# Present Value

# 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)λ −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)λ(−(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 '200' 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.

## USES OF PV

The present value calculation can be used to determine the value of a property today expected to earn at least the projected stream of cash flows in the future … or the amounts that must be invested today in order to reap desired sums at future dates.

A common use of present value calculations is to determine the value of a business an investor is thinking of acquiring. The investor is likely to have a certain fairly predictable return on his or her investments based on past experience. That value is used as the discount rate. The future cash earnings of the acquisition target are projected year by year, usually for a ten-year period and using various conservative assumptions based on the target's own history. A residual value for the 11th year is calculated, typically assuming that the business will be sold for five or six times its earnings. The resulting series of annual cash flows are then reduced to present value using the investor's own rate of return. The annual results are summed. If this value is greater than or equal to the asking price, the acquisition might be desirable. If the PV of cash flows is lower, the investor can make more money investing his or her cash in something else. In using such techniques, inflation may be accounted for separately or simply added into the discount rate.

**see also** *Discounted Cash Flow*

## BIBLIOGRAPHY

"Discounted Cash Flow." *Chartered Management Institute: Checklists: Managing Information and Finance*. October 2005.

Ross, Stephen A., Randolph W. Westerfield, and Bradford D. Jordan. *Fundamentals of Corporate Finance*. McGraw-Hill/Irwin, 2005.

"What Are You Worth? For sellers, it's back to the future, but for buyers it's here and now." *Financial Planning*. 1 May 2005.

*Darnay, ECDI*

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