years you take the proceeds and invest them for 12 years at 15 percent. How J You invest a single amount of $10,000 for 5 years at 10 percent. At the end much will you have after 17 years? Solution Appendix a FV≡PVxFⅤIF $l0000x1611=$16,110 Appendix a FV≡PⅤxFVF $16,110x5350=$86,188 9-8 Jean Splicing will receive $8, 500 a year for the next 15 years from her trust. If a 7 percent interest rate is applied, what is the current value of the future payments? Solution: ppendix d PVA=AX PVIFA(7%, 15 periods) =$8,500X9.108=$77,418 99 Phil Goode will receive $175,000 in 50 years. His friends are very jealous of him. If the funds are discounted back at a rate of 14 percent, what is the present value of his future"pot of gold"? Solution: Appendix b PV=FVX PVIF(14%0, 50 periods) $175,000x001=$175 CopyrightC 2005 by The McGray-Hill Companies, Inc. S-310
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-310 9-7. You invest a single amount of $10,000 for 5 years at 10 percent. At the end of 5 years you take the proceeds and invest them for 12 years at 15 percent. How much will you have after 17 years? Solution: Appendix A FV = PV x FVIF $10,000 x 1.611 = $16,110 Appendix A FV = PV x FVIF $16,110 x 5.350 = $86,188 9-8. Jean Splicing will receive $8,500 a year for the next 15 years from her trust. If a 7 percent interest rate is applied, what is the current value of the future payments? Solution: Appendix D PVA = A x PVIFA (7%, 15 periods) = $8,500 x 9.108 = $77,418 9-9. Phil Goode will receive $175,000 in 50 years. His friends are very jealous of him. If the funds are discounted back at a rate of 14 percent, what is the present value of his future "pot of gold"? Solution: Appendix B PV = FV x PVIF (14%, 50 periods) = $175,000 x .001 = $175
Polly graham will receive $12,000 a year for the next 15 years as a result of her patent. If a 9 percent rate is applied, should she be willing to sell out her future rights now for $100.000? Solution Appendix D PVA=AX PVIFA (9%, 15 periods) $12000x8.061=$96,732 Yes, the present value of the annuity is worth less than $100,000 9-11 Carrie Tune will receive $19, 500 for the next 20 years as a payment for a new song she has written. If a 10 percent rate is applied, should she be willing to sell out her future rights now for $160,000 Solution: Appendix d PVA=AX PVIFA(10%0, 20 periods) PVA=$19,500x8.514=$166023 o, the present value of the annuity is worth more than $160,000 9-12 The Clearinghouse Sweepstakes has just informed you that you have won $1 million. The amount is to be paid out at the rate of $20,000 a year for the next 50 years. With a discount rate of 10 percent, what is the present value of your winnings? Solution: Appendix d PVA=AXPVIFA(10%0, 50 periods) PVA=$20,000x9.915=$198,300 S-311 Copyright o 2005 by The McGraw-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-311 9-10. Polly Graham will receive $12,000 a year for the next 15 years as a result of her patent. If a 9 percent rate is applied, should she be willing to sell out her future rights now for $100,000? Solution: Appendix D PVA = A x PVIFA (9%, 15 periods) = $12,000 x 8.061 = $96,732 Yes, the present value of the annuity is worth less than $100,000. 9-11. Carrie Tune will receive $19,500 for the next 20 years as a payment for a new song she has written. If a 10 percent rate is applied, should she be willing to sell out her future rights now for $160,000. Solution: Appendix D PVA = A x PVIFA (10%, 20 periods) PVA = $19,500 x 8.514 = $166,023 No, the present value of the annuity is worth more than $160,000. 9-12. The Clearinghouse Sweepstakes has just informed you that you have won $1 million. The amount is to be paid out at the rate of $20,000 a year for the next 50 years. With a discount rate of 10 percent, what is the present value of your winnings? Solution: Appendix D PVA = A x PVIFA (10%, 50 periods) PVA = $20,000 x 9.915 = $198,300
Al Rosen invests $25,000 in a mint condition 1952 Mickey Mantle Topps baseball card. He expects the card to increase in value 12 percent per year for the next 10 years How much will his card be worth after 10 years' Solution Appendix a FV=PVX FVIF (12%, 10 periods) $25000x3.106=$77,650 9-14 Dr. Ruth has been secretly depositing $2, 500 in her savings account every December starting in 1995. Her account earns 5 percent compounded annuall How much will she have in december of 2004?(Assume that a deposit is made in 2004.) Make sure to carefully count the years Solution: ppendⅸxC FVA=AX FVIEA (5%0, 10 periods FVA=$2,500x12.578=$31,445 9-15 At a growth(interest)rate of 9 percent annually, how long will it take for a sum to double? To triple? Select the year that is closest to the correct answer Solution: Appendix a If the sum is doubling, then the interest factor must equal 2 s In Appendix A, looking down the 9% column, we find the factor closest to 2(1.993)on the 8-year row. The factor closest to 3 (3.066)is on the 13-year row CopyrightC 2005 by The McGray-Hill Companies, Inc. S-312
