posted on 06-06-2019

# Present Value (PV)

Updated October 1, 2019

## What is Present Value (PV)?

Present value describes how much a future sum of money is worth today.

## How Does Present Value (PV) Work?

The formula for present value is:

PV = CF/(1+r)n

Where:
CF = cash flow in future period
r = the periodic rate of return or interest (also called the discount rate or the required rate of return)
n = number of periods

Let's look at an example. Assume that you would like to put money in an account today to make sure your child has enough money in 10 years to buy a car. If you would like to give your child \$10,000 in 10 years, and you know you can get 5% interest per year from a savings account during that time, how much should you put in the account now? The present value formula tells us:

PV = \$10,000/ (1 + .05)10 = \$6,139.13

Thus, \$6,139.13 will be worth \$10,000 in 10 years if you can earn 5% each year. In other words, the present value of \$10,000 in this scenario is \$6,139.13.

It is important to note that the three most influential components of present value are time, expected rate of return, and the size of the future cash flow. To account for inflation in the calculation, investors should use the real interest rate (nominal interest rate - inflation rate). If given enough time, small changes in these components can have significant effects.

## Why Does Present Value (PV) Matter?

The concept of present value is one of the most fundamental and pervasive in the world of finance. It is the basis for stock pricing, bond pricing, financial modeling, banking, insurance, pension fund valuation, and even lottery payouts. It accounts for the fact that money we receive today can be invested today to earn a return. In other words, present value accounts for the time value of money.

In the stock world, calculating present value can be a complex, inexact process that incorporates assumptions regarding short and long-term growth rates, capital expenditures, return requirements, and many other factors. Naturally, such variables are impossible to predict with perfect precision. Regardless, present value provides an estimate of what we should spend today (e.g., what price we should pay) to have an investment worth a certain amount of money at a specific point in the future -- this is the basic premise of the math behind most stock- and bond-pricing models.

Present value is one of the most important concepts in finance. Luckily, it's easy to calculate once you know a few tricks. Click here to learn How to Calculate Present Value Using Excel or a Financial Calculator.