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
1460T_c06.qxd12/2/0509:28 am Page293 EQA Exercises·293 Instructions On the basis of the information above,determine the present value of the pension obligation (liability). (L0 5,E6-15 (Investment Decision)Andrew Bogut just received a signing bonus of $1,000,000.His plan is to 6) invest this payment in a fund that will earn 8%,compounded annually. Instructions (a)If Bogut plans to establish the AB Foundation once the fund grows to $1,999,000,how many years until he can establish the foundation? (b)Instead of investing the entire $1,000,000,Bogut invests $300,000 today and plans to make 9 equal annual investments into the fund beginning one year from today.What amount should the pay- ments be if Bogut plans to establish the $1,999,000 foundation at the end of 9 years? (L0 6,E6-16 (Retirement of Debt)Jesper Parnevik borrowed $70,000 on March 1,2005.This amount plus ac- 7) crued interest at 12%compounded semiannually is to be repaid March 1,2015.To retire this debt,Jesper plans to contribute to a debt retirement fund five equal amounts starting on March 1,2010,and for the next 4 years.The fund is expected to earn 10%per annum Instructions How much must be contributed each year by Jesper Parnevik to provide a fund sufficient to retire the debt on March 1,2015? (L0 7)E6-17 (Computation of Amount of Rentals)Your client,Ron Santo Leasing Company,is preparing a contract to lease a machine to Souvenirs Corporation for a period of 25 years.Santo has an investment cost of $365,755 in the machine,which has a useful life of 25 years and no salvage value at the end of that time.Your client is interested in earning an 11%return on its investment and has agreed to accept 25 equal rental payments at the end of each of the next 25 years Instructions You are requested to provide Santo with the amount of each of the 25 rental payments that will yield an 11%return on investment. (L0 5,E6-18 (Least Costly Payoff)Assume that Sonic Foundry Corporation has a contractual debt out- 7) standing.Sonic has available two means of settlement:It can either make immediate payment of $2,600,000, or it can make annual payments of $300,000 for 15 years,each payment due on the last day of the year. Instructions Which method of payment do you recommend,assuming an expected effective interest rate of 8%dur- ing the future period? (Lo 5,E6-19 (Least Costly Payoff)Assuming the same facts as those in E6-18 except that the payments 7) must begin now and be made on the first day of each of the 15 years,what payment method would you recommend? (L0 9)E6-20 (Expected Cash Flows)For each of the following,determine the expected cash flows. Probability Cash Flow Estimate Assessment (a) $3,800 20% 6,300 50% 7,500 30% (b) $5,400 30% 7,200 50% 8.400 20% (c) s(1,000) 10% 2000 80% 5,000 10% (L0 9)E6-21 (Expected Cash Flows and Present Value)Andrew Kelly is trying to determine the amount to set aside so that he will have enough money on hand in 2 years to overhaul the engine on his vintage used car.While there is some uncertainty about the cost of engine overhauls in 2 years,by conducting some research online,Andrew has developed the following estimates. Engine Overhaul Probability Estimated Cash Outflow Assessment $200 10% 450 30% 550 50% 750 10%
Exercises • 293 Instructions On the basis of the information above, determine the present value of the pension obligation (liability). E6-15 (Investment Decision) Andrew Bogut just received a signing bonus of $1,000,000. His plan is to invest this payment in a fund that will earn 8%, compounded annually. Instructions (a) If Bogut plans to establish the AB Foundation once the fund grows to $1,999,000, how many years until he can establish the foundation? (b) Instead of investing the entire $1,000,000, Bogut invests $300,000 today and plans to make 9 equal annual investments into the fund beginning one year from today. What amount should the payments be if Bogut plans to establish the $1,999,000 foundation at the end of 9 years? E6-16 (Retirement of Debt) Jesper Parnevik borrowed $70,000 on March 1, 2005. This amount plus accrued interest at 12% compounded semiannually is to be repaid March 1, 2015. To retire this debt, Jesper plans to contribute to a debt retirement fund five equal amounts starting on March 1, 2010, and for the next 4 years. The fund is expected to earn 10% per annum. Instructions How much must be contributed each year by Jesper Parnevik to provide a fund sufficient to retire the debt on March 1, 2015? E6-17 (Computation of Amount of Rentals) Your client, Ron Santo Leasing Company, is preparing a contract to lease a machine to Souvenirs Corporation for a period of 25 years. Santo has an investment cost of $365,755 in the machine, which has a useful life of 25 years and no salvage value at the end of that time. Your client is interested in earning an 11% return on its investment and has agreed to accept 25 equal rental payments at the end of each of the next 25 years. Instructions You are requested to provide Santo with the amount of each of the 25 rental payments that will yield an 11% return on investment. E6-18 (Least Costly Payoff) Assume that Sonic Foundry Corporation has a contractual debt outstanding. Sonic has available two means of