 # Present Value of Money By Yuriy Smirnov Ph.D.

## Definition

The time value of money concept states that \$1 today is worth more than \$1 in the future. The reason is rather simple. If you have \$1 today, you can invest it and receive more value in the future. So, the present value (PV) of money is the current worth of the amount that will be received at a specific date in the future. It is implied that the money is invested at a specific interest rate called the required rate of return.

Note that the present value is usually less than the future value except during times of negative interest rates!

## Formula

Calculating the present value is also called discounting and is the reverse of finding future value (FV), which is also called compounding. Furthermore, there is a relationship between the future value and the present value described by the following equation.

FVN = PV × (1 + r)N

Here FVN is a future value at the end of relevant period N, PV is a present value, r represents an interest rate earned per period, and N is a number of periods.

The equation above can be modified to find the PV as follows:

 PV = FV (1 + r)N

## Graphic Approach

As was mentioned above, the sum to be received in the future would be worth less than the same sum to be received today. Two drivers decrease the present value of a future amount of money.

1. Interest rate. The higher the interest rate, the faster the present value will decrease.
2. Number of periods. An amount of money to be received in the future even at a relatively low interest rate has very little present value. Thus, the further in the future the due date is extended, the lower the PV will be (gradually approaching zero).

## Examples

Let’s assume an investor intends to have \$100 after 5 years. The money could be invested at a 12.5% annual rate. We need to discount \$100 to find how much the money is worth now (zero point). Graphically, the discounting is shown in the figure below. We start with \$100 at the end of the fifth year and get \$88.89 worth at the end of the fourth year. Further, we discount \$88.89 and get \$79.01 at the end of the third year. This process continues for the remaining years until we get the present value of \$55.49 at the beginning of the first year (zero point on figure above).

PV End of 4th year = \$100 ÷ (1 + 0.125) = \$88.89

PV End of 3rd year = \$88.89 ÷ (1 + 0.125) = \$79.01

PV End of 2nd year = \$79.01 ÷ (1 + 0.125) = \$70.23

PV End of 1st year = \$70.23 ÷ (1 + 0.125) = \$62.43

PV Beginning of 1st year = \$62.43 ÷ (1 + 0.125) = \$55.49

The step-by-step approach demonstrated above is cumbersome, especially for a large number of periods. So we can reach the same result using the formula of PV mentioned above.

 PV = \$100 = \$55.49 (1 + 0.125)5

## Calculator and Discount Table

You can also find the present value of money using our online calculator or discount table.