# Present Value

Present value (PV) is an accounting term meaning the value today of some amount of money expected to be available one or more years in the future. The concept behind this is that money available in the future is worth less than the same amount in hand today. One hundred dollars invested for a year at a 10 percent rate of return per annum will earn \$10, hence will be worth \$110 next year. This relationship can be reversed. If I can get 10 percent interest on my money, then \$100 paid me a year from now will only be worth \$90.91 today, derived by dividing 100 by 1.1. This is known as the time value of the money. Just how high that value is depends on two variables: the amount of time and the interest rate.

The formula for calculating present value for any given year in the future is the following: PV = FV  (1 + dr)  -n.

In this formula, PV stands for present value, namely right now, in the year of analysis. Future Value (FV) is the cash projected for one of the years in the future. dr is the discount rate. A discount rate of 16.7 percent would be entered as .167. The caret symbol stands for exponentiation; n is the number of years; the negative n is the negative value of the year. Thus year 1 is 1, year 2 is 2 and so on.

When present value is calculated for multiple years of projected income, for example, two numbers in the formula would change. FV might be different from year to year. And n would be different for each year. The sum of the PVs calculated would be the present value of the entire stream. Let us assume that we have three future earnings of \$5,000, \$5,500, and \$8,750 in the years 2008, 2009, 2010. These values total to \$19,250. Now let us assume a discount rate of 15 percent. Using a Microsoft Excel spreadsheet, we could calculate the PV as follows, assuming that the current year is 2007.

We would enter the years beginning with 2008 in column A, row 1 and the values of future earnings, beginning with \$5,000, in column B, row 1. Next, we would enter the following formula into column C, row 1: = B1*(1 + 0.15)  (-(A1-2007)) This formula in column C would now produce the present value of the first year. Replicating this formula in rows 2 and 3 would produce all the new values: \$4,348, \$4,159, and \$5,753. These sum to \$14,260. Thus the present value of \$19,250, using our 15 percent discount rate, is \$14,260. Notice, incidentally, that the n term (represented by the A1-2007) would be 1 in the first, 2 in the second, and 3 in the third year because ‘2007′ is deducted from the years we keyed in.

The technique described can, of course, also be applied to quarterly or monthly income streams. In those cases the n term would be smaller increments and the discount rate would be for the shorter period. Thus a 15 percent interest rate for a quarterly calculation would be 3.75 percent and shown as 0.0375.