.) How much interest will he pay over the life of the loan? How much should he be willing to pay to get out of a 12 percent mortgage and into a 10 percent mortgage with 30 years remaining on the mortgage? Suggestion: Find the annual savings and then discount them back to the present at the current interest rate (10 percent).  Loan repayment 
You are chairperson of the investment fund for the Continental Soccer League. You are asked to set up a fund of semiannual payments to be compounded semiannually to accumulate a sum of $200,000 after 10 years at an 8 percent annual rate (20 payments). The first payment into the fund is to take place six months from today, and the last payment is to take place at the end of the 10th year. Determine how much the semiannual payment should be. (Round to whole numbers.) On the day after the sixth payment is made (the beginning of the fourth year) the interest rate goes up to a 10 percent annual rate, and you can earn a 10 percent annual rate on funds that have been accumulated as well as all future payments into the fund. Interest is to be compounded semiannually on all funds. Determine how much the revised semiannual payments should be after this rate change (there are 14 payments and compounding dates). The next payment will be in the middle of the fourth year. (Round all values to whole numbers.)  Annuity with changing interest rates 
Your younger sister, Jennifer, will start college in five years. She has just informed your parents that she wants to go to Eastern State U., which will cost $18,000 per year for four years (cost assumed to come at the end of each year). Anticipating Jennifer’s ambitions, your parents started investing $3,000 per year five yeas ago and will continue to do so for five more years. How much more will your parents have to invest each year for the next five years to have the necessary funds for Jennifer’s education? Use 10 percent as the appropriate interest rate throughout this problem (for discounting or compounding). Round all values to whole numbers.  Annuity consideration 
Jennifer (from problem 42) is now 18 years old (five years have passed), and she wants to get married instead of going to college. Your parents have accumulated the necessary funds for her education. Instead of her schooling, your parents are paying $7,000 for her current wedding and plan to take yearend vacations costing $2,000 per year for the next three years. How much money will your parents have at the end of three years to help you with graduate school, which you will start then? You plan to work on a master’s and perhaps a PhD. If graduate school costs $18,930 per year, approximately how long will you be able to stay in school based on these funds? Use 10 percent as the appropriate interest rate throughout this problem. (Round all values to whole numbers.)  ^
Philip Morris is excited because sales for his clothing company are expected to double from $500,000 to $1,000,000 next year. Philip notes that net assets (Assets  Liabilities) will remain at 50 percent of Sales. His clothing firm will enjoy a 9 percent return on total sales. He will start the year with $100,000 in the bank and is already bragging about the two Mercedes he will buy and the European vacation he will take. Does his optimistic outlook for his cash position appear to be correct? Compute his likely cash balance or deficit for the end of the year. Start with beginning cash and subtract the asset buildup (equal to 50 percent of the sales increase) and add in profit.  Growth and financing  In Problem 1 if there had been no increase in sales and all other facts were the same, what would Philip’s ending cash balance be? What lesson do the examples in Problems 1 and 2 illustrate?  Growth and financing  The Alliance Corp. expects to sell the following number of units of copper cables at the prices indicated, under three different scenarios in the economy. The probability of each outcome is indicated. What is the expected value of the total sales projection?  Sales projections  Bronco Truck Parts expects to sell the following number of units at the prices indicated under three different scenarios in the economy. The probability of each outcome is indicated. What is the expected value of the total sales projection?  Sales projections  Cyber Security Systems had sales of 3,000 units at $50 per unit last year. The marketing manager projects a 20 percent increase in unit volume sales this year with a 10 percent price increase. Returned merchandise will represent 6 percent of total sales. What is your net dollar sales projection for this year?  Sales projections  Dodge Ball Bearings had sales of 10,000 units at $20 per unit last year. The marketing manager projects a 30 percent increase in unit volume sales this year with a 5 percent price decrease (due to a price reduction by a competitor). Returned merchandise will represent 3 percent of total sales. What is your net dollar sales projection for this year?  Sales projections  Sales for Western Boot Stores are expected to be 40,000 units for October. The company likes to maintain 15 percent of unit sales for each month in ending inventory (i.e., the end of October). Beginning inventory for October is 8,500 units. How many units should Western Boot produce for the coming month?  Production requirements  Vitale Hair Spray had sales of 8,000 units in March. A 50 percent increase is expected in April. The company will maintain 5 percent of expected unit sales for April in ending inventory. Beginning inventory for April was 400 units. How many units should the company produce in April?  Production requirements  Delsing Plumbing Company has beginning inventory of 14,000 units, will sell 50,000 units for the month, and desires to reduce ending inventory to 40 percent of beginning inventory. How many units should Delsing produce?  Production requirements  On December 31 of last year, Wolfson Corporation had in inventory 400 units of its product, which cost $21 per unit to produce. During January, the company produced 800 units at a cost of $24 per unit. Assuming that Wolfson Corporation sold 700 units in January, what was the cost of goods sold (assume FIFO inventory accounting)?  