Agriculture Reference
In-Depth Information
Concepts of the time value of money
Two of the four methods used to evaluate capital investments, net present value and internal
rate of return, are based on the time value of money. So an introduction to the concepts of
time value of money is needed prior to discussing the evaluation methods. This section
develops the basic ideas underlying the time value of money. The fi rst of those ideas is that
an interest rate serves as the pricing mechanism for the time value of money. The
interest
rate
refl ects investors' time preferences for money and serves as the exchange price between
money received today versus money received at some point in the future. In essence, a dollar
received today can be exchanged for a dollar plus an amount of interest (1 + i) received one
period in the future. The value for the dollar invested for multiple periods, with the interest
added to the principal to earn interest, would be calculated by multiplying the amount of the
investment by (1 + i)
n
, in which n is the number of periods. So, the formula used to calculate
the future value is:
Future Value of the Investment
(
)
×
(
)
n
Present Value of the Invest
1i
ment
1
=
Where
i nterest Rate
nNumber of Periods
Alternatively, one dollar received one period in the future exchanges for 1 ÷ (1 + i), or the
amount of the investment multiplied by (1 + i)
-n
. The amount in today's dollars is normally
referred to as the present value. The formula used to calculate present value is:
Present Value of Investment
=
(
Future Value of Investment
)
(
)
n
r
/
io
)
1
+
n
=
(
Future Value of Investment
)
×
(
)
−
1i
+
Where
Interest Rat
i
:
i
t e
nNumber of Periods
I
t
=
For example, $1,000 invested today for one year at 10 percent will be worth $1,100 at the
end of the year. So, the present value of $1,100 received in one year, at a 10 percent discount
rate would equal $1,000. The $1,100 investment has been “discounted” to its present value
of $1,000.
So for our example:
1
Future Value
(
)
$
1
0.1
.1
)
1
$
1 1
00
=
1
1
+
,
000
and
1
Present Value
(
.
)
000
$
1
1
/
(
1
.
0
$1
1
/ 1
1
$1
1
1
+
1
1
$
/
00
00
0
or
1
Present Value
(
)
−
$
1 00
1
1
0
.
+
1
