# What is Time Value of Money?

Time Value of Money (TVM) is the concept that the money available now is worth more than the same amount in the future, given their earning power over time. Concerning the equivalence relationships between cash flows occurring on different dates, the amount of difference between two cash flows is called interest.

For example, if you pay \$10,000 today and in return receive \$9,500 today, you most likely will not accept the arrangement. However, if you receive \$9,500 today and agree to pay \$10,000 one year from now, the amount could possibly be equivalent.  An interest rate, denoted r, can illustrate the relationship between differently dated cash flows, hence considered a rate of return. In this case, \$9,500 today and \$10,000 in one-year results in \$500 earnings, which can also be called the compensation for receiving \$10,000 in one year. This is a 5.26% rate of return/interest rate calculated as \$500/\$9,500=0.0526.

### Time Value of Money & Interest Rates

Interest rates can be understood in three different ways: a required rate of return for making the investments; a discount rate that tells you the present value of a future cash flow; lastly an opportunity cost-the value of different opportunities that are forfeited by not having the cash today. In real life, an interest rate includes: the risk-free interest rate, inflation premium, default risk premium, liquidity premium and maturity premium.

### Basic Formula of Time Value of Money

FV = Future value of money (ending amount at some point in the future, usually greater than the present value)

PV = Present value of money (beginning amount/initial investment at present)

I = Interest rate (growth rate of your money over the period of the investments, often used interchangeably with discount rate and stated in percentage)

N = Number of compounding periods per year (timeline for your investment, usually measured yearly, quarterly, monthly or even daily)

T = Number of years

Based on these variables, the formula for time value of money is:

Example in the Video:

In this video, we walked through two simple examples. In the first example, we have \$1,000 today and want to hold onto the money for 10 years and save for a big house. If the interest rate is 5% and compound for 10 years, then the future value becomes:

The next example demonstrates how a potential investor can use the time value of money when considering buying a business. We are expecting the business to generate \$10,000 in year 1, \$13,000 in year 2, \$17,000 in year 3, \$22,000 and \$28,000 in the following years. If we want to know how much these cash flows worth today, the math is similar to what we already knew. Here are each of the formulas and here is what each year’s cash flow is worth today.

Well now all we must do is add this up and we get the total value of the business today. And that turns out to be \$76,039 at a 5% return. Or to say it more accurately, using a 5% discount rate.

### Effect of Compound Interest

One thing that we need to pay attention is the frequency of the deposits. If you adjust the frequency of deposits or investments don’t forget to adjust the number of periods in your formula. So, in the above example, if you added money each month and you were expecting to return 5% a year. well if you divide that 5% by the 12 months in a year, well you get a monthly return of 0.4167%, and then a 5-year investment would be 60 months period, hence raise the power of 60. They call this number of periods compounding periods. The number of compounding periods can have a drastic effect on the TVM calculations. In general, if the number of compounding periods is increased to quarterly, monthly or daily, the ending future value is higher.