Modeling and discounting future damages: income stream analysis gives a better picture of what a plaintiff really may have lost.

EXECUTIVE SUMMARY

* IN LITIGATION INVOLVING FUTURE ECONOMIC damages, experts' calculations must discount the amounts to present value. The courts have offered little guidance on appropriate discount rates.

* BUSINESS DAMAGES MAY BE FOR THE TERM of a contract, the technological life of a product or until the plaintiff could reasonably be expected to mitigate continuing losses. Opposing financial experts sometimes arrive at estimates that overstate or understate the present value of damages.

* IF THE PLAINTIFF OFFERS AN UNDISCOUNTED calculation of future economic damages at trial and the opposing counsel fails to object, the error is waived and cannot be raised on appeal.

* DISCOUNT RATES VARY WIDELY, from a "safe" investment return to much higher rates. Discount rates in general don't behave in linear and intuitive ways compared with the outcome probabilities.

* BECAUSE THE MECHANICS OF INVERSELY compounding discount rates may be puzzling to non-CPAs, a CPA damages expert may choose to testify about a computation by comparing the numbers of a "best estimate" with a "hoped-for" outcome in a spreadsheet model.

* MINIMIZING THE DIFFERENCE BETWEEN the plaintiff's and the defendant's discount rates helps a jury reach a more rational decision. Modeling future damages by examining variables that can affect future income helps to accomplish this.

CPA expert witnesses frequently testify in court about damages assessments when a plaintiff alleges future economic losses because of a defendant's wrongdoing. Some 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 of uncertainty to determine the present value. This article shows why the first approach is easier for judges and juries to understand.

When, as in the second approach, higher discount rates are applied to a short, finite damages period, they may not achieve the expert's desired result--that is, the present value of future damages. However, the first approach--"modeling" (examining the interactive components of a financial outcome) and analyzing various input factors (sensitivity analysis)--does this more accurately. Working with a spreadsheet program to address variables (risk) that influence projected earnings helps us to arrive at appropriate financial-damages information to offer in court. This article addresses business damages such as lost profits from breach of contract or patent infringement.

THE DAMAGES FRAMEWORK

The principle is deceptively simple: A calculation of a future income stream must be discounted to a present-value damages amount and entered into the record of the legal proceeding. If the plaintiff offers an undiscounted calculation of future damages at trial and the opposing party fails to object, the error is waived and cannot be raised on appeal--correction is no longer an option.

Calculating the present value of future business damages usually involves two phases. First, using a spreadsheet program, the CPA expert projects the lost stream of future income to create a model that shows lost net profits. The figure is based on a prediction of lost net sales less their saved costs such as any variable production and business expenses. For the overall period of damages (which usually begins with the occasion of the "wrongdoing" and ends some finite time thereafter), the difference between the lost net revenue and the expenses saved (variable business costs) represents the plaintiff's lost profits had the damaging act not occurred.

Next, CPA experts convert projected losses of net profits to a present value using a discount rate (see exhibit 1, page 51). A discount rate is the interest rate used to calculate future receipts or payments at their present value. (For example, $1 put in the bank today at 5% interest will be worth $1.63 in 10 years. Therefore, the present value of $1.63 to be received in 10 years is $1 today at a 5% discount rate.) The discount rate used should include a safe rate of return plus factors for risk not adjusted in the model.

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 profit streams that have not been risk-adjusted.

Those higher discount rates contain three components: a risk-free return, additional return for general equity investment and company size risk, and premia (other risk factors) for company-specific uncertainties such as a small customer base or a time-sensitive product. Specifically, the higher discount rates reflect a risk-free or virtually guaranteed interest rate plus a premium for "systematic" risk--general equity risk, a volatility modifier (beta coefficient) and, perhaps, a business size premium--and "subjective" risk factors that the expert thinks are applicable. Exhibit 1 shows examples of risk considerations that underlie the discount rate. The sum of the risk-free and systematic risk components is the "base" discount rate, which is the most objective and verifiable part of the overall discount rate.

