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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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NOTE

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, dont l'utilisation fut sanctionnde par la

by the Supreme Court of Canada in the nowfamous 1978 trilogy of damages cases, is Cour supreme en 1978 dans la d6sormais

shown by the author to introduce serious c61 bre trilogie d'arr6ts rendus sur la queserror into the process of calculating the pre- tion de '6valuation des dommages futurs, peut produire de s6rieuses erreurs dans I'6vasent money value of lost future economic values in personal injury and wrongful death luation, en valeurs actuelles, de pertes 6conomiques A venir. Ainsi, ces valeurs accases. The error typically understates the tuelles seraient syst6matiquement souspresent money value and leads to inadequate damages awards. In situations involving the estimdes, produisant ainsi des attributions replacement of losses occurring over an ex- inad6quates de dommages-int6r6ts. Par tended number of years, successful plaintiffs exemple, obi une affaire exigerait qu'on 6vamay recover as little as one-half of their lue la valeur de pertes s'6chelonnant sur une p6riode 6tendue d'ann6es, un demandeur future losses. The error introduced by the net discount concept originates when the netting pourrait se voir allou6 un montant 6quivalant of growth rates and discount rates alters a Ala demie de ses pertes futures r6elles. L'erreur se produirait lorsque l'6valuation de critical fraction in the present value formula.

l'effet combin6 des taux d'escompte et d'acThe author demonstrates how the problem croissement modifierait une fraction essencan be solved by using a serial calculation tielle la d6termination exacte de Ia valeur method.

pr6sente. L'auteur pr6sente une solution qui saurait pallier au probl~me en utilisant une m6thode de calcul sdquentiel.

Synopsis Introduction I. Purpose of Present Money Value Awards Methodological Error in the Use of Net Discount Rates H.

Impact of the Error Indu

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*Associate Professor of Finance at the University of Miami, Coral Gables, Florida. Dr Landsea has given expert testimony on the discounting process in United States Federal District Court, Administrative Law Court and Florida Circuit Court.

NOTE Introduction A discount rate is an important element in the calculation of the present money value of future economic damages in personal injury and wrongful death cases. These damage assessment calculations typically incorporate: (a) an original or current economic value, such as a pre-injury wage potential or current medical care costs, (b) the expected growth rate of the potential economic loss (including inflationary expectations), (c) the number of future time periods over which the loss is expected to persist, and (d) a discount rate.

Discounting is required to reduce future economic losses to equivalent present money value damage awards. For instance, a plaintiff who will incur an economic loss of $20,000 a year from now (e.g., because of lost wages) will be satisfied with a damages award of less than $20,000 paid to him today.

He can invest this lesser amount now so that it will be worth $20,000 by the end of the year. In this illustration the $20,000 future loss is afuture value; the lesser amount with which the plaintiff is satisfied today is apresentvalue. The financial device used to reduce future values to present values is the discount rate.

A number of recent articles have noted the recognition given by the Supreme Court of Canada to a net discount rate concept.' This concept was first applied by the Court in three cases decided together in January 1978 and collectively referred to as the trilogy.2 The net discount rate is a rate determined by subtracting the anticipated rate of future inflation from the anticipated yield on appropriate investment securities. In the trilogy, the Supreme Court accepted the argument that inflationary expectations (then of 3.5% per annum) should be netted against currently available long term bond returns (then in excess of 10%) to produce a net discount rate (then of 7% per annum).

IDexter, Murray & Pollay, Inflation, InterestRates andIndemnity: The EconomicRealities of CompensationAwards (1979) 13 U.B.C. L. Rev. 298; Paterson, Loss ofFuture Income In Actions for Damages (1980) 26 McGill L.J. 114; Gibson, Repairing the Law of Damages (1978) 8 Man. L.J. 637; Braniff & Pratt, Tragedy in The Supreme Court of Canada:New Developments in the Assessment of Damagesfor PersonalInjuries (1979) 37 U. T. Fac. L.

Rev. 1; Feldthusen & McNair, General Damages in PersonalInjury Suits: The Supreme Court's Trilogy (1978) 28 U.T. L.J. 381; Bissett -Johnson, DamagesforPersonalInjuriesThe Supreme CourtSpeaks (1978) 24 McGill L.J. 316; McLachlin, What Price Disability?A Perspective on the Law of DamagesforPersonalInjury (1981) 59 Can. Bar Rev. 1; Connell, Discount Rates - The Current Debate (1980) 2 Advocates' Q. 138; Boyle & Murray, Assessment of Damages:Economic andActuarial Evidence (1981) 19 Osgoode Hall L.J. 1.

Andrews v. Grand & Toy Alberta Ltd [1978] 2 S.C.R. 229, (1978) 83 D.L.R. (3d) 452 [hereinafter cited to S.C.R.]; Arnold v. Teno [1978] 2 S.C.R. 287, (1978) 83 D.L.R. (3d) 609 [hereinafter cited to S.C.R.]; Thornton v. Boardof School Trustees ofSchool DistrictNo. 57 (Prince George) [1978] 2 S.C.R. 267, (1978) 83 D.L.R. (3d) 480. See also Keizer v. Hanna [1978] 2 S.C.R. 342, (1978) 82 D.L.R. (3d) 449.





McGILL LAW JOURNAL [Vol. 28 The same concept has found acceptance, albeit not unanimous acceptance, in the United States as the so-called offset method.3 Other authors argue correctly that an analysis of historical data may suggest net discount rates different from the 7% per annum accepted by the Supreme Court in the trilogy.4 Additional factors such as investment expenses and portfolio distribution effects have also been suggested as reasons for deductions from the gross investment return for the purpose of determining the appropriate net discount rate.

