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# Example 20 - Present Value Calculation

This example applies to our online demo Time Value of Money Calculator. The C-Value! program for Windows works in a similar way and has a few more features. Note, our online demo TVM calculator is limited to calculations using interest rates between 2.0% and 8.9%

## The present value is today's value future cash flow or amount.

For greater detail about how values are entered into the TVM calculator, please see Example 1 - conventional mortgage or loan.

Background: The cash flow may be comprised of a single amount or a series of deposits, withdrawals or payments. When calculating the present value, the amount for the first entry is always "Unknown" and the date should be set to the current date. (This is true with two exceptions. See Existing Fixed Special Series.)

The classic PV example assumes some series of income and answers the question "How much should I accept today as a lump sum in lieu of the future income?". Such a question is often asked by an individual that is planning for an imminent retirement where they can take a lump sum amount instead of future pension payments. Attorneys will also use this calculation when advising clients on whether to accept a lump sum settlement or a series of future payments. Lottery winners will also want to use this calculation when determining if they should accept their winnings in one payment or paid out over time.

Let's assume you are the lottery winner.

The lottery commission has offered you the choice of receiving \$35,045.00 paid monthly for the next twenty years OR a single, lump sum payment of \$5,476,123.50. Which option should you select?

To calculate the present value of a cash flow, follow these steps:

1. Click the [New] button to clear any previous entries.
2. Set "Rounding" to "Ignore" by clicking on the "Rounding" button.
1. Click {Setup}. Select {Set calculation options...} to open the "Calculation Options" window. Select "Compute/Amortization Methods" tab.
1. For the "Compute Method" select the "Normal" option.
2. For the "Days Per Year" select 360.
3. Click on the [OK] button to close the Window.
1. Set compounding to "Daily".
2. Enter 5.5% for the "Nominal Annual Rate". The is the annual rate of return you are assuming you can earn on any investments you make. This is also known as your "discount rate".
3. Create the first event as a "Withdrawal". We use the withdrawal event here because we are assuming you want to "withdraw" from the lottery proceeds all the future "deposits" that will be made.
1. Set the "Date" to October 3, 2012. (mm/dd/yyyy)
2. For the "Amount", type a "U" for "Unknown".
3. Enter 1 for the "# Periods".
1. Create the 2nd event. It will be a "Deposit" event. We use the deposit event because we are going to assume that the lottery commission will be making deposits into an account for you.
1. Enter the "Date" as November 1, 2012 for this is the date the first payment would be due from the lottery commission.
2. Enter the "Amount" as \$35,045.00. This is the periodic winnings.
3. Enter 240 for "# Periods"
4. Select "Monthly" for "Frequency". The calculated "End Date" will be October 1, 2032. (The last payment from the lottery will be on this date.)

The first entry is always "Unknown" for any present value (PV) calculation.

1. Click on "Calc" to solve for the unknown present value. The result is \$5,057,830.93. In other words, assuming a future cash flow of 240 monthly deposits of \$35,045.00 each, the present value is \$5,057.830.93. This is less than the lottery is offering (\$5,476,123.50) as a single payment amount. Therefore, it would seem reasonable to accept the single payment from the lottery as having a greater value than the future deposits.
1. If you want to see a detail cash flow schedule showing what the deposits earn in interest, click on the "Schedule" tab above the input area

NOTE: This example is NOT considering tax consequences. As we all know, tax implications can be significant. You should seek the guidance of a tax professional if you were making this decision.

FURTHER NOTE: This example also does not consider risk. If you accept the single sum settlement option, will you be able to invest the money to equal the future value of the cash flow that the lottery commission is required to pay you? On the other hand, if you accept the series of future payments, what's the risk of the lottery not being able to meet their obligation? Granted, the risk might be slight. But if this example had been illustrating a settlement for a court case and a company had to pay you a future income stream, you have to asses whether or not the company will be able to meet their obligation. In that case, it might be better to take a single lump sum even if it is worth somewhat less than the future cash flow.

Our Time Value of Money calculator, C-Value!, or any other program, will never be able to make these decisions for you.

Cash flow schedule showing the calculated present value.

Schedule shows a 0.12 balance after last deposit. Nothing further is due.

Back to the online Time Value of Money Calculator.

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