## The Time Value of Money

Everyone knows that a dollar today is worth more than a dollar a year from now. The reason for this is because of the time value of money. To illustrate the time value of money, let us look at the following equation:

Where FV = Future value of an investment PV = Present value k = Investment interest rate (or cost of capital) n = Number of years

Using this formula, we can see that an investment of \$1,000 today (i.e., PV) invested at 10% (i.e., k) for one year (i.e., n) will give us a future value of \$1,100. If the investment is for two years, then the future value would be worth \$1,210.

Now, let us look at the formula from a different perspective. If an investment yields \$1,000 a year from now, then how much is it worth today if the cost of money is 10%? To solve the problem, we must discount future values to the present for comparison purposes. This is referred to as "discounted cash flows."

The previous equation can be written as:

Using the data given:

Therefore, \$1,000 a year from now is worth only \$909 today. If the interest rate, k, is known to be 10%, then you should not invest more than \$909 to get the

\$1,000 return a year from now. However, if you could purchase this investment for \$875, your interest rate would be more than 10%.

Discounting cash flows to the present for comparison purposes is a viable way to assess the value of an investment. As an example, you have a choice between two investments. Investment A will generate \$100,000 two years from now and investment B will generate \$110,000 three years from now. If the cost of capital is 15%, which investment is better?

Using the formula for discounted cash flow, we find that:

This implies that a return of \$100,000 in two years is worth more to the firm than a \$110,000 return three years from now. 