## Discounting the cost of future care: Current methods overestimate the present value.

A. Factors determining the size of an award

Three factors determine the present value of the costs of future care, and hence determine the quantum of damages.

1. The annual costs of care (or other payments) to be received by the plaintiff. These are specified in a life care plan. For simplicity we assume here that the annual payments are equal, or nearly so.1

2. The net discount rate, representing the difference of the rate of return on investment and the inflation rate. The net rate is often in the vicinity of 3%. This means, for example, that a payment to be received in one year's time has a present value of about 97% (1/1.03).

3. The plaintiff's life table.2 More precisely, what is required is the plaintiff's chance of surviving one more year, two more years, and so on.

The first factor is determined by the Court, and the second is usually specified by law for the country, state, or province. We focus here on the third, the life table, as it is here that the consistent overestimation of present value occurs.

B. The current procedure

1. Currently, the Court hears arguments about the plaintiff's life expectancy or median survival time3 and makes a determination. For example, the Court may accept that the life expectancy is 20 additional years.

2. This figure (together with the life care plan and the specified discount rate) is provided to an actuary or economist, who computes the expected present value (EPV) -- the amount of money today which is actuarially equivalent to the life-time stream of payments.

3. It is not currently recognized in legal circles that the life expectancy alone is insufficient to determine the EPV; in fact, the complete life table is required. There are infinitely many life tables that yield a given life expectancy, and all result in a different EPV.

4. An expert opinion on life expectancy should include the complete life table, not just the single number (the life expectancy) that is computed from it. In practice, however, it is generally left to the economist or actuary to invent a life table that corresponds to the given life expectancy.

5. It is here that the problem arises: the economist/actuary is not provided with the correct life table, and the standard methods used to invent one all lead to overestimation of the EPV.

C. The standard methods to create a life table corresponding to a given life expectancy

The most common methods are the following:

1. The Expectancy Method assumes that the plaintiff will live exactly to his or her life expectancy and then die. With a 20 year life expectancy, for example, one would assume the plaintiff will live exactly 20 more years. The life table implicit in this method is the "degenerate" one in which there is no variability at all in the survival time -- it is assumed to be exactly 20 years.

2. Rating Up advances the plaintiff's age to a "rated age" chosen so that the life expectancy in the general population is the required life expectancy. For example, if a boy with cerebral palsy has a life expectancy of 20 years, his rated age is 58 years -- the age at which a normal man has this life expectancy. The child's life table is then assumed to be the ordinary life table for a man of 58.

3. In The Ratio Method the age-specific death rates are all multiplied by a constant chosen to result in the required life expectancy. The suitable constant is easily found by trial and error.

As noted, all of these methods overestimate the EPV. The first -- the expectancy method -- results in the greatest overestimation of all. This is noteworthy because it is perhaps the most common approach in the U.S., and we understand that it is the method required by law in Australia.

The discrepancy between the expectancy method and use of the correct life table has been noted in the literature. Jordan (1967, p.174) refers to a "widespread misconception" that the two quantities are equal. Ben-Zion and Reddall (1985) state that the expectancy method is (a) widespread and (b) demonstrably incorrect.

Strauss et al. (2001) document the magnitude of the error resulting from all three of the above methods, and also demonstrate mathematically why all the methods overestimate the EPV rather than underestimate it. The example below, from Strauss et al. (2001), may be helpful.

```
Table 1. Expected Present Values of lifetime care for a
5-year old boy with cerebral palsy. Life expectancy is 20
years, costs are \$100,000 per year, and a 4% net discount
rate is assumed.
---------------------------------------------------------
#  Method                                             EPV
---------------------------------------------------------
1. No discounting at all                      \$ 2,000,000

2. Assuming the child lives exactly 20 years  \$ 1,385,947

3. "Rating up" (using the life table for a    \$ 1,296,538
normal male aged 58 years)

4. Ratio method                               \$ 1,298,388

5. Using the correct life table               \$ 1,149,194
---------------------------------------------------------
```

D. What is to be done?

We would suggest the following:

1. First, the legal community needs to be aware that a life expectancy opinion itself is not sufficient to determine the damages, and that a full life table is required.

2. When the plaintiff has a normal or near-normal life expectancy, the general population life table can and should be used (possibly with some modest "rating up" adjustment for smoking, obesity, and other factors). There is no possible justification for the commonly used expectancy method.

3. Where the life expectancy is reduced, as in the case of severe cerebral palsy, for example, an actuarially based life table is required. This is not within the expertise of the physician. An approximate life table can be obtained from analysis of the literature on survival rates for persons with cerebral palsy etc., but an actuarial analysis of a large data base is much more reliable. Methods for constructing the life table for persons with chronic disabilities are available in the literature (Strauss & Shavelle, 1998).

Footnotes
1. If this is not the case, then the magnitude and direction of the error in the methods discussed below cannot be predicted and individual calculations will be required.

2. See, for example, Schoen (1988), chapter 1 for a discussion of the life table.

3. Technically, a person's life expectancy is the average (mean) time survived by a cohort of individuals like himself. If one third of such people live exactly one more year, one third live exactly two more years, and one third live exactly nine more years, the life expectancy is (1 + 2 + 9)/3 = 4 years. The median survival time in this example is 2 years, the survival time of the "middle" person.

References

Ben-Zion B, Reddall R (1985). Life expectancy and actuarial present values: A note to forensic economists. Research in Law and Economics, 7: 161-171.

Jordan CW (1967). Life contingencies, Second Edition, p.174. Chicago: Society of Actuaries.

Schoen R (1988). Modeling multigroup populations. New York: Plenum Press.

Strauss DJ, Shavelle RM (1998). Life expectancies of persons with chronic disabilities. Journal of Insurance Medicine, 30: 96-108.

Strauss DJ, Shavelle RM, Pflaum C, Bruce C (2000). Incorporating the effect of reduced life expectancy into awards for future costs of care. The Expert Witness, Winter 2000, volume 5, number 4.

Strauss DJ, Shavelle RM, Pflaum C, Bruce C (2001). Discounting the cost of future care for persons with disabilities. Journal of Forensic Economics, 14:79-87.