Discount Rates
The Present Value of Future Lost Profits, and the Time Value of Money
Experts estimating the present value of a business’ future lost profits have much less direction from the courts than their counterparts estimating the present value of a person’s lost earning capacity. Professional literature has attempted to fill this gap providing many articles discussing the differing methods for analyzing lost profits (e.g., yardstick, before-and-after, but for) or how to determine the discount rate by applying a weighted cost of average capital, equity rates of return, or some form of risk premium build-up. This article moves away from these others to address the concept of the time value of money and how it applies to the discount rate applied to the future lost profits.
Experts estimating the present value of a business’ future lost profits have much less direction from the courts than their counterparts estimating the present value of a person’s lost earning capacity. Professional literature has attempted to fill this gap providing many articles discussing the differing methods for analyzing lost profits (e.g., yardstick, before-and-after, but for) or how to determine the discount rate by applying a weighted cost of average capital, equity rates of return, or some form of risk premium build-up.[1]
This article moves away from these others to address the concept of the time value of money and how it applies to the discount rate applied to the future lost profits. The time value of money is a core principle of finance. This concept should form the foundation for any discount rate to be used in estimating the present value of future lost profits.
Two Step Process
There are two steps required for calculating the present value of future lost profits. The first is projecting the cash flow that would have generated the lost profits. The second is determining the appropriate discount rate to apply to the future lost profits. The total resulting from the application of the discount rate to the future lost profits is the present value of these lost profits.
Robert Dunn and Everett Harry addressed this issue.[2] They argue the assessment of the discount rate begins with the preparation of the spreadsheet estimating the lost sales less expenses associated with the generation of those sales. The difference between these sales and costs are the lost profits. The level of reasonable certainty may impact the discount rate used. They observe that: “[s]ome CPA experts project the plaintiff’s hoped-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 present value.”[3]
Texas’ Appeals Courts have also addressed this issue. “The mere assertion that contracts were lost does not demonstrate a reasonably certain objective determination of lost profits. [cite omitted] Whether evidence is speculative or reasonably certain is a factual issue within the exclusive province of the jury to determine. [cite omitted] Reasonably, certain lost profits may be proved by relying on such factors as: (1) the experience of the business principals; (2) the nature of the business; (3) the nature of the market; (4) the nature of the client base; (5) the sales force; (6) the marketing plan; and (7) the company’s track record of sales. For example, when a business is already established and making a profit at the time the contract was breached or the tort committed, pre-existing profit, together with other facts and circumstances, may indicate with reasonable certainty the amount of lost profits. [cite omitted]”[4]
As the estimate of future sales and expenses may vary, so too the uncertainty or risk associated with the calculation. For that reason, ‘Experts’ approaches to addressing risks or uncertainties can be very different, however. Some CPA experts use discount rates that represent a return on U.S. government securities or, alternatively, the cost of funds (interest on business loans) the plaintiff will face in the future. The rates are applied to a reasonably predictable or risk-adjusted stream of lost profits—perhaps, for a wrongful contract termination, to those of a contractor who has a clear, consistent history of profitability on comparable projects. Others might use higher discount rates to arrive at present values when calculating lost profits streams that have not been risk-adjusted.”[5]
Concept of Time Value of Money
The concept of the time value of money can be simply stated as the idea that money available at the present time is worth more than the same amount in the future. “This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received.”[6]
This issue was addressed by the U.S. Supreme Court as early as 1916. “It is self-evident that a sum of money in the hand is worth more than the like sum of money payable in the future.”[7] Based on numerous federal and state court decisions, experts are expected to provide the present value of future losses. This means that any future losses in personal and commercial damages cases must be reduced to account for the time value of money.[8]
To make these calculations, experts apply a specified rate of return. The greater the discount rate (the specified rate of return) the lesser the present value of the future losses.
In the Chesapeake case, the U.S. Supreme Court called for the use of a “safest and best” interest rate for discounting personal income losses to present value. Other decisions have confirmed this position, calling for the application of a “risk free” rate.[9]
Courts have not been as limiting in setting standards for the discount rate to be applied in commercial damages cases. A review court cases shows that courts have accepted discount rates ranging from the risk free rate to nearly forty percent. This makes the determination of the appropriate discount rate in a commercial damages case controversial.
