Lost Profits and Discount Rates
What Do the Courts Want?
Finding the methodology for determining the appropriate discount rate in a lost profits case can be a convoluted journey. The numerator (the lost profits) may be adjusted through modeling. The denominator (the discount rate) may be a risk-free rate, a rate of return on investments, or the rate of return commensurate with generating the lost profits had no wrongful act occurred. And, whether modeling is used to adjust the lost profits will impact the risk premia that affects the discount rate. Experts must review the facts of each assignment and apply an approach which they believe best represents those facts. No U.S. Supreme Court decision has provided direction for discounting lost profits. This article reviews the U.S. Supreme Court‚Äôs decisions on discount rates from other areas of litigation. It also discusses various methodologies for discounting lost profits and provides insight into what other courts have said regarding the appropriate discount rate for lost profits.
Discounting lost profits to present value appears to be a straightforward mathematical calculation. This is because the formula for discounting an amount of future money to present value is commonly known.
Y / (1+r) ^t
Y is the amount of loss being discounted for a specific period of time.
r is the discount rate.
t is the period of time of the loss.
This means if you have a $1,000 projection of lost profits for the second year in the future, a discount rate of 5 percent and the time period for the second year of two. The present value of the $1,000 is $907.03.
$1,000 / (1+5%) ^2
$1,000 / (1.05 X 1.05)
$1,000 / 1.1025
Although the math is straight forward, determining the appropriate discount rate has proven difficult over the years. This article looks at financial literature regarding discounting future lost profits and how the courts have viewed discounting to present value, not only for lost profits but other areas of economic damages.
Financial literature describes two generally accepted methodologies for calculating the present value of lost profits: the certainty equivalent method and the risk-adjusted discount rate method. ‚ÄúThe certainty equivalent method entails adjusting cash flows for risk and then discounting them at a risk-free rate. The risk-adjusted discount rate method entails discounting expected cash flows at a discount rate that reflects the riskiness of the cash flows.‚ÄĚ
‚ÄúIn essence, damage experts must account for risk either in the numerator, adjusting lost profits for the probability of successful outcomes, or in the denominator by using a risk-adjusted discount rate.‚ÄĚ
This explanation of these two methodologies is a broad brush. The reality for applying either methodology is much more complex.
Because these two methodologies require quite different approaches, two differing camps of opinions have been created, both championing their side. While both sides argue for the correctness of their approach, courts across the country have found both methodologies acceptable for calculating the present value of lost profits.
No U.S. Supreme Court decision has provided a foundation for discounting lost profits. In other areas of litigation, the U.S. Supreme Court has provided guidance for what methodology experts should expect to use in discounting. This article reviews the U.S. Supreme Court‚Äôs decisions on discount rates from these other areas. It also provides insight into what other courts have said regarding the appropriate discount rate for lost profits. ¬†
U.S. Supreme Court‚ÄĒRisk-free and Risk Adjusted Rates
The U.S. Supreme Court (SCOTUS) set an early standard for discount rates in personal damages cases. SCOTUS has long agreed with the principle of finance which holds, provided money can earn interest, any amount of money is worth more the sooner it is received. In 1916, the SCOTUS stated, ‚ÄúIt is self-evident that a sum of money in the hand is worth more than the like sum of money payable in the future.‚ÄĚ The Chesapeake decision went on to say future losses should be discounted with a ‚Äúbest and safest‚ÄĚ interest rate.
This position was confirmed in SCOTUS‚Äô Pfeifer decision. ‚ÄúIt has been settled since our decision in Chesapeake and Ohio R. Co. v Kelly [cite omitted] that ‚Äėin all cases where it is reasonable to suppose that interest may be safely earned upon the amount that is awarded, the ascertained future benefits ought to be discounted in the making up of the award.‚Äô The discount rate should be based on the rate of interest that would be earned on ‚Äėthe best and safest investments.‚Äô Once it is assumed that the injured worker would definitely have worked for a specific term of years, he is entitled to a risk-free stream of future income to replace his lost wages; therefore this discount rate should not reflect the market‚Äôs premium for investors who are willing to accept some risk of default.‚ÄĚ
This was a personal damages case. As the court noted, before discounting, an expert must determine the specific number of years the injured or deceased would have worked and then determine the lost wages based on that loss period. There is assumed level of certainty and therefore, a lower level of risk, not often found in commercial damages.
