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# Ch5 homework answer - Chapter 5 1 Sum the PV of each cash...

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Chapter 5 1. Sum the PV of each cash flow and sum. PV = FV / (1 + r) t [email protected]% = \$900 / 1.10 + \$600 / 1.10 2 + \$1,100 / 1.10 3 + \$1,480 / 1.10 4 = \$3,151.36 [email protected]% = \$900 / 1.18 + \$600 / 1.18 2 + \$1,100 / 1.18 3 + \$1,480 / 1.18 4 = \$2,626.48 [email protected]% = \$900 / 1.24 + \$600 / 1.24 2 + \$1,100 / 1.24 3 + \$1,480 / 1.24 4 = \$2,318.96 Using the cash flow function: (This is different from the TVM Function.) 1. Enter the Cash flows 0 {CFj} Enters \$0 at time 0 900 {CFj} Enters \$900 as the first cash flow 1 {Yellow Shift} {Nj} Enters the number of times the \$900 is received (once) 600 {CFj} Enters \$600 as the second cash flow 1 {Yellow Shift} {Nj} Enters the number of times the \$600 is received 1100 {CFj} Enters \$1,100 as the second cash flow 1 {Yellow Shift} {Nj} Enters the number of times the \$1,100 is received 1480 {CFj} Enters \$1,480 as the second cash flow 1 {Yellow Shift} {Nj} Enters the number of times the \$1,100 is received 2. Enter the each Discount Rate and Calculate the PV for each discount rate: 10 {I/YR} Enters 10% as the discount rate {Yellow Shift} {NPV} Calculates the Net Present Value (same as the PV in this case) 18 {I/YR} Enters 18% as the new discount rate (the CFs remain unchanged) {Yellow Shift} {NPV} Calculates the Net Present Value (same as the PV in this case) 24 {I/YR} Enters 24% as the new discount rate (the CFs remain unchanged) {Yellow Shift} {NPV} Calculates the Net Present Value (same as the PV in this case) CFo \$0 CFo \$0 CFo \$0 C01 \$900 C01 \$900 C01 \$900 F01 1 F01 1 F01 1 C02 \$600 C02 \$600 C02 \$600 F02 1 F02 1 F02 1 C03 \$1,100 C03 \$1,100 C03 \$1,100 F03 1 F03 1 F03 1 C04 \$1,480 C04 \$1,480 C04 \$1,480 F04 1 F04 1 F04 1 I = 10 I = 18 I = 24 NPV CPT NPV CPT NPV CPT \$3,151.36 \$2,626.48 \$2,318.96 2. To find the PVA, we use the equation: PVA = C ({1 – [1/(1 + r) ] t } / r ) At a 5%: PVA = \$4,000{[1 – (1/1.05) 9 ] / .05 } = \$28,431.29 PVA = \$6,000{[1 – (1/1.05) 5 ] / .05 } = \$25,976.86 1

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At a 22%: [email protected]%: PVA = \$4,000{[1 – (1/1.22) 9 ] / .22 } = \$15,145.14 [email protected]%: PVA = \$6,000{[1 – (1/1.22) 5 ] / .22 } = \$17,181.84 Notice that the PV of Cash flow X has a greater PV at a 5 percent interest rate, but a lower PV at a 22 percent interest rate. The reason is that X has greater total cash flows. At a lower interest rate, the total cash flow is more important since the cost of waiting (the interest rate) is not as great. At a higher interest rate, Y is more valuable since it has larger cash flows. At a higher interest rate, these bigger cash flows early are more important since the cost of waiting (the interest rate) is so much greater.
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