What Is Present Value? Formula and Calculation

What Is Present Value?

Calculating present value allows an investor to compare the potential performance of various investments by determining the current worth of the number of dollars that each investment will return by a future date.

Present value (PV) is based on the concept that a sum of money in hand today is probably worth more than the same sum in the future because it can be invested and earn a return in the meantime.

Present value (PV) is calculated by discounting the future value by the estimated rate of return that the money could earn if invested.

Understanding Present Value

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. This is also known as the time value of money. Based on the same logic, a sum of money that will be received at a future date will not be worth as much as that same sum today.

For example, $1,000 in hand today should be worth more than $1,000 five years from now because it 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 works in reverse by calculating what a future amount of money would be worth today. 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.

Present Value Formula and Calculation

This is how to calculate the present value of a future sum of money:

$\begin{aligned} &\text{Present Value} = \dfrac{\text{FV}}{(1+r)^n}\\ &\textbf{where:}\\ &\text{FV} = \text{Future Value}\\ &r = \text{Rate of return}\\ &n = \text{Number of periods}\\ \end{aligned}$​Present Value=(1+r)nFV​where:FV=Future Valuer=Rate of returnn=Number of periods​

1. Use the future amount that you expect to receive as the numerator of the formula.
2. Estimate the interest rate that you might earn between now and the future payment date if you were to invest the money today, and plug that in as a decimal for the “r” in the denominator.
3. Indicate the time period as the exponent “n” in the denominator. So, if you want to calculate the present value of an amount you expect to receive in three years, you would plug in the number 3.

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.

It’s easier to do this using an online calculator rather than by hand.

Determining the Discount Rate

As 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 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.

Most investors 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.

Benefits of Present Value

• Present value can clarify whether an investment’s estimated rate of return makes it worth pursuing. Businesses and investors often set a hurdle rate, indicating the minimum rate of return they would need to achieve.
• Present value can be helpful to investors and companies in deciding among competing investments.

Limitations of Present Value

• Present value requires making assumptions about the discount rate, which may or may not prove accurate.
• Because they involve assumptions, present value calculations can be manipulated by those who favor a particular investment, such as corporate managers pushing a pet project.

Example of Present Value

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 $2,000) to come out even.

Calculating Future Value vs. Present Value

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 could be proved wrong if you choose the wrong estimate for your rate of return.

Explain It Like I’m Five

Present value shows what money you’ll receive in the future is worth today. Because money can earn interest over time, a dollar today is usually worth more than a dollar received later. Present value helps investors compare investment opportunities that pay off at different times.

The Bottom Line

Present value is a way of representing the current value of a future sum of money or future cash flows.

While useful, present value calculations rely on assumptions about future rates of return. These assumptions become especially tricky over longer time horizons.