settlement: It can either make immediate payment of $2,600,000, or it can make annual payments of $300,000 for 15 years, each payment due on the last day of the year. Instructions Which method of payment do you recommend, assuming an expected effective interest rate of 8% during the future period? E6-19 (Least Costly Payoff) Assuming the same facts as those in E6-18 except that the payments must begin now and be made on the first day of each of the 15 years, what payment method would you recommend? E6-20 (Expected Cash Flows) For each of the following, determine the expected cash flows. Probability Cash Flow Estimate Assessment (a) $ 3,800 20% 6,300 50% 7,500 30% (b) $ 5,400 30% 7,200 50% 8,400 20% (c) $(1,000) 10% 2,000 80% 5,000 10% E6-21 (Expected Cash Flows and Present Value) Andrew Kelly is trying to determine the amount to set aside so that he will have enough money on hand in 2 years to overhaul the engine on his vintage used car. While there is some uncertainty about the cost of engine overhauls in 2 years, by conducting some research online, Andrew has developed the following estimates. Engine Overhaul Probability Estimated Cash Outflow Assessment $200 10% 450 30% 550 50% 750 10% (L0 5, 6) (L0 6, 7) (L0 7) (L0 5, 7) (L0 5, 7) (L0 9) (L0 9) 1460T_c06.qxd 12/2/05 09:28 am Page 293
1460T_c06.qxd12/2/0509:28 am Page294 EQA 294.Chapter 6 Accounting and the Time Value of Money Instructions How much should Andrew Kelly deposit today in an account earning 6%,compounded annually,so that he will have enough money on hand in 2 years to pay for the overhaul? (L0 10)E6-22 (Determine Interest Rate)Reba McEntire wishes to invest $19,000 on July 1,2007,and have it accumulate to $49,000 by July 1,2017. Instructions Use a financial calculator to determine at what exact annual rate of interest Reba must invest the $19,000. (L0 10)*E6-23 (Determine Interest Rate)On July 17,2006,Tim McGraw borrowed $42,000 from his grand- father to open a clothing store.Starting July 17,2007,Tim has to make ten equal annual payments of $6,500 each to repay the loan. Instructions Use a financial calculator to determine what interest rate Tim is paying. (L0 10)*E6-24 (Determine Interest Rate)As the purchaser of a new house,Patty Loveless has signed a mort- gage note to pay the Memphis National Bank and Trust Co.$14,000 every 6 months for 20 years,at the end of which time she will own the house.At the date the mortgage is signed the purchase price was $198,000,and a down payment of $20,000 was made.The first payment will be made 6 months after the date the mortgage is signed. Instructions Using a financial calculator,compute the exact rate of interest earned on the mortgage by the bank. See the book's website,www.wiley.com/college/kieso,for Additional Exercises. PROBLEMS ⊕ (Interest rates are per annum unless otherwise indicated.) (L05, P6-1 (Various Time Value Situations)Answer each of these unrelated questions. 6,7) (a)On January 1,2007,Aaron Brown Corporation sold a building that cost $250,000 and that had accu- mulated depreciation of $100,000 on the date of sale.Brown received as consideration a $275,000 noninterest-bearing note due on January 1,2010.There was no established exchange price for the building,and the note had no ready market.The prevailing rate of interest for a note of this type on January 1,2007,was 9%.At what amount should the gain from the sale of the building be reported? (b) On January 1,2007,Aaron Brown Corporation purchased 200 of the $1,000 face value,9%,10-year bonds of Walters Inc.The bonds mature on January 1,2017,and pay interest annually beginning January 1,2008.Brown purchased the bonds to yield 11%.How much did Brown pay for the bonds? (c)Aaron Brown Corporation bought a new machine and agreed to pay for it in equal annual in- stallments of $4,000 at the end of each of the next 10 years.Assuming that a prevailing interest rate of 8%applies to this contract,how much should Brown record as the cost of the machine? (d)Aaron Brown Corporation purchased a special tractor on December 31,2007.The purchase agree- ment stipulated that Brown should pay $20,000 at the time of purchase and $5,000 at the end of each of the next 8 years.The tractor should be recorded on December 31,2007,at what amount, assuming an appropriate interest rate of 12%? (e) Aaron Brown Corporation wants to withdraw $100,000(including principal)from an investment fund at the end of each year for 9 years.What should be the required initial investment at the be ginning of the first year if the fund earns 11%? (L05, P6-2 (Various Time Value Situations)Using the appropriate interest table,provide the solution to each 6,7) of the following four questions by computing the unknowns (a)What is the amount of the payments that Tom Brokaw must make at the end of each of 8 years to accumulate a fund of $70,000 by the end of the eighth year,if the fund earns 8%interest,com- pounded annually? (b)Anderson Cooper is 40 years old today and he wishes to accumulate $500,000 by his sixty-fifth birthday so he can retire to his summer place on Lake Hopatcong.He wishes to accumulate this amount by making equal deposits on his fortieth through his sixty-fourth birthdays.What annual deposit must Anderson make if the fund will earn 12%interest compounded annually?
