AN INTRODUCTION TO PREJUDGMENT
INTEREST FOR ADVOCATES
 

Andre Wiggins
 
 

Law & Valuation
Professor Palmiter
Spring, 1999






Abstract


 
Abstract
Prejudgment interest promotes fairness in that it allows the plaintiff to be fully compensated for his injury, including for the time during which litigation took place where there was an opportunity cost to not having the damages money available for use since the time of the accident.  If prejudgment interest was not allowed, then defendants are not fully deterred from engaging in such injurious activity and also have an incentive to lengthen litigation, as damages can be viewed as an interest free loan from the time of the accident to the time of judgment.

ISSUES

1.  What is prejudgment interest?

2.  How should prejudgment interest be calculated?
RULES

1.  Prejudgment interest is compensation awarded for the loss of money due as damages during the time since the accrual of the claim.

2.  The court in In re Oil Spill by the Amoco Cadiz used a multiplier method where a multiplier was determined by looking at several factors and then applied to the amount of damages incurred in order to calculate the final judgment.
ANALYSIS

Prejudgment interest is to be calculated so that the parties are placed in the same position at the time of final judgment as they would have been had the damages been paid immediately after the injury occurred.  Thus, the future value of the damages incurred at the time of accident needs to be calculated for the time of judgment.  However, courts typically calculate a multiplier and then apply it to the damages incurred in order to determine the final judgment. The multiplier is calculated by determining the interest rate for the prejudgment period, the length of the prejudgment period, and finally the number of compounding periods per year.  However, each of these factors may be computed differently by different courts and different parties, leading to some difficulties, as demonstrated by Amoco Cadiz.

First, the court determined the appropriate interest rate to the used.  If the court wants to deter and punish the defendant, then its interest rate should be used.  However, if the court wants to compensate the plaintiff, then his interest rate should be used. Unjust enrichment of the defendant is a consideration, in that the defendant is in effect borrowing money from the plaintiff, and therefore the rate at which the defendants borrows money from outside sources could be used in order to prevent unjust enrichment.  For compensating the plaintiff, the lost opportunities for investing the damages during the time between the accident and the judgment should be considered.  However, this is speculative, so the defendantís borrowing rate could again be used, as it could be viewed that the plaintiff invested in the defendant.  Then there is the question of long term versus floating rates.  Floating rates are more appropriate for prejudgment interest.  This allows the plaintiff to be adequately compensated, and the defendant will not be able to benefit by delaying the litigation.  If the court does not know the defendantís rate of borrowing, then prejudgment interest should be determined using the prime rate, which is what banks charge large commercial borrowers for unsecured loans.  The biggest flaw with this is that at any point in time, the defendantís cost of unsecured borrowing is not represented.  Thus, alternative methods may be better used.  These alternative methods include looking at a floating rate at which the defendant could borrow unsecured, such as that for commercial paper, and estimating the spread of interest rates at which the defendant could have borrowed during the prejudgment period.  When calculating the interest using whatever rate is determined, the geometric mean should be used instead of the arithmetic mean.  Finally, it must be determined whether the interest will be simple or compounded.  According to common law, prejudgment interest is not to be compounded, although under federal law, the decision is left to the court.  However, compound interest would better serve the goals of prejudgment interest and would be more fair to the plaintiff as well as a better reflection of what occurs in commercial practices.  If compound interest is to be used, then the frequency of compounding must be determined.

Thus, prejudgment interest is an important consideration in any litigation involving damages.  There are numerous financial decisions that must be made when prejudgment interest is to be awarded.


Text

Introduction

Some courts and advocates are not familiar with prejudgment interest.  Many of those that are familiar with prejudgment interest have no idea how it should be calculated.  The purpose of this paper is to introduce the concept of prejudgment interest and briefly explain how it should be calculated.

