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 ). 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.
Exhibit 1
: Discount Rate
Risk Considerations 
Unsystematic or
subjective risk 
Market risk
 Barriers to market
entry
Market size or
share constraints
Strength of
competition
Buyer product or
service acceptance
Shifting buyer
preferences 

Financial risk
 Illiquidity
Unfavorable
contractual obligations
Excessive debt
 
Management risk
 Depth of management
talent
Key employee
dependence
Management’s past
experience with product or
service 
 Product risk
 Key supplier
dependence
Obsolescence
Reliance on
specific patents and licenses
Lack of productive
capacity
Commercial
impracticality of production
 
Company sales risk
 Key customer
dependence
Lack of product
diversification
Lack of geographic
sales diversification 

Business
environment risk
 General economic
conditions
Government
regulation 
“Base” rate

Systematic risk
 General equity risk
premium
Beta coefficient
for the subject industry to
modify the general equity risk
premium
Company size
premium 
 Riskfree
 U.S. Treasury
coupon bond, note or bill yield
 
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 riskadjusted 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
riskadjusted. Those higher discount rates
contain three components: a riskfree return,
additional return for general equity investment
and company size risk, and premia (other risk
factors) for companyspecific uncertainties such
as a small customer base or a timesensitive
product. Specifically, the higher discount rates
reflect a riskfree 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
riskfree and systematic risk components is the
“base” discount rate, which is the most objective
and verifiable part of the overall discount rate.
The “Total Offset” Rule
With respect to lost wages,
courts have a policy that plaintiffs
with personalinjury 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 personalinjury
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.

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 riskfree or “safe” rate to one that includes
systematic risk premia. To adjust the information
model
Obtain or prepare a spreadsheet model
of the plaintiffenvisioned “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 ).
Identify the risks the plaintiff
likely will attain lowerthanhopedfor 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) butfor
outcome.
Calculate the present value for the
riskadjusted lost profits stream by using an
appropriately riskabated 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 riskfree 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 riskadjusted model
and will likely make the plaintiff economically
whole over time.
Exhibit 2
: Discount and
Sensitivity Analysis Models
 
DISCOUNTED 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 nonCPAs, an expert may
choose to testify about a damages computation by
comparing the numbers of a “best estimate” to a
“hopedfor” 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 ). For finite damage
periods, the subjective risk premia do not change
linearly with changes in the expected outcome (the
riskadjusted 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 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
100year 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.
Exhibit 4
: Sample Subjective
Risk Rate Computation
 
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 threeyear 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 marketderived 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 riskadjusted 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
riskabated discount rates. The approach described
here is consistent with this trend.
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 210month 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% riskfree
discount rate to calculate lost profits
damages for 1994 through 2002 was not
erroneous as a matter of law.  