Instructions How much should Andrew Kelly deposit today in an account earning 6%, compounded annually, so that he will have enough money on hand in 2 years to pay for the overhaul? *E6-22 (Determine Interest Rate) Reba McEntire wishes to invest $19,000 on July 1, 2007, and have it accumulate to $49,000 by July 1, 2017. Instructions Use a financial calculator to determine at what exact annual rate of interest Reba must invest the $19,000. *E6-23 (Determine Interest Rate) On July 17, 2006, Tim McGraw borrowed $42,000 from his grandfather to open a clothing store. Starting July 17, 2007, Tim has to make ten equal annual payments of $6,500 each to repay the loan. Instructions Use a financial calculator to determine what interest rate Tim is paying. *E6-24 (Determine Interest Rate) As the purchaser of a new house, Patty Loveless has signed a mortgage note to pay the Memphis National Bank and Trust Co. $14,000 every 6 months for 20 years, at the end of which time she will own the house. At the date the mortgage is signed the purchase price was $198,000, and a down payment of $20,000 was made. The first payment will be made 6 months after the date the mortgage is signed. Instructions Using a financial calculator, compute the exact rate of interest earned on the mortgage by the bank. PROBLEMS (Interest rates are per annum unless otherwise indicated.) P6-1 (Various Time Value Situations) Answer each of these unrelated questions. (a) On January 1, 2007, Aaron Brown Corporation sold a building that cost $250,000 and that had accumulated depreciation of $100,000 on the date of sale. Brown received as consideration a $275,000 noninterest-bearing note due on January 1, 2010. There was no established exchange price for the building, and the note had no ready market. The prevailing rate of interest for a note of this type on January 1, 2007, was 9%. At what amount should the gain from the sale of the building be reported? (b) On January 1, 2007, Aaron Brown Corporation purchased 200 of the $1,000 face value, 9%, 10-year bonds of Walters Inc. The bonds mature on January 1, 2017, and pay interest annually beginning January 1, 2008. Brown purchased the bonds to yield 11%. How much did Brown pay for the bonds? (c) Aaron Brown Corporation bought a new machine and agreed to pay for it in equal annual installments of $4,000 at the end of each of the next 10 years. Assuming that a prevailing interest rate of 8% applies to this contract, how much should Brown record as the cost of the machine? (d) Aaron Brown Corporation purchased a special tractor on December 31, 2007. The purchase agreement stipulated that Brown should pay $20,000 at the time of purchase and $5,000 at the end of each of the next 8 years. The tractor should be recorded on December 31, 2007, at what amount, assuming an appropriate interest rate of 12%? (e) Aaron Brown Corporation wants to withdraw $100,000 (including principal) from an investment fund at the end of each year for 9 years. What should be the required initial investment at the beginning of the first year if the fund earns 11%? P6-2 (Various Time Value Situations) Using the appropriate interest table, provide the solution to each of the following four questions by computing the unknowns. (a) What is the amount of the payments that Tom Brokaw must make at the end of each of 8 years to accumulate a fund of $70,000 by the end of the eighth year, if the fund earns 8% interest, compounded annually? (b) Anderson Cooper is 40 years old today and he wishes to accumulate $500,000 by his sixty-fifth birthday so he can retire to his summer place on Lake Hopatcong. He wishes to accumulate this amount by making equal deposits on his fortieth through his sixty-fourth birthdays. What annual deposit must Anderson make if the fund will earn 12% interest compounded annually? 294 • Chapter 6 Accounting and the Time Value of Money (L0 5, 6, 7) (L0 10) (L0 10) (L0 10) (L0 5, 6, 7) wi el moc. y c/ ollege/kieso See the book’s website, www.wiley.com/college/kieso, for Additional Exercises. 1460T_c06.qxd 12/2/05 09:28 am Page 294
1460T_c06.qxd1/10/0602:26 am Page295 EQA Problems·295 (c)Jane Pauley has $20,000 to invest today at 9%to pay a debt of $56,253.How many years will it take her to accumulate enough to liquidate the debt? (d)Maria Shriver has a $27,600 debt that she wishes to repay 4 years from today;she has $18,181 that she intends to invest for the 4 years.What rate of interest will she need to earn annually in order to accumulate enough to pay the debt? (L05, P6-3 (Analysis of Alternatives)Assume that Wal-Mart,Inc.has decided to surface and maintain for 6,7) 10 years a vacant lot next to one of its discount-retail outlets to serve as a parking lot for customers.Man- agement is considering the following bids involving two different qualities of surfacing for a parking area of 12,000 square yards. Bid A:A surface that costs $5.25 per square yard to install.This surface will have to be replaced at the end of 5 years.The annual maintenance cost on this surface is estimated at 20 cents per square yard for each year except the last year of its service.The replacement surface will be similar to the initial surface. Bid B:A surface that costs $9.50 per square yard to install.This surface has a probable useful life of 10 years and will require annual maintenance in each year except the last year,at an estimated cost of 9 cents per square yard. Instructions Prepare