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Jason Fernando is a professional investor and writer who enjoys tackling and communicating complex business and financial problems.
Updated June 27, 2024 Fact checked by Fact checked by Ariel CourageAriel Courage is an experienced editor, researcher, and former fact-checker. She has performed editing and fact-checking work for several leading finance publications, including The Motley Fool and Passport to Wall Street.
Present value (PV) is the current value of a future sum of money or stream of cash flows. It is determined by discounting the future value by the estimated rate of return that the money could earn if invested. Present value calculations can be useful in investing and in strategic planning for businesses.
Present value is based on the concept that a particular sum of money today is likely to be worth more than the same amount in the future, also known as the time value of money. Conversely, a particular sum to be received in the future will not be worth as much as that same sum today.
For example, $1,000 today should be worth more than $1,000 five years from now because today's $1,000 can be invested for those five years and earn a return. If, let's say, the $1,000 earns 5% a year, compounded annually, it will be worth about $1,276 in five years.
Present value looks at it in reverse. For example, if you are due to receive $1,000 five years from now—the future value (FV)—what is that worth to you today? Using the same 5% interest rate compounded annually, the answer is about $784. In this formulation, the rate of return is known as the discount rate. The word "discount" refers to future value being discounted back to present value.
This is how to calculate the present value of a future sum of money:
Present Value = FV ( 1 + r ) n where: FV = Future Value r = Rate of return n = Number of periods \begin &\text = \dfrac>\\ &\textbf\\ &\text = \text\\ &r = \text\\ &n = \text\\ \end Present Value = ( 1 + r ) n FV where: FV = Future Value r = Rate of return n = Number of periods
To calculate the present value of a stream of future cash flows you would repeat the formula for each cash flow and then total them. Fortunately, you can easily do this using software or an online calculator rather than by hand.
A mentioned, the discount rate is the rate of return you use in the present value calculation. It represents your forgone rate of return if you chose to accept an amount in the future vs. the same amount today. The discount rate is highly subjective because it's simply the rate of return you might expect to receive if you invested today's dollars for a period of time, which can only be estimated.
In many cases, investors will use a risk-free rate of return as the discount rate. That is often the rate on U.S. Treasury bonds, which are considered virtually risk-free because they are backed by the U.S. government.
The higher the discount rate you select, the lower the present value will be because you are assuming that you would be able to earn a higher return on the money.
You can also incorporate the potential effects of inflation into the present value formula by using what's known as the real interest rate rather than the nominal interest rate.
As a simple example, let's say you have the choice of being paid $2,000 today or $2,200 one year from now. You expect that you could safely invest the $2,000 and earn 3% on it. Which is the better option?
In this case, $2,200 is the future value (FV), so the formula for present value (PV) would be $2,200 ÷ (1 + 0. 03) 1 . The result is $2,135.92. So if you were to be paid now you'd need to receive at least $2,135.92 (not just $2,000) to come out even.
In the present value formula shown above, we're assuming that you know the future value and are solving for present value.
It is also possible to solve for future value when you know the present value, using a formula like this: FV = PV x (1 + r) n .
So, plugging in the same numbers as in the example above:
FV= $2,000 × 1.03 = $2,060.
As both the present value and future value calculations show, you'd be better off waiting for the $2,200 a year from now than taking $2,000 now.
Of course, both calculations also hinge on whether the rate of return you chose is accurate.
Present value is calculated using three data points: the expected future value, the interest rate that the money might earn between now and then if invested, and number of payment periods, such as one in the case of a one-year annual return that doesn't compound.
With that information, you can calculate the present value using the formula:
Present Value = FV ( 1 + r ) n where: FV = Future Value r = Rate of return n = Number of periods \begin &\text = \dfrac>\\ &\textbf\\ &\text = \text\\ &r = \text\\ &n = \text\\ \end Present Value = ( 1 + r ) n FV where: FV = Future Value r = Rate of return n = Number of periods
Consider a scenario where you expect to receive a $5,000 lump sum payment in five years' time. If the discount rate is 8.25%, you want to know what that payment will be worth today. So you calculate the PV: $5,000 ÷ (1 + 0.0825) 5 = $3,363.80.
Present value is important because it allows investors and businesses to judge whether some future outcome will be worth making the investment today. It is also important in choosing among potential investments, especially if they are expected to pay off at different times in the future.
Present value is a way of representing the current value of a future sum of money or future cash flows. While useful, it is dependent on making good assumptions on future rates of return, assumptions that become especially tricky over longer time horizons.
