The Concept of Present Value: A Primer for Litigators

TIME VALUE OF MONEY PRINCIPLES

To assist in understanding the TVM principles, one should examine the reasons why a dollar today is worth more than a dollar tomorrow. Here are some basic examples:

First, money can be invested to earn interest. So if a plaintiff is offered a choice between $100,000 settlement now or a $100,000 settlement at the end of the year, they would naturally take the money now to earn a year’s interest. For example, if the interest rate is 10 percent, then

$100,000 has increased to $110,000 at year-end.

(1+.10)¹ x $100,000 = $110,000

If the person chooses to wait a year for the settlement, they would have only $100,000. [FOOTNOTE 2]

Let’s turn this around: How much do we need to invest now in order to produce $110,000 at the end of the year. Economic experts refer to this as the present value of the $110,000 payoff.

Since future value is calculated by multiplying the present investment by one plus the interest rate, to calculate present value, the future value should be divided by 1.10.

FutureValue
————– = Present Value
(1+ InterestRate)ⁱ


Or in our example,

110,000
————– = 100,000
(1+.10)¹


The purchasing power of money is the second reason why a dollar received today is worth more than a dollar received tomorrow. A dollar received next year will have less purchasing power than a dollar received this year because of the general rise in prices (inflation). For example, suppose you plan to buy a car five years from now and want to invest enough money now to pay for it. Assume the car now costs $10,000, and the interest rate you can earn on your money is 8 percent per year.

In attempting to figure out the amount to invest now, it’s natural to compute the present value of $10,000 to be received in five years at 8 percent.

PV = $10,000/1.08⁵ = $6,806

You might conclude that investing $6,806 now is adequate to pay for the car five years from now. But that would be a mistake. If the car costs $10,000 today, a similar car will cost more five years from now. How much more? That depends on the rate of inflation. If inflation in car prices is 5 percent per year, then the car will cost $10,000 x 1.05⁵ or $12,763 in five years.

The final reason why a dollar received today is worth more than a dollar received tomorrow is that the receipt of money expected in the future is, in general, uncertain. A dollar received today can be spent and enjoyed today. Even if there were no investments and no inflation, a dollar today would have greater value than a future dollar because whatever one purchases today could be enjoyed for the full year that would have been spent waiting for the future dollar. By choosing to wait until next year, one takes on the risk that the defendant may no longer have the dollar to pay to the plaintiff.

DAMAGE CALCULATIONS: CHOOSING THE APPROPRIATE DISCOUNT RATE[FOOTNOTE 3]

The lesser value of future money is reflected in damage calculations through the use of a present value discount rate. In economic terms, a present value discount rate is an “opportunity cost”, or the expected rate of return (or yield) that an investor would have to give up by investing in the subject investment — instead of in available alternative investments that are comparable in terms of risk and other investment characteristics.

For example, if an economist determines that next year’s dollar is worth 10 percent less than this year’s, the discount rate used would be ten percent. Dividing next year’s dollar by 1.10 yields how much of today’s money is required to compensate the plaintiff for the loss of next year’s dollar. This amount is called the “present value,” and is actually $0.91. Thus, if a jury decided that the plaintiff lost one dollar next year, it would be appropriate to make the plaintiff whole by awarding the plaintiff ninety-one cents today.

If the amount of time over which the lost income stream were long enough, the discount rate would make a difference in the amount of damages awarded. For example, assume the plaintiff was expected to earn $500,000 per year for ten years. Without discounting to the present value, the plaintiff’s damages would be $5 million. Discounting that income stream using a six percent rate would result in a present value of approximately $2.8 million. If, instead, the expert uses a ten percent rate, damages would be approximately $1.9 million.






This example shows the lower the discount rate, the higher the present value of damages. Thus, it is obvious why one major contention between opposing experts is the discount rate.

The choice of the discount rate is driven by the definition of economic income [FOOTNOTE 4] used in the numerator. The discount rate used in the analysis must be appropriate for the definition of the economic income and for the class of capital (or other type of investment) to which it applies.

As a practical matter, the choice of economic income may be constrained by the ability, or lack of it, to develop an empirically supportable discount rate. For this reason, you may find definitions of economic income used in market approach methods. This assumes, however, a market derived capitalization rate is available that are not used in discounting methods.

It is important that the discount rate developed be matched conceptually and empirically to the definition of economic income being discounted. Also, the discount rate must reflect the degree of risk.

A question that sometimes arises is whether a discount rate should remain constant over the projection period or whether it should vary with time. The argument for varying it is that investment risk may be greater or less later in the projection period than it is at the beginning of the projection period. This is a highly judgmental (and usually subjective) matter. Usually experts use a constant discount rate — reflecting in the average amount of investment risk throughout the projection period.

CONCLUSION

The time value money can have a significant effect on damage calculations. Understanding the time value of money and how it influences the damage calculation is a valuable asset for lawyers and consultants that will enable them to provide better representation to their clients.

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