# Value of an Annuity Calculator

Cash Flow Amount?:
Number of Cash Flows? (#):
Annual Discount Rate?:
Today's Date? (m/d/y):
//
First Cash Flow Date? (m/d/y):
//
Cash Flow Frequency?:
Compounding Frequency?:

Present Value:
Sum of Cash Flows:
Last Cash Flow Date:

## Present Value of an Annuity Help

An "annuity" is a fixed sum of money paid someone each period, typically for the rest of their life. More loosely, it means any regular cash flow stream which may or may not have an explicit declared term. If an annuity is scheduled for 10 annual payments of \$10,000 each, the sum of the payments is \$100,000. However, if instead of being paid in 10 annual installments you wanted to receive a single sum, you would not receive \$100,000. Why? Because if you receive a single sum today, there is no future risk of not receiving the amount due. Therefore, you would take less today to eliminate the risk of not collecting all payments.

If you are scheduled to receive a series of regular fixed payments of \$2,500 for 20 years, what is today's cash value, assuming a 5.5% annual discount rate? The "annual discount rate" is the rate of return that you expect to receive on your investments. This is a personal number. There is no "right" answer, though you want to use a realistic number based on your investment history. The discount rate will vary from individual to individual.

Enter \$2,500 in the "Cash Flow Amount" field (never type the currency symbol or commas). The cash flow frequency will be monthly. Enter 240 for the "Number of Cash Flows" (240 months is 20 years). Assume monthly compounding. Since the first payment isn't due until a month from now, set the "First Cash Flow Date" to one month from "Today's Date".

The PV is \$363,431.62. Thus, you could accept \$363,431.62 today in lieu of receiving \$2,500 a month for twenty years. For you, the two are equal.

A note or two about "Compounding Frequency". The "Exact/Simple" option is actually exact day simple interest. When you make this selection, the calculator uses no compounding and the exact number of days between cash flow dates are used. The "Daily" option uses the exact number of days between dates, but daily compounding is assumed. If you are considering receiving a single amount in lieu of a cash flow stream, the "Exact/Simple" compounding option is the most conservative setting. That is, it will result in the highest present value calculation.

The prior version of this calculator provided you with an option to set the "Cash Flow Timing". Since you can enter "Today's Date" and the "First Cash Flow Date" this option is no longer necessary because the calculator will calculate the exact dates the cash flow is due.

One additional point about "Today's Date". This input does not have to be set to the current date. The date you use is the date you want to know the present value. If you were closing on a deal to buy a mortgage and the deal is expected to close in a week, then you would want to use the date of the closing for "Today's Date" so you'll know the present value on the closing date.

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Currency
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Conventions:
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Update 03/04/2013 (BETA): Changed technology used which is both faster and more reliable. You also don't have to clear the calculator prior to each calculation. Even more importantly, calculator now uses actual dates to calculate the present value. This makes it suitable for use as an auditing tool and for calculating the PV of court settlements. Please let us know of any problems — contact us

The present value of a series is also known as the present value of an annuity. Annuity is a financial term used to refer to any series of fixed, regular payments (cash flows) over a specific period of time. The above present value (PV) calculator is used for calculating today's value of a series of future cash flows.

You may also use this calculator to calculate the present value of a single amount. Enter 1 for "Number of Cash Flows" and set the dates as needed. If you set the "First Cash Flow Date" to 10 years into the future, the calculator will calculate the PV of a single amount due in 10 years.

## When is the Value of an Annuity Calculator Used?

Frequently, this a calculator is used to determine the cash value of a court settlement. If a settlement dictates that \$2,500 is to be received monthly for twenty years but the party receiving the settlement is not comfortable waiting twenty years, then they could agree to settle for a lesser cash amount today. The amount they would be willing to settle for would be the present value. The PV varies from individual to individual depending upon the "annual discount rate" used. The "discount rate" is the rate of return the user expects to earn on their investments.

Investors also frequently use a present value of a series calculator. For example, mortgages are often bought and sold. When an investor buys a mortgage, they need to use a PV of an annuity calculator to determine how much to pay for a mortgage. A thirty year, fixed rate mortgage may have been issued ten years ago at a 6.5% annual rate. Today, an investor might be willing to buy a mortgage for a 4.0% return. This calculator tells them how much they can pay to realize the return they desire. Note, that even if the investor wanted to make a 6.5% return (or more), they would still need to use this calculator to know how much to pay when buying the mortgage. The investor does not pay the holder of the mortgage the balance due. Why? Because they are not receiving the balance from the debtor today. They are receiving the stream of future mortgage payments.

The date entered for "Today's Date" and "First Cash Flow Date" may be the same date.

Please click on the above "Help" button for details.

## General Periodic Interest Rate Equation

Periodic Rate = Annual Rate / Periods Per Year / 100

Example of common periods per year: Annually: 1, Monthly: 12, Weekly: 52, Daily: 365.

## Calculating Present Value of an Annuity — PV Equation

A = (1-(1+Periodic Rate)(-Total Periods+Timing)) / Periodic Rate

PV = Cash Flow Amount * (Timing + A)

Timing is the timing of the cash flows. If the cash flows are received at the start of the period, the value for timing is 1, otherwise, if the cash flows are received at the end of the period, the timing is 0.

## Example of Solving For Present Value

Your former neighbors had provided their buyer with seller financing when they sold their home a little over ten years ago. The former owner now wants all the cash and you have the opportunity to buy the mortgage. There are 230 remaining monthly payments of \$1565.81. Due to the risks you have assessed, you want to earn a 10% return. How much should you pay for the mortgage?

First, calculate the periodic rate.

Periodic Rate = 0.0083333... = 10.0% / 12 / 100

A = 102.2076766 = (1-(1+0.00833333...)(-230+0)) / 0.00833333...

PV = \$160,037.80 = 1565.81 * ( 0 + 102.2076766 )

Any price you can negotiate that is less than \$160,037.80 means that your rate of return will be better than 10.0%. This is assuming that all payments due are paid on time.