computations showing which bid should be accepted by Wal-Mart,Inc.You may assume that the cost of capital is 9%,that the annual maintenance expenditures are incurred at the end of each year,and that prices are not expected to change during the next 10 years. (L06, P6-4 (Evaluating Payment Alternatives)Terry O'Malley has just learned he has won a $900,000 prize 7) in the lottery.The lottery has given him two options for receiving the payments:(1)If Terry takes all the money today,the state and federal governments will deduct taxes at a rate of 46%immediately. (2)Alternatively,the lottery offers Terry a payout of 20 equal payments of $62,000 with the first payment occurring when Terry turns in the winning ticket.Terry will be taxed on each of these payments at a rate of25%. Instructions Assuming Terry can earn an 8%rate of return(compounded annually)on any money invested during this period,which pay-out option should he choose? (L05, P6-5 (Analysis of Alternatives)Sally Brown died,leaving to her husband Linus an insurance policy 6,7) contract that provides that the beneficiary (Linus)can choose any one of the following four options. (a)$55,000 immediate cash. (b)$3,700 every 3 months payable at the end of each quarter for 5 years. (c) $18,000 immediate cash and $1,600 every 3 months for 10 years,payable at the beginning of each 3-month period. (d)$4,000 every 3 months for 3 years and $1,200 each quarter for the following 25 quarters,all pay- ments payable at the end of each quarter. Instructions If money is worth 2%%per quarter,compounded quarterly,which option would you recommend that Linus exercise? (L0 8)P6-6 (Purchase Price of a Business)During the past year,Nicole Bobek planted a new vineyard on 150 acres of land that she leases for $27,000 a year.She has asked you as her accountant to assist her in determining the value of her vineyard operation The vineyard will bear no grapes for the first 5 years (1-5).In the next 5 years (6-10),Nicole estimates that the vines will bear grapes that can be sold for $60,000 each year.For the next 20 years(11-30)she ex- pects the harvest will provide annual revenues of $100,000.But during the last 10 years (31-40)of the vineyard's life,she estimates that revenues will decline to $80,000 per year. During the first 5 years the annual cost of pruning,fertilizing,and caring for the vineyard is estimated at $9,000;during the years of production,6-40,these costs will rise to $10,000 per year.The relevant mar- ket rate of interest for the entire period is 12%.Assume that all receipts and payments are made at the end of each year. Instructions Dick Button has offered to buy Nicole's vineyard business by assuming the 40-year lease.On the basis of the current value of the business,what is the minimum price Nicole should accept? (L0 5,P6-7 (Time Value Concepts Applied to Solve Business Problems)Answer the following questions 6,7)related to Derek Lee Inc
(c) Jane Pauley has $20,000 to invest today at 9% to pay a debt of $56,253. How many years will it take her to accumulate enough to liquidate the debt? (d) Maria Shriver has a $27,600 debt that she wishes to repay 4 years from today; she has $18,181 that she intends to invest for the 4 years. What rate of interest will she need to earn annually in order to accumulate enough to pay the debt? P6-3 (Analysis of Alternatives) Assume that Wal-Mart, Inc. has decided to surface and maintain for 10 years a vacant lot next to one of its discount-retail outlets to serve as a parking lot for customers. Management is considering the following bids involving two different qualities of surfacing for a parking area of 12,000 square yards. Bid A: A surface that costs $5.25 per square yard to install. This surface will have to be replaced at the end of 5 years. The annual maintenance cost on this surface is estimated at 20 cents per square yard for each year except the last year of its service. The replacement surface will be similar to the initial surface. Bid B: A surface that costs $9.50 per square yard to install. This surface has a probable useful life of 10 years and will require annual maintenance in each year except the last year, at an estimated cost of 9 cents per square yard. Instructions Prepare computations showing which bid should be accepted by Wal-Mart, Inc. You may assume that the cost of capital is 9%, that the annual maintenance expenditures are incurred at the end of each year, and that prices are not expected to change during the next 10 years. P6-4 (Evaluating Payment Alternatives) Terry O’Malley has just learned he has won a $900,000 prize in the lottery. The lottery has given him two options for receiving the payments: (1) If Terry takes all the money today, the state and federal governments will deduct taxes at a rate of 46% immediately. (2) Alternatively, the lottery offers Terry a payout of 20 equal payments of $62,000 with the first payment occurring when Terry turns in the winning ticket. Terry will be taxed on each of these payments at a rate of 25%. Instructions Assuming Terry can earn an 8% rate of return (compounded annually) on any money invested during this period, which pay-out option should he choose? P6-5 (Analysis of Alternatives) Sally Brown died, leaving to her husband Linus an insurance policy contract that provides that the beneficiary (Linus) can choose any one of the following four options. (a) $55,000 immediate cash. (b) $3,700 every 3 