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%:
[email protected]%:
PVA = $4,000{[1 – (1/1.05)
9
] / .05 } = $28,431.29
[email protected]%:
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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 Fall '08
 TOMNELSON
 Time Value Of Money, Net Present Value

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