PAR
1
TIME
VALUE
OF
MONE1{
1 Single
Cash
Flow
1.1
Present
Value
Problem. A single cash
tlO\\7
of
$1,000.00
\yill
be
received
in
5 periods.
For
this cnsh
11O\v,
the
appropriate discoU!lt rate
I
period
is
6.0%. What
is
the present value
of
this single cash flow')
Solution
Strategy.
We
will
calculate
the present value
ofiiJis
single
cash
flO\'v
in three
equivalent
ways.
First,
\ve
will
calculate the present value using a time line.
vvhere
each column corresponds
to
a period
of
calendar time. Second.
we
use a formula for
the
present value. Third,
we
Lise
Excel's PV
I'ul1clion
for
the
present value.
FIGURE
1.1
Spreadsheet
for Single
Cash
Flow 
Present
Value.
4
5
$0
00
$1
,000 00
1>000
$74726
$000
1,000
5
:fi1
00000
6.0%.
Present
Value
using
il
Time
Urc~
Period
.0:...,
1'__
2
Cash
Flo'vv,
.
:1,0.00:li0
00
'h0
00
Present "ialue
01
Each
I.:.ash
Flow
$0.00
$000
$000
.resent Value
"j"l~t
.
Inputs
Single Cash
F!'c'N
Discount Rate
i
Period
Number
of
Penods
How To Build
Your
Own
Spreadsheet
Model.
I.
Inputs. Enter
the
inputs
in
the range B4:B6.
2.
Present Value using a
Time
Line. Creale
<l
time line
from
period 0
to
period
5.
enter
the single
cash tlo\\
in
period
5.
Calculate the present value
of
each cash
11l1'v\
and sum the present values
as
!(l110\\S.
o
pcriorJ. Enter
U.
L 2
.....
:S.
in
the
range
Bt);(;<).
o
Cash
Fkws.
Enter $0.00
in
cell B
i
0
and
copy
it
to
the range C
to:
FlO. Enter
=134
in
eeli
GIG.
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o
Present
Value
of
Each
Cash
Flo"
=
(Cash
flo\\)
/
«(1
+
Discount
Rate/Period)
1\
Period).
Enler
=BIO/«1+$B$5)"B9)
in cell
Bll
and cop:'
it
across.
The
S signs in $BS5
lock the column as
B
and the row as S when copying.
o
Present
Value
=
Sum
over
all
periods
of
the Present Value
c"
Each Cash
Flow.
Enter
=StJl\'l(Bl1:Gl1)
in
cell
1312.
3.
Present
Value
using
the
Formula.
For
(\
single
cash
[lov,.
the formula
is
Present Value
=
(Cash
Flow) /
eel
+
Discount Rate/Period)
1\
Period). Enter
=B4/«1+B5)"B6)
in
cell
HIS
4.
Present
Value
using
the
PV
Function.
The Excel PV function can
be
used
to
calculate the
present value
or
a
singk
cash
110w.
the presenl
value
or
an
annuity, or
the
present
value
or
a bond.
For a single cash !low. the format
is
=PV(lJiscoullt
Rate!
Period. NU::lber
of
[)eriods.
O.
Single
Cac,h
F!l.m)
Enter
=I>V(B5,B6,O,B4)
in
cell
R~18.
The
PreserH Value
of
this
Single
Cash Flow
is
\
. Notice
yOU
get the saine answer
all
three
ways:
using the time lint\ using the formula. or using the PV function!
1.2
Future
Value
Problem.
A single cash flow
of$747.25
is
available
no\\o
(in period
0).
For this cash
tlovi,
the appropriate
discount
rate /
period
is
6.0%.
What is the
period
5 fulure
value
of
this
single
cash
110\0\'1
Solution
Strategy.
We
will calculate the future value
of
the single cash flow
in
three equivalent ways.
First, we
will
calculate the
future
value using a time line, where
cacb
column
corresponds to a period
of
calendar
time.
Second.
\\Ie
usc
a
fonnula
for the future value.
Third.
\VC
use
Fxccl's
FV
function
fQr
the
rlllur·~
value.
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 Spring '10
 WANG
 Future Value, Net Present Value

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