In 2004, SCOTUS addressed issues regarding interest rates to be used in cramdown interest rates for secured loans in Chapter 13 bankruptcy matters. This has been called the Till decision. This was a plurality decision. There were four justices in favor, one justice (Thomas) concurring, and four opposed. Justice Stevens, who wrote the Pfeifer decision, also wrote the Till decision.
‚Äú[Reorganization] plans that invoke the cramdown power often provide for installment payments over a period of years rather than a single payment. In such circumstances, the amount of each installment must be calibrated to ensure that, over time, the creditor receives disbursements whose total present value equals or exceeds that of the allowed claim.‚ÄĚ
The decision rejects the use of three methods for setting the appropriate interest rate: coerced loan rate, presumptive contract rate, and cost of funds rate. It approves the use of the formula approach. This approach is like the build-up method. As opposed to beginning with a risk-free rate, as the build-up method does, the formula approach begins with the national prime lending rate. To this rate, risk premiums are added depending on certain factors related to the bankruptcy. This decision also set a range of safe harbor interest rates that could be used. These rates ranged from prime plus 1 percent to prime plus 3 percent.¬†
As noted by Justice Stevens, ‚Äú[T]his requirement obligates the court to select a rate high enough to compensate the creditor for its risk but not so high as to doom the [reorganization] plan. If the court determines that the likelihood of default is so high as to necessitate an ‚Äėeye-popping‚Äô interest rate, [cite omitted] the plan probably should not be confirmed.‚ÄĚ
In this decision, SCOTUS acknowledges the need for adjusting the prime rate for risk relating to the ability of the debtor to repay the creditor. This opinion is only precedent for secured loans in Chapter 13 bankruptcies. However, many bankruptcy courts and appellant courts have found it instructive and informative for applying the same standard to secured loans in Chapter 11 matters. 
Although concurring with Justice Stevens, Justice Thomas had a different view on the appropriate interest rate. ‚ÄúThis case presents the issue of what the proper method is for discounting deferred payments to present value and what compensation the creditor is entitled to in calculating the appropriate discount rate of interest. Both the plurality and the dissent agree that ‚Äė[a] debtor‚Äôs promise of future payments is worth less than an immediate payment of the same total amount because the creditor cannot use the money right away, inflation may cause the value of the dollar to decline before the debtor pays, and there is always some risk of nonpayment.‚Äô [cite omitted] Thus, the plurality and the dissent agree that the proper method for discounting deferred payments to present value should take into account each of these factors, but disagree over the proper starting point for calculating the risk of nonpayment.‚ÄĚ
Justice Thomas goes on to state that in order to satisfy the Bankruptcy Code, ‚Äúthe plan need only propose an interest rate that will compensate a creditor for the fact that if he had received the property immediately rather than at a future date, he could have immediately made use of the property. In most, if not all, cases, where the plan proposes simply a stream of cash payments, the appropriate risk-free rate should suffice.‚ÄĚ
In concurring with the plurality, he allowed the formula approach to become the acceptable method for determining a cramdown interest rate for secured debt. However, Justice Thomas argues a risk-free rate will suffice. This would pay the creditor for the time value of money without consideration of risk factors beyond the risk of default.
Both decisions set precedents in areas where economic experts may be asked to testify as to the appropriate interest rate. They are instructive and informative on the thinking of the high court. But they do not specifically address discount lost profits.
Lost Profits, Financial Literature, and the Courts: Question of Fact
While courts have been unclear on how to determine an appropriate discount rate, the federal courts have been consistent whether an appropriate discount rate is a question of fact or law. In the Energy Capital case, it was noted, ‚ÄúThe appropriate discount rate is a question of fact.‚ÄĚ Other federal decisions have held this same position.
Because the appropriate discount rate is a question of fact and the facts of each litigation will be different, the assessment of the appropriate discount rate will be different. Therefore, the expert assigned to estimate future lost profits and discount them to present value must determine the best method for determining the appropriate discount rate for that specific case.
