Agriculture Reference
In-Depth Information
Hence, there are two aspects of the time value of money. One is to take a present amount and
determine what that amount would equal at some point in the future, if invested at a given
interest rate, or compounding. The second is to take an amount in the future and determine
what that amount would equal in present dollars at a given interest or discount rate, or dis-
counting. Both aspects are discussed in the following sections.
Compounding
Compounding
is a method of calculating interest earned periodically, when that interest is
added to the principal and becomes part of the principal base on which future interest is
earned. A simple example is used to illustrate this method. Suppose the relative of a high
school graduate invests $1,000 at the time of graduation and plans to leave that money
invested during the next four years, while the graduate attends college. The relative plans to
give the college graduate the $1,000, plus the interest earned after four years, as a graduation
present. How much will the $1,000 be worth at the end of four years, if interest is 5 percent
and it is compounded annually?
Compounded annually means that interest earned during the fi rst year of our example
($1,000.00 × 0.05 = $50.00) will be added to the original investment (
principal
) ($1,000.00
+ $50.00 = $1,050.00), so that in year two, the entire principal investment ($1,050.00) will
earn interest at the 5 percent rate. Each year additional interest earned is added to the invest-
ment, and it too earns interest. When the formula discussed above is used the result would
be as follows:
4
(
)
$,
,
1
0.
.
$
$ ,
215 5
0
+
.
000
To make calculations simpler, managers often use tables of future values (
Table 13.1)
or use
fi nancial calculators or spreadsheets to quickly calculate the future value of an investment.
The factors presented in the tables are simply the factor calculations using the respective
interest rates and number of periods.
1.2155. So, the calculation would be:
(
)
$,
,
1
.
$ ,
1 215 5
0
.
000
Discounting
Discounting
is a method of converting a future value to a
present value
by adjusting the
future value by its discount rate. Suppose in this example, a relative gives a new high school
graduate a note promising him or her $1,000 upon graduation from college four years later.
Assuming that the time value of money is 5 percent (interest rate), what is the present value
of that gift? Although the formula is the same as before, this is more diffi cult to calculate.
4
Present Value
)
(
$
1
000
/
(
.
5
1
(
)
$1
/
1
000
5151
×
515
0
1
51
5
=
.
.
5151
×
1
.
51
.
.
000
822
$1
000
/1
2155
$.
7
0
=
=
