This suit by a widow for compensation for her husband's death raises primarily a somewhat esoteric, yet recurring, issue in the calculation of damages for lost future wages: Whether the present value of future wages, calculated by discounting back to the event that caused the loss, should bear prejudgment interest from date of loss to date of trial, and, if so, at what rate? This issue arises on an appeal by Hawaiian Independent Refinery, Inc. and Pacific Resources, Inc. from the March 16, 1990, judgment of the District Court for the Southern District of New York (Robert L. Carter, Judge), awarding Louanna Duffy $434,395 in an admiralty action. In re Connecticut National Bank, 733 F. Supp. 14 (S.D.N.Y.1990). The District Court discounted lost future wages and the value of lost future services by 2 percent back to the date of death and added 12 percent prejudgment interest on the discounted sum for the three and one-quarter years from the death to the trial. We conclude that the calculation method was proper but that the prejudgment interest rate might have been excessive. We therefore remand for further consideration of the appropriate prejudgment interest rate.

Plaintiff's decedent, James W. Duffy, was killed on October 28, 1986, as a result of a fire and an explosion while working in the engine department of the appellants' vessel, S/S OMI YUKON. Louanna Duffy, his widow and personal representative, sued under the Death on the High Seas Act, 46 U.S.C. app. Sec. 761 et seq. (1988), the Jones Act, 46 U.S.C. app. Sec. 688 (1988), and general maritime law. By agreement, the damages aspects of her claim under the Death on the High Seas Act were bifurcated for non-jury trial before Judge Carter.

The District Court determined damages in the following manner. First, Judge Carter estimated the likely future wages of the decedent by averaging his wages for the four years from 1981 to 1984. From that average, $50,993, he then deducted taxes. From the balance, he deducted approximately 25 percent attributable to the decedent's likely consumption in order to arrive at the net sum that would have been available to the widow. This yielded an annual payment of $29,912. Judge Carter then multiplied this amount by 10.8, representing the number of years of the decedent's estimated work expectancy. He then discounted the total net benefit from future wages back to the date of death (i.e., over 10.8 years) at a discount rate of 2 percent.1 The discounted sum was $288,506. Judge Carter then estimated, for the same 10.8 years, the value of the services the decedent would have rendered at home and similarly discounted this sum back to the date of death at 2 percent. The discounted sum for services was $11,077. To the total of the discounted sums for net benefit from future wages and for the value of services, $299,583, the District Judge then added interest at 12 percent for 3.25 years, covering the interval from the date of death to the date of trial. The interest was $134,812. The total award was $434,395.

Appellants challenge the award in two respects. Primarily, they contend that it was error to award prejudgment interest on the entire discounted sum. In their view, the effect of doing so was to allow prejudgment interest on future (post-trial) lost wages, a result they consider irrational. They argue that the prejudgment interest should have been awarded only on the payments attributable to the lost wages for the 3.25 years between death and trial, with the payments for the remaining 7.55 years from trial until the end of work expectancy discounted back to the date of trial. Second, they contend that the deduction from future wages to reflect the decedent's consumption should have been at least 50 percent.

Appellants' challenge to the allowance of prejudgment interest on the total discounted sum comprehends two complaints, which require separate consideration. The first concerns the appropriateness of permitting prejudgment interest to run on the entirety of the discounted sum. The second concerns the rate of prejudgment interest. We turn first to the allowance of interest on the entire discounted sum.

A. Prejudgment interest on discounted sum. There are two ways to perform the calculation for the present value discount of a stream of payments that span an interval beginning prior to a trial and ending at some future point after the trial. Appellants argue for a two-step method, whereby the payments that would have been received for the period after the trial are discounted back to the date of the trial, and the payments that would have been made prior to the trial are awarded with compound interest on those payments from the dates they would have been received until the date of the trial. The District Court used a one-step method whereby all of the payments, both the pretrial and post-trial payments, are discounted back to the date of death, with compound interest awarded on the total discounted sum from date of death to date of trial.

