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Len Watkins
Joshua Genser
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Offices
in Point Richmond and Emeryville
125 Park Place, Suite 210
Point Richmond, CA 94801
Phone: 510-237-6916
Fax: 510-236-9851
2200 Powell Street, Suite 890
The Watergate Office Towers
Emeryville, CA 94608
Phone: 510-237-6916
Fax: 510-236-9851
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Explaining
the Inexplicable: A Primer on Present Value
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Half
of any lawsuit is the question of damages. After all,
what difference does it make who’s at fault if the
plaintiff wouldn’t be entitled to recover money in
any event? Damages are usually a future stream of income
the plaintiff would have received but for defendant’s
wrongful act. The parties usually retain an accountant
or economist to estimate that future lost income stream.
At the trial, however, the plaintiff is going to be awarded only
a single lump-sum, not a stream of future payments. Thus, the parties’
damages experts will be asked to figure out what present lump-sum
would be sufficient to make up for the loss of a stream of future
income.
The present lump-sum amount of damages is less than the total of
all lost future income because money to come is worth less than money
now. That is, a dollar in your wallet today is worth more than is
a dollar that won’t make it into your wallet until next year.
Although this is, perhaps, obvious, an examination of the reasons
why it is true will assist in understanding the practical applications
of the principle. There are three reasons why a dollar today is worth
more than a dollar next year.
One reason is that a dollar today may be invested and a return obtained
on that investment in the course of a year. The person who has and
invests a dollar now in, for example, a certificate of deposit paying
three percent interest, would, at the end of the year, have $1.03.
The person who didn’t even get the dollar until the year had passed
would have only $1.00.
Inflation is the second reason why a dollar received today is worth
more. A dollar received next year will not purchase as much as will
a dollar received this year, because prices will have increased in
the meantime. If inflation is four percent, then next year’s dollar
will buy only about 96% of what you could’ve bought this year. (To
calculate the effect of inflation on the present value of a future
dollar, divide the dollar by one plus the amount of inflation (1
divided by 1.04 = .961538461). Do not simply subtract the rate of
inflation from the dollar; even though the results of both calculations
will be similar, the differences become significant if the total
dollar amounts are sufficiently large or if the rate of inflation
is high.)
Finally, a dollar received today is worth more than a dollar received
next year because you can spend it and enjoy it today. Even if there
were no investments and no inflation, a dollar today would have greater
value than the future dollar because whatever you bought today could
be enjoyed for the full year while you waited for your future dollar.
The lower value of future money is reflected in the damages calculations
by a discount rate, usually expressed as a percentage. For example,
if the economist decides that next year’s dollar is worth six percent
less than this year’s, then she is using a "discount
rate" of six percent. If you divide next year’s dollar by 1.06, then you find out
how much of today’s money is required to compensate the plaintiff
for the loss of next year’s dollar. That amount, called the "net present value," is actually $0.9433962. Thus, if the jury decided that the plaintiff lost one
dollar next year, it would be appropriate to make the plaintiff whole
by awarding the plaintiff ninety-five cents.
Of course, juries usually award more than $1, if they award anything,
and the lost income usually covers a period of more than one year.
If the sums are large enough or the amounts of time over which the
income stream was lost are long enough, the discount rate can make
a tremendous difference in the amount of damages to be awarded. For
example, assume the plaintiff was expected to earn $200,000 per year
for ten years. Without discounting to the present value, the plaintiff’s
damages would be $2 million. Discounting that income stream using
a discount rate of six percent would result in a net present value
of $1,472,017.41. If, instead, a discount rate of twelve percent
is used, the result is $1,130,044.61.
In case you hadn’t already noticed, the lower the discount rate the
better for the plaintiff. The parties, therefore, often litigate
over the discount rate.
The appropriate discount rate is determined using all three of the
concepts explained above: the rate of return the plaintiff could
get on investments, inflation, and the value of immediate gratification.
Actually, investment rates of return are often accepted as proxies
for the other two concepts. That is, people will only make an investment
if the expected rate of return is sufficient to make up for delaying
the gratification of spending the money immediately and to cover
anticipated inflation. The type of investment used as a proxy for
the discount rate, and, thus, the rate of return, is chosen so that
its risk reflects the level of uncertainty of the plaintiff’s future
income. That is, the less certain it is that the plaintiff would
have made the amount of income the economist is predicting, the higher
should be the discount rate.
Take, for example, the case of a white-collar wage earner with a
long work history for a large, solid company. The economist can be
highly confident that, but for the wrongful act of the defendant,
the plaintiff would remain employed and making a predictable wage
for the balance of the plaintiff’s expected work life. In that case,
the rate of return component of the discount rate should be chosen
from low-risk investment vehicles. In contrast, if the plaintiff
is a start-up business, it could be that its profits would skyrocket,
or that it would fail completely. That variability would be better
reflected by using for the discount rate a higher rate of return
promised for high-risk investments.
