1460T_c06.qxd12/2/0509:28 am Page288 EQA 288.Chapter 6 Accounting and the Time Value of Money Entering N=180(12 X 15 years),I =8.4,PMT =-700,FV =0,and pressing PV,you find a present value of $71,509.81-the maximum house price you can afford,given that you want to keep your mortgage payments at $700.Note that by changing any of the variables,you can quickly conduct "what-if"analyses for different factual situations. Individual Retirement Account (IRA) Assume you opened an IRA on April 15,1997,with a deposit of $2,000.Since then you have deposited $100 in the account every 2 weeks(26 deposits per year,with the first $100 deposit made on April 29,1997).The account pays 7.6%annual interest com- pounded semi-monthly(with each deposit).How much will be in the account on April 15,2007?Illustration 6A-9 depicts this problem. ILLUSTRATION 6A-9 Calculator Solution for Inputs: 260 7.6 -2.000 -100 IRA Balance N PV PMT FV Answer: 43,131.79 By entering N =260 (26 X 10 years),I=7.6,PV =-2,000,PMT =-100,and press- ing FV,you determine the future value of $43,131.79.This is the amount that the IRA will grow to over the 10-year period.Note that in this problem we use four of the keys and solve for the fifth.Thus,we combine the future value of a single sum and of an annuity.Other problems similar to this are illustrated in Chapters 7 and 14. SUMMARY OF LEARNING OBJECTIVE FOR APPENDIX 6A 10.Use a financial calculator to solve time value of money problems.Financial calcula- tors can be used to solve the same and additional problems as those solved with time value of money tables.One enters into the financial calculator the amounts for all but one of the unknown elements of a time value of money problem(periods,interest rate,payments,future or present value).Particularly useful situations involve inter- est rates and compounding periods not presented in the tables. Note:All asterisked Exercises and Problems relate to material contained in the chap- ter appendix.You will need a calculator for these assignments. QUESTIONS 1.What is the time value of money?Why should account- 4.What are the components of an interest rate?Why is it ants have an understanding of compound interest,an- important for accountants to understand these compo- nuities,and present value concepts? nents? 2.Identify three situations in which accounting measures 5.Presented are a number of values taken from compound interest tables involving the same number of periods and are based on present values.Do these present value ap- the same rate of interest.Indicate what each of these four plications involve single sums or annuities,or both sin- gle sums and annuities?Explain. values represents. (a)6.71008 (c).46319 3.What is the nature of interest?Distinguish between "simple interest"and "compound interest." (b)2.15892 (d)14.48656
288 • Chapter 6 Accounting and the Time Value of Money By entering N 260 (26 10 years), I 7.6, PV 2,000, PMT 100, and pressing FV, you determine the future value of $43,131.79. This is the amount that the IRA will grow to over the 10-year period. Note that in this problem we use four of the keys and solve for the fifth. Thus, we combine the future value of a single sum and of an annuity. Other problems similar to this are illustrated in Chapters 7 and 14. SUMMARY OF LEARNING OBJECTIVE FOR APPENDIX 6A 10. Use a financial calculator to solve time value of money problems. Financial calculators can be used to solve the same and additional problems as those solved with time value of money tables. One enters into the financial calculator the amounts for all but one of the unknown elements of a time value of money problem (periods, interest rate, payments, future or present value). Particularly useful situations involve interest rates and compounding periods not presented in the tables. Note: All asterisked Exercises and Problems relate to material contained in the chapter appendix. You will need a calculator for these assignments. Entering N 180 (12 15 years), I 8.4, PMT 700, FV 0, and pressing PV, you find a present value of $71,509.81—the maximum house price you can afford, given that you want to keep your mortgage payments at $700. Note that by changing any of the variables, you can quickly conduct “what-if” analyses for different factual situations. Individual Retirement Account (IRA) Assume you opened an IRA on April 15, 1997, with a deposit of $2,000. Since then you have deposited $100 in the account every 2 weeks (26 deposits per year, with the first $100 deposit made on April 29, 1997). The account pays 7.6% annual interest compounded semi-monthly (with each deposit). How much will be in the account on April 15, 2007? Illustration 6A-9 depicts this problem. 4. What are the components of an interest rate? Why is it important for accountants to understand these components? 5. Presented are a number of values taken from compound interest tables involving the same number of periods and the same rate of interest. Indicate what each of these four values represents. (a) 6.71008 (c) .46319 (b) 2.15892 (d) 14.48656 QUESTIONS 1. What is the time value of money? Why should accountants have an understanding of compound interest, annuities, and present value concepts? 2. Identify three situations in which accounting measures are based on present values. Do these present value applications involve single sums or annuities, or both single sums and annuities? Explain. 3. What is the nature of interest? Distinguish between “simple interest” and “compound interest.” N Inputs: 260 7.6 –2,000 –100 ? Answer: I PV PMT FV 43,131.79 ILLUSTRATION 6A-9 Calculator Solution for IRA Balance 1460T_c06.qxd 12/2/05 09:28 am Page 288