THE CONTEXT FOR DISCOUNTS

At trial, the jury (or judge or other trier of fact--for simplicity we use jury throughout) assesses damages, Because opposing CPA and other financial experts' estimates sometimes materially overstate or understate the discounted value of damages, the jury considers all evidence presented, including testimony from nonfinance experts and witnesses who may discuss risk considerations related to products, services or markets--although seldom in terms of discount rates.

If the "wrongdoing" happened well before trial, some CPA experts project damages from the time it took place. If certain business risks--for example, the actual pretrial sales a patent infringer made--have been settled prior to trial, past (time frame from wrongdoing to resolution) and future (time frame from risk resolution to future liability cutoff) damages can be valued separately. Business damages can be for the term of a contract, the "life" of a product or until the plaintiff could reasonably expect to stop its losses.

HOW TO "MODEL" THE PRESENT VALUE

Minimizing the difference between the plaintiff's and the defendant's discount rates is the key to helping the jury reach an accurate and rational decision. If the CPA expert addresses risk to the maximum practical extent in the model, he or she can employ a discount rate ranging from the risk-free or "safe" rate to one that includes systematic risk premia. To adjust the information model

* Obtain or prepare a spreadsheet model of the plaintiff-envisioned "success" outcome, which reflects the lost sales revenue, saved expenses and lost-net profits. The data should be arranged by interim time segment (by year, for example) across the damages period. Automate the spreadsheet model to use formulas and links that respond to changes in a key input factors table (see exhibit 2, page 52).

* Identify the risks the plaintiff likely will attain lower-than-hoped-for results. For example, could the future economic returns be less than projected because unit sales would be lower, unit prices would be lower or variable expenses would be higher?

* Adjust the spreadsheet model for these identified risks with the objective of generating a stream of undiscounted lost profits that reasonably approximates the most likely or "expected" (in a probability sense) but-for outcome.

* Calculate the present value for the risk-adjusted lost profits stream by using an appropriately risk-abated discount rate.

* Prepare a suitable courtroom exhibit (not necessarily a spreadsheet) to display the information (see "An Expert Witness Can Make or Break a Case" JofA, Aug.01, page 37).

If the expert believes the damages model represents the lost income stream with a high degree of certainty, he or she may elect to use only a safe rate for discounting. But a discount rate greater than the risk-free level may be appropriate if the facts warrant it. For example, the weighted average cost of capital can be used if it is consistent with the risk-adjusted model and will likely make the plaintiff economically whole over time.

DISCOUNT RATES BEHAVE IN UNEXPECTED WAYS

For business litigation, the courts have held that future damages must be discounted but historically have offered little guidance on appropriate discount rates. Because the mechanics of discount rates may be puzzling to non-CPAs, an expert may choose to testify about a damages computation by comparing the numbers of a "best estimate" to a "hoped-for" outcome in a spreadsheet model.

Discount rates in general, and subjective risk premia in particular, don't behave in linear and intuitive ways compared with the outcome probabilities of various events considered in the damages model. Except for a perpetuity--a very long time horizon--there is no obvious relationship between the probability of an outcome and the subjective risk premia in the total discount rate (see exhibit 3, page 54). For finite damage periods, the subjective risk premia do not change linearly with changes in the expected outcome (the risk-adjusted but undiscounted lost profits).

Holding constant all other aspects of the damages model, including the stream of lost income, the discount rate--when modeling outcome probabilities for situations that have less than 100% certainty--declines as the damage period increases, and it falls exponentially in the first few years. (An average juror might expect the opposite result by assuming growing uncertainty as the time horizon lengthens.)

However, for linearly increasing model outcome uncertainty (expressed as a decreasing percentage of the "success" model's prospective economic income stream), the discount rate neither remains constant nor increases pro rata; in fact, it increases dramatically. See the accompanying table of subjective risk premia in exhibit 3.