Compensation is the primary purpose of damage awards in civil actions.  However, the life of the average lawsuit spans a number of years.[1]  Thus, if a judgment, given years after the injury, provides the amount of damages sustained by the plaintiff at the time of the incident, the plaintiff will have some opportunity cost.  The plaintiff will have lost the opportunity to invest the amount of the damages and to earn a return on that investment.  His compensation will not be complete since he has not recovered damages for the opportunity costs incurred between the time of the injury and the time of judgment.  The longer a plaintiff must wait in obtaining judgment, the more inadequate the judgment becomes.[2]

Prejudgment Interest

Interest is defined as "payment for the use or forbearance of money, or as damages for its detention."[3]  Prejudgment interest is compensation "allowed by law as additional damages for loss of use of the money due as damages, during the lapse of time since the accrual of the claim."[4]  Awarding prejudgment interest will convert time-of-accident damages in to time-of-judgment damages and thereby allow the plaintiff to be fully compensated.  If justice were immediate, there would never be an award of prejudgment interest.  However, since justice is not immediate, interest should be added to judgments to complete compensation.[5]  The law of most jurisdictions provides for interest that covers the time from when the claim arose until the date of judgment.  This interest is prejudgment interest.[6]
A.  Purposes of Prejudgment Interest
Prejudgment interest promotes fairness and efficiency.  Fairness requires that a plaintiff be fully compensated for his loss and that the defendant pay this amount.[7]  In turn, with regard to efficiency, full compensation ensures that prospective parties have the appropriate incentives to take precautions when engaging in the same activity that led to the judgment.[8]  Since compensation is incomplete without prejudgment interest, prospective defendants will not be fully deterred and cannot be expected to take sufficient precautions.[9]  Thus, by allowing for full compensation, prejudgment interest ensures that prospective defendants take sufficient precautions.

Second, where prejudgment interest is not allowed, defendants have a powerful incentive to lengthen litigation.[10] Effectively, the defendant has an interest free loan from the plaintiff until judgment. Since the defendant would normally have to pay interest on a loan, it is in his best interest to stretch the litigation.[11]  Awarding prejudgment interest reduces the defendant's incentive to delay settlement or judgment.

B.  Acceptance of Prejudgment Interest and its Application Varies by Jurisdiction

Despite the benefits of prejudgment interest, its acceptance is far from universal.  Frequently, it is left to the discretion of the court whether to award prejudgment interest or not.  In some jurisdictions, its availability depends on the source of the claim and the nature of the inquiry.  For example, under the common-law, prejudgment interest was allowed for liquidated claims but not for unliquidated claims.  The logic was that only a defendant who knew exactly what he owed could improperly withhold payment.[12]  The modern trend is towards allowing prejudgment interest.[13]

The rationale for awarding prejudgment interest was articulated by the Seventh Circuit using as an example the costs incurred by French plaintiffs to clean up the Brittany coast following the Amoco Cadiz [14] oil spill.[C]onsider what would have happened if the French parties had borrowed $60 million to finance the cleanup in April 1978, and Amoco had put that sum in trust to fund an award of damages . . . The victims would have had to pay the market rate of interest . . .If they arranged to repay the debt in a single balloon payment at the end (when they recouped from Amoco), and if the rate of interest averaged 12%, then by April 1991 the victims would owe their creditors $262 million.  Meanwhile the trust fund, lending out its assets at the market rate of 12%, would have grown to $262 million.  Scores would be fully settled if Amoco tendered its interest in the fund: it would thus "pay" $60 million as of 1978, and the victims would receive $60 million as of 1978; the lenders who financed the cleanup would receive full payment for the use of their money.[15]

Victims who finance their own cleanup are lending to themselves to pay for a project that is not of their choosing.[16]  Tortfeasors who choose to reinvest their money in their own business rather than create a trust fund in anticipation of judgment should not complain when called upon to pay prejudgment interest.[17]  However, fairness and efficiency not only require that prejudgment interest be calculated but that it also be calculated correctly.

