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# «How Workable are Net Discount Rates? William F. Landsea* L'auteur d6montre que le taux d'escompte The net discount rate, a concept sanctioned net, ...»

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The assumption implicit in this procedure is that discounting an annuity by a net discount rate will produce a present value award equivalent to that obtained in the preceding example with separate serial calculations. This assumption is incorrect. To further understand the error inherent in the net discount method, consider the situation when the method is used to determine the present money value of the lost wage stream discussed earlier. In that case the income in the last year preceding the disability was \$9,090.91. This becomes the annual annuity amount to be discounted at the net discount rate of 5% (Dm = 15% and g = 10%) for a 3 year period. The net discount-annuity method determines the present money value to be \$24,756.80. '6Note that this present value is approximately 1% less than the present money value as determined previously by the serial calculation method under the same basic assumptions (DM = 15%, g = 10%, WA = \$9,090.91 and n = 3 years) in Part 1.17 Table 2 demonstrates the incompatability of the two methods of present value calculation. In Table 2 an investment of \$24,756.80 (the net discountannuity present value) is made at a yield of 15% per annum and the income is consumed along with portions of the investment to produce amounts necessary in an attempt to replace the forecasted lost wages. In the third year the income plus the remaining balance of the investment fund is insufficient to replace the forecasted \$12,100.00 annual wage. The shortfall is \$323.00 or nearly 3% of the forecast income for that year.

The reason for the understatement is that the net discount rate concept incorrectly combines the gross discount rate with the wage growth rate. This imprecision thereby alters a critical fraction created in the present value formula when the growth factor is divided by the discounting factor.,8

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The differences of 1% in the total present value and 3% in the final year's wage replacement sum may not seem overly significant in that they are relatively small compared to the total damages award. Two observations may be made at this point. First, in this instance and in many other possible circumstances the differences are small and the results are reasonable approximations of the true present value calculated by the serial method. However, as shown above, the net discount-annuity present value approximations are not mathematically accurate calculations. In inflationary times the calculations systematically undercompensate the plaintiff. There can be little excuse for a court resorting to an inaccurate approximation when absolute accuracy is possible with the serial method. It cannot even be argued that the net discountannuity method is easier to apply - the serial method formula can be reduced to an equally convenient one-step calculation. 9 Perhaps more significant is that the net discount-annuity method is sometimes a poor approximation.

Table 3 shows the percentage by which the net discount-annuity method

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understates the present value as compared to the serial method for various combinations of gross discount rates, growth rates and number of years of economic loss. From the Table a number of generalizations can be made.

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First, as would be expected, longer time periods result in greater distortion. The maximum percentage understatement found occurs at fifty years the longest time period calculated on the Table. The hardest hit by the inaccuracies of the net discount rate concept will be the young plaintiff whose life expectancy has not been reduced significantly by the disability suffered. 0 Second, the understatement caused by the net discount-annuity method is greater when the gross discount rate is high. This can be seen by comparing figures in (A), where a 15% per annum gross discount rate was assumed, with those in (B), based on a 10% rate. This holds true even when the net discount rate is identical (e.g., the understatement is greater when the net discount rate is 1% if this 1% is the result of a gross discount rate of 15% and a growth rate of 14%, rather than 10% and 9% respectively). Thus, in long periods of high interest rates, damage awards calculated under the net discount rate method will be understated more seriously.

Third, when growth rates approach the gross discount rate (i.e., when net discount rates approach zero) the relative understatement caused by the net discount rate method is minimized. Recent economic literature suggests that conditions leading to this result are rather commonplace." Finally, when the growth rate moves down from the gross discount rate (i.e., when the net discount rate grows larger) the relative understatement at first increases, then decreases as the growth rate approaches zero. Table 3 shows that the approximation of present value afforded by the net discount-annuity method varies from one set of circumstances to another, and that in some cases it produces understatements of almost 7% from the true figures.

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amount.

