Present Value

# Present Value Moneyzine Editor
Last updated 23rd Sep 2022
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The concept of present value doesn't have to be difficult to understand. However, it is an important investment theory to know because it's aligned with a second important concept: the time value of money. Calculations involving present value are used when creating business cases, examining annuities, as well as determining cash flows in perpetuity.

In this article, we're going to be talking about the concept of present value. As part of that discussion, we'll talk about the time value of money, and why a dollar received 10 years from now doesn't have the same value as a dollar received today. We'll also talk about some of the more common calculations that leverage this concept. Finally, we'll provide a link to our online calculator.

## Present Value Theory

The assumption behind all present value calculations is that a dollar received in the future does not have the same value as a dollar received today. For example, an investor will place a greater value on \$1,000 received today than \$1,000 received 12 months from now. That's because the investor has the option of taking the \$1,000 received today and investing it in a relatively low risk account such as a money market fund or certificate of deposit that will earn interest.

In other words, the investor has the opportunity to put the \$1,000 to work and earn interest, or create additional value. The opportunity to earn more money on the original investment means the worth of that investment will be greater than \$1,000 in 12 months. Using the same reasoning, \$1,000 received in 12 months, will have a present value that is less than \$1,000. These examples demonstrate how this concept supports the time value of money theory.

### Present Value Calculations

The calculation of present value is relatively straightforward, and can be used to solve several different types of problems. The two most commonly used forms include:

• Discounting the future value of an investment
• Determining the value of a cash flow that goes on forever (in perpetuity).

Each of these calculations is detailed in the sections below.

#### Example 1: Present and Future Value

The relationship between the present value and future value of an investment is demonstrated using the following formula:

PV = FV / (1+i)N

where:

• PV = present value of the investment
• FV = future value of the investment
• i = the interest rate, also referred to as the discount rate
• N = number of periods

In this first example, we're going to determine the present value of \$1,000 received 10 years from now, using a discount rate of 10% per year. Using the above formula:

• FV = \$1,000
• i = 10% / year
• N = 10 years

Solving this example:

PV =\$1,000 / (1+0.10)10 PV =\$1,000 / (1.10)10 PV =\$1,000 / 2.59374 PV = \$385.54

#### Example 2: Present Value and Perpetuities

In this second example, we're going to find the present value of a cash flow that goes on in perpetuity. An example of a cash flow in perpetuity is an annuity that pays indefinitely. The relationship between the present value and this type of perpetuity is as follows:

PV = C / i

where:

• PV = present value of the investment
• C = cash payment received in perpetuity
• i = the interest rate on the investment

In this second example, we're going to determine the present value of \$1,000 received each year, in perpetuity, using an interest rate of 10% per year. Using the above formula, we know:

• C = \$1,000
• i = 10% or 0.10

Solving this example:

PV =\$1,000 / 0.10 PV =\$10,000

### Present Value Calculators

As promised, we're going to provide links to several useful online calculators. The first is a simple present value calculator. That tool can be used to solve problems that are similar to the first example above. The second is a present value of an annuity calculator, which can be used to solve problems similar to the second example appearing in this article.

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