1460T_c06.qxd12/2/0509:28 am Page289 EQA Brief Exercises·289 6.Bill Jones is considering two investment options for a interest rate (to the nearest percent)was used to deter- $1,000 gift he received for graduation.Both investments mine the amount of the annuity?(Assume end-of-year have 8%annual interest rates.One offers quarterly com- payments.) pounding;the other compounds on a semiannual basis. 16.Greg Norman Enterprises leases property to Tiger Which investment should he choose?Why? Woods,Inc.Because Tiger Woods,Inc.is experiencing fi- 7.Brenda Starr deposited $18,000 in a money market cer- nancial difficulty,Norman agrees to receive five rents of tificate that provides interest of 10%compounded quar- $10,000 at the end of each year,with the rents deferred terly if the amount is maintained for 3 years.How much 3 years.What is the present value of the five rents dis- will Brenda Starr have at the end of 3 years? counted at 12%? 8.Charlie Brown will receive $50,000 on December 31,2012 17.Answer the following questions. (5 years from now)from a trust fund established by his (a)On May 1,2007,Liselotte Neumann Company sold father.Assuming the appropriate interest rate for dis- counting is 12%(compounded semiannually),what is some machinery to Tee-off Company on an install- ment contract basis.The contract required five equal the present value of this amount today? annual payments,with the first payment due on May 9.What are the primary characteristics of an annuity?Dif- 1,2007.What present value concept is appropriate ferentiate between an "ordinary annuity"and an "an- for this situation? nuity due." (b)On June 1,2007,Mike Brisky Inc.purchased a new 10.Linus,Inc.owes $30,000 to Peanuts Company.How machine that it does not have to pay for until May 1, much would Linus have to pay each year if the debt is 2009.The total payment on May 1,2009,will include retired through four equal payments(made at the end both principal and interest.Assuming interest at a of the year),given an interest rate on the debt of 12%? 12%rate,the cost of the machine would be the total (Round to two decimal places.) payment multiplied by what time value of money 11.The Forths are planning for a retirement home.They es- concept? timate they will need $160,000,4 years from now to pur- (c)Kelly Gibson Inc.wishes to know how much money chase this home.Assuming an interest rate of 10%,what it will have available in 5 years if five equal amounts amount must be deposited at the end of each of the 4 of $35,000 are invested,with the first amount in- years to fund the home price?(Round to two decimal vested immediately.What interest table is appropri- places.) ate for this situation? 12.Assume the same situation as in Question 11,except that (d)Patty Sheehan invests in a "jumbo"$200,000,3-year the four equal amounts are deposited at the beginning certificate of deposit at First Wisconsin Bank.What of the period rather than at the end.In this case,what table would be used to determine the amount accu- amount must be deposited at the beginning of each pe- mulated at the end of 3 years? riod?(Round to two decimals.) 18.Recently Vickie Maher was interested in purchasing a 13.Explain how the future value of an ordinary annuity Honda Acura.The salesperson indicated that the price interest table is converted to the future value of an an- of the car was either $27,000 cash or $6,900 at the end of nuity due interest table. each of 5 years.Compute the effective interest rate to the 14.Explain how the present value of an ordinary annuity nearest percent that Vickie would pay if she chooses to interest table is converted to the present value of an make the five annual payments. annuity due interest table. 19.Recently,property/casualty insurance companies have 15.In a book named Treasure,the reader has to figure out been criticized because they reserve for the total loss as where a 2.2 pound,24 kt gold horse has been buried. much as5 years before it may happen.The IRS has joined If the horse is found,a prize of $25,000 a year for the debate because they say the full reserve is unfair from 20 years is provided.The actual cost of the publisher to a taxation viewpoint.What do you believe is the IRS purchase an annuity to pay for the prize is $210,000.What position? BRIEF EXERCISES PLUS (L05) BE6-1 Steve Allen invested $10,000 today in a fund that earns 8%compounded annually.To what amount will the investment grow in 3 years?To what amount would the investment grow in 3 years if the fund earns 8%annual interest compounded semiannually? (L05) BE6-2 Itzak Perlman needs $20,000 in 4 years.What amount must he invest today if his investment earns 12%compounded annually?What amount must he invest if his investment earns 12%annual interest compounded quarterly?