How Prejudgment Interest Should be Calculated

A final judgment should place the parties in the same position they would have been in had the original judgment been paid immediately.  This amount is known as the future value of the original judgment, or rather, the amount the original judgment would have grown over the interim period.  The general formula for the future value of the original judgment is:
 

FV=J(1 + r sub1/n)(1 + r sub2/2)...(1 + r subi/n)...(1 + r subnT)[18]
In reality, courts don't normally follow this equation. Final awards are most often figured by first calculating a multiplier.  The multiplier is then applied to the original judgment producing the final judgment.
FV=J X m. (m is the multiplier)

The multiplier is commonly calculated as follows:

M=(1 + r subm/n)subnT

In order to set the multiplier the court must first decide three preliminary matters.  First, the court must set the interest rate for the prejudgment period.  Next, the court must define the length of the prejudgment period.  Last, the court must also calculate the number of compounding periods per year.  The miscalculation of how often interest should be compounded often leads to substantial miscalculations of interest.

A.  Amoco Cadiz as an Example

The Amoco Cadiz Court used the multiplier method.  The French plaintiffs convinced the court to set r equal to the average prime rate over the 1980s[19]  and to set n equal to one.  Interestingly, the prejudgment period was not calculated to start from the time the spill occurred.[20]  It started on January 1, 1980 and ended July 24, 1990 when the district court issued its final report.  Therefore, the prejudgment period was 10.5616 years.   See Amoco Cadiz v. Amoco Transport (argument about how many days in year for interest calculation)[21] Thus, r = 11.85%, n = 1, and T = 10.6 (if rounded up).  Plugging into the equation M?(1 + r subm/n)subnT and the multiplier is 3.2775.[22]  See Knoll, A Primer on Prejudgment Interest.  An original judgment of $65 would then become a final award of $213.037 million.

B.  Choosing an Interest Rate

The first major issue for a court is the appropriate interest rate to apply.  Should it be the defendant's interest rate or the plaintiff's?  If the judgment is intended to punish the defendant, force him to give up any profits that might have been made, or to encourage parties in similar circumstances to take greater precaution, then the court should look to the defendant. If on the other hand, the circumstances of the case are such that the goal of the court is to compensate the plaintiff or to prevent parties in the future from taking too much precaution, then the court should look to the plaintiff for the interest rate.  In many cases, the reasons are mixed and the court will find that there is not one single clear interest rate to use.  It is especially unlikely that one interest rate is applicable when one of the parties is an individual.

1.  Courts Concerned with Unjust Enrichment

In the Amoco case, the Court was interested in making certain that the defendants did not profit from their mistakes.[23]  Thus, they looked to the defendant's interest rate.  The court reasoned that the defendant's decision to not pay the plaintiff earlier implied that it elected to borrow money from the plaintiff.  The defendant could have borrowed the money from an outside source, paid the plaintiff much earlier and then repaid the loan.  The "loan" from the plaintiff effectively replaced a loan from an outside source. Financing through the plaintiff is attractive to the defendant if it knows or suspects that the prejudgment interest rate will be lower than what it pays to an outside creditor.  Thus, if the court wants to keep the defendant from being unjustly enriched it must use the defendant=s borrowing rate to calculate interest.

2.   Courts Concerned With Compensation of Plaintiff

If a court decides that it wants to compensate the plaintiff then it will look to the plaintiff's interest rate. The question becomes, how do you calculate the plaintiff's interest rate when any plaintiff has unlimited investment opportunities?  The interest rate that the defendant pays to borrow money is once again the appropriate rate to use.

Had restitution been immediate, the plaintiff could have invested in other businesses through stock or debt, or made nonbusiness investments by purchasing U.S. Treasury securities or shares of common stock. There is no method to figure what the plaintiff's returns would have been.  However, while we don't know how the plaintiff would have invested had he received immediate restitution, we know how the proceeds were actually invested. The defendant had them.  Thus, since return is a function of risk, the plaintiff's return should reflect the risk of investing in the defendant.  Therefore, the interest rate that the defendant pays to borrow money is once again the appropriate rate to use.[24]

C.  Long-term Versus Floating Rates

Floating interest rates should be applied to meet the goals of awarding prejudgment interest.  Interest rates normally vary with the duration of the investment.  Short-term rates are less than long-term rates.  Deciding whether a short-term or long-term rate is appropriate requires the following brief analysis.

