Pertemuan 12
Perhitungan Nilai
Waktu Uang
Time Value of Money
Business investments
extend over long periods
of time, so we must
recognize the time value
of money.
Investments that promise
returns earlier in time are
preferable to those that
promise returns later in
time.
McGraw-Hill/Irwin
© The McGraw-Hill Companies, Inc., 2003
Time Value of Money
A dollar today is worth
more than a dollar a
year from now since a
dollar received today
can be invested,
yielding more than a
dollar a year from now.
McGraw-Hill/Irwin
© The McGraw-Hill Companies, Inc., 2003
Interest and the Time Value of Money
If $100 is invested today at 8% interest,
how much will you have in two years?
At the end of one year:
$100 + 0.08  $100 = (1.08)  $100 = $108
At the end of two years:
(1.08)$108 = $116.64
or
(1.08)2 × $100 = $116.64
McGraw-Hill/Irwin
© The McGraw-Hill Companies, Inc., 2003
Interest and the Time Value of Money
If P dollars are invested today at the
annual interest rate r, then in n years
you would have Fn dollars computed as
follows:
Fn = P(1 +
McGraw-Hill/Irwin
n
r)
© The McGraw-Hill Companies, Inc., 2003
Interest and the Time Value of Money
The present value of any sum to be
received in the future can be computed
by turning the interest formula around
and solving for P:
P = Fn
McGraw-Hill/Irwin
1
(1 + r)n
© The McGraw-Hill Companies, Inc., 2003
Time Value of Money
Excerpt from Present Value of $1 Table in
the Appendix to Chapter 14
Periods
1
2
3
4
5
McGraw-Hill/Irwin
10%
0.909
0.826
0.751
0.683
0.621
Rate
12%
0.893
0.797
0.712
0.636
0.567
14%
0.877
0.769
0.675
0.592
0.519
© The McGraw-Hill Companies, Inc., 2003
Interest and the Time Value of Money
A bond will pay $100 in two years. What is
the present value of the $100 if an investor
can earn a return of 12% on investments?
1
P = 100 (1 + .12)2
P = $100 (0.797)
P = $79.70
McGraw-Hill/Irwin
© The McGraw-Hill Companies, Inc., 2003
Interest and the Time Value of Money
A bond will pay $100 in two years. What is
the present value of the $100 if an investor
can earn a return of 12% on investments?
Present Value = $79.70
What does this mean?
If $79.70 is put in the bank today,
it will be worth $100 in two years.
In that sense, $79.70 today is
equivalent to $100 in two years.
McGraw-Hill/Irwin
© The McGraw-Hill Companies, Inc., 2003
Interest and the Time Value of Money
Let’s verify that if we put $79.70 in the bank
today at 12% interest that it would grow to
$100 at the end of two years.
Year 1
Beginning balance $ 79.70
Interest @ 12%
$ 9.56
Ending balance
$ 89.26
Year 2
$ 89.26
$ 10.71
$ 99.97
We can also determine the present
value using present value tables.
McGraw-Hill/Irwin
© The McGraw-Hill Companies, Inc., 2003
Time Value of Money
Excerpt from Present Value of $1 Table in
the Appendix to Chapter 14
Periods
1
2
3
4
5
McGraw-Hill/Irwin
10%
0.909
0.826
0.751
0.683
0.621
Rate
12%
0.893
0.797
0.712
0.636
0.567
14%
0.877
0.769
0.675
0.592
0.519
© The McGraw-Hill Companies, Inc., 2003
Time Value of Money
$100 × 0.797 = $79.70 present value
Periods
1
2
3
4
5
10%
0.909
0.826
0.751
0.683
0.621
Rate
12%
0.893
0.797
0.712
0.636
0.567
14%
0.877
0.769
0.675
0.592
0.519
Present value factor of $1 for 2 periods at 12%.
Atau dapat dihitung dengan mempergunakan kalkulator. Caranya: Tekan angka 1
dan tekan bagi 1,12, terus tekan sama dengan, yang akan menghasilkan 0.893 untuk
tahun pertama. Lalu tekan sama dengan lagi untuk menghasikan 0.797, dan
seterusnya.