Justice Stevens recognized the availability of both methods in footnote 22 of his opinion in Jones & Laughlin Steel Corp. v. Pfeifer, 462 U.S. 523, 538 n. 22, 103 S. Ct. 2541, 2551 n. 22, 76 L. Ed. 2d 768 (1983), and suggested that it is "both easier and more precise" to use the one-step method. Id. See Taliercio v. Compania Empressa Lineas Argentina, 761 F.2d 126, 129 (2d Cir.1985) (one-step method "better" than two-step method). In fact, the two methods, properly applied,2 yield identical results, provided the same rate is used both for the present value discount and for the prejudgment interest. We will shortly consider that proviso, but, for the moment, we will demonstrate the equivalency, using an example of ten annual payments of $10,000 each to compensate for payments lost because of a death, a trial held at the end of the third year after the death (three pretrial payments and seven post-trial payments), and an interest rate of 2 percent, used both for present value discount and for prejudgment interest. Using the two-step method, we find, from standard tables, that the present value of the right to receive seven annual payments of $10,000, discounted (back to the date of trial) at 2 percent, is $64,720.3 Since present value tables are constructed on the assumption that the payment will be withdrawn from the invested fund at the end of each specified interval (one year, in our example), it is appropriate to calculate the interest on the three pretrial payments by assuming that each of these payments was made at the end of the year. Since the $10,000 payment for the first year would have been received two years before the trial, it should bear two years of compound interest ($404), the $10,000 payment for the second year, which would have been received one year before the trial, bears one year of interest ($200), and the $10,000 payment for the third year, which would have been received on the day of the trial, bears no interest. The sum of the pretrial payments, with interest, is $30,604. The total of the three pretrial payments, with interest, and the discounted value of the seven post-trial payments is $95,324.

Using the one-step method, we find, again from standard tables, that the present value of the right to receive ten annual payments of $10,000, discounted (back to the date of death) at 2 percent, is $89,826.4 Since present value tables are constructed on the assumption that the discounted sum will be available for investment at the beginning of the first interval, it is appropriate to calculate compound interest on the ten-year discounted sum for three years from date of death to date of trial. The interest payments total $5,498. The total of the discounted amount plus interest is $95,324, precisely the result obtained under the two-step method. See In re Air Crash Disaster Near Chicago, Illinois on May 25, 1979 ("Chicago Air Crash"), 644 F.2d 633, 643-44 (7th Cir.1981) (demonstrating equivalency of two methods with similar example).

Thus, appellants are simply incorrect in contending that there is something improper in allowing prejudgment interest on the entirety of the sum of the pretrial and the post-trial payments, discounted back to the date of death.5 Prejudgment interest must be awarded on the sum of the payments discounted back to date of death, just as it would be awarded on the pretrial payments alone if post-trial payments were discounted back to date of trial. Though the one-step method gives the superficial appearance of awarding prejudgment interest on future payments, as appellants contend, what really occurs is the award of prejudgment interest on the present value of those future payments, which is not at all irrational and which in fact is essential to make the two methods of discounting equivalent.6 When the discounted sum of posttrial and pretrial payments is discounted back to date of death, this sum will not yield the expected stream of payments unless it bears interest from date of death to date of trial. The discounted sum will yield the expected payments only if invested upon receipt, and it must bear interest from date of death to date of trial (i.e., date of receipt) to reflect the growth that the invested fund would have achieved by the time of the trial had the discounted sum been received at date of death.

B. Rate of prejudgment interest. The rate of prejudgment interest on a sum of payments discounted back to date of death (or other event causing loss) is a more complicated matter. Selection of the appropriate rate will often have a significant effect on the total award. In this case, for example, the prejudgment interest compounded for 3.25 years at 12 percent was $134,812. At 2 percent, which was the discount rate, the interest would have been $19,926. Appellants, convinced that the problem is the application of a prejudgment rate to post-trial payments, recalculate the award using the two-step method; they discount the post-trial payments at 2 percent back to the date of trial and add the 3.25 years of pretrial payments, with prejudgment interest at 12 percent on these 3.25 years of payments.7 This calculation yields a total award of $356,424, compared to the District Court's award of $434,395.

For her part, appellee is content simply to point out that a district court exercising admiralty jurisdiction has discretion concerning the rate of prejudgment interest, see Independent Bulk Transport, Inc. v. Vessel "Morania Abaco", 676 F.2d 23, 27 (2d Cir.1982). We think the appropriate rate of prejudgment interest in a case involving the one-step method of discounting future payments requires more analysis than either side has given the matter.

Our analysis must begin with consideration of the discount rate. In this case, Judge Carter used a 2 percent rate, a rate we suggested in Doca v. Marina Mercante Nicaraguense, S.A., 634 F.2d 30, 39 (2d Cir.1980), cert. denied, 451 U.S. 971, 101 S. Ct. 2049, 68 L. Ed. 2d 351 (1981), and one falling within the 1-3 percent range of discount rates deemed acceptable by the Supreme Court in Pfeifer, 462 U.S. at 548-49, 103 S.Ct. at 2556. What must be appreciated is the significance of that rate. It is an inflation-free rate, selected to represent, on average, the true cost of money without regard to the premium that lenders charge above the true cost of money in order to compensate themselves for the fact that inflation can be expected to diminish the purchasing power of the money they lend by the time it is repaid. See Pfeifer, 462 U.S. at 538-39, 103 S.Ct. at 2551; O'Shea v. Riverway Towing Co., 677 F.2d 1194, 1199-1200 (7th Cir.1982) (Posner, J.); Doca, 634 F.2d at 37-38. The virtue of an inflation-free discount rate is that it avoids the need to make any estimate of future inflation. The recipient of the sum of future payments, discounted at 2 percent, may make an investment at whatever interest rates are prevailing and will obtain an interest rate that, on average, will be composed of the 2 percent real cost of money plus the financial community's estimate of future inflation.

