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Learning objectives of this
article:
-
Define and explain present
value.
-
How is present value of a single
sum calculated?
-
What are the uses of present value concepts?
Contents:
We can divide present value concept
into two types. These are: (1) present value of a
single sum and (2) present value of an annuity. In
this article present value of a single sum is
explained. To understand the concept of the present
value of an annuity read present value of an
annuity article.
The present value concept implies
that a dollar in hand today is not equivalent to a
dollar in hand at some point in future. It is
because we can invest it to earn interest income and
at some point in future we will have more than a dollar.
Suppose $1 is invested at 12% interest. It will grow
to $1.12 after one year because the interest is
added to $1. After second year, it will grow to
$1.2544 because the interest for the second year is
calculated on $1.12. After third year it will grow
to 1.4049 as calculated below:
| At the beginning
of the first year |
No interest |
|
$1 |
| At the end of
the first year |
[$1 + ($1
×
12/100)] |
= |
$1.12 |
| At the end of
the second year |
[$1.12 + ($1.12
×
12/100)] |
= |
1.2544 |
| At the end of
the third year |
[$1.2544 + ($1.2544
×
12/100)] |
= |
1.4049 |
|
Notice that the interest for the
second year is calculated on $1.12 - principle ($1)
plus interest for the first year ($.12). When
interest is computed not only on the principle but
also on the interest, it is called compound
interest. The calculation of present value is the
reverse of compounding process. The $1 is the
present value of $1.4049 and $1.4049 is the future
value of $1 at 12% interest rate. Thus, if the rate
of interest is 12%, you would be indifferent to
either $1 today or $1.4049 after three years.
The present value of a single sum
can be easily calculated by the the following
formula:
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Where;
PV = Present value
FV = Future value
1/(1+i)n = Present value factor
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A young man has recently received an inheritance.
He wants to take a portion of inheritance and invest
it for his later years. His goal is to accumulate
$300,000 in 15 years. How much of the inheritance
should be invested if the money will earn 12 percent
per year compounded annually?
Solution:
We want to calculate the amount of money that is
required today to receive $300,000 after 15 years at
12% interest. In other words, we want to know the
present value of $300,000 at a 12% interest rate. It
is calculated as follows:
The present value concept is very often used in
businesses to evaluate proposed projects which will
generate cash flows in different periods. Today,
$20,000 of revenue is not equivalent to $20,000 in
revenue 10 years from now. Thus, businesses very
often use the present value concept to translate all
cash flows associated with a project into equivalent
dollars at one common point in time.
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