Cost of goods sold—FIFO  At the end of January, Higgins Data Systems had an inventory of 600 units, which cost $16 per unit to produce. During February the company produced 850 units at a cost of $19 per unit. If the firm sold 1,100 units in February, what was its cost of goods sold (assume LIFO inventory accounting)?  Cost of goods sold—FIFO  The Bradley Corporation produces a product with the following costs as of July 1, 2007: Beginning inventory at these costs on July 1 was 3,000 units. From July 1 to December 1, 2007, Bradley produced 12,000 units. These units had a material cost of $3, labor of $5, and overhead of $3 per unit. Bradley uses FIFO inventory accounting. Assuming that Bradley sold 13,000 units during the last six months of the year at $16 each, what is its gross profit? What is the value of ending inventory?  Gross profit and ending inventory  Assume in Problem 12 that the Bradley Corporation used LIFO accounting instead of FIFO; what would its gross profit be? What would be the value of ending inventory?  Gross profit and ending inventory  Sprint Shoes, Inc., had a beginning inventory of 9,000 units on January 1, 2007. The costs associated with the inventory were: During 2007, the firm produced 42,500 units with the following costs: Sales for the year were 47,250 units at $39.60 each. Sprint Shoes uses LIFO accounting. What was the gross profit? What was the value of ending inventory?  Gross profit and ending inventory  Victoria’s Apparel has forecast credit sales for the fourth quarter of the year as: Experience has shown that 20 percent of sales receipts are collected in the month of sale, 70 percent in the following month, and 10 percent are never collected. Prepare a schedule of cash receipts for Victoria’s Apparel covering the fourth quarter (October through December).  Schedule of cash receipts  Simpson Glove Company has made the following sales projections for the next six months. All sales are credit sales. Sales in January and February were $41,000 and $39,000 respectively. Experience has shown that of total sales receipts, 10 percent are uncollectible, 40 percent are collected in the month of sale, 30 percent are collected in the following month, and 20 percent are collected two months after sale. Prepare a monthly cash receipts schedule for the firm for March through August.  Schedule of cash receipts  Watt’s Lighting Stores made the following sales projection for the next six months. All sales are credit sales. Sales in January and February were $33,000 and $32,000, respectively. Experience has shown that of total sales, 10 percent are uncollectible, 30 percent are collected in the month of sale, 40 percent are collected in the following month, and 20 percent are collected two months after sale. Prepare a monthly cash receipts schedule for the firm for March through August. Of the sales expected to be made during the six months from March through August, how much will still be uncollected at the end of August? How much of this is expected to be collected later?  Schedule of cash receipts  Ultravision, Inc., anticipates sales of $240,000 from January through April. Materials will represent 50 percent of sales and because of level production, material purchases will be equal for each month during the four months of January, February, March, and April. Materials are paid for one month after the month purchased. Materials purchased in December of last year were $20,000 (half of $40,000 in sales). Labor costs for each of the four months are slightly different due to a provision in the labor contract in which bonuses are paid in February and April. The labor figures are: Fixed overhead is $6,000 per month. Prepare a schedule of cash payments for January through April.  Schedule of cash payments  The Denver Corporation has forecast the following sales for the first seven months of the year: Monthly material purchases are set equal to 30 percent of forecasted sales for the next month. Of the total material costs, 40 percent are paid in the month of purchase and 60 percent in the following month. Labor costs will run $4,000 per month, and fixed overhead is $2,000 per month. Interest payments on the debt will be $3,000 for both March and June. Finally, the Denever salesforce will receive a 1.5 percent commission on total sales for the first six months of the year, to be paid on June 30. Prepare a monthly summary of cash payments for the sixmonth period from January through June. (Note: Compute prior December purchases to help get total material payments for January.)  Schedule of cash payments  The Boswell Corporation forecasts its sales in units for the next four months as follows: Boswell maintains an ending inventory for each month in the amount of one and onehalf times the expected sales in the following month. The ending inventory for February (March’s beginning inventory) reflects this policy. Materials cost $5 per unit and are paid for in the month after production. Labor cost is $10 per unit and is paid for in the month incurred. Fixed overhead is $12,000 per month. Dividends of $20,000 are to be paid in May. Five thousand units were produced in February. Complete a production schedule and a summary of cash payments for March, April, and May. Remember that production in any one month is equal to sales plus desired ending inventory minus beginning inventory.  Schedule of cash payments  The Volt Battery Company has forecast its sales in units as follows: Volt Battery always keeps an ending inventory equal to 120 percent of the next month’s expected sales. The ending inventory for December (January’s beginning inventory) is 960 units, which is consistent with this policy. Materials cost $12 per unit and are paid for in the month after purchase. Labor cost is $5 per unit and is paid in the month the cost is incurred. Overhead costs are $6,000 per month. Interest of $8,000 is scheduled to be paid in March, and employee bonuses of $13,200 will be paid in June. Prepare a monthly production schedule and a monthly summary of cash payments for January through June. Volt produced 600 units in December.  