Next, for the subjective risk component of a business valuation discount rate, it alone neither remains constant nor changes proportionately with variations in the underlying "base" discount rate. To the contrary, the higher the "base" discount rate, the higher the collective subjective risk premia for the overall discount rate is. Damages experts often treat the "base" and subjective discount rate components as behaving independently, which is not the case.

Exhibit 3 presents scenarios using "base" discount rates of 5%, 10% or 15%, varying damage periods and varying probabilities of attaining a stream of constant lost net profits. The exhibit shows how much each "base" discount would have to be increased to attain equivalent present values for the following calculations:

* The projected stream of lost income adjusted to the expected outcome, then discounted at the "base" rate.

* The projected stream of lost income, unadjusted for uncertainties, and discounted at the "base" discount rate plus the additional rate increment to be determined.

The chart in exhibit 4, page 55, illustrates this process for one subjective risk rate calculation. For any given "base" discount rate and outcome probability, the subjective risk component decreases as the period of damage increases. For any given "base" discount rate and period of damages, the subjective risk premia increase exponentially as the chance of success decreases. For any given damage period and outcome probability less than 100% but greater than 0%, the subjective risk premia increase as the "base" discount rate increases. Exhibit 3 illustrates that the discount rate component for subjective risk (thus the overall discount rate) doesn't begin to stabilize until well into a 100-year period, far longer than nearly all litigation damage periods. The subjective risk component is most volatile at 20 or fewer years and extremely sensitive at 10 years or less--the period for which most litigation damage computations are performed.

It's difficult to expect anyone to fully understand the ballooning discount rates required for shorter damage periods and relatively higher probabilities that the lost profits will not be achieved. For example, assuming a 15% "base" discount rate, a three-year damage period, level annual lost profits and a 25% outcome probability, a subjective risk premia factor of 152% is required--or a total discount rate of 167%--to achieve the same present value as reducing the model stream by 75% (that is, 100% less 25% outcome probability), then discounting at the "base" rate.

IN PURSUIT OF CLARITY

Although opposing experts typically present damages scenarios as impartial and based upon the experts' experience or market-derived data, they're likely to be related to other companies' data, may not be comparable and, usually, are not defined for plaintiff's risks. Therefore, damages assessments that address risk through model adjustments and sensitivity analyses (evaluation of changing input factors), and minimize risk considerations in the discount rate can better serve the court.

Using a risk-adjusted model helps jurors identify, understand and resolve uncertainty about what the prospective income stream would have been but for the wrongdoing (if liability is proved). An appropriate present value is more easily determined, and the need for discount rate modifications in the damages award is minimized if not eliminated. Judicial decisions in business litigation are beginning to reflect a trend toward risk-abated discount rates. The approach described here is consistent with this trend.

Exhibit 1: Discount Rate Risk Considerations

Unsystematic    Market risk      * Barriers to market entry
or subjective                    * Market size or share constraints
risk                             * Strength of competition
                                 * Buyer product or service
                                   acceptance
                                 * Shifting buyer preferences

                Financial        * Illiquidity
                risk             * Unfavorable contractual
                                   obligations
                                 * Excessive debt

                Management       * Depth of management talent
                risk             * Key employee dependence
                                 * Management's past experience
                                   with product or service

                Product          * Key supplier dependence
                risk             * Obsolescence
                                 * Reliance on specific patents
                                   and licenses
                                 * Lack of productive capacity
                                 * Commercial impracticality of
                                   production

                Company sales    * Key customer dependence
                risk             * Lack of product diversification
                                 * Lack of geographic sales
                                   diversification

                Business         * General economic conditions
                environment      * Government regulation
                risk

"Base" rate     Systematic       * General equity risk premium
                risk             * Beta coefficient for the subject
                                   industry to modify the general
                                   equity risk premium
                                 * Company size premium