First, providing prejudgment interest at the long-term rate does not compromise the court's objective of fairness.  Neither the defendant nor the plaintiff is advantaged or disadvantaged by using the long-term rate.  Further, since it is fair and the plaintiff is fully compensated, the defendant is deterred from acting in the same manner in the future.  Thus, the efficiency goal of deterrence can also be met using the long-term rate.

However, using the long-term rate does adversely effect the parties desire to settle a case. If intererst rates rise, defendants will be borrowing below the market rate which will be an incentive to extend the litigation.    The plaintiff will want to speed up the litigation, but it is the nature of our system that it is easier to unilaterally delay than it is to expedite it.  Thus, long-term rates should not be used when calculating prejudgment interest.

Interest should be calculated on a floating rate basis to be fair.  It will produce lower awards, but this is not unfair to plaintiffs since it is unnecessary to compensate plaintiffs for the risk that interest rates will rise.  The interest rates are calculated after the fact so there is no danger that the rate will later change.[25]  With a floating interest rate, the plaintiff is fully compensated for judgment delay and the defendant is not able to benefit from the delay.  Further, a floating interest rate does not give either party an incentive to prolong litigation.  Thus, floating interest rates allow the court to meet the goals of fairness and efficiency.

E.  The Prime Rate Can Act as a Default

Even though a court may know the criteria that the interest rate should meet, it still may not be able to know which interest rate to apply.  Realizing this, the Seventh Circuit has held that in lieu of information about the defendant's cost of unsecured borrowing or an applicable statutory rate, prejudgment interest should be assessed at the prime rate.[26]  The prime rate is the rate that banks charge large, creditworthy, commercial borrowers for unsecured loans.  The prime rate over the 1980s was used by the Amoco Cadiz Court.[27]

Two major advantages to using the prime rate are, first, it is widely published and easily ascertainable; second, the prime rate is market determined and varies over time as interest rates change.  The one disadvantage is that at any given time it may not adequately reflect the defendant's cost of unsecured borrowing.  It simply cannot reflect the risk of an unsecured investment in a particular defendant.[28]  An accurate calculation of prejudgment interest generally requires additional effort by the court.

1.  Alternatives Methods of Calculating Interest

There are two methods of calculating interest rates that may more accurately reflect the risk of defendant's unsecured debt. Neither is perfect.  However, they are simple and will yield credible results when used with care.  The first method is to look at a floating or short-term rate at which the defendant is borrowing or could borrow unsecured.  The second method is for the court to estimate the spread of the rate at which the defendant could have borrowed over the term of the prejudgment period.

a.  Commercial Paper

Applying the first method to the Amoco case, we see that Amoco borrowed through the commercial paper market during the prejudgment period.(Standard Oil Company (Indiana), which became Amoco on April 23, 1985, had $100 million of outstanding commercial paper at the end of 1983 and also at the end of 1984.[29]  Commercial paper are short-term, unsecured promissory notes.[30]  Only the most creditworthy borrowers, like Amoco, can issue commercial paper.

If the Amoco Court had used the commercial paper rate instead of the prime rate to calculate the prejudgment interest, the final award would have been $42 million less.[31]  The mean interest rate for commercial paper, calculated in the same manner as the Amoco Cadiz court used to calculate the mean prime rate, is 9.57%.  Using the same method of calculating the final award produces an award of $171 million.[32]  When the defendant is a corporation that issues commercial paper, using the average commercial paper rate will produce a more accurate award than one calculated based on the prime rate.[33]

b.  Using a Spread During Prejudgment Period

The second method is for the court to estimate the spread of the rate at which the defendant could have borrowed during the prejudgment period.  The court would start with a rating of the corporation's unsecured long-term debt, and then, using information from the bond rating services on the risk premiums for various risk classes.[34]  The court would then calculate the interest rate that the defendant would have paid on similarly rated short-term or floating debt.  The difference between the index and the rate the defendant would have paid is added to the index=s average over the prejudgment period.  The result is the prejudgment interest rate.