10One fund for the provision for future care of an infant plaintiff, Diane Teno, was calculated on 2 basis of 57 years, see Arnold v. Teno, supra, note 2, 335.

the 11lbbotson & Sinquefield, Stocks, Bonds, Bills and Inflation: Year-by-Year Historical Returns (1926-1974) (1976) 49 J. Bus. U. Chi. 11,40; lbbotson & Sinquefield, Stocks, Bonds,

-Billsand Inflation: Updates (1979) 35 Financial Analysts J. 40, 43.

"Especially given the imprecision inherent in the estimation of gross investment rates, inflation rates and the level of economic losses themselves.

3The average amount awarded for pecuniary damages in the trilogy was \$586,183.

1982] NOTE Even more serious, however, is the effect this understatement in present value has on future values. The present value understatement leads to shortfalls of much larger proportions in the replacement of future losses because of the cumulative effect of the loss of interest that would otherwise accrue 24 on the present value shortfall. For example, in the illustration given in Table 2, the \$323.00 future value shortfall is a greater proportion of the total future wage loss of \$33,100.00 (the total of the Column (4) amounts) than the present value understatement of \$212.38 is of the correct present value of the loss, \$24,969.18.

As shown in Table 4, when losses occur over an extended number of years and the gross discount rate is high, the understatement of present value caused by the use of the net discount method creates a very large shortfall in the replacement of future lost wages. For example, at an 8% growth rate, 15% gross discount rate, and 40 year period of economic loss, the present value damage award is understated by 5.96%. However, in that case the insufficient award dooms the plaintiff to a recapture of only 51% of lostfuture wages a shortfall of 49%.26 It should be noted, however, that this 49% shortfall in dollar value does not mean correspondingly that the plaintiff will not be receiving payments for the last 49% of the years of his 40 year period of economic loss. In fact, his losses will be replaced fully for 31 years of the 40 year period, and partially replaced in the 32d year. Because the growth rate results in geometrically increasing annual payment amounts, the last 8 and a fraction years (i.e. just over 20% of the years) account for 49% of the total future dollar loss.

An examination of the shortfall in future values presented in Table 4 dramatizes clearly the inadequacy of the net-discount method. It is submitted that the focus on future value shortfalls (as opposed to the relatively smaller present value understatements shown in Table 3) is justified since the object of present value discounting is to arrive at present money values which compensate for all lost potential future values. Large shortfalls, such as are illustrated in Table 4, are particularly troublesome because full compensation is now the rule in the assessment of pecuniary damages. 2 The net discount approach is clearly not an acceptable method of calculation.

"Theoretically at the gross discount rate.

"See Table 3, supra.

'Even this figure is conservative in that it does not compensate the plaintiff for the lost opportunity cost of future funds not collected due to the net discount method's initial understatement of present value.

'Andrews v. Grand & Toy Alberta Ltd, supra, note 2, 240-2.

REVUE DE DROIT DE McGILL [Vol. 28

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Conclusion The 1978 trilogy of personal injury cases introduced major advances in damage assessment techniques. Unfortunately, the cases also marked the Supreme Court's acceptance of the net discount rate - a concept with considerable common sense appeal.

NOTE 1982] However, the net discount rate has been shown to be an inaccurate approximation of the combined effect of gross discount rates and economic growth factors, as used in present value calculations. In inflationary times, use of the net discount rate will systematically undercompensate the plaintiff, conceivably up to 7% of the present value damages award to which he is entitled. The present value error leads in turn to a shortfall of even larger proportions in the replacement of future lost values, to the extent that plaintiffs could conceivably recover as little as 50% of their future losses.

Fortunately there is a correct procedure for reducing future economic damages to present money values - the serial method of calculation presented herein. This method takes into account all the factors recognized by the Supreme Court in the trilogy and applies them in a mathematically correct fashion. Furthermore, the serial method is just as easy to apply as the net discount rate approach. It is to be hoped that the courts will, in the future, adopt the more accurate method.

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