                Risk-free        * U.S. Treasury coupon bond, note
                                   or bill yield
Exhibit 2: Discount and Sensitivity Analysis Models

                           Plaintiff's lost profits with risk
                            calculated through discount rate

Description                    Year 1       Year 2       Year 3

"But-for" unit sales           10,000       11,000       12,100
Less: Projected after
contract breach                (8,000)      (9,200)     (10,580)

Lost unit sales                 2,000        1,800        1,520
Sales price/unit               $1,000        1,050        1,103

Lost revenue               $2,000,000    1,890,000    1,675,800
Less: 50% saved
manufacturing costs       ($1,000,000)    (945,000)    (837,900)
Less: 20% other
saved expenses              ($400,000)    (378,000)    (335,160)

Lost net profits per
plaintiff                    $600,000     $567,000     $502,740
Present value at 53.84%      $390,027     $239,590     $138,093

                             Risk primarily addressed through
                                         the model

Description                    Year 1       Year 2       Year 3

"But-for" unit sales            9,500       10,260       11,081
Less: Projected after
contract breach                (8,000)      (8,910)      (9,941)

Lost unit sales                 1,500        1,350        1,140
Sales price/unit                 $952        1,000        1,050

Lost revenue               $1,428,570    1,349,999    1,196,999
Less: 56% saved
manufacturing costs         ($799,999)    (755,999)    (670,319)
Less: 23% other saved
expenses                    ($328,571)    (310,500)    (275,310)

Risk-adjusted lost
net profits                  $300,000     $283,500     $251,370
Present value at 12%         $267,857     $226,004     $178,920

                                   Model input factors

                                   Plaintiff's "hoped
                                      for" outcome

Year 1 but-for unit sales                10,000
But-for unit sales growth                    10%
Impaired year 1 unit sales                8,000
Impaired unit sales growth                   15%
Year 1 unit sales price                  $1,000
Unit sales price growth                       5%
Variable manufacturing costs                 50%
Other variable costs                         20%

                           Plaintiff's lost profits with risk
                            calculated through discount rate

Description                        Year 4       Year 5

"But-for" unit sales               13,310       14,641
Less: Projected after
contract breach                   (12,167)     (13,992)

Lost unit sales                     1,143          649
Sales price/unit                    1,158        1,216

Lost revenue                    1,323,165      788,803
Less: 50% saved
manufacturing costs              (661,583)    (394,401)
Less: 20% other
saved expenses                   (264,633)    (157,761)

Lost net profits per
plaintiff                        $396,950     $236,641
Present value at 53.84%           $70,877      $27,467

                             Risk primarily addressed through
                                         the model

Description                        Year 4      Year 5

"But-for" unit sales               11,967      12,925
Less: Projected after
contract breach                   (11,110)    (12,438)

Lost unit sales                       857         487
Sales price/unit                    1,102       1,158

Lost revenue                      945,117     563,430
Less: 56% saved
manufacturing costs              (529,265)   (315,521)
Less: 23% other saved
expenses                         (217,377)   (129,589)

Risk-adjusted lost
net profits                      $198,475    $118,320
Present value at 12%             $126,135     $67,138

                                         Model input factors

                                            Risk-adjusted
                                             expectation

Year 1 but-for unit sales                      9,500
But-for unit sales growth                          8%
Impaired year 1 unit sales                     8,000
Impaired unit sales growth          11.4% up to 12.0% (approx.)
Year 1 unit sales price                         $952
Unit sales price growth                            5%
Variable manufacturing costs                      56%
Other variable costs                              23%

                            Plaintiff's lost profits with risk
                             calculated through discount rate

Description                            Total

"But-for" unit sales                  61,051
Less: Projected after
contract breach                      (53,939)

Lost unit sales                        7,112
Sales price/unit                      $1,080    Average