Again, the Amoco case can be used as an example.  Amoco's long term unsecured debt had a rating of AAA by Standard and Poor's and a rating of Aaa by Moody's Investor Services.[35]  Both of these ratings are the highest available by the respective agencies.  Because of the very low probability of default, this debt pays very low interest rates, just slightly above U.S. Treasury securities.  Data from the prejudgment period indicates that the spread over the T-bills for AAA debt averaged forty-seven points.[36]  During this same period, the short-term T-bill rate averaged 8.85%.  Thus, we add Forty-seven points to this rate and find that the interest rate used to calculate prejudgment interest would be 9.32%.[37]  The final judgment for the plaintiff would be about $167 million,[38] which is $46 million less than when the court used the prime rate.  This method takes into account the risk of long term investment in the defendant corporation.

c.   Applying the Alternative Methods to Amoco

Had Amoco made an argument for either of the above methods they would have possibly reduced their total liability by about 40 million.  The rule in the Seventh Circuit was that the prime rate would be used as a default unless either side produced evidence of the cost of the defendant's unsecured borrowing.[39]

F.  Finding the Average Rate Over the Prejudgment Period

Courts should use the geometric mean rather than the arithmetic mean when calculating the interest rate that existed during the prejudgment period.  The geometric mean is appropriate due to the principle of compounding.  Since the accumulated value of an investment will grow by the forward factor over each compounding period, the compound average rate of growth is the geometric mean.[40]

The plaintiffs in the Amoco case claimed that the average prime interest rate over the prejudgment period was 11.9%.[41]  The arithmetic mean of the interest rate over this period was 11.85%.[42]  The geometric mean was 11.80%.[43]  The following table[44] sets out the multiplier, total award, and interest component of the Amoco award utilizing both the arithmetic and geometric means.

Method used        Mean    Multiplier    Total Award     Interest

                                                                    Millions            Millions
Arithmetic            11.85     3.2775          213.037              148.037
Geometric             11.80     .2620             212.030             147.030
While it is theoretically incorrect to use the arithmetic mean to calculate prejudgment interest, the difference in results from using it rather than the geometric mean is probably relatively small.  In the Amoco case, the difference was about $1 million.  That constituted less than one percent of the interest component of the award.  While some commentators argue that the "practical significance of calculating the interest rate in the proper way is likely to be small in most cases",[45] it seems ludicrous for plaintiffs in a case like Amoco to not have an expert do the calculation correctly.

G. Interest Should Be Compounded

One of the issues that is frequently contested with regard to prejudgment interest is whether the court should award simple of compound interest.[46]  Simple interest is calculated off the base amount year after year.[47]  For example, ten percent of $100 is $10 year after year.  On the other hand, with compound interest, the interest is calculated each period by adding to the last period's ending base the interest calculated over that period. For example, at the end of the first year the $10 interest will be added to the base of $100 to make $110.  In the second year, there is $11 interest which is added to the new base of $110 to make $121.  Obviously, compound interest will produce a larger award over the same period of time.

The common law rule is that prejudgment interest is not compounded.[48]  Some states now have statutes that explicitly do not allow for compounded interest.[49]  Others are silent on the issue.  Under federal law, whether to award compound or simple interest is left to the discretion of the court.[50]

To meet the stated objectives of compensation, it is proper to use compound interest.  It is consistent with commercial practices and therefore reflects what is actually occurring.  Since prejudgment interest is not paid until the judgment is enforced, it is not paid to the plaintiff as it accrues.  For each passing day, the defendant=s obligation to the plaintiff increases.  On the other hand, if prejudgment interest was paid to the plaintiff as it accrued, the plaintiff would still get the benefit of compounding because the interest received could be reinvested elsewhere, generating compound interest.[51]

1.  Simple Interest is Not Fair to Plaintiff

Simple interest favors the defendant.  He does not pay for the full harm that he has caused.  Since the plaintiff is not fully compensated by the defendant, it follows that the defendant is not fully deterred from engaging in the behavior that caused the harm.  Further, simple interest may encourage defendants to stretch legal proceedings.  If defendant has to only pay simple when he can earn compound interest, then it is rationale to avoid payment for as long as possible.  The decision to award simple or compound interest can be crucial in terms of the dollar amount of a judgment.  Using the Amoco case as an example, if that Court awarded simple interest rather than compound, it would have reduced the award by over $66 million.

