Chapter 6 HomeworkPg. 268 ST-2; ST-4 Pg. 270 6-6; 6-10 Pg. 271 6-12 Pg. 274 6-25 Pg. 268 ST-2 In the introduction to this chapter we asked whether you would prefer to invest $5,500 today and receive either $7,020 in five years or $8,126 in eight years. You should now be able to determine which investment alternative is better. a. Based only on the return you would earn from each investment, which is better? b. Can you think of any factors other than the expected return that might be important to consider when choosing between the two investment alternatives? 500(1+i)8 8. 020 8.Pg.500 1 2 3 4 5 6 7 8 7.27641/5 1.2764 1. 268 ST-2a 0 Option A -5.500 Option B -5.4775 = FVIF5%.126/5.8 Table Lookup 1.500 1.500(1+i)5 = (1+i)5 = (1+i)5 = (1+i) = (1+i) = 5% Option B 8.0500 i = 5.126 = 5.020/5.126 FVn = PV(1+i)n Option A 7.4775 = FVIFi.020 7.8 .500 = (1+i)8 1. 268 ST-2b Other Factors to Consider: – Risk of 8-year investment vs. 5-year – Timing – Rate Expectations .Pg. Your bank compounds interest at an eight percent annual rate.000 .Pg. 2004. and you will need $1. ‘00 8% ‘01 ‘02 ‘03 ‘04 1. 268 ST-4 Assume that it is now January 1. 2000.000 on January 1. 000 on January 1.83 .‘00 8% Pg.000 a. to have a balance of $1.000[1/(1+0.000[0.08)3] = 1. 268 ST-4 ‘01 ‘03 ‘02 PV=? ‘04 1. 2001.7938] = 793. How much must you deposit on January 1. 2004? PV=FV[1/(1+i)n] PV PV PV = 1. 000 = PMT(4.000/4. 268 ST-4 ‘01 ‘03 ‘02 PMT PMT PMT ‘04 PMT 1.‘00 8% Pg.5061 = 221.92 .n) 1.5061) 1. If you want to make equal payments to each January 1 from 2001 through 2004 to accumulate the $1. how large must each of the four payments be? FVAn = PMT(FVIFAi.000 b.000. .78 You should take the payments of $221. If your father were to offer either to make the payments calculated in part (b) ($221.000) instead of the $750 on 1/1/01 which will only be worth $944. 268 ST-4 ‘01 ‘03 ‘02 750 ‘04 FV c.92 (FV = $1.‘00 8% Pg.92) or to give you a lump sum of $750 on January 1.78. 2001. which would you choose? Input: Output: 3 8 -750 N I/Y PV 0 PMT FV 944. what interest rate.33331/3 1. 2004? FV = PV(1+i)n 1. 2001.000 1. If you have on $750 on January 1.‘00 ?% Pg. would you have to earn to have the necessary $1. 268 ST-4 ‘01 ‘03 ‘02 750 ‘04 1. compounded annually.000 d.000 on January 1.1006 i = 750(1+i)3 = (1+i)3 = (1+i) = (1+i) =10.06% .000/750 1. must you seek out to achieve your goal? Input: 1.29 -186.000.99 0 -186.000 on January 1.29 -186.29 on each January 1 from 2001 through 2004. with annual compounding.29 1. but you still need $1. 2004.000 4 N I/Y Output: 19.29 PV PMT FV . What interest rate.00 Suppose you can deposit $186. 268 ST-4 ‘01 ‘03 ‘02 -186.‘00 ?% Pg. -186.29 ‘04 e. To help you reach your $1. If all of this money is deposited in a bank that pays eight percent.‘00 8% Pg. how large must each of the six payments be? Part 1 Input: 6 4 400 N I/Y PV Output: Part 2 Input: Output: 6 4 0 0 PMT FV 506.87 N I/Y PV PMT 74.13 493. 2001. your father offers to give you $400 on January 1.000 f. 268 ST-4 ‘01 ‘03 ‘02 -400 PMT PMT PMT PMT PMT ‘04 PMT 1. You will get a part-time job and make six additional payment of equal amounts each six months thereafter.000 goal. compounded semiannually.46 FV . What is the effective annual rate being paid by the bank in part f? Effective Annual Rate = EAR = [1+(isimple/m)]m-1 Where: m = # of compounding periods per year EAR EAR = [1+(. 268 ST-4 ‘01 ‘03 ‘02 ‘04 g.08/2)]2-1 = 8.16% .‘00 8% Pg. 270 6-6 Find the present values of the following cash flow streams under the following conditions: Year 1 2 3 4 5 Cash Stream A $100 400 400 400 500 Cash Stream B $300 400 400 400 100 .Pg. 94 $400 0.17 PVA $1.9259 $92.8573 $342.00 100.7938 $317.7350 $294. i = 8% Stream A: 8% Year 1 2 3 4 5 Rate FV PVIFi.00 8.00 1.251.00 400.25 Stream B: CF CFo= C01= F01= C02= F02= C03= F03= CPT NPV 0.Pg.59 $400 0. 