In fact the net discount rate concept suffers from even more fundamental problems. This note demonstrates that the rate is a mathematically inaccurate approximation 6 and leads to substantial error in the determination of the present money'value of future economic losses.

The errors introduced into the calculations by the net discount rate concept typically understate the present money value. When the present money value is understated, it follows that future economic losses cannot be made whole and, as a consequence, serious economic harm will be done to recipients of the understated judgment amounts. Given factors which are likely to occur in today's economy, understatements of present money value as small as 6% are shown to lead to shortfalls of almost 50% in the replacement of lost future values.

There is, however, a correct method for reducing forecasted future economic damages to present money values.7 The correct method does not ignore the factors recognized by the Supreme Court and by the various authors, but combines them in a manner more likely to make the plaintiff economically whole. It is to be hoped that the courts will recognize this essential deficiency in the net discount rate concept and remedy it with the same regard for precision that was exhibited in the trilogy judgments.8 See Feldmanv. Allegheny Airlines, Inc. 524 F.2d 384 (2d Cir. 1975); McCough, Future Inflation, ProspectiveDamages and the Circuit Court (1977) 63 Va L. Rev. 105; Wainscott, Computation of Lost FuturdEarningsin PersonalInjury and Wrongful DeathActions (1978) 11 4Indiana L. Rev. 647.

Dexter, Murray & Pollay, supra, note 1, 301-6; Paterson, supra, note 1; Gibson, supra, note 1, 650-2; Braniff & Pratt, supra, note 1, 25-8; Feldthusen & McNair, supra, note 1, 393-401; McLachlin, supra,note 1,25-6; Connell, supra, note 1; Rea, Inflation, Taxation and Damage Assessment (1980) 58 Can. Bar Rev. 280, 281-6; Boyle & Murray, supra, note 1, 3-7;

K. Cooper-Stephenson & I. Saunders, PersonalInjury Damages in Canada (1981) 269.

5McLachlin, supra, note 1, 27; Connell, supra, note 1, 145-6. Such deductions were made by Southey J. in Julian v. Northern and Central Gas CorporationLtd (1978) 5 C.C.L.T.

148, 159-60 (Ont. H.C.) and were not challenged on appeal (1979) 31 O.R. (2d) 388 (C.A.).

See infra, Part II especially Table 2.

See infra, Part I especially Table 1 and note 19.

8The trilogy did introduce several advances contributing to greater precision in the assessment of damages. First, the awards made in the cases were itemized rather than merely NOTE I. Purpose of Present Money Value Awards Generally, the purpose of present money value awards for future economic losses is to provide a one-time immediate payment to compensate for expected future losses. 9 For example, if an individual is injured and becomes permanently unable to earn an income he may seek damages for lost prospective future wage earnings. An award, if justified by a finding of liability, would give the plaintiff a sum to invest now to replace the expected future lost wages. Ideally, the invested sum would produce an annual income that, together with the timely consumption of a portion of the body of the award, would equal exactly the amounts lost in future wages at the time they would have been earned.

For example, assume that in a particular case lost future wages are predicated in part upon the injured party's earnings history. This history shows wages of $9,090.91 in the income year immediately prior to the plaintiffs disability. The expected future yearly wages are forecast to be, successively, $10,000.00, $11,000.00 and $12,000.00 over a three year period. 0Assuming that investment returns at the time are 15% per annum, the present money value of the lost future earnings is calculated to be $24,969.18." The present money value in this case is calculated in a series of

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steps, each year in turn. These serial calculations are necessary since each year's future value is different in amount from the values in other years.

Table 1 illustrates how the lost future wages will be replaced by interest earned on the award at 15% per annum together with partial consumption of the award in each period. Note that in the first year the $24,969.18 investment fund will earn $3,745.38 in interest at the 15%per annum rate. Since the first year's forecasted lost wages are $10,000.00, this leaves a $6,254.62 shortfall to be made up by consumption of a portion of the investment fund. In the second year the remaining investment of $18,714.56 produces $2,807.18 in interest earnings. To make up the balance of the $11,000.00 forecasted lost wages for the second year an additional $8,192.82 of the investment fund must be consumed. At the beginning of the third and final year, only $10,521.74 of the investment fund remains. This amount is entirely consumed along with the year's interest of $1,578.26 to exactly replace the $12,100.00 of forecasted lost wages.

Assuming that there are no transaction costs on the investment and no management costs after the investment was made (or alternatively considering the 15% per annum discount rate to be an investment return net of these expenses), it can be seen that the investment of the serially-calculated award at the 15% per annum rate produces enough income, along with the timely consumption of parts of the award, to provide a future payments stream exactly equal to the plaintiff's forecasted lost wage stream.

II. Methodological Error in the Use of Net Discount Rates Net discount rates, as defined by the Supreme Court in the trilogy, are being used today to assess the present value of damages in the types of situations illustrated above.'" The example given in Part I implicitly assumed a 10% wage growth rate per annum '1 and explicitly cited a 15% per annum gross discount rate. This results in a 5% per annum net discount rate.

In brief, the net discount method treats the lost future wage stream as an annuity 11 be discounted at the net discount rate. The usual form of present to See Lewis v. Todd, supra, note 9.

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value equation for an annuity is then employed,1rather than separate serial calculations for each year as was done in Part I.



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