Chapter 5The Time Value of MoneyCHAPTER 5THE TIME VALUE OF MONEYSOLUTIONS TO PROBLEMS:1.a.FV3= $1,000(FVIF.06,3) = $1,000(1.191) =$1,191b. FV5= $1,000(FVIF.06,5) = $1,000(1.338) =$1,338c. FV10= $1,000(FVIF.06,10) = $1,000(1.791) =$1,7912.a. Present value of $5,000 today =$5,000b. Present value of $15,000 received in 5 years at 9%:PV0= $15,000(PVIF.09,5) = $15,000 (0.650) =$9,750 (tables)$9749 (calculator)c. Present value of a 15 year, $1,000 annuity at 9%:PVAN0= $1,000 (PVIFA.09,15) = $1,000(8.061) =$8,061Therefore, you prefer $15,000 in five years because it has the highestpresent value.3.FVAND8= $20,000(FVIFA.09,8)(1 + 0.09) = $20,000(11.028)(1.09)=$240,410.40($240,420.73 with a calculator)4.Alternative a:PVAND0= $1,200(PVIFA.08,12)(1 + 0.08) = $1,200(7.536)(1.08)=$9,766.66 (tables);$9,766.76 (calculator)Alternative b:Present value cost equals$10,000(given).Therefore, choose5-1Internal

Chapter 5The Time Value of MoneyAlternative (a) because it has a lower present value cost.5.a. PV0= $50,000 /[1 + (0.06/2)]2x5=$37,204.70 (calculator)b.PV0= $50,000 /[1 + (0.06/4)]4x5=$37,123.52 (calculator)6.$1,000 = $333.33(FVIFi,9)FVIFi,9= 3.000i13%from Table I. (12.98% by calculator)7.a. PV0= $800(PVIF.04,8) = $800 (0.731) =$584.80 (tables)$584.55 (calculator)b. PV0= $800(0.540) =$432c. PV = $800(PVIF.05,32) =$167.89(by calculator)d. PV = $800(1.000) =$8008.PVAN0= $60,000 - $10,000 = $50,000$50,000 = PMT(PVIFA.10,25) = PMT(9.077)PMT = $5,508.43 (tables)$5,508.40 (calculator)Interest (first year) = .10($50,000) = $5,000Principal reduction = $5,508.43 - $5,000 =$508.439.$200,000 = $41,067(PVIFAi,20)PVIFAi,20= 4.870;From Table IV,i = 20%10.$600,000 = PMT(FVIFA.09,25) = PMT(84.701)5-2Internal

Chapter 5The Time Value of MoneyPMT =$7,083.74 (tables);$7,083.75 (calculator)11.a. PV0= $70(PVIFA.05,25) + $1000(PVIF.05,25) = $70(14.094) +$1000(0.295) =$1,281.58 (tables); $1,281.88 (calculator)b. PV0= $70(11.654) + 1000(0.184) =$1,000($999.78 usingtables; difference from $1,000 due to rounding)c. PV0= $70(7.843) + $1000(0.059) =$608.01 (tables)$607.84 (calculator)12. ieff= [ 1 + (inom/m)]m- 1 = [ 1 + (.08/4)]4-1 =0.0824 or 8.24%13.NPV1= -$10,000 + $5,000(0.909) + $6,000(0.826) + $7,000(0.751)+ $8,000(0.683) =$10,222NPV2= -$10,000 + $8,000(0.909) + $7,000(0.826) + $6,000(0.751)+ $5,000(0.683) =$10,975This is the preferred alternative.14.PVAN0= $80,000 = PMT(PVIFA.10,10) = PMT(6.145)PMT =$13,018.71(Calculator solution = $13,019.63)15.PVAN0= $30,000 - $5,000(down) - $750 (loan origination fee)= $24,250Origination fee = 0.03 x $25,000 = $750$24,250 = $3,188(PVIFAi,15)PVIFAi,15= 7.607Therefore,i10%from Table IV and calculator16.a. PV0= $6,000(PVIFA.12,5) + $4,000(PVIFA.12,5)(PVIF.12,5)5-3Internal

Chapter 5The Time Value of Money= $6,000(3.605) + $4,000(3.605)(0.567) =$29,806 (tables)$29,810 (calculator)(Note:$4,000(PVIFA.12,5) gives the present value of that annuity atthe end of five years.Hence, it must be discounted back to time 0 ata 12% rate.)

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