Brief Exercises • 289 6. Bill Jones is considering two investment options for a $1,000 gift he received for graduation. Both investments have 8% annual interest rates. One offers quarterly compounding; the other compounds on a semiannual basis. Which investment should he choose? Why? 7. Brenda Starr deposited $18,000 in a money market certificate that provides interest of 10% compounded quarterly if the amount is maintained for 3 years. How much will Brenda Starr have at the end of 3 years? 8. Charlie Brown will receive $50,000 on December 31, 2012 (5 years from now) from a trust fund established by his father. Assuming the appropriate interest rate for discounting is 12% (compounded semiannually), what is the present value of this amount today? 9. What are the primary characteristics of an annuity? Differentiate between an “ordinary annuity” and an “annuity due.” 10. Linus, Inc. owes $30,000 to Peanuts Company. How much would Linus have to pay each year if the debt is retired through four equal payments (made at the end of the year), given an interest rate on the debt of 12%? (Round to two decimal places.) 11. The Forths are planning for a retirement home. They estimate they will need $160,000, 4 years from now to purchase this home. Assuming an interest rate of 10%, what amount must be deposited at the end of each of the 4 years to fund the home price? (Round to two decimal places.) 12. Assume the same situation as in Question 11, except that the four equal amounts are deposited at the beginning of the period rather than at the end. In this case, what amount must be deposited at the beginning of each period? (Round to two decimals.) 13. Explain how the future value of an ordinary annuity interest table is converted to the future value of an annuity due interest table. 14. Explain how the present value of an ordinary annuity interest table is converted to the present value of an annuity due interest table. 15. In a book named Treasure, the reader has to figure out where a 2.2 pound, 24 kt gold horse has been buried. If the horse is found, a prize of $25,000 a year for 20 years is provided. The actual cost of the publisher to purchase an annuity to pay for the prize is $210,000. What interest rate (to the nearest percent) was used to determine the amount of the annuity? (Assume end-of-year payments.) 16. Greg Norman Enterprises leases property to Tiger Woods, Inc. Because Tiger Woods, Inc. is experiencing financial difficulty, Norman agrees to receive five rents of $10,000 at the end of each year, with the rents deferred 3 years. What is the present value of the five rents discounted at 12%? 17. Answer the following questions. (a) On May 1, 2007, Liselotte Neumann Company sold some machinery to Tee-off Company on an installment contract basis. The contract required five equal annual payments, with the first payment due on May 1, 2007. What present value concept is appropriate for this situation? (b) On June 1, 2007, Mike Brisky Inc. purchased a new machine that it does not have to pay for until May 1, 2009. The total payment on May 1, 2009, will include both principal and interest. Assuming interest at a 12% rate, the cost of the machine would be the total payment multiplied by what time value of money concept? (c) Kelly Gibson Inc. wishes to know how much money it will have available in 5 years if five equal amounts of $35,000 are invested, with the first amount invested immediately. What interest table is appropriate for this situation? (d) Patty Sheehan invests in a “jumbo” $200,000, 3-year certificate of deposit at First Wisconsin Bank. What table would be used to determine the amount accumulated at the end of 3 years? 18. Recently Vickie Maher was interested in purchasing a Honda Acura. The salesperson indicated that the price of the car was either $27,000 cash or $6,900 at the end of each of 5 years. Compute the effective interest rate to the nearest percent that Vickie would pay if she chooses to make the five annual payments. 19. Recently, property/casualty insurance companies have been criticized because they reserve for the total loss as much as 5 years before it may happen. The IRS has joined the debate because they say the full reserve is unfair from a taxation viewpoint. What do you believe is the IRS position? BRIEF EXERCISES BE6-1 Steve Allen invested $10,000 today in a fund that earns 8% compounded annually. To what amount will the investment grow in 3 years? To what amount would the investment grow in 3 years if the fund earns 8% annual interest compounded semiannually? BE6-2 Itzak Perlman needs $20,000 in 4 years. What amount must he invest today if his investment earns 12% compounded annually? What amount must he invest if his investment earns 12% annual interest compounded quarterly? (L0 5) (L0 5) 1460T_c06.qxd 12/2/05 09:28 am Page 289