Schedule of cash payments  Lansing Auto Parts, Inc., has projected sales of $25,000 in October, $35,000 in November, and $30,000 in December. Of the company’s sales, 20 percent are paid for by cash and 80 percent are sold on credit. The credit sales are collected one month after sale. Determine collections for November and December. Also assume that the company’s cash payments for November and December are $30,400 and $29,800, respectively. The beginning cash balance in November is $6,000, which is the desired minimum balance. Prepare a cash budget with borrowing needed or repayments for November and December. (You will need to prepare a cash receipts schedule first.)  Cash budget
 Harry’s Carryout Stores has eight locations. The firm wishes to expand by two more stores and needs a bank loan to do this. Mr. Wilson, the banker, will finance construction if the firm can present an acceptable threemonth financial plan for January through March. The following are actual and forecasted sales figures: Of the firm’s sales, 40 percent are for cash and the remaining 60 percent are on credit. Of credit sales, 30 percent are paid in the month after sale and 70 percent are paid in the second month after the sale. Materials cost 30 percent of sales and are purchased and received each month in an amount sufficient to cover the following month’s expected sales. Materials are paid for in the month after they are received. Labor expense is 40 percent of sales and is paid for in the month of sales. Selling and administrative expense is 5 percent of sales and is also paid in the month of sales. Overhead expense is $28,000 in cash per month. Depreciation expense is $10,000 per month. Taxes of $8,000 will be paid in January, and dividends of $2,000 will be paid in March. Cash at the beginning of January is $80,000, and the minimum desired cash balance is $75,000. For January, February, and March, prepare a schedule of monthly cash receipts, monthly cash payments, and a complete monthly cash budget with borrowings and repayments.  Complete cash budget  Archer Electronics Company’s actual sales and purchases for April and May are shown here along with forecasted sales and purchases for June through September. The company makes 10 percent of its sales for cash and 90 percent on credit. Of the credit sales, 20 percent are collected in the month after the sale and 80 percent are collected two months later. Archer pays for 40 percent of its purchases in the month after purchase and 60 percent two months after. Labor expense equals 10 percent of the current month’s sales. Overhead expense equals $12,000 per month. Interest payments of $30,000 are due in June and September. A cash dividend of $50,000 is scheduled to be paid in June. Tax payments of $25,000 are due in June and September. There is a scheduled capital outlay of $300,000 in September. Archer Electronics’s ending cash balance in May is $20,000. The minimum desired cash balance is $10,000. Prepare a schedule of monthly cash receipts, monthly cash payments, and a complete monthly cash budget with borrowing and repayments for June through September. The maximum desired cash balance is $50,000. Excess cash (above $50,000) is used to buy marketable securities. Marketable securities are sold before borrowing funds in case of a cash shortfall (less than $10,000).  Complete cash budget
 Owen’s Electronics has 9 operating plants in seven southwestern states. Sales for last year were $100 million, and the balance sheet at yearend is similar in percentage of sales to that of previous years (and this will continue in the future). All assets (including fixed assets) and current liabilities will vary directly with sales. The firm is working at full capacity. Owen’s has an aftertax profit margin of 7 percent and a dividend payout ratio of 40 percent. If sales grow by 10 percent next year, determine how many dollars of new funds are needed to finance the growth.  Percentofsales method  The Manning Company has financial statements as shown below, which are representative of the company’s historical average. The firm is expecting a 20 percent increase in sales next year, and management is concerned about the company’s need for external funds. The increase in sales is expected to be carried out without any expansion of fixed assets, but rather through more efficient asset utilization in the existing store. Among liabilities, only current liabilities vary directly with sales. Using the percentofsales method, determine whether the company has external financing needs, or a surplus of funds. (Hint: A profit margin and payout ratio must be found from the income statement.)  Percentofsales method
 Conn Man’s Shops, Inc., a national clothing chain, had sales of $300 million last year. The business has a steady net profit margin of 8 percent and a dividend payout ratio of 25 percent. The balance sheet for the end of last year is shown below. The firm’s marketing staff has told the president that in the coming year there will be a large increase in the demand for overcoats and wool slacks. A sales increase of 15 percent is forecast for the company. All balance sheet items are expected to maintain the same percentofsales relationships as last year,^{*} except for common stock and retained earnings. No change is scheduled in the number of common stock shares outstanding, and retained earnings will change as dictated by the profits and dividend policy of the firm. (Remember the net profit margin is 8 percent.) Will external financing be required for the company during the coming year? What would be the need for external financing if the net profit margin went up to 9.5 percent and the dividend payout ratio was increased to 50 percent? Explain.  Percentofsales method  ^{*}This included fixed assets as the firm is at full capacity.   