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Time Value of Money Question
±
You are offered two options to receive a
cash payment.
²
Option A: $100 today
Prof. Q. Ma
HADM 2222: Time Value of Money
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Option B: $107 in future year t
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Which one is more valuable to you?
General Question
Earlier time
Later time
Prof. Q. Ma
HADM 2222: Time Value of Money
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Time Line
$$$$
(PV)
$$$$$$
(FV)
Learning Objectives
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Be able to compute
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The FV of a cash payment made today
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The PV of cash at some future date
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The return (r) on an investment
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The number of periods (T) that equates a PV
Prof. Q. Ma
HADM 2222: Time Value of Money
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The number of periods (T) that equates a PV
and an FV given an interest rate (r)
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Be able to use a financial calculator to
solve TVM problems
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Future Value
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Suppose you invest $100 for one year at 6% per
year.
What do you have in one year?
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Interest = 100 * .06 = 6
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Value in one year = principal + interest = 100 + 6
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Future Value (FV) = 100 * (1 + .06)
Prof. Q. Ma
HADM 2222: Time Value of Money
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Suppose you leave the money in for another year.
How much will you have two years from now?
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FV = 106 + 106 * .06 = 106 * (1+.06)
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FV = 100 * (1+.06)
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Future Value – General Formula
FV = PV (1 + r)
T
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FV = future value
Prof. Q. Ma
HADM 2222: Time Value of Money
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PV = present value
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r = period interest rate, expressed as a
decimal
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T = number of periods
Definitions
Earlier time
Later time
Time Line
PV
FV
Prof. Q. Ma
HADM 2222: Time Value of Money
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Present Value – earlier money on a time line
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Future Value – later money on a time line
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Interest rate – “exchange rate” between earlier money and later
money
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Discount rate; required return
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Cost of capital; opportunity cost of capital
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Effect of Compounding
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Simple interest
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Compound interest
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= simple interest + interest on interest
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Consider the previous example (two years)
Prof. Q. Ma
HADM 2222: Time Value of Money
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FV with simple interest = 100 + 6 + 6 = 112
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FV with compound interest = 112.36
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The extra $.36 comes from the interest of the first
interest payment.
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.06(6) = .36
FV Interest Factor
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FVIF = (1 + r)
T
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FVIF Increases with time (T).
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FVIF increases with interest rate (r).
Prof. Q. Ma
HADM 2222: Time Value of Money
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FVIF = (1 + r)
T
400
5.00
6.00
7.00
1
5%
10%
20%
Prof. Q. Ma
HADM 2222: Time Value of Money
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0.00
1.00
2.00
3.00
4.00
01234567891
0
Year
FV of $1
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FV of $1 at 5% for 100 years
80
100
120
140
Prof. Q. Ma
HADM 2222: Time Value of Money
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0
20
40
60
1 1
12
13
14
15
16
17
18
19
11
0
1
Present Value – One Period
Suppose you need $10,000 in one year for the
down payment on a new sports car. If you can
earn 7% annually, how much do you need to
invest today?
Prof. Q. Ma
HADM 2222: Time Value of Money
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Present Value – General Formula
±
PV = FV / (1 + r)
T
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PV = present value
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FV = future value
Prof. Q. Ma
HADM 2222: Time Value of Money
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±
r = period interest rate, expressed as a
decimal
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T = number of periods
5
PVIF = 1/(1+r)
T
0.8
1
1.2
1
5%
10%
20%
Prof. Q. Ma
HADM 2222: Time Value of Money
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0
0.2
0.4
0.6
01234567891
0
Year
PV of $
PV & FV: Their Relation
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PV = FV / (1 + r)
T
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FV = PV
(1 + r)
T
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There are four parts in these equations
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PV, FV, r and T
Prof. Q. Ma
HADM 2222: Time Value of Money
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From any three, we can get the fourth
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Sign convention when using financial
calculator to solve for r or T.
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This note was uploaded on 10/09/2009 for the course H ADM 211 at Cornell University (Engineering School).
 '07
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