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So (1+i)
t
= (1+i)·(1+i)·(1+i)·(1+i)·(1+i)·(1+i)·(1+i)… ·(1+i) for “t” times
KEY RELATIONHSIP:
FV = PV x (1+i)
t
KEY RELATIONHSIP:
PV = FV ÷ (1+i)
t
KEY RELATIONHSIP:
(1+i)
t
=FV÷PV
(1+i) = (FV÷PV)
1/t
FV
= PV x (1+i
1
) x (1+i
2
) x (1+i
3
) x … x (1+i
t
).
Long way.
Short Way
The interest factor on that payment is 1.
The first payment earns interest for t1 periods, not t periods.
Use Short Cut
Formula
MGMT 235
Dr. Sharp
Review Fundamentals of Valuation
These class notes review this material and also provide some help for a financial
calculator. It also has some selftest questions and problems.
Class notes are necessarily
brief.
See any principles of finance book for a more extensive explanation.
Eugene F. Brigham, Joel F. Houston
Fundamentals of financial management
HG 4026 B6693 1998
Ross, Stephen A, Westerfield, and Jordan
Fundamentals of corporate finance
HG 4026 .R677 1995
PART I
:
Single Sum.
Time Value of Money: Know this terminology and notation
FV
Future Value
(1+i)
t
Future Value Interest Factor [FVIF]
PV
Present Value
1/(1+i)
t
Present Value Interest Factor
[PVIF]
i
Rate per period
t
# of time periods
Question: Why are (1+i) and (1+i)
t
called interest factors?
Answer: 1. Start with simple arithmetic problem on interest:
How much will $10,000 placed in a bank account paying 5% per year be worth
compounded annually?
Answer:
Principal
+
Interest
$10,000 + $10,000 x .05 = $10,500
2. Factor
out the $10,000.
10,000 x (1.05) = $10,500
3. This leaves (1.05) as the factor
.
1.
Find the value of $10,000 earning 5% interest per year after
two
years.
Start with the amount after one year and multiply by the factor for each year.
[
Amount after one year
]
x
(1.05)
=
[
$10,000
x
(1.05)
]
x
(1.05)
=
$10,000 x (1.05)
2
=
$11,025.
.
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View Full DocumentA.
Future Value
Find the value of $10,000 in 10 years. The investment earns 5% per year.
FV = $10,000
·
(1+i)
·
(1+i)
·
(1+i)
·
(1+i)
·
(1+i)
·
(1+i)
·
(1+i)
·
(1+i)
·
(1+i)
·
(1+i)
FV = $10,000
·
(1.05)
·
(1.05)
·
(1.05)
·
(1.05)
·
(1.05)
·
(1.05)
·
(1.05)
·
(1.05)
·
(1.05)
·
(1.05)
FV = $10,000 x (1.05)
10
=
$10,000 x 1.62889
= $16,289
Find the value of $10,000 in 10 years.
The investment earns 8% for four years and
then earns 4% for the remaining six years.
FV = $10,000
·
(1+i)
·
(1+i)
·
(1+i)
·
(1+i)
·
(1+i)
·
(1+i)
·
(1+i)
·
(1+i)
·
(1+i)
·
(1+i)
FV = $10,000
·
(1.08)
·
(1.08)
·
(1.08)
·
(1.08)
·
(1.04)
·
(1.04)
·
(1.04)
·
(1.04)
·
(1.04)
·
(1.04)
FV = $10,000 x (1.08)
4
x (1.04)
6
FV = $17,214.53
B.
Present Value
:
Same idea, but begin at the end. Rearrange the Future value equation to look
like this:
PV = FV÷ [(1+i)
·
(1+i)
·
(1+i)
·
(1+i)
·
(1+i)
·
(1+i)
·
(1+i)
·
(1+i)
·
(1+i)
·
(1+i)]
PV = FV ÷ (1+i)
t
[2]
Example: How much do I need to invest at 8% per year, in order to have $10,000 in__.
a.
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 Spring '09
 Staff
 Management

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