A review of financial literature shows three categories for determining the discount rate for calculating the present value of future lost profits.
- A rate of return on a safe investment (determined as a matter of law)
- The injured party‚Äôs rate of return when investing the award (determined as a matter of fact)
- The rate of return commensurate with the risk in receiving the lost profits (determined as a matter of fact)
Rate of Return on a Safe Investment
The rate of return on a safe investment is most often considered as a risk-free investment. This is generally seen as the investment yields on U.S. Treasury securities.
Some decisions have allowed for the use of a risk-free rate when discounting lost profits to present value. In the Northern Helex Co. case, the U.S. Court of Claims applied ‚Äúa discount rate of 9 percent derived from currently available conservative investment instruments‚ÄĚ to the damage award for a breach of contract.
This decision was written during a period of high inflation and interest rates. A review of interest rates in 1980 showed the average annual yield on U.S. Treasury securities maturing in three years was 11.51 percent. The yield on U.S. Treasury securities maturing in 10 years was 11.43 percent. And, the yield on U.S. Treasury securities maturing in 30 years was 11.27 percent. Based on these reported yields on U.S. Treasury securities, the 9 percent yield applied by the court was a risk-free rate.
Some states have allowed the use of a risk-free rate in discounting lost profits. In Knox v Taylor, a Texas Appellant Court found the use of a 7 percent risk-free discount rate to calculate lost profits damages for 1994 through 2002 was not erroneous as a matter of law.
Perhaps the most telling comment on using a risk-free rate comes from the Energy Capital case.
‚ÄúEnergy Capital argues that the sole purpose in discounting is to account for the time value of money. Again, we disagree. When calculating the value of an anticipated cash flow stream pursuant to the discounted cash flow (DCF) method, the discount rate performs two functions:¬† it accounts for the time value of money; and¬† it adjusts the value of the cash flow stream to account for risk.
We do not hold that in every case a risk-adjusted discount rate is required. Rather, we merely hold that the appropriate discount rate is a question of fact. In a case where lost profits have been awarded, each party may present evidence regarding the value of those profits, including the appropriate discount rate.‚ÄĚ
While applying a risk-free rate is not, by law, inappropriate, many courts expect a risk adjusted rate to be used for discounting lost profits. The 7th Circuit Court of Appeals has noted the discount rate must reflect risk in the income stream being discounted. Several federal decisions were found to quote Franconia Associates v United States. ‚ÄúThe appropriate discount rate must reflect risk.‚ÄĚThe Injured Party‚Äôs Rate of Return When Investing the Award
In some cases, experts claim the appropriate discount rate is the rate of return the injured party can earn by investing the court awarded money. This analysis involves considering avenues available for the injured party to invest.
‚ÄúAn example illustrates some issues that might arise in the calculation of the investment rate of return. If one assumes that the injured firm is General Electric (GE), then this company will have different opportunities to invest a court award than a smaller, private company. GE might invest an award back into its operations, and it might earn its weighted average cost of capital as a return. In that case, one might reason that the company‚Äôs weighted average cost of capital is the appropriate discount rate. Alternatively, a small private firm will not have the same investment opportunities as GE, and thus it is likely to have a different investment rate of return.‚ÄĚ
This example alone brings up the issue of differing weighted average costs of capital and whether the smaller, private company would have business related opportunities for investing a court award.
Because of these factors, the range of discount rates under this method vary greatly. Some of the options are:
- Rate of return on conservative investments
- Rate of return on an investment portfolio
- The injured firm‚Äôs cost of debt
- The injured firm‚Äôs weighted cost of capital
- The injured firm‚Äôs cost of capital
- Rate of return from investing in a similar type business as the one of the injured firm
One of the most well-known cases applying the reinvestment rate is Diesel Machinery, Inc. v B.R. Lee Industries, Inc. In this matter, the plaintiff‚Äôs expert applied a 17.5 percent discount rate reflecting the return the injured firm would receive on a lump sum award. The 8th Circuit Court of Appeals said the methodology was sound but inappropriate for this case. According to their interpretation, South Dakota law required lost profits be discounted by a risk-free rate. Therefore, while being an acceptable rate for discounting lost profits to present value, it did not meet the standards for South Dakota and therefore could not be used.
