# Present Value Factor

Present value factor (PVF) (also called present value interest factor (PVIF)) is the equivalent value today of $1 in future or a series of $1 in future. A table of present value factors can be used to work out the present value of a single sum or annuity.

There are multiple ways to find present value of a single value or an annuity: using the present value formula, using Microsoft Excel PV function, using some financial calculator or using present value tables.

Present value tables list present value factor for multiple interest rates and time periods. The interest rates are normally listed in the top row and time periods are tabulated in the first column and we need to find the value that is at the intersection of our given interest rate and time period.

## Formula

Present value factor of a single sum is given by the following formula:

PVF of a Single Sum = | 1 |

(1 + r/m)^{(n×m)} |

Present value factor of an ordinary annuity can be worked out by the following formula:

PVF of an Annuity = | 1 − (1 + r/m)^{-(n×m)} |

r/m |

The relationship between present value factor of an ordinary annuity and an annuity due is expressed below:

PVF of Annuity Due = PVF of Annuity × (1 + r/m)

Where **r** is the annual percentage interest rate, **n** is the number of years and **m** is the number of compounding periods per year.

## Example

If the interest rate is 10%, the present value factor for an amount received 10 years with semi-annual compounding is 0.3769:

PVF of a Single Sum = | 1 | = 0.3769 |

(1 + 10%/2)^{(10×2)} |

We just need to multiply the factor with the amount received to get the relevant present value:

Present Value of $5,0000 = $5,000 × 0.3769 = $1,884

The present value factor for an (ordinary) annuity with monthly compounding for 5 years at 10% APR is 47.0654:

PVF of an Annuity = | 1 − (1 + 10%/12)^{-(5×12)} | = 47.0654 |

10%/12 |

The present value factor for an annuity due with monthly compounding for 5 years at 10% APR is 47.4576:

PVF of Annuity Due = PVF of Annuity × (1 + 10%/12) = 47.4576

Written by Obaidullah Jan, ACA, CFA and last modified on