1460T_c06.qxd1/10/0605:35 am Page290 EQA 290.Chapter 6 Accounting and the Time Value of Money (L0 5)BE6-3 Natalie Portman will invest $30,000 today.She needs $222,000 in 21 years.What annual interest rate must she earn? (L0 5)BE6-4 Dan Webster will invest $10,000 today in a fund that earns 5%annual interest.How many years will it take for the fund to grow to $13,400? (LO 6)BE6-5 Anne Boleyn will invest $5,000 a year for 20 years in a fund that will earn 12%annual interest. If the first payment into the fund occurs today,what amount will be in the fund in 20 years?If the first payment occurs at year-end,what amount will be in the fund in 20 years? (Lo 6)BE6-6 William Cullen Bryant needs $200,000 in 10 years.How much must he invest at the end of each year,at 11%interest,to meet his needs? (L0 5)BE6-7 Jack Thompson's lifelong dream is to own his own fishing boat to use in his retirement.Jack has recently come into an inheritance of $400,000.He estimates that the boat he wants will cost $350,000 when he retires in 5 years.How much of his inheritance must he invest at an annual rate of 12%(compounded annually)to buy the boat at retirement? (Lo 5)BE6-8 Refer to the data in BE6-7.Assuming quarterly compounding of amounts invested at 12%,how much of Jack Thompson's inheritance must be invested to have enough at retirement to buy the boat? (L0 6)BE6-9 Luther Vandross is investing $12,961 at the end of each year in a fund that earns 10%interest.In how many years will the fund be at $100,000? (L0 7)BE6-10 Grupo Rana wants to withdraw $20,000 each year for 10 years from a fund that earns 8%inter- est.How much must he invest today if the first withdrawal is at year-end?How much must he invest today if the first withdrawal takes place immediately? (L07) BE6-11 Mark Twain's VISA balance is $1,124.40.He may pay it off in 18 equal end-of-month payments of $75 each.What interest rate is Mark paying? (L07) BE6-12 Corinne Dunbar is investing $200,000 in a fund that earns 8%interest compounded annually. What equal amounts can Corinne withdraw at the end of each of the next 20 years? (L0 6)BE6-13 Bayou Inc.will deposit $20,000 in a 12%fund at the end of each year for 8 years beginning ⊕ December 31,2007.What amount will be in the fund immediately after the last deposit? (LO 7)BE6-14 Hollis Stacy wants to create a fund today that will enable her to withdraw $20,000 per year for 8 years,with the first withdrawal to take place 5 years from today.If the fund earns 8%interest,how much must Hollis invest today? (L0 8)BE6-15 Acadian Inc.issues $1,000,000 of 7%bonds due in 10 years with interest payable at year-end. The current market rate of interest for bonds of similar risk is 8%.What amount will Acadian receive when it issues the bonds? (LO 7)BE6-16 Walt Frazier is settling a $20,000 loan due today by making 6 equal annual payments of $4,864.51. Determine the interest rate on this loan,if the payments begin one year after the loan is signed. (LO 7)BE6-17 Consider the loan in BE6-16.What payments must Walt Frazier make to settle the loan at the same interest rate but with the 6 payments beginning on the day the loan is signed? PLUS EXERCISES (Interest rates are per annum unless otherwise indicated.) (L0 3)E6-1 (Using Interest Tables)For each of the following cases,indicate (a)to what rate columns,and (b)to what number of periods you would refer in looking up the interest factor. 1.In a future value of 1 table Annual Number of Rate Years Invested Compounded a.9% 9 Annually b.12% Quarterly c.10% 15 Semiannually
290 • Chapter 6 Accounting and the Time Value of Money BE6-3 Natalie Portman will invest $30,000 today. She needs $222,000 in 21 years. What annual interest rate must she earn? BE6-4 Dan Webster will invest $10,000 today in a fund that earns 5% annual interest. How many years will it take for the fund to grow to $13,400? BE6-5 Anne Boleyn will invest $5,000 a year for 20 years in a fund that will earn 12% annual interest. If the first payment into the fund occurs today, what amount will be in the fund in 20 years? If the first payment occurs at year-end, what amount will be in the fund in 20 years? BE6-6 William Cullen Bryant needs $200,000 in 10 years. How much must he invest at the end of each year, at 11% interest, to meet his needs? BE6-7 Jack Thompson’s lifelong dream is to own his own fishing boat to use in his retirement. Jack has recently come into an inheritance of $400,000. He estimates that the boat he wants will cost $350,000 when he retires in 5 years. How much of his inheritance must he invest at an annual rate of 12% (compounded annually) to buy the boat at retirement? BE6-8 Refer to the data in BE6-7. Assuming quarterly compounding of amounts invested at 12%, how much of Jack Thompson’s inheritance must be invested to have enough at retirement to buy the boat? BE6-9 Luther Vandross is investing $12,961 at the end of each year in