# Present Value

##### By David R. Henderson

Present value is the value today of an amount of money in the future. If the appropriate interest rate is 10 percent, then the present value of $100 spent or earned one year from now is $100 divided by 1.10, which is about $91. This simple example illustrates the general truth that the present value of a future amount is less than that actual future amount. If the appropriate interest rate is only 4 percent, then the present value of $100 spent or earned one year from now is $100 divided by 1.04, or about $96. This illustrates the fact that the lower the interest rate, the higher the present value. The present value of $100 spent or earned twenty years from now is, using an interest rate of 10 percent, $100/(1.10)^{20}, or about $15. In other words, the present value of an amount far in the future is a small fraction of the amount.

The fact that a dollar one year from now is less than a dollar today would be true even if the inflation rate were zero. The reason is that we prefer current availability to future availability: we want it now. That is why there is interest even when expected inflation is zero.

The concept of present value is very useful. One can, for example, determine what a lottery prize is really worth. The California state government advertises the worth of one of its lottery prizes as $1 million. But that is not the value of the prize. Instead, the California government promises to pay $50,000 a year for twenty years. If the discount rate is 10 percent and the first payment is received immediately, then the present value of the lottery prize is “only” $468,246.

Present value also helps us with such practical issues as the location of an airport. Suppose someone argues that an airport, say Denver International Airport, should be built twenty miles from the edge of the city because twenty-five years from now the city will have expanded to reach the airport. That means that for twenty-five years, people will spend valuable time going the long distance to and from the airport. The gain is that twenty-five years from now the airport will be appropriately situated. But because the gain from appropriately locating the airport is so far in the future, the present value of this gain is small; therefore, building the airport so far away today probably does not make sense.

## About the Author

David R. Henderson is the editor of this encyclopedia. He is a research fellow at Stanford University’s Hoover Institution and an associate professor of economics at the Naval Postgraduate School in Monterey, California. He was formerly a senior economist with President Ronald Reagan’s Council of Economic Advisers.

## Further Reading

*The Theory of Interest.*New York: Macmillan, 1930. Online at: http://www.econlib.org/library/YPDBooks/Fisher/fshToI.html.