The present value is the value of a future sum of money expressed in today’s dollars at a certain interest rate. Present value relies on the concept of the time value of money, where one dollar today is worth more than a dollar received in the future. You can invest the dollar you have today, and it can grow over time at a rate of return or interest. Conversely, the dollar you will receive “tomorrow” cannot be invested today and thus does not have the same potential to increase in value.
Definitions and Examples of Present Value
The basic principle behind the time value of money is simple: one dollar today is worth more than a dollar received in the future. You can invest the dollar you have today, and it can grow over time at a rate of return or interest. The dollar you will receive “tomorrow” cannot be invested today and thus does not have the same potential to increase in value.
Note: Present value is the value of future cash flows received today at an interest rate 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 an annual interest rate of 2%, it will be worth $1,020 at the end of the year ($1,000 × 1.02). Therefore, $1,000 is the present value of $1,020 in one year at a 2% interest rate or discount rate.
The discount rate significantly affects present value. What if we change the discount rate in our example from 2% to 5%? How much money do we need to invest at 5% to get $1,020 at the end of the year? The calculation would look like this: $971.43 × 1.05 = $1,020.
So instead of needing $1,000, we only need $971.43 to reach the same future amount. We will talk about this calculation later.
Types of Present Value
Present Value of a Single Sum
Think of the present value of a future single sum as the amount you need to invest today at a compound interest rate to accumulate to the required amount in the future. In the example above, the amount of money you need to invest today to accumulate to $1,020 next year at 2% is $1,000.
Present Value of a Series of Equal Cash Flows
Retirement. Joseph and Josephine have decided they will need an income of $80,000 per year when they reach age 65, expecting to live until age 85. Joseph and Josephine need to know the amount of money they need at age 65 to produce an income of $80,000 for 20 years, assuming they will earn 4% (the discount rate).
Retirement payment = $80,000
Years of payment = 20
Discount rate = 4%
Retirement factor from present value table = 13.9503
Present value = $80,000 × 13.9503 = $1,116,024
By the time they reach age 65, Joseph and Josephine will need $1,116,024 to produce an income of $80,000 for 20 years at a 4% rate.
Present Value of Unequal Cash Flows
When businesses invest in new equipment or projects, it may take time to see results. The forecasts for revenues or cash flows may be low at first but increase over time. When making investment decisions, businesses should analyze the present value of unequal cash flows.
How Does Present Value Work?
The easiest way to calculate present value is to use one of the many free online calculators or a financial calculator app like the HP12C Financial Calculator, available on Google Play and the Apple App Store. Most spreadsheet programs also have present value functions.
Present value tables
Method
Another easy way to calculate present value is to use a present value table. These tables contain factors and interest rates for annual payments and large sums of money. It looks like this:
Present Value Table for a Lump Sum
Years 1% 2% 3% 4% 5%
1 0.990 0.980 0.971 0.962 0.952
2 0.980 0.961 0.943 0.925 0.907
Present Value Table for a Series of Equal Cash Flows
Years 1% 2% 3% 4% 5%
1 0.9901 0.9804 0.9709 0.9615 0.9524
2 1.9704 1.9416 1.9133 1.8861 1.8594
If we want to know the present value of $100,000 after two years at a rate of 4%, for example, the calculation would be as follows:
Future Value = $100,000
Present Value Factor at 4% for two years = 0.925 (see the first table above)
Present Value = 100,000 × 0.925 = $92,500
A real-life example of present value
Joseph and Josephine are planning for their retirement. They have decided that they will need an income of $80,000 per year when they reach the age of 65, and they expect to live until age 85. Joseph and Josephine need to know how much money they will need at age 65 to generate an income of $80,000 for 20 years, assuming they will earn 4% (discount rate).
Retirement Payment = $80,000
Payment Years = 20
Discount Rate = 4%
Retirement Factor from the Present Value Table = 13.9503
Present Value = $80,000 × 13.9503 = $1,112,024
By the time they reach age 65, Joseph and Josephine will need $1,112,024 to generate an income of $80,000 for 20 years at a rate of 4%.
Present Value vs Future Value
We can also measure future value. Future value is what an amount of money invested today will grow to over time at a given interest rate.
As discussed earlier, a deposit of $1,000 in a savings account at an annual interest rate of 2% has a future value of $1,020 at the end of the first year. Let’s take a look at what happens at the end of the second year:
The $1,000 deposit becomes $1,040.40. The additional change is a return of 2% on the $20 earned at the end of the first year. The process of earning interest on interest is called “compounding,” and it has a powerful effect on the future value of an investment.
Future value is the reverse image of present value.
Taking the Lesson
Present value measures the impact of time on money. Present value is the value of a monetary amount or a series of cash flows that will be paid in the future valued at today’s money at a rate of interest known as the “discount rate.” Present value is used for planning financial goals and making investment decisions.
Source: https://www.thebalancemoney.com/what-is-present-value-5194661
Leave a Reply