By focusing on the rate of return from investing the award, this method disconnects the numerator (the lost profits) from the denominator (the risk adjusted discount rate). This method appears consistent with the present value calculations for personal damages where the numerator is the lost future compensation and the denominator is the rate of return the injured person will receive by investing the court award at a risk-free rate. However, it does not address the argument that the risk adjusted rate used to discount the lost profits should reflect the risk for generating that amount of lost profits.
The Rate of Return Commensurate with the Risk in Receiving the Lost Profits
This method applies a discount rate that reflects the rate of return commensurate with the risk that the injured firm would have incurred in generating the profits had the wrongful act not occurred. This calculation allows the numerator and the denominator to address the damage caused by the alleged wrongful act. The numerator reflects the estimated future lost profits and the denominator includes risk factors the injured firm would have incurred to generate the estimated lost profits.¬†
‚ÄúThis approach relates discount rate to the risk that the injured firm would have taken on if it had received the future lost profits. Following finance theory, future lost profits that are less certain result in a higher discount rate and, therefore, a lower present value (all things being equal). Conversely, future lost profits that are more certain of being received use a lower discount rate and result in a higher present value (all other things being equal).‚ÄĚ
This statement appears to provide support for Robert Dunn and Everett Harry‚Äôs position on modeling:
‚ÄúCPA expert witnesses frequently testify in court about damages assessments when a plaintiff alleges future economic losses because of a defendant‚Äôs wrongdoing. Some CPA experts project the plaintiff‚Äôs hope-for income stream, modify those losses to a realistic expectation by factoring in future risks and then discount the adjusted future losses to a present value at a risk-reduced, relatively low discount rate. Other experts project the hoped-for-but lost amounts and then apply a higher discount rate that already incorporates risk or uncertainty to determine the present value.‚ÄĚ
Dunn and Harry go on to state the first approach is easier for the judges and juries to understand. ‚ÄúWhen, as in the second approach, higher discount rates are applied to a short, finite damages period, they may not achieve the expert‚Äôs desired results‚ÄĒthat is, the present value of future damages. However, the first approach‚ÄĒ‚Äėmodeling‚Äô (examining the interactive components of a financial outcome) and analyzing the various input factors (sensitivity analysis)‚ÄĒdoes this more accurately.‚ÄĚ
The Dunn and Harry article contains a list of risk considerations. This list includes market risk, financial risk, management risk, product risk, company sales risk, business environment risk, and systematic risk. All or none of these may provide a risk premium factor to be added to the risk-free rate through the build-up method.
They do not set a specific approach for determining the appropriate discount rate. They note experts have used a risk-free rate or the injured firm‚Äôs borrowing rate as the discount rate for firms with a ‚Äúclear, consistent history of profitability on comparable projects.‚ÄĚ Experts not modeling their lost profit calculations will include additional risk premia and ‚Äúsubjective‚ÄĚ factors they feel necessary to show the appropriate risk in their discount rate.¬†
Finding the methodology for determining the appropriate discount rate in a lost profits case can be a convoluted journey. The numerator (the lost profits) may be adjusted through modeling. The denominator (the discount rate) may be a risk-free rate, a rate of return on investments, or the rate of return commensurate with generating the lost profits had no wrongful act occurred. And, whether modeling is used to adjust the lost profits will impact the risk premia that affects the discount rate. Experts must review the facts of each assignment and apply an approach which they believe best represents those facts.
Attorney Robert Lloyd has noted:
‚ÄúCase law relating to discounting lost profits damages gives trial courts a great deal of discretion. Financial experts must use their best judgement under the facts and circumstances of each case and be prepared to defend their selection of a discount rate. For this reason, it is important for the attorney and expert to carefully consider both the economic application as well as the legal precedent for the determination of the appropriate discount rate in a lost profits damages calculation.‚ÄĚ
I believe it is best for experts to be consistent by using one of the recommended approaches whenever possible. Obviously, a venue or the specific facts of an assignment may require a different approach. But consistency is a great support to an expert.