There is a further significance to using an inflation-free rate, which has a crucial bearing on this case. Use of an inflation-free discount rate reflects an assumption that the future inflation rate will not only affect the rate of return on the invested sum of the discounted payments but would also have resulted in a roughly comparable increase in the amount of payments that the wage-earner would have received. See Pfeifer, 462 U.S. at 542, 103 S.Ct. at 2553; O'Shea, 677 F.2d at 1199; Doca, 634 F.2d at 38. To account for inflation, a future stream of earnings could be increased, before discounting, to reflect cost-of-living increases likely to occur because of inflation; if such increases are made, then the appropriate discount rate is the estimated future market rate of interest, i.e., a rate that includes a component to reflect inflation. Alternatively, inflation can be accounted for by using an inflation-free discount rate, in which event no increase should be made to the stream of earnings because of inflation: The recipient's opportunity to take the sum, discounted only at a low, inflation-free rate, and invest it at a higher prevailing interest rate is assumed to compensate approximately for the cost-of-living increases that the wage-earner would have received. See Pfeifer, 462 U.S. at 542, 103 S.Ct. at 2553; O'Shea, 677 F.2d at 1199; Doca, 634 F.2d at 39-40. What is essential is that inflation be accounted for consistently, either reflected both in the future stream of earnings and the discount rate, or in neither. Pfeifer, 462 U.S. at 547, 103 S.Ct. at 2556 ("[T]he discount rate should be chosen on the basis of the factors that are used to estimate the lost stream of future earnings."); McCrann v. United States Lines, Inc., 803 F.2d 771, 773 (2d Cir.1986); Doca, 634 F.2d at 34-38.

Thus, in this case, when Judge Carter used a discount rate of 2 percent, he was implicitly assuming not only that Mrs. Duffy could invest her award at interest rates exceeding the true cost of money by the likely future inflation rate, but also that, if her husband had lived, his wages, and hence the net payments to Mrs. Duffy, would have increased at approximately that same future inflation rate. Furthermore, when Judge Carter, following Pfeifer and Taliercio, discounted the payments back to date of death, he was implicitly assuming that the inflationary effect upon the wages her husband would have received would have begun to be realized from the date of death. That is why he was correct not only to allow prejudgment interest on the discounted sum from date of death but also correct to select an interest rate above 2 percent--a rate that would include a component for inflation. See McCrann, 803 F.2d at 774.

Whether he was correct in selecting a rate as high as 12 percent, however, is less clear. If Mrs. Duffy could have earned that rate on relatively risk-free investments, had she received the discounted payments at date of death, the 12 percent rate would have reflected the financial community's prediction of an annual inflation rate of 10 percent (12 minus 2) starting with the year of Duffy's death and would also have reflected, though with less certainty, a likely annual increase in her husband's wages of 10 percent, attributable solely to inflation. To see the effect of such anticipated inflation, we return to the example, previously discussed, of ten equal payments of $10,000 a year, with three due before trial and seven due after trial. Using the one-step method, we now apply a 12 percent prejudgment interest rate to the stream of payments, which was discounted back to date of death at 2 percent. The discounted sum of $89,826, with 12 percent interest compounded (on an assumption of investment at the start of the first year) for three years, totals $126,199. This is the sum that would be awarded in our example, under the calculation used by Judge Carter.

Though that sum is considerably larger than the sum that would be produced by the two-step method urged by appellants, even if a 12 percent prejudgment interest rate is applied to the pretrial payments totaled in the second step,8 the increase simply reflects the assumed effect on wages of an assumed annual inflation rate of 10 percent during the pretrial years, assumptions that are inherent in the application of a 12 percent prejudgment interest rate to the sum of a stream of payments discounted at 2 percent back to the date of loss. To whatever extent the prejudgment interest rate exceeds the 2 percent discount rate (10 percent, in the instant case), the effect is to increase by that rate increment each year the payments that could have been withdrawn at the end of each of the years for which prejudgment interest was added. The further effect, if we assume that after the trial the fund balance, from which the pretrial (inflated) payments are assumed to have been withdrawn each year, is invested at only 2 percent, is that the fund will produce a series of post-trial payments, each equal to the amount of the last (inflated) payment that could have been withdrawn prior to trial. If the fund can be invested, after the trial, at a rate above 2 percent, the effect would be to increase still further the size of each payment by a percent approximately equal to the difference between the investment interest rate and the 2 percent discount rate.