a fund that earns 10% interest. In how many years will the fund be at $100,000? BE6-10 Grupo Rana wants to withdraw $20,000 each year for 10 years from a fund that earns 8% interest. How much must he invest today if the first withdrawal is at year-end? How much must he invest today if the first withdrawal takes place immediately? BE6-11 Mark Twain’s VISA balance is $1,124.40. He may pay it off in 18 equal end-of-month payments of $75 each. What interest rate is Mark paying? BE6-12 Corinne Dunbar is investing $200,000 in a fund that earns 8% interest compounded annually. What equal amounts can Corinne withdraw at the end of each of the next 20 years? BE6-13 Bayou Inc. will deposit $20,000 in a 12% fund at the end of each year for 8 years beginning December 31, 2007. What amount will be in the fund immediately after the last deposit? BE6-14 Hollis Stacy wants to create a fund today that will enable her to withdraw $20,000 per year for 8 years, with the first withdrawal to take place 5 years from today. If the fund earns 8% interest, how much must Hollis invest today? BE6-15 Acadian Inc. issues $1,000,000 of 7% bonds due in 10 years with interest payable at year-end. The current market rate of interest for bonds of similar risk is 8%. What amount will Acadian receive when it issues the bonds? BE6-16 Walt Frazier is settling a $20,000 loan due today by making 6 equal annual payments of $4,864.51. Determine the interest rate on this loan, if the payments begin one year after the loan is signed. BE6-17 Consider the loan in BE6-16. What payments must Walt Frazier make to settle the loan at the same interest rate but with the 6 payments beginning on the day the loan is signed? EXERCISES (Interest rates are per annum unless otherwise indicated.) E6-1 (Using Interest Tables) For each of the following cases, indicate (a) to what rate columns, and (b) to what number of periods you would refer in looking up the interest factor. 1. In a future value of 1 table Annual Number of Rate Years Invested Compounded a. 9% 9 Annually b. 12% 5 Quarterly c. 10% 15 Semiannually (L0 3) (L0 5) (L0 5) (L0 6) (L0 6) (L0 5) (L0 5) (L0 6) (L0 7) (L0 7) (L0 7) (L0 6) (L0 7) (L0 8) (L0 7) (L0 7) 1460T_c06.qxd 1/10/06 05:35 am Page 290
1460T_c06.qxd12/2/0509:28 am Page291 EQA Exercises·291 2.In a present value of an annuity of 1 table Annual Number of Number of Frequency Rate Years Involved Rents Involved of Rents a.9% 25 25 Annually b.10% 15 30 Semiannually C.12% 28 Quarterly (L02, E6-2 (Simple and Compound Interest Computations)Alan Jackson invests $20,000 at 8%annual in- 5) terest,leaving the money invested without withdrawing any of the interest for 8 years.At the end of the 8 years,Alan withdrew the accumulated amount of money Instructions (a)Compute the amount Alan would withdraw assuming the investment earns simple interest. (b) Compute the amount Alan would withdraw assuming the investment earns interest compounded annually. (c) Compute the amount Alan would withdraw assuming the investment earns interest compounded semiannually. (L05, E6-3 (Computation of Future Values and Present Values)Using the appropriate interest table,answer 6,7) each of the following questions.(Each case is independent of the others.) (a)What is the future value of $7,000 at the end of 5 periods at 8%compounded interest? (b)What is the present value of $7,000 due 8 periods hence,discounted at 11%? (c) What is the future value of 15 periodic payments of $7,000 each made at the end of each period and compounded at 10%? (d)What is the present value of $7,000 to be received at the end of each of 20 periods,discounted at 5%compound interest? (L0 6,E6-4 (Computation of Future Values and Present Values)Using the appropriate interest table,answer 7) the following questions.(Each case is independent of the others). (a)What is the future value of 20 periodic payments of $4,000 each made at the beginning of each period and compounded at 8%? (b)What is the present value of $2,500 to be received at the beginning of each of 30 periods,dis- counted at 10%compound interest? (c) What is the future value of 15 deposits of $2,000 each made at the beginning of each period and compounded at 10%?(Future value as of the end of the fifteenth period.) (d)What is the present value of six receipts of $1,000 each received at the beginning of each period, discounted at 9%compounded interest? (L0 6,E6-5 (Computation of Present Value)Using the appropriate interest table,compute the present val- 7) ues of the following periodic amounts due at the end of the designated periods. (a)$30,000 receivable at the end of each period for 8 periods compounded at 12% (b)$30,000 payments to be made at the end of each period for 16 periods at 9%. (c) $30,000 payable at the end of the seventh,eighth,ninth,and tenth periods at 12%. (L0 5,E6-6 (Future Value and Present Value Problems)Presented below are three unrelated situations. 