If you were offered $100 today or $100 a year from now, which would you choose? Would you rather have $100,000 today or $1,000 a month for the rest of your life?

Net present value (NPV) provides a simple way to answer these types of financial questions. This calculation compares the money received in the future to an amount of money received today while accounting for time and interest. It's based on the principle of time value of money (TVM), which explains how time affects the monetary worth of things.

The TVM calculation may sound complicated, but with some understanding of NPV and how the calculation works–along with its basic variations, present value and future value—we can start putting this formula to use in common application.

## A Rationale for the Time Value of Money

If you were offered $100 today or $100 a year from now, which would be the better option and why?

This question is the classic method in which the TVM concept is taught in virtually every business school in America. The majority of people asked this question choose to take the money today. And they'd be right, according to TVM, which holds that money available at the present time is worth more than the identical sum in the future. But why? What are the advantages and, more importantly, the disadvantages of this decision?

There are three basic reasons to support the TVM theory. First, a dollar can be invested and earn interest over time, giving it potential earning power. Also, money is subject to inflation, eating away at the spending power of the currency over time, making it worth a lesser amount in the future. Finally, there is always the risk of not actually receiving the dollar in the future, whereas, if you hold the dollar now, there is no risk of this happening (as the old bird-in-the-hand-is-better-than-two-in-the-bush saying goes). Getting an accurate estimate of this last risk isn't easy and, therefore, it's harder to use in a precise manner.

#### Understanding The Time Value Of Money

## Illustrating the Net Present Value

Would you rather have $100,000 today or $1,000 a month for the rest of your life?

Most people have some vague idea of which they'd take, but a net present value calculation can tell you precisely which is better, from a financial standpoint, assuming you know how long you will live and what rate of interest you'd earn if you took the $100,000.

Specific variations of the time value of money calculations are:

**Net Present Value**(lets you value a stream of future payments into one lump sum today, as you see in many lottery payouts)**Present Value**(tells you the current worth of a future sum of money)**Future Value**(gives you the future value of cash that you have now*)*

Say someone asks you, which would you prefer: $100,000 today or $120,000 a year from now? The $100,000 is the "present value" and the $120,000 is the "future value" of your money. In this case, if the interest rate used in the calculation is 20%, there is no difference between the two.

## Determining the Time Value of Your Money

There are five factors in a TVM calculation. They are:

1. Number of time periods involved (months, years)

2. Annual interest rate (or discount rate, depending on the calculation)

3. Present value (what you currently have in your pocket)

4. Payments (If any exist; if not, payments equal zero.)

5. Future value (The dollar amount you will receive in the future. A standard mortgage will have a zero future value because it is paid off at the end of the term.)

## Calculating Future and Present Value

Many people use a financial calculator to quickly solve TVM questions. By knowing how to use one, you could easily calculate a present sum of money into a future one, or vice versa. With four of the above five components in-hand, the financial calculator can easily determine the missing factor.

But you can also calculate future value (FV) and present value (PV) by hand. For future value, the formula is:

$\text{FV}=\text{PV}\times\left(1+i\right)^n$

And for present value, the formula would be:

$\begin{aligned} &\text{PV}=\text{FV}/\left(1+i\right)^n\\ &\textbf{where:}\\ &\text{FV}=\text{Future value of money}\\ &\text{PV}=\text{Present value of money}\\ &\text{i}=\text{Interest rate}\\ &\text{n}=\text{Number of compounding periods per year}\\ \end{aligned}$

## Applying Net Present Value Calculations

Net present value calculations can also help you discover answers for financial queries like determining the payment on a mortgage, or how much interest is being charged on that short-term Christmas expenses loan. By using a net present value calculation, you can find out how much you need to invest each month to achieve your goal. For example, in order to save $1 million to retire in 20 years, assuming an annual return of 12.2%, you must save $984 per month.

Below is a list of the most common areas in which people use net present value calculations to help them make financial decisions.

- Mortgage payments
- Student loans
- Savings for college
- Home, auto, or other major purchases
- Credit cards
- Money management
- Retirement planning
- Investments
- Financial planning (both business and personal)

## The Bottom Line

The net present value calculation and its variations are quick and easy ways to measure the effects of time and interest on a given sum of money, whether it is received now or in the future. The calculation is perfect for short- and- long-term planning, budgeting, or reference. When plotting out your financial future, keep these formulas in mind. (For related reading, see "Why the Time Value of Money (TVM) Matters to Investors")