Method of Calculation      Multiplier      Total           Interest

                                                                       (Millions)  (Millions)
Simple                                  2.2561              146.647          81.647
Compound                         3.2775              213.037          148.037[52]
2.  How Often Interest Should Be Compounded

Assuming the court recognizes the importance of compounding interest, it must then decide the length of the compounding period.  A yearly compounding period would mean that the interest would be compounded just once a year (so n=1); monthly would mean that it is compounded once a month (so n=12).  The more frequent the compounding, the greater the amount of interest. The Amoco Court used a prime rate of interest but compounded yearly despite the fact that the prime rate would have been compounded quarterly.  Had the plaintiff made the argument they could have received an award of about $11 million more.[53]

Conclusion

To meet the judicial goals of fairness and efficiency, courts must not only award prejudgment interest but do so based on sound financial principles.  The court must define the length of the prejudgment period.  Then they must find the market interest rate during the prejudgment period.  The prime rate may serve as a default when no other evidence is presented.  Last, the court should decide the length of compounding periods. Advocates should learn at least the basics of prejudgment valuation in order to ensure that their clients be fully compensated for their injuries.

[1] Rosenberg & Sovern, Delay and the Dynamics of Personal Injury Litigation, 59 COLUM. L. REV. 115, 1122-23 (1959).
[2]  Dana v. Fiedler, 12 N.Y. 40, 50 (1854); See also T. SEDGWICK, A TREATISE ON THE MEASURE OF DAMAGES ss 113, at 201 (A. Sedgwick & J. Beale 9th rev. ed. 1920).
[3]  Brown v. Hiatts, 82 U.S. 177, 185 (1872).
[4] C. MCCORMICK, DAMAGES ss 5 (1935).
[5]  See West Virginia v. United States, 479 U.S. 305, 310 (1987).
[6] See  1 DAN B. DOBBS, DOBBS LAW OF REMEDIES: DAMAGES, EQUITY, RESTITUTIONS s 3.6(1), at 335 (2d ed. 1993).
[7]  See West Virginia v. United States, 479 U.S. 305, 310 (1987).
[8]  See Richard A. Posner, Economic Analysis of Law 163-65 (4th ed. 1992).
[9] See James A. Henderson, Jr., Product Liability and the Passage of Time: The Imprisonment of Corporate Rationality, 58 N.Y.U. L. REV. 765, 775-76 (1983).
[10] See James D. Wilson et al., Prejudgment Interest in Personal Injury, Wrongful Death and Other Actions, 30 Trial Law, Guide 105, note 3 at 110 (1986).
[11] See Henderson, Jr., supra  note 9 at 775-76.
[12]  See Martin Oyos, Note, Prejudgment Interest in South Dakota, 33 S.D.L. REV. 484, 487 (1988).
[13] See Bank of Chicago v. Standard Bank, 1999 WL 166920, 7 (7th Cir. (Ill.))
[14] On March 16, 1978, the supertanker Amoco Cadiz broke apart in a severe storm off the coast of Brittany dumping crude oil into the sea.  The oil slick was eighty miles long, one-fourth of the Breton coast.  4,400 men and 50 vessels were dispatched to aid in the clean up operations. In re Oil Spill By The Amoco Cadiz, 954 F.2d 1279 (1992).
[15] Id. at 1331.
[16] See Fishman v. Wirtz, 807 F.2d 520, 55-60 (7th Cir. 1986).
[17] See Amoco Cadiz, 954 F.2d at 1331.
[18] Where J is the original judgment, r is the (annual) interest rate for period I, n is the number of compounding periods in a year, and T is the time in years between the injury and the issuance of an enforceable judgment. The full amount the court should award is FV, with prejudgment interest, I, equal to the difference between FV and J.  Each of the individual terms of the form (1K r/n) is called a forward factor.  The ith forward factor is the amount that $1 at the beginning of period I will grow to by the end of period I.
[19] The arithmetic mean prime rate over the 1980s calculated to three decimal places is 11.9%.  Given the size of the judgment, rounding to the nearest tenth of a percent, instead of the nearest hundredth, would have increased the award to $214.049 million.  That is an increase of more than $1 million.  Further, the geometric mean should have been used.  This will be discussed, infra.
