## What Is Present Value?

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 were invested.
- Calculating present value involves assuming that a rate of return could be earned on the funds over the period.
- Present value is calculated by taking the expected cash flows of an investment and discounting them to the present day.

## Understanding Present Value

Present value is the concept that states that 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? Because an investor can invest that $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 Reduces Future Value

Inflation is the rise in prices of goods and services over time. If you receive money today, you can buy goods at today's prices. As inflation causes the price of goods to rise in the future, your purchasing power decreases.

Consequently, money that you don't spend today could be expected to lose value in the future by some implied annual rate (which could be the inflation rate or the rate of return if the money were 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 investment rate of return.

## Present Value 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 in the number three.
- A number of online calculators are available, including this present value calculator.
- Present value can be helpful to investors' and companies' financial and investment decision-making. It can provide valuable insight into whether or not to make certain investments over others.
- Present value can clarify whether an investment's estimated rate of return is enough to make the future result of the investment worthwhile.
- In addition, it can serve as a fundamental comparison tool during the investment selection process.
- Understanding the meaning of present value and employing its formula can shed light on the economic impact of the changing value of money across high inflation periods.
- Present value involves an assumption about the discount rate (rate of return). So, those deciding on corporate projects or preparing financial analysis reports can get the results they need by altering that assumption. This isn't helpful for a company's performance or decision-making integrity.
- Rates of return must be realistic to make a calculation of present value useful. Unfortunately, projected rates of return (and rates of inflation, as well) are just that—projections. So exact values aren't possible.
- It's important to consider that for any investment decision, no interest rate is guaranteed and inflation can erode value as well.
- Using the present value formula, the calculation is $2,200 / (1 +. 03)
^{1}= $2,135.92 - 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 it could earn 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.

## Determining the Discount Rate

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 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 or Excel 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.

## Benefits of Present Value

## Limitations of Present Value

Future returns are usually compared to a baseline equal to the yield on a U.S. Treasury Bond, rather than zero. This is because Treasurys are considered extremely low risk, and they are used to represent the risk-free rate of return.

## 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?

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.

## 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 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 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.

## How Do You Calculate Present Value?

Present value is calculated by taking the future cash flows expected from an investment and discounting them back to the present day. To do so, the investor needs three key data points: the expected cash flows, the number of years in which the cash flows 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 the 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 Is An Example of Present Value?

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: $5,000/(1 + 0.0825)^{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. Calculating present value (and future value) can help investors when they are presented with the choice of earning a fixed sum for the investment at some point in the future, or gaining a percentage of the principal.

Present value calculations are often needed in areas such as investment analysis, risk management, and business financial planning, but the concept is also useful outside of business. For example, understanding the present and future values of an annuity can help you when predicting your retirement income.

## The Bottom Line

Present value is a way of representing the current value of future cash flows, based on the principle that money in the present is worth more than money in the future. Present value is used to value the income from loans, mortgages, and other assets that may take many years to realize their full value. Investors use these calculations to compare the value of assets with very different time horizons.