By Expert No. 9025, Ph.D.
I have been attacked by the opposing expert for not using the yield of Treasury Bonds. Using short-term Treasury securities (T-Bills) is justified to remove inflation/interest rate risk that may occur with longer term Treasuries (bonds). It is not usually financially prudent to ‘lock-in’ to a Treasury Bond yield when future interest rates are expected to rise due to inflation. Further, the yield on Treasuries can change from the time when the report was written to the conclusion of trial. Using some historic average of shorter-term Treasuries provides this needed flexibility.
Moreover, for approximately one and a half years (Nov 2005 to May 2007) the yield curve flattened and then became inverted for the most part. What this means is that the yield on long term Treasuries (bonds) was actually less than that of the short-term T-Bills. This rarely happens and when it does it makes the business news. In the Nov 3rd 2006 issue of Value Line, the yield on a 10-year Treasury was 4.76%, while the yield of a 3-month Treasury was 5.11%. In the May 18th 2007 issue of Value Line, those figures are 4.66% and 4.85%, respectively.
Typically, the longer the date to maturity the higher the yield because of the economic principle of forgoing liquidity and undertaking interest rate risk. But, one can see from the preceding paragraph, sometimes this is not the case.
In actual fact, it is really the net discount rate that ultimately matters most (discount rate minus growth rate of wages). To justify my use of Treasury Bill yields and net discount rate, I offer the following case law and brief literature review.
The courts have not set the appropriate method for determining the discount rate. The parties normally receive a fairly wide latitude in arguing how future damages should be reduced to their present value. [e.g., Noble v. Tweedy (1949) 90 Cal.App.2d 738, 747-748, 203 P.2d 778, 783] But until evidence is taken on this present value issue (or comparable judicial notice), no present value instruction may be rendered. [Wilson v. Gilbert (1972) 25 Cal.App.3d 607, 102 Cal.Rptr. 31]
Which party has the burden of proof? No known reported court decision has firmly resolved which side has the burden of proving the appropriate reduction to present value. The courts have determined that a risk-free rate is the appropriate rate. The argument then turns to determining which is the appropriate risk-free rate.
The support for a (net) discount rate along the very lines I have described above is clear from the review of the literature given below.
The National Association Forensic Economics peer-reviewed Journal of Forensic Economics devoted an entire issue (April 1989) to the discount rate controversy:
In the article by Colella, a net discount rate of zero (total offset method) is supported. This implies the wage growth rate and discount rate are equivalent. He states Alaska and Pennsylvania have legislated this. Obviously, the courts feel this net discount rate will allow the plaintiff to ‘become whole.’
The article by Conley is in support of the low net discount rate of 1 for most typical cases. He argues for the use of short to intermediate maturity safest securities as the discount rate and a wage growth rate of usually one percentage point less.
In Falero’s article, he supports the use of a variety of rates in his reports. Specifically, he supports the use of a short-term rate in all his reports. He suggests a 6-month T-Bill as the appropriate risk-free rate for the reasons I described above.
In the article by Ray, he argues against choosing a discount rate that has a maturity date that corresponds with the termination of future claims because this rate may change from the time of report to settlement. Plaintiff may incur loss. He suggests a twenty-year average for 90-day T-Bills may be ‘much more appropriate’ (p.95).
Slesinger in his article substantiates the disagreement among economists regarding the appropriate discount rate. He computes long-term average of the net discount rates for a variety of securities, representing a variety of risk levels including BAA rated corporate bonds. This range takes values from 1.35% to nearly 3%, representing different risk levels.
Continuing, in the article by Albrecht (Journal of Forensic Economics 6(3) 1993 pp. 271-272), support for a risk-free rate is given.
Further, in the article by Romans and Floss (Journal of Forensic Economics 5(3) 1993 pp. 265-266) the authors offer four guidelines in the selection of a discount rate in order to reduce the controversy. These are (1) the discount rate should be a default risk-free rate. This implies Treasury bond rates; (2) the discount rate should be inflation risk-free rate. This implies a fairly short-term rate, such as Treasury Bills; (3) the discount rate should be a tax-free rate. This implies a Treasury rate minus some effective tax rate; (4) the discount rate should be an average over some reasonable time period since the use of short-term rates require reinvesting. The authors state the averaging period should be identical to the earnings growth period. They argue that an average of three to five year Treasury bond rates would be at the high end of the band of discount rate selection. At the lower end, would be an average of Treasury bill rates or municipal bond rates. They favor fairly short term government rate with a tax adjustment and municipal bond rates which may, in part, account for this tax issue.
[See generally, Trevino v. United States (9th Cir. 1986) 804 F.2d 1512, 1519, cert.den. (1987) 484 U.S. 816; Jones & Laughlin Steel Corp. v. Pfeifer (1983) 462 U.S. 523, 541-546, 103 S.Ct. 2541, 2552-2555; Schiernbeck v. Haight (1992) 7 Cal.App.4th 869, 9 Cal.Rptr.2d 716, 721]
The ‘controversy’ surrounding the selection of the (net) discount rate is ‘much ado about nothing.’ It seems clear a short-term Treasury yield has strong support.
Expert No. 9025, Ph.D. has been a professor of economics, finance and quantitative analysis at the University of California, California State University and several other universities in the state. He also serves as an expert witness for cases involving personal injury, wrongful death, housing and employment discrimination, wrongful termination, business valuations, public finance issues, breach of contract, and other economic damages. He is highly experienced in economic analysis; areas include economic impact studies, efficiency studies, benefit/cost analysis, modeling and forecasting, strategic management and planning, environmental economics, international economics, and public policy.