[20]  The spill occurred on March 16, 1978. Amoco Cadiz, 954 F.2d at 1331.
[21] July 24 is the 205th day of the year (non leap year).  Therefore, 56.16% of 1990 took place through July 24.  NOTE: In 1993, this case was back in court to decide the issue of "how many days are in a year" for the purpose of calculating interest.  Plaintiffs argued it should be calculated as 365 while Amoco argues for 360.  It is an important question as 5 more days a year signifies a difference in award of almost a half million dollars.  The court found that the banking industry did use 365 more often than 360 but that it was not an abuse of discretion by the lower court to apply 360.  Thus, judgment affirmed for 360. See Amoco Cadiz v. Amoco Transport, 4 F.3d 997 (1993).
[22] This multiplier is not exactly the same as found by the Amoco Court.  I was unable to duplicate their multiplier of 3.3162 using the methods described by the court. The findings here are consistent with those found by other commentators.  See Michael S. Knoll, A Primer On Prejudgment Interest, 75 TEX. L. REV. 292, 303.
[23]  See Amoco Cadiz, 954 F.2d at 1331-32; See General Motors Corp. v. Devex Corp., 461 U.S. 648, 655-56 (1983) Court stated that in a typical patent case an award of prejudgment interest is necessary to ensure that the patent owner is placed in as good as position as he would have been in had the infringer entered into a reasonable royalty agreement.  An award of interest from the time that the royalty payments would have been received merely serves to make the patent owner whole, since his damages consist not only of the value of the royalty payments but also of the foregone use of the money between the time of infringement and the date of the judgment.
[24]  However, "[t]he interest rate should not compensate the plaintiff for the risk of losing the case because doing so would overcompensate plaintiffs relative to a system in which justice was immediate.  To see this, assume that a plaintiff has a claim for $1,000, but the state of legal precedent or the reliability of the evidence is such that the plaintiff has only a 50% chance of winning at trial. Assume further that the claim will take two years to litigate and that defendant=s unsecured borrowing cost is 10%.  In this case, the plaintiff, if successful, should receive $210 in prejudgment interest in addition to a $1000 judgment.  The expected present value of such a judgment is $500, which equals what the expected present value would be if the case were decided immediately and the judgment would be for $1000 if the plaintiff won.  Adjusting the interest rate to compensate for the risk of the plaintiff losing the case would require doubling the award to $2420, which implies an annual interest rate of 56%.  The present value of such an award, discounted at 10%, is $2000.  Because the plaintiff's chance of winning is 50%, such an award would have an expected present value of $1000.  This is twice the value of the case to the plaintiff with an immediate decision.  Moreover, if the plaintiff's chance of winning were smaller, say 25%, the award would have to be quadrupled to $4840.  In effect, adjusting the interest rate for the risk that the plaintiff will lose is equivalent to eliminating the plaintiff's ex ante risk of losing at trial."  Knoll, supra note 22, at 374.
[25] The conclusion that variable interest rates are preferred over long-run rates is based in large part on the liquidity preference theory.  This theory holds that investors are risk averse and normally have a shorter investment horizon than do most issuers.  If these investors are going to hold long-term bonds they have to receive a premium in the early years.  A premium compensates for the risk that investors will sell the bonds when interest rates are high and bond prices are low, which causes a larger loss then what an investor would receive form holding short-term bonds.
