**Present value** is what a sum of money in the future is worth in today’s dollars at a rate of interest.

## Definitions and Examples of Present Value

The basic principle behind the time value of money is simple: One dollar today is worth more than one dollar you will receive in the future. This is because you can invest the dollar you have today, and it can grow over time at a rate of return, or interest. The dollar you receive “tomorrow” can’t be invested today, and therefore doesn’t have the same potential to increase in value.

### Note

Present value is what cash flow received in the future is worth today at a rate of interest called the “discount” rate.

Here’s an easy way to look at present value. If you invest $1,000 in a savings account today at a 2% annual interest rate, it will be worth $1,020 at the end of one year ($1,000 x 1.02). Therefore, $1,000 is the present value of $1,020 one year from now at a 2% interest, or discount, rate.

The discount rate has a big impact on the present value. What if we changed the discount rate in our example from 2% to 5%? How much money do we need to invest at 5% to have $1,020 at the end of one year? The calculation would look like this: $971.43 X 1.05 = $1,020.

So instead of needing $1,000, we only need $971.43 to reach the same resulting amount. More on this calculation later.

## Types of Present Value

### Present Value of a Lump Sum

Think of the present value of a lump sum in the future as the money you would need to invest today at a rate of interest that would accumulate to the desired amount in the future. In the example above, the amount of money you need to invest today that will accumulate to $1,020 a year in the future at 2% is $1,000.

### Present Value of an Annuity

An annuity is a series of equal payments received for a fixed period of time. For example, lottery winners often have the option to receive their prize money in equal payments over 20 years.

The present value of an annuity is the value of all the payments received over a period of time in the future in today’s dollars, at a certain discount rate.

One way to think of the present value of an annuity is a car loan. The initial loan is the present value. The annuity is the principal and interest payments you make every month until the balance of the loan is zero.

### Present Value of Unequal Cash Flows

When a business invests in new equipment or a project, it may take time to see results. The revenue or cash flow projected may be low at first but grow over time.

### Note

When making investment decisions, a business has to analyze the present value of unequal cash flows.

## How Present Value Works

The easiest way to calculate present value is to use one of the many free calculators on the internet, or a financial calculator app like the HP12C Financial Calculator, available on Google Play and in the Apple App Store. Most spreadsheet programs have present-value functions as well.

### Present Value Tables

Another easy way to calculate present value is to use a present value table. These tables have factors and interest rates for annuity payments and lump sums. They look like this:

Present Value of a Lump Sum | |||||
---|---|---|---|---|---|

Years |
1% |
2% |
3% |
4% |
5% |

1 |
.990 | .980 | .971 | .962 | .952 |

2 |
.980 | .961 | .943 | .925 | .907 |

Present Value of an Annuity | |||||
---|---|---|---|---|---|

Years |
1% |
2% |
3% |
4% |
5% |

1 |
.9901 | .9804 | .9709 | .9615 | .9524 |

2 |
1.9704 | 1.9416 | 1.9133 | 1.8861 | 1.8594 |

If we want to know the present value of $100,000 two years in the future at 4%, for instance, the calculation is:

Future value = $100,000

Present value factor at 4% for two years = .925 (see first table above)

Present value = $100,000 X .925 = $92,500

### Real-World Example of Present Value

Joseph and Josephine are planning for their retirement. They decide that they will need an income as of age 65 of $80,000 a year, and they project living to age 85. Joseph and Josephine need to know how much money they need at age 65 to produce $80,000 of income for 20 years, assuming they will earn 4% (the discount rate).

Annuity payment = $80,000

Years paid = 20

Discount rate = 4%

Annuity factor from a present value table = 13.9503

Present value = $80,000 X 13.9503 = $1,116,024

At age 65, Joseph and Josephine will need $1,116,024 to produce $80,000 of income for 20 years at 4%.

### Unequal Cash Flows

No matter what method you use–spreadsheet, calculator, table, or formula–calculating the present value of unequal cash flows takes a bit of work. An Excel spreadsheet is the easiest way to use the NPV (net present value) function; however, here’s an example of how to use the tables.

Year |
Cash Flow |
4% Present Value Factor |
Present Value |

1 |
$4,500 | .962 | $4,329 |

2 |
$5,200 | .925 | $4,810 |

3 |
$8,000 | .889 | $7,112 |

4 |
$9,200 | .855 | $7,866 |

5 |
$10,000 | .822 | $8,220 |

Total |
$36,900 | $32,337 |

## Present Value vs. Future Value

We can also measure future value. Future value is what a sum of money invested today will be worth over time, at a specified rate of interest.

As discussed earlier, $1,000 deposited in a savings account at a 2% annual interest rate has a future value of $1,020 at the end of one year. Let's look at what happens at the end of two years:

That $1,000 deposit becomes $1,040.40. The extra change is the 2% return on the $20 earned at the end of Year 1. The process of interest earning interest is called “compounding,” and it has a powerful effect on the future value of an investment.

Future value is the mirror image of present value.

### Key Takeaways

- Present value measures the effect of time on money.
- Present value is what a sum of money or a series of cash flows paid in the future is worth today at a rate of interest called the “discount” rate.
- Present value is used to plan for financial goals and to make investment decisions.