Introduction to the Time Value of Money

One of the most fundamental concepts in finance is the Time Value of Money. It states that money today is worth more than money in the future.

Imagine you are lucky enough to have someone come up to you and say, "I want to give you $500. You can either have $500 right now, or I can give you $500 in a year. What would you prefer?" Presumably, you would ask for the $500 right now. If you take the money now, you can use it to buy a TV.

If you chose to take the money in one year, you could still use it to buy the same TV, but there is a cost. The TV might not be for sale; inflation may mean the TV now costs $600, or simply, you would have to wait a year to do so and should be paid for having to wait. Since there is no cost to taking the money now, you might as well take it.

However, there is some value that you could be paid in one year that would be worth the same to you as $500 today. Say it is $550 – you are completely indifferent between taking $500 today and $550 next year because even if you had to wait a year to get your money, you think $50 is worth waiting.

In finance, there are special names for each of these numbers to help ensure that everyone is talking about the same thing. The $500 you get today is called the Present Value (PV). This is what the money is worth right now. The $550 is called the Future Value (FV).

This is what $500 today is worth after the time period (t) – one year in this example. Money with a PV of $500 has an FV of $550. The rate that you must pay per year to avoid having the money is called an interest rate (i or r).

The equation ties together all four variables (PV, FV, r, and t). Do not worry if this seems confusing; the concept will be explored in more depth later.

\(FV = PV \cdot (1 + rt)\)

Simple Interest Formula Simple interest is when interest is only paid on the amount you originally invested (the principal). You do not earn interest on interest you previously earned.

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The time value of money is a concept integral to all business. A business does not want to know just what an investment is worth today­it wants to know its total value. What is the investment worth in total?

Let's take a look at a couple of examples.

Suppose you are one of the lucky people who won the lottery. You are given two options on how to receive the money.

1. Option 1: Take $5,000,000 right now.
   
   
2. Option 2: Get paid $600,000 annually for the next 10 years.

In Option One, you get $5,000,000, and in Option Two, you get $6,000,000. Option Two may seem like the better bet because you get an extra $1,000,000, but the time value of money theory says that since some of the money is paid to you in the future, it is worthless.

By figuring out how much Option Two is worth today (through a process called discounting), you​ can make an apples−to−apples comparison between the two options. If Option Two turns out to be worthless than $5,000,000 today, you should choose Option One, or vice versa.

Let's look at another example. Suppose you go to the bank and deposit $100. Bank One says that if you promise not to withdraw the money for five years, they will pay you an interest rate of 5% each year. Before you sign up, consider that there is a cost to you for not having access to your money for five years. At the end of five years, Bank One will give you back $128.

But you also know that you can go to Bank Two and get a guaranteed 6% interest rate, so your money is worth 6% a year for every year you do not have it. Converting our present cash worth into future value using the two different interest rates offered by Banks One and Two, we see that putting our money in Bank 1 gives us roughly 128 in five years, while Bank Two's interest rate gives 134.

Between these two options, Bank Two is the better deal for maximizing future value.

\(FV = PV \cdot (1+i)^t\)

Compound Interest In this formula, your deposit ($100) is PV, i is the interest rate (5% for Bank One, 6% for Bank Two), t is time (5=five years), and FV is the future value.