270 6-6 a.53 $400 0.01 $300 0.n PV $100 0.00 3.00 300.32 I = NPV CPT .6806 $204.00 1.00 1.300. Pg.0000 $400.00 $300 1.00 $400 1.00 I = NPV CPT .0000 $300.00 1.00 PVA $1.00 3.00 1.600. 270 6-6 b.00 Stream B: CF CFo= C01= F01= C02= F02= C03= F03= CPT NPV 0.0000 $400.00 $400 1.00 0.00 400. i = 0% Stream A: 0% Year 1 2 3 4 5 Rate FV PVIFi.00 300.0000 $400.00 100.00 $400 1.600.n PV $100 1.0000 $100.00 1. Pg.32 .272. FV of $400 each six months for five years at a simple rate of 12 percent. compounded semiannually. 270 6-10a Find the future values of the following ordinary annuities: a. Input: 10 6 0 N I/Y PV -400 PMT FV Output: 5. 374. FV of $200 each three months for five years at a simple rate of 12 percent. Input: 20 3 0 -200 PMT N I/Y PV FV Output: 5. 270 6-10b Find the future values of the following ordinary annuities: b.07 .Pg. compounded quarterly. yet the annuity in part (b) ears $101. 270 6-10c Find the future values of the following ordinary annuities: c. The annuities described in parts (a) and (b) have the same amount of money paid into them during the fiveyear period and both earn interest at the same simple rate. Why does this occur? The first payment is made 3 months earlier in (b) than in (a) and the effect of more frequent compounding both contribute to the higher earnings.Pg.76 more than the one in part (a) over the five years. . a. just borrowed $25. b.Pg. . and the interest rate is ten percent. Set up an amortization schedule for the loan.000.000? Assume that the interest rate remains at ten percent and that the loan is paid off over five years. The loan is to be repaid in equal installments at the end of each of the next five years. 271 6-12 Lorkay Seidens Inc. How large must each annual payment be if the loan is for $50. 094.94) 3 ($6.40 $0.500.445.36) ($5.94) 2 ($6.69) In Excel: Payment = PMT(rate.594.58) ($599.Nper.Type) Balance = Loan Amount -Principal .594.FV) Principle = PPMT(rate.94) 5 ($6.76 $5.090.87) ($5.000 Principal Balance ($4.FV.00) $20.Pg.144.63 $11.905.504.Per.40) ($25.94) Interest ($2.51) ($1.94) ($4.Per.Nper.594.640. 10% Interest Year Payment 1 ($6.PV.974.54) Loan Amount 25.450.594.PV. 271 6-12a a.594.PV.995.00) ($2.400.995.69) ($7.974.06) ($1.Type) Interest = IPMT(rate.000.06 $16.Nper.43) ($4.00 ($32.954.FV.94) 4 ($6. 271 6-12b a.Per.52 $11.909.008.900.FV) Principle = PPMT(rate.01) ($3.79) ($50.13) ($2.Nper.990.801. 10% Interest Year Payment 1 ($13.00) $41.Type) Interest = IPMT(rate.Nper.15) ($1.189.37) In Excel: Payment = PMT(rate.949.75) ($10.79 $0.PV.86) ($9.FV.00) ($4.189.810.Pg.000.189.181.189.280.87) 5 ($13.72) ($11.949.PV.87) ($9.13 $32.Type) Balance = Loan Amount -Principal .87) 2 ($13.189.26 $22.87) Interest ($5.87) 3 ($13.891.000.Per.00 ($65.87) 4 ($13.FV.199.37) ($15.000 Principal Balance ($8.289.08) Loan Amount 50.Nper.990.189.PV. 949. however the same principal ($50. Why are these payments not half as large as the payments on the loan in part (b)? Input: Output: 10 10 50.000. The total interest paid on the 10-year loan is $31. the interest rate is ten percent. . while the total for the 5-year loan is $15.27 Because the payments are spread out over a longer period of time.137.000) is repaid over a longer period of time so that the total payment per year is not doubled. but the payments are spread out over twice as many periods. more interest must be paid. How large must each payment be if the loan is for $50. 271 6-12c c. and the loan is paid off in equal installments at the end of each of the next ten years? This loan is for the same amount as the loan in part (b).000 PMT 0 N I/Y PV FV 8.373.Pg. how long. 274 6-25 While Steve Bouchard was a student at the University of Florida.500 per year. If Steve repays $1. will it take him to repay the loan? PVAn = PMT(PVIFAi.000 in student loans at an annual interest rate of nine percent. to the nearest year.500 I/Y PV PMT 0 FV .77 9 12.000 1. he borrowed $12.Pg.n) Input: N Output: 14.