Present Value

Present Value describes the process of determining what a cash flow to be received in the future is worth in today's dollars. Therefore, the Present Value of a future cash flow represents the amount of money today which, if invested at a particular interest rate, will grow to the amount of the future cash flow at that time in the future. The process of finding present values is called Discounting and the interest rate used to calculate present values is called the discount rate. For example, the Present Value of $100 to be received one year from now is $90.91 if the discount rate is 10% compounded annually. This can be demonstrated as follows: (Refer to the Future Value page if you are unfamiliar with the calculations.)

One Year

$90.91(1 + 0.10) = $100 or $90.91 = $100/(1 + 0.10)

Notice that the Future Value Equation is used to describe the relationship between the present value and the future value. Thus, the Present Value of $100 to be received in two years can be shown to be $82.64 if the discount rate is 10%.

Two Years

$82.64(1 + 0.10)2 = $100 or $82.64 = $100/(1 + 0.10)2

A pattern should be becoming apparent. The following equation can be used to calculate the Present Value of a future cash flow given the discount rate and number of years in the future that the cash flow occurs. (This equation can be obtained algebraically from the Future Value Equation.)

where

• PV = Present Value
• CF_t = Future Cash Flow which occurs t years from now
• r = the interest or discount rate
• t = the number of years