## What is the Present Value Factor?

The **Present Value Factor (PVF)** estimates the present value (PV) of cash flows expected to be received on a future date. The formula to calculate the present value factor (PVF) divides one by (1 + discount rate), raised to the period number.

## How to Calculate Present Value Factor (PVF)

The present value factor (PVF), often referred to as the “present value interest factor” (PVIF), is used to determine the present value of a cash flow anticipated to be received at a future point in time.

The core premise of the present value factor (PVF) is based upon the time value of money (TVM) concept, a core principle in corporate finance that sets the foundation for performing a cash flow analysis.

Simply put, the time value of money (TVM) states that a dollar received today is worth more than a dollar received in the future.

Why? The opportunity cost of capital is a critical part of analyzing the future cash flows expected to be generated by a company or project.

Given the present value factor (PVF), the current worth of a future cash flow (or stream of future cash flows) expected to be received on a later date can then be estimated.

In practice, the present value factor (PVF) is an integral component in estimating the future free cash flow (FCF) generated by a company, most often in the context of performing a discounted cash flow (DCF) analysis.

By understanding the present value factor (PVF), corporations and institutional investors such as hedge funds can make financially sound decisions in their capital allocation strategies, among other high-stake applications.

The steps to calculate the present value factor (PVF) and determine the present value (PV) of a cash flow are as follows.

- Step 1 → Divide 1 by (1 + Discount Rate) Raised to the Period Number
- Step 2 → Estimate the Future Value (FV) of a Cash Flow
- Step 3 → Multiply the Future Value (FV) by 1 ÷ (1 + Discount Rate) Raised to the Coinciding Period

## Present Value Factor Formula

The formula to calculate the present value factor (PVF) on a per-dollar basis is one divided by (1 + discount rate), raised to the period number.

**Present Value Factor (PVF) =**1

**÷**(1

**+**Discount Rate)

**^**Period

Where:

- Discount Rate (r) → The discount rate is the rate of return, or interest rate, expected to be earned on a particular investment.
- Period (n) → The period is the number of compounding periods from the present date on which the corresponding cash flow is expected to be received.

The more practical application of the present value factor (PVF) – from which the present value (PV) of a cash flow can be derived – multiplies the future value (FV) by the earlier formula.

**Present Value (PV) =**Future Value (FV)

**×**[1

**÷**(1

**+**r)

**^**Period]

The present value (PV) of a future cash flow is inversely proportional to the period number, wherein more time is required before the receipt of the cash proceeds reduces its present value (PV).

On that note, the present value factor (PVF) for later periods will be less than one under all circumstances, and reduce the further out the cash flow is expected to be received.

## Present Value of One Table (PV)

n | 1% | 2% | 3% | 4% | 5% | 6% | 8% | 10% |
---|---|---|---|---|---|---|---|---|

1 | 99.01% | 98.04% | 97.09% | 96.15% | 95.24% | 94.34% | 92.59% | 90.91% |

2 | 98.03% | 96.12% | 94.26% | 92.46% | 90.70% | 89.00% | 85.73% | 82.65% |

3 | 97.06% | 94.23% | 91.51% | 88.90% | 86.38% | 83.96% | 79.38% | 75.13% |

4 | 96.10% | 92.39% | 88.85% | 85.48% | 82.27% | 79.21% | 73.50% | 68.30% |

5 | 95.15% | 90.57% | 86.26% | 82.19% | 78.35% | 74.73% | 68.06% | 62.09% |

6 | 94.21% | 88.80% | 83.75% | 79.03% | 74.62% | 70.50% | 63.02% | 56.45% |

7 | 93.27% | 87.06% | 81.31% | 75.99% | 71.07% | 66.51% | 58.35% | 51.32% |

8 | 92.35% | 85.35% | 78.94% | 73.07% | 67.68% | 62.74% | 54.03% | 46.65% |

9 | 91.43% | 83.68% | 76.64% | 70.26% | 64.46% | 59.19% | 50.03% | 42.41% |

10 | 90.53% | 82.04% | 74.41% | 67.56% | 61.39% | 55.84% | 46.32% | 38.55% |

11 | 89.63% | 80.43% | 72.24% | 64.96% | 58.47% | 52.68% | 42.89% | 35.05% |

12 | 88.75% | 78.85% | 70.14% | 62.46% | 55.68% | 49.70% | 39.71% | 31.86% |

13 | 87.87% | 77.30% | 68.10% | 60.06% | 53.03% | 46.88% | 36.77% | 28.97% |

14 | 87.00% | 75.79% | 66.11% | 57.75% | 50.51% | 44.23% | 34.05% | 26.33% |

15 | 86.14% | 74.30% | 64.19% | 55.53% | 48.10% | 41.73% | 31.52% | 23.94% |

16 | 85.28% | 72.85% | 62.32% | 53.39% | 45.81% | 39.37% | 29.19% | 21.76% |

17 | 84.44% | 71.42% | 60.50% | 51.34% | 43.63% | 37.14% | 27.03% | 19.78% |

18 | 83.60% | 70.02% | 58.74% | 49.36% | 41.55% | 35.03% | 25.03% | 17.99% |

19 | 82.77% | 68.64% | 57.03% | 47.46% | 39.57% | 33.05% | 23.17% | 16.35% |

20 | 81.95% | 67.30% | 55.37% | 45.64% | 37.69% | 31.18% | 21.46% | 14.86% |

21 | 81.14% | 65.98% | 53.76% | 43.88% | 35.89% | 29.42% | 19.87% | 13.51% |

22 | 80.34% | 64.68% | 52.19% | 42.20% | 34.19% | 27.75% | 18.39% | 12.29% |

23 | 79.54% | 63.42% | 50.67% | 40.57% | 32.56% | 26.18% | 17.03% | 11.19% |

24 | 78.76% | 62.17% | 49.19% | 39.01% | 31.01% | 24.70% | 15.77% | 10.15% |

25 | 77.98% | 60.95% | 47.76% | 37.51% | 29.53% | 23.30% | 14.60% | 9.23% |