Discount Rates for Lost Profits
Commercial damages literature discusses three methods for determining the appropriate discount rate.
- Safe rate of return;
- Rate of return from investing the award; and
- Rate of return commensurate with the risk in receiving the lost profits.[10]
The safe rate of return is seldom used for discounting for future lost profits. However, both federal and state cases have allowed for such application. In the Northern Helix case, the appellant court upheld the application of a discount rate “derived from currently available conservative investment instruments.”[11] Texas appellant courts have also allowed the using of a safe rate of return stating, “The use of a risk-free discount rate to calculate lost profits damages…was not erroneous as a matter of law.”[12]
The federal appellant court in the Energy Capital Corp. case noted, “The appropriate discount rate is a question of fact.”[13] This decision goes on to discuss factors impacting the discount rate. “Energy 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: (i) it accounts for the time value of money; and (ii) 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.”[14]
Occasionally, this risk adjustment may reflect the rate of return the injured company may earn by investing the court award. This method assumes the company will receive all of the future lost profits at one time (as opposed to earning them over the period of recovery). Because the company received the lost profits in a lump sum, they could be invested and earn money for the company during the recovery period. Therefore, these future lost profits must be discounted by the rate of return the company will earn on these lost profits during the recovery period to prevent overpaying the damaged party.
More commonly, experts determine a discount rate that is commensurate to the risk that would have been assumed by the injured company to achieve the future lost profits. The greater the risk relating to the company achieving the projected profits, under normal business circumstances, the greater the discount rate. Many experts use a build-up method for determining this discount rate. The build-up begins with a risk-free rate and adds various risk premiums that, when totaled, provide the discount rate. These risk premiums may include market risk, financial risk, sales risk, product risk, and many others.[15]
Period of Recovery
One of the areas not receiving a great deal of notice in damages literature is the period of recovery for calculating lost profits. The period of recovery is the number of days, months, or years over which the injured company may claim lost profits. Some cases may be able to show losses for seventeen years (the life of a patent) or ten years (the life of a trademark agreement), but most commercial damage cases will have shorter loss periods.
Many contracts or agreements include notice periods allowing the parties to provide a notice and end their relationship in a number of days. In some cases, courts have upheld these notices in breach of contract matters shortening the recovery period to as short as thirty days.
Other cases have allowed companies to pursue recovery periods beyond the notice period. This is particularly true when: “a termination in violation of a notice provision could have a severe impact on the continuation of a well-established business and might include the loss of customer goodwill or damaged customer relationships.”[16]
Time Value of Money, Recovery Period, and the Discount Rate
The length of the recovery period may directly affect the discount rate. This concept ties directly to the time value of money. Traditionally, the longer the maturity before money will be received, the greater the interest rate that needs to be paid on that money. This can be seen in a normal yield curve; the shorter-term bonds provide lesser interest rates than bonds with longer maturities. As an example, below are the yields for U.S. Treasury securities on November 17, 2015.
| Maturity | Yield |
| 90 days | 0.11% |
| 180 days | 0.33% |
| 365 days | 0.48% |
| 2 years | 0.86% |
| 5 years | 1.68% |
| 10 years | 2.29% |
| 30 years | 3.08% |
These yields reflect the time value of money as reflected on a normal yield curve.[17]
The build-up method used to provide a risk adjusted discount rate calls for using the risk-free rate as its base rate. This rate should vary depending on the recovery period. Using the November 17 data, if the future recovery period is two years, the base for the build-up should be 0.86%. If the future loss is ten years, the risk-free base would be 2.29%. That is a 143 basis points difference.
In addition, consider the risk premiums to be included in the build-up. The risk projecting cash flows over the next two years with reasonable certainty should be less than assessing cash flows over ten years.
Conclusion
It is seldom that I have been involved in a matter where lost profits run more than five years into the future. By using the date of trial as the date of measurement, a portion of the lost profits fall into the past and are therefore, not discounted to present value. This division of the recovery period, naturally, reduces the period for estimating future lost profits.