[26]  See Amoco Cadiz  at 1332.
[27]  "The prime rate will be too low then the defendant's unsecured debt has a relatively high probability of default.  This is likely to occur when the defendant=s business is volatile or its leverage is high.  The prime rate will be too high when that default probability is relatively low.  This is most likely to occur for well?established companies with little leverage." See id.
[28]  See STANLEY B. BLOCK & GEOFFREY A. HIRT, FOUNDATIONS OF FINANCIAL MANAGEMENT 204, 212 (6th ed. 1992).
[29] See  Standard Oil Co. (Indiana), 1984 Annual Report, available in LEXIS, Corp Library, ANNRPT file.  Amoco reported commercial paper borrowings of $346 million at the end of 1985 and $174 million at the end of 1986.  Amoco Corp., 1986 Annual Report, available in LEXIS, Corp Library, ANNRPT file.
[30]  See BLOCK & HIRT, supra note 28 at 210.
[31] The interest component of the award is reduced by 28%.
[32] This calculation assumes an original judgment of $65 million and a prejudgment period of 10.6 years.
[33] See  Knoll, supra note 22 at 374.
[34]  Id.   If there is not a single class of unsecured debt outstanding, but rather several classes of senior and subordinated debt, then the court should take a weighted average of the ratings, in which the weights are the outstanding balances, to estimate the appropriate rating for the claim.  The difference between the yield on the corporation's unsecured debt and Treasury securities with the same duration is another method of revealing the spread.
[35] Moody's Investors Service, Inc., Moody's Industrial Manual (1979-92); Standard and Poor's Bond Guide (1979-92).
[36]  The prejudgment period is from January 1, 1980 through July 24, 1990. Amoco Cadiz, 954 F.2d 1279, 1290, 1337 (7th Cir. 1992).
[37]  This happens to be 2.58% below the interest rate the Amoco Court used. See Id. at 1337.
[38] This calculation assumes an original judgment of $65 million and a prejudgment period of 10.6 years.
[39] See Gorenstein Enters., Inc. v. Quality Care--USA, Inc., 874 F.2d 431, 437 (7th Cir. 1989).
[40] See  ZVI BODIE ET. AL. INVESTMENTS 441, 721 (1989). The formula for the geometric mean rate of return for a T-year investment, r/n is given by:
r subG/n-[(1 + r sub1/n(1 + r sub2/n)...(1 + r subi/n...(1 + subn T/n)]1/nT-1.  Note: r/n is the return in each period.
[41] Amoco Cadiz, 954 F.2d 1279, 1335 (7th Cir. 1992).
[42]  See ECONOMIC REPORT OF THE PRESIDENT at 358 tbl.B-72 (1995) (listing the bond yields and interest rates from 1929-1994).
[43]  See id.
[44]  The table assumes an original judgment of $65 million and a prejudgment period of 10.6 years with annual compounding.
[45] Knoll, supra note 22 at 333 ; See Michael Brookshire & Frank Slesnick, 1993 Survey of NAFE Members: A Follow-up Survey of Economic Methodology, 7 J. Forensic Econ. 25, 31-32 (1993).
[46]  See Anthony E. Rothschild, Comment, Prejudgment Interest: Survey and Suggestion, 77 NW. U.L. REV. 192, 217 (1982).
[47] See  Stephen A. Ross et al., Corporate Finance, 82 (3d ed. 1993).
[48]  See Restatement (Second) of Contracts s 354 cmt a (1981).
[49] See  Minn. Stat. s. 549.09(1)(c)(1996); Tex. Rev. Civ. Stat. Ann. Art. 5069-1.05  s. 6(g)(Vernon Supp. 1996).
[50] See Bio-Rad Lab., Inc. v. Nicolet Instrumental Corp., 807 F.2d 964, 969 (Fed. Cir. 1986).
[51] See Rothschild, supra note 46 at 218.
[52]  See Knoll supra note 22 at 374.
[53]  A loan that pays interest of 11.85%, if compounded quarterly, actually pays interest at 2.9625% each quarter.  Over the prejudgment period (10.6 years), there are 42 quarterly compounding periods (full ones), and 40% of one more.  The multiplier can be calculated as follows: (1 + .1185/4)42.4-(1.029625)42.4-3.4482. Therefore, the total award can be calculated as follows: $65 million X 3.4482-$224.133 million. This shows an increase of $11 million from the final award actually given.  Had the interest been correctly compounded it would have increased the award by about 7.5%.  See Knoll supra note 22 at 374.