6,7) (a)Dwayne Wade Company recently signed a lease for a new office building,for a lease period of 10 years.Under the lease agreement,a security deposit of $12,000 is made,with the deposit to be returned at the expiration of the lease,with interest compounded at 10%per year.What amount will the company receive at the time the lease expires? (b)Serena Williams Corporation,having recently issued a $20 million,15-year bond issue,is com- mitted to make annual sinking fund deposits of $600,000.The deposits are made on the last day of each year and yield a return of 10%.Will the fund at the end of 15 years be sufficient to retire the bonds?If not,what will the deficiency be? (c)Under the terms of his salary agreement,president Rex Walters has an option of receiving either an immediate bonus of $40,000,or a deferred bonus of $70,000 payable in 10 years.Ignoring tax consid- erations,and assuming a relevant interest rate of 8%,which form of settlement should Walters accept? (LO 8)E6-7 (Computation of Bond Prices)What would you pay for a $50,000 debenture bond that matures in 15 years and pays $5,000 a year in interest if you wanted to earn a yield of: (a)8%？b)10%？(c)12%？ (LO 8)E6-8 (Computations for a Retirement Fund)Clarence Weatherspoon,a super salesman contemplating retirement on his fifty-fifth birthday,decides to create a fund on an 8%basis that will enable him to
Exercises • 291 2. In a present value of an annuity of 1 table Annual Number of Number of Frequency Rate Years Involved Rents Involved of Rents a. 9% 25 25 Annually b. 10% 15 30 Semiannually c. 12% 7 28 Quarterly E6-2 (Simple and Compound Interest Computations) Alan Jackson invests $20,000 at 8% annual interest, leaving the money invested without withdrawing any of the interest for 8 years. At the end of the 8 years, Alan withdrew the accumulated amount of money. Instructions (a) Compute the amount Alan would withdraw assuming the investment earns simple interest. (b) Compute the amount Alan would withdraw assuming the investment earns interest compounded annually. (c) Compute the amount Alan would withdraw assuming the investment earns interest compounded semiannually. E6-3 (Computation of Future Values and Present Values) Using the appropriate interest table, answer each of the following questions. (Each case is independent of the others.) (a) What is the future value of $7,000 at the end of 5 periods at 8% compounded interest? (b) What is the present value of $7,000 due 8 periods hence, discounted at 11%? (c) What is the future value of 15 periodic payments of $7,000 each made at the end of each period and compounded at 10%? (d) What is the present value of $7,000 to be received at the end of each of 20 periods, discounted at 5% compound interest? E6-4 (Computation of Future Values and Present Values) Using the appropriate interest table, answer the following questions. (Each case is independent of the others). (a) What is the future value of 20 periodic payments of $4,000 each made at the beginning of each period and compounded at 8%? (b) What is the present value of $2,500 to be received at the beginning of each of 30 periods, discounted at 10% compound interest? (c) What is the future value of 15 deposits of $2,000 each made at the beginning of each period and compounded at 10%? (Future value as of the end of the fifteenth period.) (d) What is the present value of six receipts of $1,000 each received at the beginning of each period, discounted at 9% compounded interest? E6-5 (Computation of Present Value) Using the appropriate interest table, compute the present values of the following periodic amounts due at the end of the designated periods. (a) $30,000 receivable at the end of each period for 8 periods compounded at 12%. (b) $30,000 payments to be made at the end of each period for 16 periods at 9%. (c) $30,000 payable at the end of the seventh, eighth, ninth, and tenth periods at 12%. E6-6 (Future Value and Present Value Problems) Presented below are three unrelated situations. (a) Dwayne Wade Company recently signed a lease for a new office building, for a lease period of 10 years. Under the lease agreement, a security deposit of $12,000 is made, with the deposit to be returned at the expiration of the lease, with interest compounded at 10% per year. What amount will the company receive at the time the lease expires? (b) Serena Williams Corporation, having recently issued a $20 million, 15-year bond issue, is committed to make annual sinking fund deposits of $600,000. The deposits are made on the last day of each year and yield a return of 10%. Will the fund at the end of 15 years be sufficient to retire the bonds? If not, what will the deficiency be? (c) Under the terms of his salary agreement, president Rex Walters has an option of receiving either an immediate bonus of $40,000, or a deferred bonus of $70,000 payable in 10 years. Ignoring tax considerations, and assuming a relevant interest rate of 8%, which form of settlement should Walters accept? E6-7 (Computation of Bond Prices) What would you pay for a $50,000 debenture bond that matures in 15 years and pays $5,000 a year in interest if you wanted to earn a yield of: (a) 8%? (b) 10%? (c) 12%? E6-8 (Computations for a Retirement Fund) Clarence Weatherspoon, a super salesman contemplating retirement on his fifty-fifth birthday, decides to create a fund on an 8% basis that will enable him to (L0 2, 5) (L0 5, 6, 7) (L0 6, 7) (L0 6, 7) (L0 5, 6, 7) (L0 8) (L0 8) 1460T_c06.qxd 12/2/05 09:28 am Page 291
