## What Is Present Value (PV)?

Present value (PV) is the current value of a future sum of money or stream of cash flows given a specified rate of return. Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower the present value of the future cash flows. Determining the appropriate discount rate is the key to properly valuing future cash flows, whether they be earnings or debt obligations.

### Key Takeaways

- Present value states that an amount of money today is worth more than the same amount in the future.
- In other words, present value shows that money received in the future is not worth as much as an equal amount received today.
- Unspent money today could lose value in the future by an implied annual rate due to inflation or the rate of return if the money was invested.
- Calculating present value involves assuming that a rate of return could be earned on the funds over the period.

#### Present Value

## Understanding Present Value (PV)

Present value is the concept that states an amount of money today is worth more than that same amount in the future. In other words, money received in the future is not worth as much as an equal amount received today.

Receiving $1,000 today is worth more than $1,000 five years from now. Why? An investor can invest the $1,000 today and presumably earn a rate of return over the next five years. Present value takes into account any interest rate an investment might earn.

For example, if an investor receives $1,000 today and can earn a rate of return of 5% per year, the $1,000 today is certainly worth more than receiving $1,000 five years from now. If an investor waited five years for $1,000, there would be an opportunity cost or the investor would lose out on the rate of return for the five years.

## Inflation and Purchasing Power

Inflation is the process in which prices of goods and services rise over time. If you receive money today, you can buy goods at today's prices. Presumably, inflation will cause the price of goods to rise in the future, which would lower the purchasing power of your money.

Money not spent today could be expected to lose value in the future by some implied annual rate, which could be inflation or the rate of return if the money was invested. The present value formula discounts the future value to today's dollars by factoring in the implied annual rate from either inflation or the rate of return that could be achieved if a sum was invested.

## Discount Rate for Finding Present Value

The discount rate is the investment rate of return that is applied to the present value calculation. In other words, the discount rate would be the forgone rate of return if an investor chose to accept an amount in the future versus the same amount today. The discount rate that is chosen for the present value calculation is highly subjective because it's the expected rate of return you'd receive if you had invested today's dollars for a period of time.

In many cases, a risk-free rate of return is determined and used as the discount rate, which is often called the hurdle rate. The rate represents the rate of return that the investment or project would need to earn in order to be worth pursuing. A U.S. Treasury bond rate is often used as the risk-free rate because Treasuries are backed by the U.S. government. So, for example, if a two-year Treasury paid 2% interest or yield, the investment would need to at least earn more than 2% to justify the risk.

The discount rate is the sum of the time value and a relevant interest rate that mathematically increases future value in nominal or absolute terms. Conversely, the discount rate is used to work out future value in terms of present value, allowing a lender to settle on the fair amount of any future earnings or obligations in relation to the present value of the capital. The word "discount" refers to future value being discounted to present value.

The calculation of discounted or present value is extremely important in many financial calculations. For example, net present value, bond yields, and pension obligations all rely on discounted or present value. Learning how to use a financial calculator to make present value calculations can help you decide whether you should accept such offers as a cash rebate, 0% financing on the purchase of a car, or pay points on a mortgage.

## PV Formula and Calculation

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

- Input the future amount that you expect to receive in the numerator of the formula.
- Determine the interest rate that you expect to receive between now and the future and plug the rate as a decimal in place of "r" in the denominator.
- Input 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 the number three in for "n" in the denominator.
- There are a number of online calculators, including this present value calculator.

## Future Value vs. Present Value

A comparison of present value with future value (FV) best illustrates the principle of the time value of money and the need for charging or paying additional risk-based interest rates. Simply put, the money today is worth more than the same money tomorrow because of the passage of time. Future value can relate to the future cash inflows from investing today's money, or the future payment required to repay money borrowed today.

Future value (FV) is the value of a current asset at a specified date in the future based on an assumed rate of growth. The FV equation assumes a constant rate of growth and a single upfront payment left untouched for the duration of the investment. The FV calculation allows investors to predict, with varying degrees of accuracy, the amount of profit that can be generated by different investments.

Present value (PV) is the current value of a future sum of money or stream of cash flows given a specified rate of return. Present value takes the future value and applies a discount rate or the interest rate that could be earned if invested. Future value tells you what an investment is worth in the future while the present value tells you how much you'd need in today's dollars to earn a specific amount in the future.

## Criticism of Present Value

As stated earlier, calculating present value involves making an assumption that a rate of return could be earned on the funds over the time period. In the discussion above, we looked at one investment over the course of one year. However, if a company is deciding to go ahead with a series of projects that has a different rate of return for each year and each project, the present value becomes less certain if those expected rates of return are not realistic. It's important to consider that in any investment decision, no interest rate is guaranteed, and inflation can erode the rate of return on an investment.

## Example of Present Value

Let's say you have the choice of being paid $2,000 today earning 3% annually or $2,200 one year from now. Which is the best option?

- Using the present value formula, the calculation is $2,200 / (1 +. 03)
^{1}= $2135.92 - PV = $2,135.92, or the minimum amount that you would need to be paid today to have $2,200 one year from now. In other words, if you were paid $2,000 today and based on a 3% interest rate, the amount would not be enough to give you $2,200 one year from now.
- Alternatively, you could calculate the future value of the $2,000 today in a year's time: 2,000 x 1.03 = $2,060.

Present value provides a basis for assessing the fairness of any future financial benefits or liabilities. For example, a future cash rebate discounted to present value may or may not be worth having a potentially higher purchase price. The same financial calculation applies to 0% financing when buying a car.

Paying some interest on a lower sticker price may work out better for the buyer than paying zero interest on a higher sticker price. Paying mortgage points now in exchange for lower mortgage payments later makes sense only if the present value of the future mortgage savings is greater than the mortgage points paid today.

## How Do You Calculate Present Value?

Present value is calculated by taking the future cashflows expected from an investment and discounting them back to the present day. To do so, the investor needs three key data points: the expected cashflows, the number of years in which the cashflows will be paid, and their discount rate. The discount rate is a very important factor in influencing the present value, with higher discount rates leading to a lower present value, and vice-versa. Using these variables, investors can calculate present value using the formula:

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

## What Are Some Examples of Present Value?

To illustrate, consider a scenario where you expect to earn 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 = $5000/(1.0825)5 = 3,363.80.

## Why Is Present Value Important?

Present value is important because it allows investors to judge whether or not the price they pay for an investment is appropriate. For example, in our previous example, having a 12% discount rate would reduce the present value of the investment to only $1,802.39. In that scenario, we would be very reluctant to pay more than that amount for the investment, since our present value calculation indicates that we could find better opportunities elsewhere. Present value calculations like this play a critical role in areas such as investment analysis, risk management, and financial planning.