### PRESENT VALUE

Present value (PV) is an accounting term that measures how money money needs to be invested today in over to finance future business initiatives, projects, and obligations. In order to determine the present value of future costs, accountants use formulas based on the time value of money. These formulas features variables such as the length of time involved and the prevailing interest rate. In other words, the present value of an amount to be received in the future is the discounted face value considering the length of time the receipt is deferred and the required rate of return (or appropriate discount rate under the circumstances). Present value is the result of the time value of money concept, which recognizes that today's dollar is worth more than the same dollar received at a future point in time.

The standard formula for calculating the present value of a series of future receipts is:

PV = cash flow 1 / (1 + interest rate) 1 + cash flow 2 / (1 + interest rate) 2 + … + cash flow n / (1 + interest rate)n

Where cash flows 1 to n are the future receipts, the interest rate is the discount rate appropriate for the stated period, and n is the number of periods over which future receipts occur.

The interest, or discount, rate used in PV calculations is a key element in determining the PV. This importance is emphasized when the future amounts occur over an extended period of time, due to the power of compounding. For example, the final payment on a 30-year loan at 7 percent interest would be worth approximately 13.1 percent of its face amount on a present value basis at the date of loan origin [1/ (1 + .07)30]. By contrast, the 30th payment on a loan with a 9 percent interest rate would be worth only 7.5 percent [1/(1 + .09)30] of its face amount in present value terms at the origin. This example shows the power of compounding when time periods are long.

The discount rate used in a given circumstance must compensate the lender of funds for three elements of return:

Inflation. In order to remain even in terms of buying power, the return of money at a future date must be appended by the Consumer Price Index rate. In other words, if a person lends an amount of money adequate to buy a loaf of bread at t=0, he will require repayment at t=1 of the original amount plus the fraction of that amount representing the CPI increase over the period. That way he will be able to buy the same loaf of bread at t=1.

Time value of money (TVM). In addition to keeping pace with inflation, the investor or lender has a natural inclination for consumption sooner rather than later. The cost of compensating for this aspect of human nature has been found to be about 1 to 2 percent per year.

Risk. In addition to postponing the preferred immediate consumption and having to reimburse for inflation's erosion of buying power, many types of investment involve a risk of default. Compensating for this element of required return can be the most expense of the elements under consideration.