This risk can also be taken into account in the determination of
future income, but, if so, then the discount rate should be adjusted
so that the risk is not double-counted. For example, in estimating
the lost future profits of a high-risk start-up company, the economist
could assume that its profits would continue to increase at its historically
high rate, and then compensate for the high level of uncertainty
by using a high discount rate. However, the economist might, instead,
use a conservative projection of future income by, for example, averaging
best and worst cases for the company, in which case a lower discount
rate would be appropriate.
The lowest-risk investment vehicle is usually assumed to be United
States government treasury bills. Higher-risk investments might include
any manner of securities, but economists often use bonds, because
the various ratings are already accepted measures of relative risk.
Determining the appropriate discount rate for a business may be different,
more precise, than doing so for an individual. That is because there
may already be market rates of return on investments in the income
to be generated by that particular type of business. That is, investors,
whether purchasers of equity in the business or lenders to the business,
demand returns on their investments appropriate to the risks they
are taking. Thus, the rate of return offered by such businesses to
their investors, the "capitalization
rate," is an excellent indicator of the appropriate discount rate.
The capitalization rate is a weighted average of the rates of return
the industry provides on equity and on debt. "Equity" refers,
generally, to stock, so the rate of return on investments in equity
is the rate of return demanded by stockholders. The rate of return
on debt is the interest rate the industry must pay on bonds in order
to entice investors to purchase them.
Assume, for example, if the plaintiff is a business of a type whose
stock is publicly traded. (It is not vital that the plaintiff’s stock
be publicly traded, only that there be some similar businesses that
are.) The rate of return demanded by investors in that business’
equity can be determined by comparing the industry’s profit per share
with the price of the stock. For example, if the stock is selling
at $10 per share and the profits per share have been $1.10, then
the rate of return on equity is 11%.
The capitalization rate is determined by taking the industry average
rate of return on equity and the industry average interest rate paid
on bonds, and multiplying each figure by the relative amount of each
type of financing used by the industry. That is, if 70% of the industry’s
capitalization comes from sale of stock, and 30% from debt, and stockholders
demand a return of 11% and bondholders demand 15%, then the capitalization
rate would be 70% times 11% plus 30% times 15%, or 12.2%.
The discount rate can also depend upon how far into the future losses
are projected. For example, in the case of our stable, white-collar
employee of a blue chip company, we have assumed that the risk that
his income stream would have been interrupted but for the wrongful
act of the defendant is very low. Thus, use of a discount rate equal
to the rate of return being paid on Treasury Bills is appropriate.
However, Treasury Bills with different maturity dates have different
rates of return. Longer-term securities pay higher interest than
those that mature sooner. For example, a five-year T-Bill might pay
4%, but a ten-year T-Bill might pay 6%.
Many economists, therefore, use discount rates equal to rates of
return on investments of a term equal to the future time period being
studied. Thus, if the plaintiff lost income over an anticipated ten-year
period, the economist would use as the discount rate the rate of
return on ten-year T-Bills. This would, however, overstate the discount
rate, because the income the plaintiff would have earned in the next
year should be discounted only at the rate of return on one-year
T-Bills.
The most accurate means of discounting future income would be to
use a different discount rate for each year into the future income
is forecast. That is, the first year’s income would be discounted
at a rate equal to the return paid on a one-year T-Bill, the fifth
year’s income discounted at a rate equal to the interest paid on
a five-year T-bill, and so on.
Of course, there is no seven-year T-Bill. However, T-Bills are traded
on an open market. Thus, there is a market price for T-Bills that
originally had longer maturities of which only seven years is left.
The rate of return on those T-Bills is the amount of interest, determined
by multiplying the interest rate shown on the face of the T-Bill
by the original purchase price of the T-Bill, divided by the purchase
price now.
There is also no requirement that the discount rate used be constant,
or even derived from the same source. It may be that the economist
anticipates future changes in the appropriate market, which might
dramatically change the risks of that particular business. For example,
the future profitability of a video rental business might be reasonably
assured for five years into the future, but the economist might believe
that digital cable television with pay-per-view on demand will suddenly
reduce demand for video rentals when the technology becomes widely
available thereafter. Thus, a much higher discount rate should be
applied to estimated losses for periods more than five years into
the future.
As always seems to be the case, there is a trade-off between scientific
rigor and the ability to explain the calculations to a jury. Before
deciding how much accuracy to sacrifice for simplicity, an attorney
would be well-advised to determine how much difference it would make
to the result of the calculation. A large difference is a sign that
your economist would be vulnerable to an effective cross-examination.
Even where the difference is small, however, the attorney should
understand the principles and what compromises have been made so
that the expert can be rehabilitated if these compromises are brought
to light. |
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