Post on 14-Jan-2016
The Time Value
of Money
The Time Value of Money
Future Value
Investment Interest or YieldYield
10%
Investment
$1,000
10___x 100
1 ___
10= .1= =
$100 Annual Yield
10% =
50% =
8% =
6.5% =
Compound InterestHow often is interest added to
investment principalExamples: annually, monthly, weekly, daily Annually $1,000 @ 12% =
$120 Monthly $1,000 @ 12% =
$126.83$1,000 x .12
/12 = $10
Month 1 $1,010
x .12/12 = $10.10
Month 2
Monthly Interest = $10
-- Interest earning interest
$1,020 x .12
/12 = $10.30
Month 3
.1 .5 .08 .065
The Time Value of Money
Future Value ComputationBeginning of
YearEnd of Year
Investment
x$1,00
0=
$1,000
1
Income x$1,00
0=
.08
80_____$1,080
1.08
x$1,000
=$1,0801.
08x
$1,080
=$1,166
(1 + Interest Rate)
xInvestme
nt=
Future ValueFuture Value
=(1 + int)xPresent Value P
V x(1 + int)
2
End of year 1
= Future Value End of year 2
PV x (1 + int) n = Future Value
Number of Payment Periods
1 =100%
The Time Value of Money
FUTURE VALUE
The Time Value of Money
FUTURE VALUEFuture Value ComputationBeginning of
YearEnd of Year
Investment
x$100,000
=$100,00
01
Income x$100,000
=.08
8,000_______$108,0
001.08
x$100,000
=$108,0001.
08x$108,
000=
$116,640
The Time Value of Money
The Time Value of Money
Click the ‘Insert Function’ (fx) icon
FUTURE VALUE
EXCEL
The Time Value of Money
FUTURE VALUE
EXCEL
The ‘Insert Function’ Box Appears
The Time Value of Money
FUTURE VALUE
EXCEL
The ‘Insert Function’ Box Appears
Type ‘fv’Then click on the ‘Go’ icon
Then click ‘OK’
The Time Value of Money
FUTURE VALUE
EXCELThe ‘Function Arguments’ Box Appears
Type ‘.08’Type ‘2’
Type ‘0’Type ‘-100000’
The ‘function’ formula Excel utilizes appears as you type
Then click ‘OK’The calculated answer appears here even before you click the ‘OK’ icon
Positive and Negative Numbers
IN your pocket = type in a POSITIVE NumberOUT of your pocket = type in a NEGATIVE Number
Ask yourself “Does this financial transaction allow me to put money IN
my pocket or require me to take money OUT of my pocket?
If you take $100,000 and put it in an investment where did the
$100,000 come from?OUT of your pocket
After 2 years the investment gives you
= -100,000
IN your pocket
$116,640
The Time Value of Money
The Time Value of Money
Positive and Negative Numbers
Future Value of a Stream of Payments
Future Value ComputationBeginning of
YearEnd of Year
Investment
x$100,000
=$100,00
01
Income x$100,000
=.08
8,000_______$108,0
00Investm
ent
+ $100,00
0=
$208,000
Income x$208,000
=.08
16,640_______
$224,640
The Time Value of Money
The Time Value of Money
EXCEL Click on function icon (fx)
Type ‘fv’ (future value)
Click on ‘OK’
Future Value of a Steam of Payments
The Time Value of Money
EXCELThe ‘Function Arguments’ Box Appears
Type ‘.08’Type ‘2’
Type ‘-100,000’Type ‘0’Type ‘1’
Then click ‘OK’
Future Value of a Stream of Payments
The Time Value of Money
EXCEL
Type is a value representing the timing of the payment:
Payment at the beginning of the period = 1
Payment at the end of the period = 0 or omitted
Investment Contribution
Debt Payment
Future Value of a Stream of Payments
First Pension Check
Type
The Time Value of Money
CompoundingWhat if your money compounds
monthly or payments are made monthly instead of annually?12 percent
interestannually
= .12
monthly
= .12/12
paymentsannual
ly= 1
monthly
= 1 * 12
quarterly
= .12/4
quarterly
= 1 * 4
PRESENT VALUEPresent Value
ComputationBeginning of Year
End of Year
Investment
/$100,000
=$92,5931.08
$92,593 x 1.08 = $100,000
Investment
/$92,593
=$85,7341.08
The Time Value of Money
The Time Value of Money
EXCEL Click on function icon (fx)
Type ‘pv’ (present value)
Click on ‘OK’
PRESENT VALUE
The Time Value of Money
EXCELThe ‘Function Arguments’ Box Appears
Type ‘.08’Type ‘2’
Type ‘0’Type ‘100000’Type ‘0’
Then click ‘OK’
PRESENT VALUE
Present Value Computation Beginning of
YearEnd of Year
Investment
/$100,000
=$92,5931.08Investm
ent/$100,
000=$85,7341.0
82
Investment
/$100,000
=$79,3831.08
3
The Time Value of Money
Present Value of a Stream of Payments
Present Value Computation Beginning of
YearEnd of Year
Investment
/$100,000
=$92,5931.08Investm
ent/$100,
000=$85,7341.0
82
Investment
/$100,000
=$79,3831.08
3
$257,710
________
The Time Value of Money
Present Value of a Stream of Payments
The Time Value of Money
EXCEL Click on function icon (fx)
Type ‘pv’ (present value)
Click on ‘OK’
Present Value of a Stream of Payments
The Time Value of Money
EXCELThe ‘Function Arguments’ Box Appears
Type ‘.08’Type ‘3’
Type ‘100,000’Type ‘0’Type ‘0’
Then click ‘OK’
Present Value of a Stream of Payments
FourPractic
e Proble
ms
The Time Value of Money
The Time Value of Money
Future Value of a Lump Sum
The Time Value of Money
Future Value of a Stream of Payments
The Time Value of Money
Future Value of a Stream of Payments
The Time Value of Money
Future Value of a Future Lump Sum