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CF
473.32
5
Winter 2014
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The Time Value of Money
ch 5
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Time Value of Money
What is the Present Value
• of $ received in future?
Future Value• of $ given today?
Interest Rate• during the periods between?
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Present Value
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$1,000
-$900
Present Value
FP
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$1,000
-$900
Present Value
-$800
P F
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$1,000
-$900
Present Value
-$800
P
-$700
F
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$1,000
-$900
Present Value
-$800
P
-$700
F
-$600
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$1,000
-$900
Present Value
-$800
P
-$700
F
-$600-$500
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$1,000
-$500 -$600 -$700 -$800 -$900
Present Value
FV5PV0
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? ? ? ? ?
Present Value
tr
FVPV
1
$1,000-$500 -$600 -$700 -$800 -$900
FV
1=t
10%=r
$1,000=FV
= ?PV
t
“discounting”
110.1
000,1
PV
vfvp
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PV
Present Value
tr
FVPV
1
$1,000-$909.09
FV
1=t
10%=r
$1,000=FV
= -$909.09PV
t
“discounting”
09.909
10.1
000,11
PV
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? PV
Present Value
tr
FVPV
1
$1,000-$909.09
FV
2=t
10%=r
$1,000.00=FV
= ?PV
t
“discounting”
210.1
00.000,1
PV
-$826.45
t
45.826
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Present Value
tr
FVPV
1
$1,000
FV
=t
10%=r
$1,000.00=FV
=PV
“discounting”
-$751.31-$683.01-$620.92 -$909.09-$826.45
1…5
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PV FV
Future Value
trPVFV )1(
=t
10%=r
?=FV
= -$1,000PV
$1,100-$1,000
t
1
?
1)10.1(000,1 FV
100,1
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PV FV
Future Value
trPVFV )1(
=t
10%=r
$1,210=FV
= -$1,000PV
$1,100-$1,000
t
2
?
2)10.1(000,1 FV
210,1
t
“compounding”
Why not $1,200?
$1,210
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Future Value
trPVFV )1(
=t
10.00%=r
=FV
= -$1,000.00PV
$1,100.00-$1,000.00
1…5
“compounding”
$1,210.00
t=4 t=5t=3t=2t=1
$1,331.00 $1,464.10 $1,610.51
PV
FV
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Future Value
also works as a general growth formula suppose we
• currently sell 1,000 widgets/year
• expect to increase sales at 10%/year for 5 years
how many will we be selling in five years?
useful for figuring out building projects & capital needs
trPVFV )1( 5
)10.1(00.000,1 51.610,1
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tt
rPVFV )1(
=r
?=t
$1,100.00=FV
= -$1,000.00 PV
$1,100.00-$1,000.00
10%
“time periods”
PV
r
PVFVt
1log
loglog
FV
$2,000.00
$2,000.00
years 72.7t
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rt
rPVFV )1(
=t
?=r
$1,100.00=FV
= -$1,000.00 PV
$1,100.00-$1,000.00
1
“discount rate”
FVPV
1
1
t
PV
FVr
100.000,1
00.100,1 1
1
r 10.
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r
=t
?=r
$1,420.00=FV
= -$1,000.00 PV
$1,420.00-$1,000.00
1
“discount rate”
FVPV
1
1
t
PV
FVr
100.000,1
00.420,1 1
1
r 42. %00.42
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r
=t
?=r
$1,420.00=FV
= -$1,000.00 PV
$1,420.00-$1,000.00
5
“discount rate”
FVPV
1
1
t
PV
FVr
100.000,1
00.420,1 5
1
r 0726. %26.7
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r “discount rate” interest rate IRR
• internal rate of return
ERR• equivalent rate of return
CAGR• compound annual growth rate
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Time Value of Money
useful for choosing between options suppose we can choose between
a. investing $500 in a company receiving $600 in 5 years
b. putting $500 in the bank at 4%
which is better?
r ?
FV ?$608.33
3.71%
trPVFV )1(
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Remember
this is the most important chapter
read work on problems meet think
next Tue report due