Lost revenue                      $7,677,768
Less: 50% saved
manufacturing costs              ($3,838,884)
Less: 20% other
saved expenses                   ($1,535,554)

Lost net profits per
plaintiff                         $2,303,330
Present value at 53.84%             $866,054

                             Risk primarily addressed through
                                         the model

Description                            Total

"But-for" unit sales                  55,733
Less: Projected after
contract breach                      (50,399)

Lost unit sales                        5,334
Sales price/unit                      $1,028    Average

Lost revenue                      $5,484,115
Less: 56% saved
manufacturing costs              ($3,071,103)
Less: 23% other saved
expenses                         ($1,261,346)

Risk-adjusted lost
net profits                       $1,151,665    50% of above
Present value at 12%                $866,054
Exhibit 3: Varying Subjective Risk Rates

         5% base discount rate

              Outcome probability

Years    100%      75%      50%       25%

    5   0.00%   11.36%   31.42%    83.51%
   10   0.00%    6.40%   17.50%    45.96%
   15   0.00%    4.60%   12.57%    33.24%
   20   0.00%    3.67%   10.08%    26.97%
   25   0.00%    3.12%    8.61%    23.33%
   30   0.00%    2.75%    7.64%    21.00%
   35   0.00%    2.49%    6.98%    19.42%
   40   0.00%    2.31%    6.51%    18.31%
   45   0.00%    2.17%    6.16%    17.50%
   50   0.00%    2.06%    5.89%    16.91%
   55   0.00%    1.98%    5.69%    16.47%
   60   0.00%    1.92%    5.54%    16.13%
   65   0.00%    1.87%    5.42%    15.88%
   70   0.00%    1.83%    5.33%    15.68%
   75   0.00%    1.79%    5.26%    15.53%
   80   0.00%    1.77%    5.20%    15.41%
   85   0.00%    1.75%    5.16%    15.32%
   90   0.00%    1.73%    5.12%    15.26%
   95   0.00%    1.72%    5.10%    15.20%
  100   0.00%    1.71%    5.08%    15.15%

         10% base discount rate

              Outcome probability

Years    100%      75%      50%       25%

    5   0.00%   12.34%   34.34%    92.41%
   10   0.00%    7.30%   20.23%    54.65%
   15   0.00%    5.52%   15.41%    42.50%
   20   0.00%    4.64%   13.13%    36.96%
   25   0.00%    4.15%   11.88%    34.06%
   30   0.00%    3.86%   11.15%    32.43%
   35   0.00%    3.67%   10.71%    31.48%
   40   0.00%    3.55%   10.44%    30.90%
   45   0.00%    3.47%   10.27%    30.56%
   50   0.00%    3.42%   10.17%    30.34%
   55   0.00%    3.39%   10.11%    30.21%
   60   0.00%    3.37%   10.07%    30.13%
   65   0.00%    3.36%   10.04%    30.08%
   70   0.00%    3.35%   10.03%    30.05%
   75   0.00%    3.34%   10.02%    30.03%
   80   0.00%    3.34%   10.01%    30.02%
   85   0.00%    3.34%   10.01%    30.01%
   90   0.00%    3.34%   10.00%    30.00%
   95   0.00%    3.33%   10.00%    30.00%
  100   0.00%    3.33%   10.00%    30.00%

         15% base discount rate

              Outcome probability

Years    100%      75%      50%       25%

    5   0.00%   13.36%   37.41%   101.84%
   10   0.00%    8.29%   23.29%    64.47%
   15   0.00%    6.59%   18.77%    53.38%
   20   0.00%    5.82%   16.83%    48.90%
   25   0.00%    5.43%   15.90%    46.88%
   30   0.00%    5.23%   15.45%    45.92%
   35   0.00%    5.12%   15.22%    45.45%
   40   0.00%    5.06%   15.11%    45.22%
   45   0.00%    5.03%   15.06%    45.11%
   50   0.00%    5.02%   15.03%    45.06%
   55   0.00%    5.01%   15.01%    45.03%
   60   0.00%    5.00%   15.01%    45.01%
   65   0.00%    5.00%   15.00%    45.01%
   70   0.00%    5.00%   15.00%    45.00%
   75   0.00%    5.00%   15.00%    45.00%
   80   0.00%    5.00%   15.00%    45.00%
   85   0.00%    5.00%   15.00%    45.00%
   90   0.00%    5.00%   15.00%    45.00%
   95   0.00%    5.00%   15.00%    45.00%
  100   0.00%    5.00%   15.00%    45.00%