1460T_c06.qxd1/10/0602:26 am Page292 EQA 292 Chapter 6 Accounting and the Time Value of Money withdraw $20,000 per year on June 30,beginning in 2014 and continuing through 2017.To develop this fund,Clarence intends to make equal contributions on June 30 of each of the years 2010-2013. Instructions (a)How much must the balance of the fund equal on June 30,2013,in order for Clarence Weather- spoon to satisfy his objective? (b)What are each of Clarence's contributions to the fund? (L05) E6-9 (Unknown Rate)LEW Company purchased a machine at a price of $100,000 by signing a note payable,which requires a single payment of $123,210 in 2 years.Assuming annual compounding of in- terest,what rate of interest is being paid on the loan? (L0 5)E6-10 (Unknown Periods and Unknown Interest Rate)Consider the following independent situations. (a)Mike Finley wishes to become a millionaire.His money market fund has a balance of $92,296 and has a guaranteed interest rate of 10%.How many years must Mike leave that balance in the fund in order to get his desired $1,000,000? (b)Assume that Serena Williams desires to accumulate $1 million in 15 years using her money mar- ket fund balance of $182,696.At what interest rate must Serena's investment compound annually? (LO 7)E6-11 (Evaluation of Purchase Options)Sosa Excavating Inc.is purchasing a bulldozer.The equip- ment has a price of $100,000.The manufacturer has offered a payment plan that would allow Sosa to make 10 equal annual payments of $16,274.53,with the first payment due one year after the purchase. Instructions (a)How much total interest will Sosa pay on this payment plan? (b) Sosa could borrow $100,000 from its bank to finance the purchase at an annual rate of 9%.Should Sosa borrow from the bank or use the manufacturer's payment plan to pay for the equipment? (Lo 5,E6-12 (Analysis of Alternatives)The Black Knights Inc.,a manufacturer of high-sugar,low-sodium, 6,7)low-cholesterol TV dinners,would like to increase its market share in the Sunbelt.In order to do so,Black Knights has decided to locate a new factory in the Panama City area.Black Knights will either buy or lease a site depending upon which is more advantageous.The site location committee has narrowed down the available sites to the following three buildings. ⊕ Building A:Purchase for a cash price of $600,000,useful life 25 years. Building B:Lease for 25 years with annual lease payments of $69,000 being made at the beginning of the year. Building C:Purchase for $650,000 cash.This building is larger than needed;however,the excess space can be sublet for 25 years at a net annual rental of $7,000.Rental payments will be received at the end of each year.The Black Knights Inc.has no aversion to being a landlord. Instructions In which building would you recommend that The Black Knights Inc.locate,assuming a 12%cost of funds? (LO 8)E6-13 (Computation of Bond Liability)Lance Armstrong Inc.manufactures cycling equipment.Re- cently the vice president of operations of the company has requested construction of a new plant to meet the increasing demand for the company's bikes.After a careful evaluation of the request,the board of di- rectors has decided to raise funds for the new plant by issuing $2,000,000 of 11%term corporate bonds on March 1,2007,due on March 1,2022,with interest payable each March 1 and September 1.At the time of issuance,the market interest rate for similar financial instruments is 10%. Instructions As the controller of the company,determine the selling price of the bonds. (L0 8)E6-14 (Computation of Pension Liability)Nerwin,Inc.is a furniture manufacturing company with 50 employees.Recently,after a long negotiation with the local labor union,the company decided to ini- tiate a pension plan as a part of its compensation plan.The plan will start on January 1,2007.Each em- ployee covered by the plan is entitled to a pension payment each year after retirement.As required by accounting standards,the controller of the company needs to report the pension obligation (liability).On the basis of a discussion with the supervisor of the Personnel Department and an actuary from an insur- ance company,the controller develops the following information related to the pension plan. Average length of time to retirement 15 years Expected life duration after retirement 10 years Total pension payment expected each year after retirement for all employees.Payment made at the end of the year. S700,000 per year The interest rate to be used is 8%
