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TIME VALUE OF MONEY
Page 1
FUTURE AND PRESENT VALUE FACTORS
Interest rate
10%
Present value
1,000
First of
End of
% of
Year
Year
Initial
Year
Balance
Interest
Balance
Investment
1
1,000
100
1,100
110%
2
1,100
110
1,210
121%
3
1,210
121
1,331
133%
4
1,331
133
1,464
146%
% of Initial Investment ( Future Value Factor )
=
( 1 + Interest Rate ) ^ # of Years
Present Value Factor
= 1 / ( 1 + Interest Rate ) ^ # of Years
A
B
C
D
E
F
G
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
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Page 2
AMORTIZATON TABLE
The following amortization table shows the link between the present value (amount
borrowed), cash flow (payment) and discount rate (interest rate) on a fiveyear loan.
Interest rate
10%
Payment
1,000
Amount borrowed
3,791
Beginning
Plus
Less
Ending
Year
Balance
Interest
Payment
Balance
1
3,791
379
(1,000)
3,170
2
3,170
317
(1,000)
2,487
3
2,487
249
(1,000)
1,736
4
1,736
174
(1,000)
909
5
909
91
(1,000)
0
A
B
C
D
E
F
G
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
TIME VALUE OF MONEY
Page 3
PRESENT VALUE CALCULATION
The following shows how to calculate the present value as the sum of the present values
of the cash flows.
Interest rate
10%
Payment
1,000
Year
0
1
2
3
4
5
Payment
1,000
1,000
1,000
1,000
1,000
Present value factor
100%
91%
83%
75%
68%
62%
PV of payment
909
826
751
683
621
PV of all payments
3,791
A
B
C
D
E
F
G
H
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
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Page 4
SPREADSHEET FUNCTIONS
Given the number of periods (or number of payments), any two of the following determine
the third:
present value, cash flow, discount rate.
Be careful about the signs!
1. The present value is computed as PV(interest rate, # of periods, cash flow).
Discount rate
10%
Number of periods
5
Cash flow
1,000
Present value
(3,791)
2. The present value can also be computed as NPV(interest rate, series of cash flows).
Year
0
1
2
3
4
5
Cash flow
1,000
1,000
1,000
1,000
1,000
PV of cash flows
3,791
3. The cash flow is computed as PMT(discount rate, # of periods, present value).
Discount rate
10%
Number of periods
5
Present value
3791
Cash flow
(1,000)
4. The discount rate is computed as IRR(series of present value and cash flows).
Year
0
1
2
3
4
5
Cash flow
(3,791)
1,000
1,000
1,000
1,000
1,000
Internal rate of return
10%
A
B
C
D
E
F
G
H
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
TIME VALUE OF MONEY
Page 5
MONTHLY COMPOUNDING
Annual interest rate
10%
Monthly interest rate
0.83%
( Annual rate / 12 )
Future
Beginning
Ending
Value
Month
Balance
Interest
Balance
Factor
1
100.00
0.83
100.83
100.83%
2
100.83
0.84
101.67
101.67%
3
101.67
0.85
102.52
102.52%
4
102.52
0.85
103.38
103.38%
5
103.38
0.86
104.24
104.24%
6
104.24
0.87
105.11
105.11%
7
105.11
0.88
105.98
105.98%
8
105.98
0.88
106.86
106.86%
9
106.86
0.89
107.75
107.75%
10
107.75
0.90
108.65
108.65%
11
108.65
0.91
109.56
109.56%
12
109.56
0.91
110.47
110.47%
Effective annual rate
10.47%
Effective annual rate
=
FVF  100%
=
( 1 + Monthly Rate )^12  100%
A
B
C
D
E
F
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
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This note was uploaded on 12/14/2011 for the course MGT 268 taught by Professor Paragkosalge during the Spring '08 term at Grand Valley State University.
 Spring '08
 ParagKosalge

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