# Robust discount rates

The case for a low discount rate is stronger than you think. If we are uncertain what is the right discount rate, and we count **values** in our averaging (rather than averaging discount rates per se), lower discount rates get more weight in the expected value calculation. In his book on catastrophe, Richard Posner writes:

Suppose there’s an equal chance that the applicable interest rate throughout this and future centuries will be either 1 percent or 5 percent. The present value of $1 in 100 years is 36.9 cents if the interest rate used to compute the present value is 1 percent but only .76 cents (a shade over three-quarters of a cent) if it is 5 percent. Now consider the 101

^{st}year and remember the assumption that the two alternative discount rates are equally probable. If the interest rate used to discount the future to the present value is 1 percent, then the present value of $1 at the end of that year will have shrunk from 36.9 cents to 36.6 cents. If instead the interest rate used is 5 percent, the present value of .76 cents will have shrunk to about .75 cents. This means that theaveragepresent value of $1 at the end of the 101^{st}year will be 18.68 cents, implying an average discount rate of less than 2 percent, rather than 3 percent. The reason is that the more rapid decline in value under the higher discount rate (5 percent) reduces its influence on present value.

**The bottom line**: If we are unsure what is the right discount rate, in practice that usually means something like a low discount rate.