292 • Chapter 6 Accounting and the Time Value of Money withdraw $20,000 per year on June 30, beginning in 2014 and continuing through 2017. To develop this fund, Clarence intends to make equal contributions on June 30 of each of the years 2010–2013. Instructions (a) How much must the balance of the fund equal on June 30, 2013, in order for Clarence Weatherspoon to satisfy his objective? (b) What are each of Clarence’s contributions to the fund? E6-9 (Unknown Rate) LEW Company purchased a machine at a price of $100,000 by signing a note payable, which requires a single payment of $123,210 in 2 years. Assuming annual compounding of interest, what rate of interest is being paid on the loan? E6-10 (Unknown Periods and Unknown Interest Rate) Consider the following independent situations. (a) Mike Finley wishes to become a millionaire. His money market fund has a balance of $92,296 and has a guaranteed interest rate of 10%. How many years must Mike leave that balance in the fund in order to get his desired $1,000,000? (b) Assume that Serena Williams desires to accumulate $1 million in 15 years using her money market fund balance of $182,696. At what interest rate must Serena’s investment compound annually? E6-11 (Evaluation of Purchase Options) Sosa Excavating Inc. is purchasing a bulldozer. The equipment has a price of $100,000. The manufacturer has offered a payment plan that would allow Sosa to make 10 equal annual payments of $16,274.53, with the first payment due one year after the purchase. Instructions (a) How much total interest will Sosa pay on this payment plan? (b) Sosa could borrow $100,000 from its bank to finance the purchase at an annual rate of 9%. Should Sosa borrow from the bank or use the manufacturer’s payment plan to pay for the equipment? E6-12 (Analysis of Alternatives) The Black Knights Inc., a manufacturer of high-sugar, low-sodium, low-cholesterol TV dinners, would like to increase its market share in the Sunbelt. In order to do so, Black Knights has decided to locate a new factory in the Panama City area. Black Knights will either buy or lease a site depending upon which is more advantageous. The site location committee has narrowed down the available sites to the following three buildings. Building A: Purchase for a cash price of $600,000, useful life 25 years. Building B: Lease for 25 years with annual lease payments of $69,000 being made at the beginning of the year. Building C: Purchase for $650,000 cash. This building is larger than needed; however, the excess space can be sublet for 25 years at a net annual rental of $7,000. Rental payments will be received at the end of each year. The Black Knights Inc. has no aversion to being a landlord. Instructions In which building would you recommend that The Black Knights Inc. locate, assuming a 12% cost of funds? E6-13 (Computation of Bond Liability) Lance Armstrong Inc. manufactures cycling equipment. Recently the vice president of operations of the company has requested construction of a new plant to meet the increasing demand for the company’s bikes. After a careful evaluation of the request, the board of directors has decided to raise funds for the new plant by issuing $2,000,000 of 11% term corporate bonds on March 1, 2007, due on March 1, 2022, with interest payable each March 1 and September 1. At the time of issuance, the market interest rate for similar financial instruments is 10%. Instructions As the controller of the company, determine the selling price of the bonds. E6-14 (Computation of Pension Liability) Nerwin, Inc. is a furniture manufacturing company with 50 employees. Recently, after a long negotiation with the local labor union, the company decided to initiate a pension plan as a part of its compensation plan. The plan will start on January 1, 2007. Each employee covered by the plan is entitled to a pension payment each year after retirement. As required by accounting standards, the controller of the company needs to report the pension obligation (liability). On the basis of a discussion with the supervisor of the Personnel Department and an actuary from an insurance company, the controller develops the following information related to the pension plan. Average length of time to retirement 15 years Expected life duration after retirement 10 years Total pension payment expected each year after retirement for all employees. Payment made at the end of the year. $700,000 per year The interest rate to be used is 8%. (L0 5) (L0 5) (L0 7) (L0 5, 6, 7) (L0 8) (L0 8) 1460T_c06.qxd 1/10/06 02:26 am Page 292