months payable at the end of each quarter for 5 years. (c) $18,000 immediate cash and $1,600 every 3 months for 10 years, payable at the beginning of each 3-month period. (d) $4,000 every 3 months for 3 years and $1,200 each quarter for the following 25 quarters, all payments payable at the end of each quarter. Instructions If money is worth 21 ⁄2% per quarter, compounded quarterly, which option would you recommend that Linus exercise? P6-6 (Purchase Price of a Business) During the past year, Nicole Bobek planted a new vineyard on 150 acres of land that she leases for $27,000 a year. She has asked you as her accountant to assist her in determining the value of her vineyard operation. The vineyard will bear no grapes for the first 5 years (1–5). In the next 5 years (6–10), Nicole estimates that the vines will bear grapes that can be sold for $60,000 each year. For the next 20 years (11–30) she expects the harvest will provide annual revenues of $100,000. But during the last 10 years (31–40) of the vineyard’s life, she estimates that revenues will decline to $80,000 per year. During the first 5 years the annual cost of pruning, fertilizing, and caring for the vineyard is estimated at $9,000; during the years of production, 6–40, these costs will rise to $10,000 per year. The relevant market rate of interest for the entire period is 12%. Assume that all receipts and payments are made at the end of each year. Instructions Dick Button has offered to buy Nicole’s vineyard business by assuming the 40-year lease. On the basis of the current value of the business, what is the minimum price Nicole should accept? P6-7 (Time Value Concepts Applied to Solve Business Problems) Answer the following questions related to Derek Lee Inc. Problems • 295 (L0 5, 6, 7) (L0 6, 7) (L0 5, 6, 7) (L0 8) (L0 5, 6, 7) 1460T_c06.qxd 1/10/06 02:26 am Page 295
1460T_c06.qxd1/10/0602:26 am Page296 EQA 296 Chapter 6 Accounting and the Time Value of Money (a)Derek Lee Inc.has $572,000 to invest.The company is trying to decide between two alternative uses of the funds.One alternative provides $80,000 at the end of each year for 12 years,and the other is to receive a single lump sum payment of $1,900,000 at the end of the 12 years.Which al- ternative should Lee select?Assume the interest rate is constant over the entire investment. (b) Derek Lee Inc.has completed the purchase of new Dell computers.The fair market value of the equipment is $824,150.The purchase agreement specifies an immediate down payment of $200,000 and semiannual payments of $76,952 beginning at the end of 6 months for 5 years.What is the interest rate,to the nearest percent,used in discounting this purchase transaction? (c) Derek Lee Inc.loans money to John Kruk Corporation in the amount of $600,000.Lee accepts an 8%note due in 7 years with interest payable semiannually.After 2 years(and receipt of interest for 2 years),Lee needs money and therefore sells the note to Chicago National Bank,which demands interest on the note of 10%compounded semiannually.What is the amount Lee will receive on the sale of the note? (d)Derek Lee Inc.wishes to accumulate $1,300,000 by December 31,2017,to retire bonds outstand- ing.The company deposits $300,000 on December 31,2007,which will earn interest at 10%com- pounded quarterly,to help in the retirement of this debt.In addition,the company wants to know how much should be deposited at the end of each quarter for 10 years to ensure that $1,300,000 is available at the end of 2017.(The quarterly deposits will also earn at a rate of 10%,compounded quarterly.)(Round to even dollars.) (L0 6,P6-8 (Analysis of Alternatives)Homer Simpson Inc.,a manufacturer of steel school lockers,plans to 7) purchase a new punch press for use in its manufacturing process.After contacting the appropriate ven- dors,the purchasing department received differing terms and options from each vendor.The Engineer- ing Department has determined that each vendor's punch press is substantially identical and each has a useful life of 20 years.In addition,Engineering has estimated that required year-end maintenance costs will be $1,000 per year for the first 5 years,$2,000 per year for the next 10 years,and $3,000 per year for the last 5 years.Following is each vendor's sale package. Vendor A:$45,000 cash at time of delivery and 10 year-end payments of $15,000 each.Vendor A offers all its customers the right to purchase at the time of sale a separate 20-year maintenance service contract, under which Vendor A will perform all year-end maintenance at a one-time initial cost of $10,000. ⊕ Vendor B:Forty seminannual payments of $8,000 each,with the first installment due upon delivery. Vendor B will perform all year-end maintenance for the next 20 years at no extra charge Vendor C:Full cash price of $125,000 will be due upon delivery. Instructions Assuming that both Vendor A and B will be able to perform the required year-end maintenance,that Simpson's cost of funds is 10%,and the machine will be purchased on January 1,from which vendor should the press be purchased? (L05, P6-9 (Analysis of Business Problems)Jean-Luc is a financial executive with Starship Enterprises 6,7) Although Jean-Luc has not had any formal training in finance or accounting,he has a "good sense"for numbers and has helped the company grow from a very small company($500,000 sales)to a large oper- ation($45 million in sales).With the business growing