Understanding the concept of present value and how to calculate the present value of a single amount is important in real-life situations. Examples include investing, valuing financial assets, and calculating cash flow.
Calculating Present Value
Let’s say you just graduated from college and you’re going to work for a few years, but your dream is to own your own business. You have some money now, but you don’t know how much, if any, you will be able to save before you buy your business in five years.
You can use the calculation for present value of a single amount to find out how much you should deposit or invest today if the interest rate (or capital gains plus dividends) is 5% and you will need $25,000 to buy your business in five years.
Calculating Present Value Using the Formula
Here is the formula for present value of a single amount (PV), which is the exact opposite of future value of a lump sum:
PV = FV x [1/(1 +i)t]
In this formula:
- FV = the future value
- i = interest rate
- t = number of time periods
You can fill in the formula with your specific information including the future value of the money you'll need to buy your business ($25,000), the interest rate you'll receive in this time (5%), and the time period in which you hope to buy your business (five years):
PV = $25,000 x [1/(1 + .05)5]
PV = $19,588
In this case, if you have $19,588 now and you can earn 5% interest on it for the next five years, you can buy your business for $25,000 without adding any more money to your account. This is the concept of present value of a single amount. It shows you how much a sum that you are supposed to have in the future is worth to you today. We are applying the concept to how much money we need to buy a business. Given our time frame of five years and a 5% interest rate, we can find the present value of that sum of money.
Note
Calculating present value is calleddiscounting. Discounting cash flows, like our $25,000, simply means that we take inflation and the fact that money can earn interest into account. Since you do not have the $25,000 in your hand today, you cannot earn interest on it, so it is discounted today.
Calculating Present Value Using the Tables
A set of tables, known as the time value of money interest factor tables, were developed and can be used in place of the formula to simplify the calculation. The value in the table is used in place of this part of the formula: [1/(1 + i)t]
:max_bytes(150000):strip_icc()/ScreenShot2020-02-06at1.30.36PM-07a6d5deff0d48c2a44378f0d3f4000c.png "Calculating the Present Value of a Sum of Money (1)")
In order to get the value that you will insert into the formula in the example used in this problem from earlier, we can use the table in the image above.
Go down the left column to the number of time periods (five) and across the row to the interest rate column that matches your interest rate (5%). You will find the number .7835. Insert this number into the formula in place of [1/(1 + i)t], like so:
PV = $25,000 x .7835
PV= $19,588
Calculating Present Value Using a Financial Calculator
You can calculate the present value of a single amount with just about any financial calculator. With some variations based on the brand of calculator, you can enter the following based on the numbers from the previous example:
- Press 5 N
- Press 5 I/YR
- Press 0 PMT
- Press 25000 FV
- You will get 19,588. Drop the negative symbol in front of it.
Calculating Present Value Using a Spreadsheet
Spreadsheets, such asMicrosoft Excel or Google Sheets, are well-suited for calculating time-value-of-money problems and other mathematical functions. Here's how it works:
- Open a new worksheet and click on Financial function.
- Scroll down the menu and click on PV.
- This opens a box in a cell in which the information for the problem you are trying to solve will be entered.
In the example used in our problem from earlier, you can enter:
- The interest rate as 0.05
- The time period as 5
- The payments as 0
- The future value as $25,000, expressed as a positive number
- If payments are made at the end (0) or the beginning (1)
It will look like this once all of the info is added:
PV = (5%, 5, 0, 25000, 0)
Click enter on your keyboard and you'll see the value returned is -19,588. Remove the negative symbol in front of it and you get 19,588 or $19,588, as we got with our other formulas.
The Bottom Line
The present value of a single amount allows us to determine what the value of a lump sum to be received in the future is worth to us today. It is worth more than today due to the power of compound interest.
There are five key elements in all time-value-of-money calculations. These elements are present value and future value, as well as the interest rate, the number of payment periods, and the payment principal sum.
