## Present Value Factor

A Present Value Factor (PVF) is a figure used in the calculation of the present value of a future sum of money or stream of cash flows. The PVF acts as a multiplier which converts future cash flows into today’s dollars.

The Present Value Factor is calculated using the following formula:

PVF = 1 / (1 + r)^n

Where:

- r is the discount rate or rate of return
- n is the number of periods until the cash flow occurs

The PVF is used in the present value formula as follows:

PV = FV * PVF

Where:

- PV is the present value
- FV is the future value

The present value factor can be thought of as the discounting part of the present value calculation, as it represents the effect of discounting the future value back to the present.

The PVF is often presented in the form of a table, known as a Present Value of $1 table (or PVIF table), which provides the PVFs for various combinations of r (discount rate) and n (number of periods). These tables are used to simplify present value calculations.

## Example of a Present Value Factor

Imagine you are set to receive $10,000 in 5 years, and you want to determine the present value of this future sum. You’ve decided to use a discount rate of 5% per annum for your calculations.

First, calculate the Present Value Factor using the formula:

PVF = 1 / (1 + r)^n

Where:

- r is the discount rate = 5% or 0.05
- n is the number of periods = 5 years

So,

PVF = 1 / (1 + 0.05)^5

PVF = 1 / 1.27628

PVF = 0.783526

This is your Present Value Factor.

Now, you use this factor to find the present value of the $10,000 to be received in 5 years:

PV = FV * PVF

PV = $10,000 * 0.783526

PV = $7,835.26

Therefore, the present value of $10,000 received 5 years from now at a 5% discount rate is approximately $7,835.26. The Present Value Factor helped us discount the future value to today’s dollars, reflecting the time value of money principle.