steadily,however,the company needs to make a number of difficult financial decisions in which Jean-Luc feels a little "over his head."He therefore has decided to hire a new employee with"numbers"expertise to help him.As a basis for determining whom to employ,he has decided to ask each prospective employee to prepare answers to questions relating to the following situations he has encountered recently.Here are the questions. (a)In 2005,Starship Enterprises negotiated and closed a long-term lease contract for newly con- structed truck terminals and freight storage facilities.The buildings were constructed on land owned by the company.On January 1,2006,Starship took possession of the leased property.The 20-year lease is effective for the period January 1,2006,through December 31,2025.Advance rental payments of $800,000 are payable to the lessor (owner of facilities)on January 1 of each of the first 10 years of the lease term.Advance payments of $300,000 are due on January 1 for each of the last 10 years of the lease term.Starship has an option to purchase all the leased facilities for $1 on December 31,2025.At the time the lease was negotiated,the fair market value of the truck terminals and freight storage facilities was approximately $7,200,000.If the company had borrowed the money to purchase the facilities,it would have had to pay 10%interest.Should the company have purchased rather than leased the facilities? (b)Last year the company exchanged a piece of land for a non-interest-bearing note.The note is to be paid at the rate of $12,000 per year for 9 years,beginning one year from the date of disposal of the land.An appropriate rate of interest for the note was 11%.At the time the land was origi- nally purchased,it cost $90,000.What is the fair value of the note?
(a) Derek Lee Inc. has $572,000 to invest. The company is trying to decide between two alternative uses of the funds. One alternative provides $80,000 at the end of each year for 12 years, and the other is to receive a single lump sum payment of $1,900,000 at the end of the 12 years. Which alternative should Lee select? Assume the interest rate is constant over the entire investment. (b) Derek Lee Inc. has completed the purchase of new Dell computers. The fair market value of the equipment is $824,150. The purchase agreement specifies an immediate down payment of $200,000 and semiannual payments of $76,952 beginning at the end of 6 months for 5 years. What is the interest rate, to the nearest percent, used in discounting this purchase transaction? (c) Derek Lee Inc. loans money to John Kruk Corporation in the amount of $600,000. Lee accepts an 8% note due in 7 years with interest payable semiannually. After 2 years (and receipt of interest for 2 years), Lee needs money and therefore sells the note to Chicago National Bank, which demands interest on the note of 10% compounded semiannually. What is the amount Lee will receive on the sale of the note? (d) Derek Lee Inc. wishes to accumulate $1,300,000 by December 31, 2017, to retire bonds outstanding. The company deposits $300,000 on December 31, 2007, which will earn interest at 10% compounded quarterly, to help in the retirement of this debt. In addition, the company wants to know how much should be deposited at the end of each quarter for 10 years to ensure that $1,300,000 is available at the end of 2017. (The quarterly deposits will also earn at a rate of 10%, compounded quarterly.) (Round to even dollars.) P6-8 (Analysis of Alternatives) Homer Simpson Inc., a manufacturer of steel school lockers, plans to purchase a new punch press for use in its manufacturing process. After contacting the appropriate vendors, the purchasing department received differing terms and options from each vendor. The Engineering Department has determined that each vendor’s punch press is substantially identical and each has a useful life of 20 years. In addition, Engineering has estimated that required year-end maintenance costs will be $1,000 per year for the first 5 years, $2,000 per year for the next 10 years, and $3,000 per year for the last 5 years. Following is each vendor’s sale package. Vendor A: $45,000 cash at time of delivery and 10 year-end payments of $15,000 each. Vendor A offers all its customers the right to purchase at the time of sale a separate 20-year maintenance service contract, under which Vendor A will perform all year-end maintenance at a one-time initial cost of $10,000. Vendor B: Forty seminannual payments of $8,000 each, with the first installment due upon delivery. Vendor B will perform all year-end maintenance for the next 20 years at no extra charge. Vendor C: Full cash price of $125,000 will be due upon delivery. Instructions Assuming that both Vendor A and B will be able to perform the required year-end maintenance, that Simpson’s cost of funds is 10%, and the machine will be purchased on January 1, from which vendor should the press be purchased? P6-9 (Analysis of Business Problems) Jean-Luc is a financial executive with Starship Enterprises. Although Jean-Luc has not had any formal training in finance or accounting, he has a “good sense” for numbers and has helped the company grow from a very small company ($500,000 sales) to a large operation ($45 million in sales). With the business growing steadily, however, the company needs to make a number of difficult financial decisions in which Jean-Luc feels a little “over his head.” He