How to Calculate the Present Value of a Single Amount
Understanding the present value of a single amount of money is an important concept in investing, calculating valuations and cash flow, and in many other financial situations.
Three approaches to solving the problem of calculating the present value of a single amount (one type of time value of money calculation) are commonly employed: present value of a single amount formula; a financial calculator; or a spreadsheet application, such as Excel.
Calculating Present Value
The first thing to remember is that present value of a single amount is the exact opposite of future value. Here is the formula:
PV = FV [1/(1 + I)t]
Consider this problem:
Let's say that you have been promised $1,464 four years from today and the interest rate is 10%. The year (t) is year 4. We want to know what that $1,464 is worth today (the present value) given that the interest rate is 10% and the year is 4. Using the present value of a single amount formula, we can calculate the present value of $1,464 if the interest rate is 10% at the end of 4 years using the formula:
PV = 1,464 [1/(1 + .10)]4 = $1,000
Calculating present value is called discounting. Discounting cash flows, like our $1,464, simply means that we take inflation and the fact that money can earn interest into account. Since you do not have the $1,464 in your hand today, you cannot earn interest on it, so it is discounted today.
Clearly, using the formula is the long way to do present value problems. Using a financial calculator or a spreadsheet application is a more efficient way to calculate present value.
Calculating Present Value Using a Financial Calculator
You can find the present value of a single amount with any calculator with an exponential function, even non-financial calculators. It is best to use financial calculators because they have five keys which correspond to the five variables in time value of money equations. This present value of a single amount equation that we calculated above uses only four of those variables. Look at your financial calculator. Here are the key and inputs that you punch:
Punch N and 4 (for 2 years)
Punch I/YR and 10 (for the interest rate of 5%)
Punch FV and 1,464 (for the amount of money we are calculating interest on in year 4)
Punch PMT and PMT (there are no payments beyond the first one)
Punch PV and you will have your answer of $1,000
Calculating Present Value Using a Spreadsheet
Spreadsheets, such as Microsoft Excel, are well-suited for calculating time value of money problems and other mathematical functions. The function used for present value of a lump sum on an Excel spreadsheet is:
- Go to an Excel worksheet and click on Financial function.
- Pull down a menu and click on PV.
- This opens a box in which the information for the problem you are trying to solve is entered.
In the example we are using:
- Interest rate of 0.10
- Time period of 4 (years)
- Payments of 0
- Future value of $1,464 expressed as a positive number
- 0 is entered for the last item, which means that a payment, if any, would be at the end of the time period
This completes the function above. Go to the right-hand side of the worksheet at the top and click on Calculate. You will get the answer of $1,000.
This video lesson will help you with practicing calculations for present value of a single amount.