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Discounting the future

Long-horizon bond yield data from the US Treasury

The FRED Blog has discussed data from the High-Quality Market (HQM) corporate bond yields release reported by the US Department of the Treasury. In short, that executive agency of the federal government uses the spot rate yields of actual high-quality (that is, low-risk-of-default) corporate bonds to calculate the interest rates of 200 individual bonds with maturity dates extending far into the future. Up to 100 years in the future, in fact.

The FRED graph above shows the calculated interest rate of a hypothetical 100-year bond. The latest data available at the time of this writing is from December 2023: As of that date, the yield of a bond maturing in December 2123, had it been possible then to buy one, was projected to be 5.1%.

This information is used by the Internal Revenue Service (IRS) to calculate the present value of payment from defined benefit plans. The standard formula to compute the present value (PV) of a future value (FV) payment is PV=FV*(1/(1+i)^n), where i is the interest rate and n is the number of periods between now and the future date. The Treasury data provide the value of the interest rates in the IRS’s present value calculations.

So, how are the present values of very distant future payments looking lately? The FRED graph shows that the 100-year interest rate followed a decreasing trend between January 1984 and August 2020. Basic algebra shows that lower values of interest rates, holding constant future values and the number of periods, boost the present value of future payments. The inverse is true when interest rates rise and that has generally been the case during the past three years. Thus, as the present values of very distant future payments decrease, perhaps we should conclude this post by saying carpe diem.

How this graph was created: Search the alphabetical list of FRED releases for “Corporate Bond Yield Curve” and select “Corporate Bond Spot Rates by Maturity, Monthly, Not Seasonally Adjusted.” Scroll all the way down the page to select the series “100-year.”

Suggested by Diego Mendez-Carbajo.

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