therefore has decided to hire a new employee with “numbers” expertise to help him. As a basis for determining whom to employ, he has decided to ask each prospective employee to prepare answers to questions relating to the following situations he has encountered recently. Here are the questions. (a) In 2005, Starship Enterprises negotiated and closed a long-term lease contract for newly constructed truck terminals and freight storage facilities. The buildings were constructed on land owned by the company. On January 1, 2006, Starship took possession of the leased property. The 20-year lease is effective for the period January 1, 2006, through December 31, 2025. Advance rental payments of $800,000 are payable to the lessor (owner of facilities) on January 1 of each of the first 10 years of the lease term. Advance payments of $300,000 are due on January 1 for each of the last 10 years of the lease term. Starship has an option to purchase all the leased facilities for $1 on December 31, 2025. At the time the lease was negotiated, the fair market value of the truck terminals and freight storage facilities was approximately $7,200,000. If the company had borrowed the money to purchase the facilities, it would have had to pay 10% interest. Should the company have purchased rather than leased the facilities? (b) Last year the company exchanged a piece of land for a non-interest-bearing note. The note is to be paid at the rate of $12,000 per year for 9 years, beginning one year from the date of disposal of the land. An appropriate rate of interest for the note was 11%. At the time the land was originally purchased, it cost $90,000. What is the fair value of the note? 296 • Chapter 6 Accounting and the Time Value of Money (L0 6, 7) (L0 5, 6, 7) 1460T_c06.qxd 1/10/06 02:26 am Page 296
1460T_c06.qxd12/2/0509:28 am Page297 EQA Problems·297 (c)The company has always followed the policy to take any cash discounts on goods purchased.Re- cently the company purchased a large amount of raw materials at a price of $800,000 with terms 2/10,n/30 on which it took the discount.Starship has recently estimated its cost of funds at 10% Should Starship continue this policy of always taking the cash discount? (L0 5,P6-10 (Analysis of Lease vs.Purchase)Jose Rijo Inc.owns and operates a number of hardware stores 6,7)in the New England region.Recently the company has decided to locate another store in a rapidly grow- ing area of Maryland.The company is trying to decide whether to purchase or lease the building and related facilities. Purchase:The company can purchase the site,construct the building,and purchase all store fixtures. The cost would be $1,650,000.An immediate down payment of $400,000 is required,and the remaining $1,250,000 would be paid off over 5 years at $300,000 per year(including interest).The property is expected to have a useful life of 12 years,and then it will be sold for $500,000.As the owner of the property,the company will have the following out-of-pocket expenses each period. Property taxes (to be paid at the end of each year) $40,000 Insurance(to be paid at the beginning of each year) 27.000 Other(primarily maintenance which occurs at the end of each year) 16,000 S83,000 Lease:First National Bank has agreed to purchase the site,construct the building,and install the appropriate fixtures for Rijo Inc.if Rijo will lease the completed facility for 12 years.The annual costs for the lease would be $240,000.Rijo would have no responsibility related to the facility over the 12 years. The terms of the lease are that Rijo would be required to make 12 annual payments(the first payment to be made at the time the store opens and then each following year).In addition,a deposit of $100,000 is required when the store is opened.This deposit will be returned at the end of the twelfth year,assuming no unusual damage to the building structure or fixtures. Currently the cost of funds for Rijo Inc.is 10%. Instructions Which of the two approaches should Rijo Inc.follow? (L0 8)P6-11 (Pension Funding)You have been hired as a benefit consultant by Maugarite Alomar,the owner of Attic Angels.She wants to establish a retirement plan for herself and her three employees.Maugarite has provided the following information:The retirement plan is to be based upon annual salary for the last year before retirement and is to provide 50%of Maugarite's last-year annual salary and 40%of the last-year annual salary for each employee.The plan will make annual payments at the beginning of each year for 20 years from the date of retirement.Maugarite wishes to fund the plan by making 15 annual deposits beginning January 1,2007.Invested funds will earn 12%compounded annually.Information about plan participants as of January 1,2007,is as follows. Maugarite Alomar,owner:Current annual salary of $40,000;estimated retirement date January 1, 2032. Kenny Rogers,flower arranger:Current annual salary of $30,000;estimated retirement date January 1, 2037. Anita Baker,sales clerk:Current annual salary of $15,000;estimated retirement date January 1,2027. Willie Nelson,part-time bookkeeper:Current annual salary of $15,000;estimated retirement date January 1,2022. In the past,Maugarite has given herself and each employee a year-end salary increase of 4%.Maugarite plans to continue this policy in the future. Instructions (a)Based upon the above information,what will be the annual retirement benefit for each plan par- ticipant?