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-312 9-13. Al Rosen invests $25,000 in a mint condition 1952 Mickey Mantle Topps baseball card. He expects the card to increase in value 12 percent per year for the next 10 years. How much will his card be worth after 10 years? Solution: Appendix A FV = PV x FVIF (12%, 10 periods) = $25,000 x 3.106 = $77,650 9-14. Dr. Ruth has been secretly depositing $2,500 in her savings account every December starting in 1995. Her account earns 5 percent compounded annually. How much will she have in December of 2004? (Assume that a deposit is made in 2004.) Make sure to carefully count the years. Solution: Appendix C FVA = A x FVIFA (5%, 10 periods) FVA = $2,500 x 12.578 = $31,445 9-15. At a growth (interest) rate of 9 percent annually, how long will it take for a sum to double? To triple? Select the year that is closest to the correct answer. Solution: Appendix A If the sum is doubling, then the interest factor must equal 2. * In Appendix A, looking down the 9% column, we find the factor closest to 2 (1.993) on the 8-year row. The factor closest to 3 (3.066) is on the 13-year row
cred itor accept in payment immed iately if she could earn 12 percent on herour If you owe $40,000 payable at the end of seven years, what amount should mone Solution Appendix b PⅤ=FⅤxPVF(12%,7 periods) PV=$40.000X452=$18,080 9-17 Jack Hammer invests in a stock that will pay dividends of $2.00 at the end of the first year; $2. 20 at the end of the second year; and $2.40 at the end of the third year. Also, he believes that at the end of the third year he will be able to ll the stock for $33. What is the present value of all future benefits if a discount rate of 1 l percent is applied?(Round all values to two places to the right of the decimal point. Solution: ppendix B PⅤ=FⅤI Discount rate =11% $200x.901=$1.80 2.20x.802 79 2.40x.731=175 33.00x.731=24.12 $2946 -313 CopyrightC2005 by The McGraw-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-313 9-16. If you owe $40,000 payable at the end of seven years, what amount should your creditor accept in payment immediately if she could earn 12 percent on her money? Solution: Appendix B PV = FV x PVIF (12%, 7 periods) PV = $40,000 x .452 = $18,080 9-17. Jack Hammer invests in a stock that will pay dividends of $2.00 at the end of the first year; $2.20 at the end of the second year; and $2.40 at the end of the third year. Also, he believes that at the end of the third year he will be able to sell the stock for $33. What is the present value of all future benefits if a discount rate of 11 percent is applied? (Round all values to two places to the right of the decimal point.) Solution: Appendix B PV = FVIF Discount rate = 11% $ 2.00 x .901 = $ 1.80 2.20 x .802 = 1.79 2.40 x .731 = 1.75 33.00 x .731 = 24.12 $29.46
Les moore retired as president of Good man Snack Foods Company but is currently on a consulting contract for $35,000 per year for the next 10 years a. If Mr. Moore's opportunity cost(potential return)is 10 percent, what is the present value of his consulting contract? b. Assume Mr Moore will not retire for two more years and will not start to receive his 10 payments until the end of the third year, what would be the value of his deferred annuity? Solution: ppendix d a. PVA=AX PVIFA (10%, 10 periods) PVA=$35000X6.145=$215,075 b Deferred annuity-Appendix d PVA=AX PVIFA (I=10%, 10 periods) PVA=$35,000×6145=$215075 Now, discount back this value for 2 periods PⅤ=FⅤxPⅤF(1=10%,2 periods) Appendix e $215075X826=$177,652 OR A dix D PⅤA=$35,000(6814-1.7360 where n=12,n=2andi=10%) $35,000(5078)=$177,730 The answer is slightly different from the answer above due to rounding in the tables CopyrightC 2005 by The McGray-Hill Companies, Inc. -314
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-314 9-18. Les Moore retired as president of Goodman Snack Foods Company but is currently on a consulting contract for $35,000 per year for the next 10 years. a. If Mr. Moore's opportunity cost (potential return) is 10 percent, what is the present value of his consulting contract? b. Assume Mr. Moore will not retire for two more years and will not start to receive his 10 payments until the end of the third year, what would be the value of his deferred annuity? Solution: Appendix D a. PVA = A x PVIFA (10%, 10 periods) PVA = $35,000 x 6.145 = $215,075 b. Deferred annuity—Appendix D PVA = A x PVIFA (i = 10%, 10 periods) PVA = $35,000 x 6.145 = $215,075 Now, discount back this value for 2 periods PV = FV x PVIF (i = 10%, 2 periods) Appendix B $215,075 x .826 = $177,652 OR Appendix D PVA = $35,000 (6.814 – 1.7360 where n = 12, n = 2 and i = 10%) = $35,000 (5.078) = $177,730 The answer is slightly different from the answer above due to rounding in the tables