The total discount rate is the sum of the "base" rate and a
subjective risk premium. Computations assume a constant stream of
lost economic income.
Exhibit 4: Sample Subjective Risk Rate Computation

                                          End-of-year payment

                                 Year 1    Year 2    Year 3    Year 4

Subjective        Projected      $1,000    $1,000    $1,000    $1,000
  risks           Probability
  addressed         of payment       50%       50%       50%       50%
  in model        Expected
                    receipt        $500      $500      $500      $500

                                                        10%
                                                      discount
                                                        rate

                                            Present value = $1,895.39

                                                       44.34%
                                                      discount
                                                        rate

All risks
  addressed in
  discount rate   Projected      $1,000    $1,000    $1,000    $1,000

                                 End-of-year payment

                                        Year 5

Subjective        Projected             $1,000
  risks           Probability
  addressed         of payment              50%
  in model        Expected
                    receipt               $500

                                         34.34%
                                       difference

All risks
  addressed in
  discount rate   Projected             $1,000

The "Total Offset" Rule

With respect to lost wages, courts have a policy that plaintiffs with personal-injury claims should be awarded a dollar amount equivalent to the stream of income adjusted for inflation and invested at a safe rate of return--that the plaintiff might have realized but for the injury. In such a framework, a discount rate doesn't reflect factors such as that a company might have failed or that the individual might have lost his or her job anyway. The discount rate for future lost individual income in personal-injury cases therefore typically has been about 1% to 3%. Some states, such as Alaska, apply the "total offset" rule--inflation plus growth offsets the rate of return or discount rate--and do not discount future lost earnings at all, but this rule doesn't apply to business damages.

Business Loss Discount Rate Case Law

Only four judicial decisions have considered what the authors believe is the proper discount rate for future lost profits in business litigation. None of these has approved a discount rate above 20%.

* American List Corp. v. U.S. News & World Report, Inc., 72 N.Y. 2d 38, 550 N.Y.S.2d 590 (1989)--An 18% discount rate was applied at trial but was reversed as being too high. The plaintiff in a breach of contract action was not required to factor in the risk that the plaintiff might not have been able to perform the contract which the defendant had repudiated, thereby excusing plaintiff's performance.

* Burger King Corp. v. Barnes, 1 F. Supp. 2d 1367 (S.D. Florida, 1998)--A 9% discount rate was approved in an action by a franchiser for breach of contract by a franchisee. The 9% rate was used to discount the franchiser's future lost net royalties over a 210-month period to present value.

* Olson v. Nieman's, Inc., 579 N.W. 2d 299 (Iowa, 1998)--A discount rate of 19.4% was approved for future hypothetical patent royalties based on an expert's testimony to a 14.4% rate of return for publicly held corporations plus 5% for market risk.

* Knox v. Taylor, 992 S.W.2d 40 (Tex. App. 1999)--The use of a 7% risk-free discount rate to calculate lost profits damages for 1994 through 2002 was not erroneous as a matter of law.

ROBERT L. DUNN, JD, has conducted commercial litigation for over 30 years and is the author of Recovery of Damages for Lost Profits. His e-mail address is [e-mail]. EVERETT P. HARRY, CPA, is a small-firm owner. He has served on the AICPA litigation services subcommittee and is the author of numerous articles. His e-mail address is [e-mail].