In my practice, I follow the Dunn and Harry recommendation and model the estimated cash flow whenever possible. Because of this modeling, the risk adjusted discount rate is less than for non-modeled cash flows. I have found good acceptance in the courts to this approach.
I also know experts who do not model and apply a greater discount rate that includes additional risk premia. Where I may use a borrowing rate, they may use the weighted average cost of capital. They have found comfort with their approach and it has been accepted by courts as well. ¬†
Knowing the legal terrain and being comfortable with the selected approach is the foundation for a quality expert report. Perhaps the most important aspect in this is understanding the relevant court decisions and being able to address those decisions when applying the expert‚Äôs selected approach. Adding this information to the expert‚Äôs book of knowledge will assist in the successful defense of the expert‚Äôs work.
Allyn Needham, PhD, CEA, is a partner at Shipp Needham Economic Analysis, LLC, a Fort Worth-based litigation support consulting expert services and economic research firm. Prior to joining Shipp Needham Economic Analysis, he was in the banking, finance, and insurance industries for over twenty years. As an expert, he has testified on various matters relating to commercial damages, personal damages, business bankruptcy, and business valuation. Dr. Needham has published articles in the area of financial and forensic economics and provided continuing education presentations at professional economic, vocational rehabilitation, and bar association meetings.
Dr. Needham can be contacted at (817) 348-0213, or by e-mail to firstname.lastname@example.org
 In other words, the loss amount is divided by a figure which resulted from one plus the discount rate being raised to the power of the time covering the loss period.
 Risk-Adjusted Lost Profits: Why Some Methodologies Overcompensate Plaintiffs, Gene Trevino, The Value Examiner, November/December 2019, p. 8.
 Ibid p. 9.
 Chesapeake and O.R. Co. v Kelly, 241 U.S. 485, 489 (1916).
 Jones and Laughlin Steel Corp. v Pfeifer, 462 U.S. 523, 536-537, (1983).
 Till v SCS Credit Corp, 541 U.S. 465 (2004).
 Ibid. 469.
 Ibid. 480‚Äď481.
 e.g. In re: Texas Grand Prairie Hotel Realty, LLC, 710 F.3d 324, (5th Cir., 2013).
 Till, 485.
 Ibid. 487.
 Energy Capital Corp. v United States, 302 F.3d 1314, 1332, (Fed. Cir 2002).
 e.g. Sonoma Apartment Associates v United States, 134 Fed. Cl. 90 (2017); Elk v United States, 87 Fed. Cl. 70 (2009); Franconia Associates v United States, 61 Fed. Cl. 718 (2004), PSKS, Inc. v Leegin Creative Leather Products, Inc., 171 Fed. Appx. 464, (5th Cir. 2006).
 The Comprehensive Guide to Lost Profits and Other Commercial Damages, 3rd Ed., Vol. 1, Nancy Fannon, Jonathan Dunitz, BVR, 2014, 347.
 Northern Helex Co. v United States, 634 F.2d 567, 564 (Ct. Cl. 1980).
 Annual Average Yields taken from Table B-25, Economic Report of the President 2018.
 Knox v Taylor, 992 S.W.2d 40 (Tex. App. 1999).
 Energy Capital Corp. V United States, 302 F.3d 1314, 1333 (2002).
 Douglas v Hustler Magazine, Inc., 769 F.2d 1128 (7th Cir. 1985).
 Franconia Associates v United States, 61 Fed Cl. 718, 764 (2004).
 The Comprehensive Guide to Lost Profits and Other Commercial Damages, 349.
 Diesel Machinery, Inc. v B.R. Lee Industries, Inc., 418 F.3d 820 (8th Cir. 2005).
 The Comprehensive Guide to Lost Profits and Other Commercial Damages, 350.
 Modeling and Discounting Future Damages, Robert Dunn, Everett Harry, Journal of Accountancy, January 2002, www.aicpa.org/pubs/jofa/jan2002/dunn.htm, 1.
 Ibid, 1.
 The Comprehensive Guide to Lost Profits and Other Commercial Damages, 371