Chapter 9 Discussion Questions 9-1 How is the future value(Appendix a)related to the present value of a single sum(Appendix B)? The future value represents the expected worth of a single amount, whereas the present value represents the current worth FV=PV(1+r future value Present va lu (1+i 9-2 How is the present value of a single sum(Appendix b)related to the present value of an annuity(Appendix D)? The present value of a single amount is the discounted value for one future payment, whereas the present value of an annuity represents the discounted value of a series of consecutive payments of equal amount why does money have a time value? Money has a time value because funds received today can be reinvested to reach a greater value in the future. a person would rather receive $1 today than I in ten years, because a dollar received today, invested at 6 percent, is worth $.791 after ten years Does inflation have anything to do with making a dollar today worth more than a dollar tomorrow? Inflation makes a dollar tod ay worth more than a dollar in the future. Because inflation tends to erode the purchasing power of money, funds received today will be worth more than the same amount received in the future S-305 Copyright C2005 by The McGra-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-305 Chapter 9 Discussion Questions 9-1. How is the future value (Appendix A) related to the present value of a single sum (Appendix B)? The future value represents the expected worth of a single amount, whereas the present value represents the current worth. FV = PV (1 + I) n future value ( ) Present va lue 1 1 PV FV + = n i 9-2. How is the present value of a single sum (Appendix B) related to the present value of an annuity (Appendix D)? The present value of a single amount is the discounted value for one future payment, whereas the present value of an annuity represents the discounted value of a series of consecutive payments of equal amount. 9-3. Why does money have a time value? Money has a time value because funds received today can be reinvested to reach a greater value in the future. A person would rather receive $1 today than $1 in ten years, because a dollar received today, invested at 6 percent, is worth $1.791 after ten years. 9-4. Does inflation have anything to do with making a dollar today worth more than a dollar tomorrow? Inflation makes a dollar today worth more than a dollar in the future. Because inflation tends to erode the purchasing power of money, funds received today will be worth more than the same amount received in the future
Adjust the annual formula for a future value of a single amount at 12 percent for 10 years to a semiannual compound ing formula. What are the interest factors(FVIE) before and after? Why are they different? FV=PVxFⅤ( Appendix A) i=12%,n=10 3.106 Annual 6%.n=20 3.207 Semiannual The more frequent compounding under the semiannual compound ing assumption increases the future value 9-6 If, as an investor, you had a choice of daily ly, or quarterly compounding, which would you choose? Why? The greater the number of compounding periods, the larger the future value The investor should choose daily compounding over monthly or quarterly What is a deferred annuity? a deferred annuity is an annuity in which the equal payments will begin at some future point in time 9-8 List five different financial applications of the time value of money Different financial applications of the time value of money Equipment purchase or new product decision, Present value of a contract providing future payments, Future worth of an investment Regular payment necessary to provide a future sum, Regular payment necessary to amortize a loan Determination of return on an investment Determination of the value of a bond CopyrightC 2005 by The McGray-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-306 9-5. Adjust the annual formula for a future value of a single amount at 12 percent for 10 years to a semiannual compounding formula. What are the interest factors (FVIF) before and after? Why are they different? ( ) i 6%, n 20 3.207 Semiannual i 12%, n 10 3.106 Annual FV PV FVIF Appendix A = = = = = The more frequent compounding under the semiannual compounding assumption increases the future value. 9-6. If, as an investor, you had a choice of daily, monthly, or quarterly compounding, which would you choose? Why? The greater the number of compounding periods, the larger the future value. The investor should choose daily compounding over monthly or quarterly. 9-7. What is a deferred annuity? A deferred annuity is an annuity in which the equal payments will begin at some future point in time. 9-8. List five different financial applications of the time value of money. Different financial applications of the time value of money: Equipment purchase or new product decision, Present value of a contract providing future payments, Future worth of an investment, Regular payment necessary to provide a future sum, Regular payment necessary to amortize a loan, Determination of return on an investment, Determination of the value of a bond