© The McGraw-Hill Companies, Inc., 2003
McGraw-Hill/Irwin
Time Value of Money
An investment that involves a series
of identical cash flows at the end of
each year is called an annuity.
$100
$100
1
McGraw-Hill/Irwin
$100
2
$100
3
$100
4
$100
5
6
© The McGraw-Hill Companies, Inc., 2003
Quick Check 
How much would you have to put in the bank
today to have $100 at the end of five years if the
interest rate is 10%?
a. $62.10
b. $56.70
c. $90.90
d. $51.90
McGraw-Hill/Irwin
© The McGraw-Hill Companies, Inc., 2003
Quick Check 
How much would you have to put in the bank
today to have $100 at the end of five years if the
interest rate is 10%?
a. $62.10 $100  0.621 = $62.10
b. $56.70
c. $90.90
d. $51.90
McGraw-Hill/Irwin
© The McGraw-Hill Companies, Inc., 2003
Time Value of Money
Lacey Inc. purchased a tract of land on
which a $60,000 payment will be due
each year for the next five years. What is
the present value of this stream of cash
payments when the discount rate is 12%?
McGraw-Hill/Irwin
© The McGraw-Hill Companies, Inc., 2003
Time Value of Money
We could solve the problem like this . . .
Look in Appendix C of this Chapter for the
Present Value of an Annuity of $1 Table
Periods
1
2
3
4
5
McGraw-Hill/Irwin
10%
0.909
1.736
2.487
3.170
3.791
12%
0.893
1.690
2.402
3.037
3.605
14%
0.877
1.647
2.322
2.914
3.433
© The McGraw-Hill Companies, Inc., 2003
Time Value of Money
We could solve the problem like this . . .
Periods
1
2
3
4
5
10%
0.909
1.736
2.487
3.170
3.791
12%
0.893
1.690
2.402
3.037
3.605
14%
0.877
1.647
2.322
2.914
3.433
$60,000 × 3.605 = $216,300
McGraw-Hill/Irwin
© The McGraw-Hill Companies, Inc., 2003
Quick Check 
If the interest rate is 14%, how much would you
have to put in the bank today so as to be able to
withdraw $100 at the end of each of the next
five years?
a. $34.33
b. $500.00
c. $343.30
d. $360.50
McGraw-Hill/Irwin
© The McGraw-Hill Companies, Inc., 2003
Quick Check 
If the interest rate is 14%, how much would you
have to put in the bank today so as to be able to
withdraw $100 at the end of each of the next
five years?
a. $34.33
b. $500.00
c. $343.30 $100  3.433 = $343.30
d. $360.50
McGraw-Hill/Irwin
© The McGraw-Hill Companies, Inc., 2003
Quick Check 
If the interest rate is 14%, what is the present
value of $100 to be received at the end of the
3rd, 4th, and 5th years?
a. $866.90
b. $178.60
c. $ 86.90
d. $300.00
McGraw-Hill/Irwin
© The McGraw-Hill Companies, Inc., 2003
Quick Check 
If the interest rate is 14%, what is the present
value of $100 to be received at the end of the
3rd, 4th, and 5th years?
a. $866.90
b. $178.60
c. $ 86.90
d. $300.00
$100(3.433-1.647)= $1001.786 = $178.60
or
$100(0.675+0.592+0.519)= $1001.786 = $178.60
McGraw-Hill/Irwin
© The McGraw-Hill Companies, Inc., 2003
Typical Cash Outflows
Repairs and
maintenance
Working
capital
Initial
investment
Incremental
operating
costs
McGraw-Hill/Irwin
© The McGraw-Hill Companies, Inc., 2003
Typical Cash Inflows
Salvage
value
Release of
working
capital
Reduction
of costs
Incremental
revenues
McGraw-Hill/Irwin
© The McGraw-Hill Companies, Inc., 2003
Akhir Pertemuan 12:
Terima kasih
McGraw-Hill/Irwin
© The McGraw-Hill Companies, Inc., 2003