(Round to the nearest dollar.)(Hint:Maugarite will receive raises for 24 years.) (b)What amount must be on deposit at the end of 15 years to ensure that all benefits will be paid? (Round to the nearest dollar.) (c)What is the amount of each annual deposit Maugarite must make to the retirement plan? (L0 8)P6-12 (Pension Funding)James Qualls,newly appointed controller of KBS,is considering ways to reduce his company's expenditures on annual pension costs.One way to do this is to switch KBS's pen- sion fund assets from First Security to NET Life.KBS is a very well-respected computer manufacturer that recently has experienced a sharp decline in its financial performance for the first time in its 25-year history.Despite financial problems,KBS still is committed to providing its employees with good pension and postretirement health benefits
(c) The company has always followed the policy to take any cash discounts on goods purchased. Recently the company purchased a large amount of raw materials at a price of $800,000 with terms 2/10, n/30 on which it took the discount. Starship has recently estimated its cost of funds at 10%. Should Starship continue this policy of always taking the cash discount? P6-10 (Analysis of Lease vs. Purchase) Jose Rijo Inc. owns and operates a number of hardware stores in the New England region. Recently the company has decided to locate another store in a rapidly growing area of Maryland. The company is trying to decide whether to purchase or lease the building and related facilities. Purchase: The company can purchase the site, construct the building, and purchase all store fixtures. The cost would be $1,650,000. An immediate down payment of $400,000 is required, and the remaining $1,250,000 would be paid off over 5 years at $300,000 per year (including interest). The property is expected to have a useful life of 12 years, and then it will be sold for $500,000. As the owner of the property, the company will have the following out-of-pocket expenses each period. Property taxes (to be paid at the end of each year) $40,000 Insurance (to be paid at the beginning of each year) 27,000 Other (primarily maintenance which occurs at the end of each year) 16,000 $83,000 Lease: First National Bank has agreed to purchase the site, construct the building, and install the appropriate fixtures for Rijo Inc. if Rijo will lease the completed facility for 12 years. The annual costs for the lease would be $240,000. Rijo would have no responsibility related to the facility over the 12 years. The terms of the lease are that Rijo would be required to make 12 annual payments (the first payment to be made at the time the store opens and then each following year). In addition, a deposit of $100,000 is required when the store is opened. This deposit will be returned at the end of the twelfth year, assuming no unusual damage to the building structure or fixtures. Currently the cost of funds for Rijo Inc. is 10%. Instructions Which of the two approaches should Rijo Inc. follow? P6-11 (Pension Funding) You have been hired as a benefit consultant by Maugarite Alomar, the owner of Attic Angels. She wants to establish a retirement plan for herself and her three employees. Maugarite has provided the following information: The retirement plan is to be based upon annual salary for the last year before retirement and is to provide 50% of Maugarite’s last-year annual salary and 40% of the last-year annual salary for each employee. The plan will make annual payments at the beginning of each year for 20 years from the date of retirement. Maugarite wishes to fund the plan by making 15 annual deposits beginning January 1, 2007. Invested funds will earn 12% compounded annually. Information about plan participants as of January 1, 2007, is as follows. Maugarite Alomar, owner: Current annual salary of $40,000; estimated retirement date January 1, 2032. Kenny Rogers, flower arranger: Current annual salary of $30,000; estimated retirement date January 1, 2037. Anita Baker, sales clerk: Current annual salary of $15,000; estimated retirement date January 1, 2027. Willie Nelson, part-time bookkeeper: Current annual salary of $15,000; estimated retirement date January 1, 2022. In the past, Maugarite has given herself and each employee a year-end salary increase of 4%. Maugarite plans to continue this policy in the future. Instructions (a) Based upon the above information, what will be the annual retirement benefit for each plan participant? (Round to the nearest dollar.) (Hint: Maugarite will receive raises for 24 years.) (b) What amount must be on deposit at the end of 15 years to ensure that all benefits will be paid? (Round to the nearest dollar.) (c) What is the amount of each annual deposit Maugarite must make to the retirement plan? P6-12 (Pension Funding) James Qualls, newly appointed controller of KBS, is considering ways to reduce his company’s expenditures on annual pension costs. One way to do this is to switch KBS’s pension fund assets from First Security to NET Life. KBS is a very well-respected computer manufacturer that recently has experienced a sharp decline in its financial performance for the first time in its 25-year history. Despite financial problems, KBS still is committed to providing its employees with good pension and postretirement health benefits. Problems • 297 (L0 5, 6, 7) (L0 8) (L0 8) 1460T_c06.qxd 12/2/05 09:28 am Page 297