Introduction to the Time Value of Money

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.