This article does not address using the date of trial (ex-post) or the date of injury (ex-ante) as the measurement date for present value calculations. Unless required by the court, my practice assumes the date of trial as the date of measurement. I, therefore, provide an ex-post present value calculation to the court.[18]
Based on the time value of money, these shorter recovery periods should allow for lower discount rates. In addition, the shorter recovery period should allow for less risk in projecting the loss. If a case included a longer recovery period (ten years or more for patent or trademark infringement), greater discount rates should reflect the additional risk in projecting the cash flow and the time value of money.
Many experts calculating lost profits come from a business valuation background. I have seen many discount rates that reflect this. While a high discount rate is almost certainly appropriate for a business valuation, it may not be appropriate for discounting lost profits. This is because discount rates are expected to correlate with the reasonable certainty of the spreadsheet calculations. To project a twenty-five to thirty percent discount rate for a recovery period of less than five years questions the reasonableness of the projected cash flow and creates a sense of speculation with those calculations.
Because a business valuation calculation attempts to capture all of the future profits that would be generated by the business, it is reasonable to assume high discount rates. This is also true in a business destruction case where the business value captures all of the future lost profits at the time of the destroying event. The capitalization rate (discount rate less a growth rate) used in this analysis would account for the recovery period of the loss.[19]
With the business valuation capturing all of the company’s future profits, there is greater risk related to the reasonable certainty of the cash flow analysis. For that reason alone, the discount rate would be greater, and many cases, much greater, than the discount rate for a recovery period of less than five years. The time value of money concept would support this difference.
Calculating the present value of future lost profits is a two-step process. During this first step of the process, an expert will decide to adjust the projected cash flow figures for realistic expectations or leave them in a hoped-for-but-lost format. This decision will impact the risk premiums to be included in the discount rate. In the second step, the appropriate discount rate is determined. This discount rate will be based on the reasonable certainty of the cash flow projections, the risks associated with the generation of the estimated lost profits, and the period of recovery. In the end, the discount rate should reflect the facts and figures relating to that specific case and the time value of money.
[1] These types of articles may be found on QuickRead by searching “Lost Profits”
[2] Modeling and Discounting Future Damages, Journal of Accountancy, Robert Dunn, Everett Harry, January 2002
[3] Ibid, 1
[4] Toshiba Machine Co., America v. SPM Flow Control, Inc., 180 S.W.3d 761, 777, (Tex. App. 2005)
[5] Dunn, Harry, 2
[6] Time Value of Money, www.investopedia.com
[7] Chesapeake & O.R. Co. v. Kelly, 241 U.S. 485, 489 (1916)
[8] States may have differing standards for discounting. An expert should always discuss the discounting standards for a specific jurisdiction with attaining counsel prior to making a present value calculation.
[9] As example see Jones & Laughlin Steel Corp. v. Pfeifer, 462 U.S. 523 (1983)
[10] The Comprehensive Guide to Lost Profits and Other Commercial Damages, 3rd Ed, Nancy Fannon, Jonathan Dunitz, BVR, 2014, Vol. 1, pages 346-354
[11] Northern Helex Co. v. U.S., 634 F.2d 557 (1980)
[12] Knox v. Taylor, 992 S.W.2d 40 (Tex. App. 1999)
[13] Energy Capital Corp. v. U.S., 302 F.3d 1314, 1333 (2002)
[14] Ibid. 1333
[15] For a more detailed list of the various systematic and unsystematic risks see Modeling and Discounting Future Damages, Dunn, Harry, 2
[16] Mood v. Kronos Products, Inc., 245 S.W.3d 8, 13 (Tex. App. 2007)
[17] U.S. Bond and Market Rates, 11/17/2015, www.Bloomberg.com
[18] For discussion of this issue see Economic Damages: Discounting Concepts and Alternatives, Peter Schulman, The Colorado Lawyer, 1999. 28, No. 1
[19] Recovery of Damages for Lost Profits, 6th Ed., Robert Dunn, Supplement September 2015, 219, 225
Allyn Needham, PhD, CEA, is a partner at Shipp, Needham & Durham, LLC, a Fort Worth-based litigation support consulting expert services and economic research firm. Dr. Needham has been in the banking, finance, and insurance industries for over 20 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 economics and forensic economics and provided continuing education presentations at professional economic, vocational rehabilitation and bar association meetings. Dr. Needham can be reached at: (817) 348-0213, or by e-mail to: aneedham@shippneedham.com.