Problems You invest $3,000 a year for 3 years at 12 percent a. What is the value of your investment after one year? Multiply $3,000x 1.12 b. What is the value of your investment after two years? multiply your answer to part a by 1.12 c. What is the value of your investment after three years? Multiply your answer to part b by 1. 12. This gives you your final answer d. Confirm that your final answer is correct by going to Appendix A(future value ofa $1), and looking up the future value for n=3, and i=12 percent Multiply this tabular value by $3,000 and compare your answer to the answer in part c. There may be a slight difference due to round ing Solution: a.$3.000x1.12 $3.360.00 b.$3,360x1.12=$3.763.20 C.$3,763.20x1.12=$4,214.78 d.$3,000X1.405=$4,21500( Appendix a) 9-2 What is the present value of a. $9,000 in 7 years at 8 percent? b. $20,000 in 5 years at 10 percent? c. $10,000 in 25 years at 6 percent? d. $1,000 in 50 years at 16 percent? Solution: appendix b PⅤ=FⅤⅹPv a.$9,000x583=$5,247 b.$20000X.621=$12420 C.$10,000×233=$2,30 d.$1000x.001=$1 -307 oyrightC2005 by The McGraw-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-307 Problems 9-1. You invest $3,000 a year for 3 years at 12 percent. a. What is the value of your investment after one year? Multiply $3,000 x 1.12. b. What is the value of your investment after two years? Multiply your answer to part a by 1.12. c. What is the value of your investment after three years? Multiply your answer to part b by 1.12. This gives you your final answer. d. Confirm that your final answer is correct by going to Appendix A (future value of a $1), and looking up the future value for n = 3, and i = 12 percent. Multiply this tabular value by $3,000 and compare your answer to the answer in part c. There may be a slight difference due to rounding. Solution: a. $3,000 x 1.12 = $3,360.00 b. $3,360 x 1.12 = $3,763.20 c. $3,763.20 x 1.12 = $4,214.78 d. $3,000 x 1.405 = $4,215.00 (Appendix A) 9-2. What is the present value of: a. $9,000 in 7 years at 8 percent? b. $20,000 in 5 years at 10 percent? c. $10,000 in 25 years at 6 percent? d. $1,000 in 50 years at 16 percent? Solution: Appendix B PV = FV x PVIF a. $ 9,000 x .583 = $5,247 b. $20,000 x .621 = $12,420 c. $10,000 x .233 = $2,330 d. $ 1,000 x .001 = $1
If you invest $9, 000 today, how much will you have a. In 2 years at 9 percent? b. In 7 years at 12 percent? c. In 25 years at 14 percent? d. In 25 years at 14 percent(compounded semiannually )? Solution: ppendix a FVEPVXFVIE a.$9.000x1.188=$10692 b.$9,000x2211=$19899 c.$9,000X26462=$238,158 d.$9000x29457=$265,113(7%,50 periods Your uncle offers you a choice of $30,000 in 50 years or $95 today. If money discounted at 12 percent, which should you choose? Solution: appendix b PV=FVX PVIF(12%, 50 periods) PV=$30.000X.003=$90 Choose $95 today CopyrightC 2005 by The McGray-Hill Companies, Inc. -308
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-308 9-3. If you invest $9,000 today, how much will you have: a. In 2 years at 9 percent? b. In 7 years at 12 percent? c. In 25 years at 14 percent? d. In 25 years at 14 percent (compounded semiannually)? Solution: Appendix A FV = PV x FVIF a. $9,000 x 1.188 = $ 10,692 b. $9,000 x 2.211 = $ 19,899 c. $9,000 x 26.462 = $238,158 d. $9,000 x 29.457 = $265,113 (7%, 50 periods) 9-4. Your uncle offers you a choice of $30,000 in 50 years or $95 today. If money is discounted at 12 percent, which should you choose? Solution: Appendix B PV = FV x PVIF (12%, 50 periods) PV = $30,000 x .003 = $90 Choose $95 today
How much would you have to invest today to receive a. $15,000 in 8 years at 10 percent? b.$20,000in12 at 13 c. $6,000 each year for 10 years at 9 percent? d. $50,000 each year for 50 years at 7 percent? Solution: ppendix b(a and b) PⅤ=FⅤ X PVIE a.$15000X467=$7005 b.$20,000x.231=$4620 Appendix d(c and d) C.$6000x6418=$38508 d.$50,000x13.801=$690050 If you invest $2,000 a year in a retirement account, how much would you have a. In 5 years at 6 percent? b. In 20 years at 10 perc c. In 40 years at 12 percent? Solution: Appendix c FVA=AxFⅤ a.$2,000X5637=$11,274 b.$2,000x57275=$114,550 C.$2.000x76709=$1.534180 -309 Copyright C2005 by The McGra-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-309 9-5. How much would you have to invest today to receive: a. $15,000 in 8 years at 10 percent? b. $20,000 in 12 years at 13 percent? c. $6,000 each year for 10 years at 9 percent? d. $50,000 each year for 50 years at 7 percent? Solution: Appendix B (a and b) PV = FV x PVIF a. $15,000 x .467 = $7,005 b. $20,000 x .231 = $4,620 Appendix D (c and d) c. $ 6,000 x 6.418 = $ 38,508 d. $50,000 x 13.801 = $690,050 9-6. If you invest $2,000 a year in a retirement account, how much would you have: a. In 5 years at 6 percent? b. In 20 years at 10 percent? c. In 40 years at 12 percent? Solution: Appendix C FVA = A x FVIFA a. $2,000 x 5.637 = $ 11,274 b. $2,000 x 57.275 = $ 114,550 c. $2,000 x 767.09 = $1,534,180