# Chapter 5_Solutions_14thEdition.doc - Chapter5...

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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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