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Present Value of a Single Sum:

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Learning objectives of this article:

  1. Define and explain present value.
  2. How is present value of a single sum calculated?
  3. What are the uses of present value concepts?


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.

Definition and Explanation:

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:


PV = Present value

FV = Future value

1/(1+i)n = Present value factor


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?


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:

FV = $300,000

n = 15

i = 12%

PV = $300,000 0.18270*

= 54,810

*Present value of $1 table - 1/(1+i)n).

Uses of Present Value Concept in Business:

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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More study material from this topic:

Methods for the evaluation of capital investment analysis
Average rate of return or accounting rate of return method
Cash payback method
Net present value method
Internal rate of return method
Simple interest
Future value of a single sum
Future value of an annuity
Present value of a single sum
Present value of an annuity
Qualitative consideration in capital investment analysis
Capital investment analysis and unequal proposal lives
Capital rationing decision process
Difference between simple interest and compound interest
Difference between nominal and effective interest rate
Future value of $1 table
Present value of $1 table
Present value of ordinary annuity table
Future value of ordinary annuity table



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