These effects can be demonstrated by further calculations in our example of ten payments of $10,000, three pretrial and seven post-trial, and a discount rate of 2 percent. We now take the present value of all ten payments, discounted back to date of loss, and apply a 12 percent prejudgment interest rate. We start with $89,826, add 12 percent (representing the first year's interest), subtract $11,000 (the first year's payment of $10,000 increased by 10 percent for inflation), add 12 percent to the balance (representing the second year's interest), subtract $12,100 (the second year's payment of $10,000 increased by two years' worth of 10 percent annual inflation), add 12 percent to the balance (representing the third year's interest), and subtract $13,310 (the third year's payment of $10,000 increased by three years' worth of 10 percent annual inflation). The balance is then $85,539. That sum, if invested at 2 percent (the rate used to discount the stream of payments), will yield approximately seven more payments of $13,310 (actually six payments of $13,310 plus a final, slightly short payment of $12,617).

Thus, the selection of a prejudgment interest rate to be applied to the sum of a discounted stream of payments has more significance than in the typical case where a rate is applied to compensate a plaintiff for the fact that a sum certain that was due at some date in the past is not paid until judgment. In the typical case, use of a prejudgment interest rate slightly higher than the rate at which the plaintiff might actually have invested the money wrongfully withheld from him provides a bonus, but has no implication for the future (other than the plaintiff's opportunity to invest the bonus). In our case, however, the prejudgment interest rate, to the extent that it exceeds 2 percent, inflates the size of all the payments that will be received in the future. It is not necessarily incorrect to do so. If, during the three and one-quarter years from Duffy's death to the trial, inflation had been 10 percent each year, then it might well be appropriate to select a prejudgment interest rate of 12 percent that will yield payments increased by 10 percent a year through the date of trial and to continue those inflated payments for the remainder of his work expectancy. If inflation had occurred at a rate of 10 percent each year, his wages might well have increased at that rate during the interval prior to trial and, even if no further inflation occurred, remained at the inflated level for the remainder of his work expectancy. On the other hand, a 12 percent prejudgment interest rate should not be selected unless the trier of fact concludes that the wages of the deceased (and hence the net payments to his wife) would have risen, because of inflation, by approximately 10 percent annually during the period between death and trial.

In this respect, the one-step method of discounting diverges in effect from the two-step method whenever the prejudgment interest rate applied to the sum of the discounted payments exceeds the discount rate. Under the two-step method, with the stream of payments discounted back to the trial, the payments after trial are not increased at all by whatever inflation occurred between date of death and date of trial;9 the payments for the period before trial are, in effect, increased by the pretrial inflation by virtue of the inflation component of the prejudgment interest rate applied to those pretrial payments. Under the one-step method, as we have seen, the inflation component of the prejudgment interest rate inflates the pretrial payments and also continues that inflation increment for all future payments. That dual effect is proper, but it underscores the need to select a prejudgment interest rate that includes a component for inflation no greater than the inflation that occurred during the interval between date of loss and date of trial.

Since the rate of inflation prior to trial is ascertainable, it should be considered in selecting a prejudgment interest rate that will have such a significant effect on the entire stream of payments. Under the two-step method, it is tolerable to make the assumption, applicable to future payments, that inflation would have increased those payments by the inflation component of whatever interest rate the recipient can obtain on the invested fund. The assumption may not always be true, but it is an acceptable assumption to make in the inevitably uncertain exercise of predicting the future. Under the one-step method, however, which Pfeifer instructs us to apply, it is unacceptable to assume that the inflation component of interest rates equals the inflation of wages during a period in the past for which this equivalency can be checked and the actual inflation rate can be ascertained.10

Since the District Judge gave no indication of the basis for selecting the 12 percent prejudgment interest rate, we cannot assume that he chose it to reflect an assumed annual inflation rate of 10 percent. In fact, the annual increases in the consumer price index for the years 1987, 1988, and 1989, were 3.7 percent, 4.1 percent, and 4.8 percent, respectively. See Lab. Rel. Expediter (BNA) LRX 430:742-47 (all urban consumers). Though an admiralty court has discretion in selecting a rate of prejudgment interest, that discretion must be exercised with particularity in a case such as this, where the rate has such significance, especially on future payments. On remand, the Court should carefully select a prejudgment interest rate, giving consideration to the interest rate the plaintiff could likely have received on relatively risk-free investments and giving particular attention to the inflation rate during the three and one-quarter years prior to trial.

In calculating the likely payment Mrs. Duffy would have received from her husband's wages, net after his consumption, Judge Carter considered the 50 percent deduction from after-tax wages that Judge Weinfeld deemed appropriate for a wife with no dependents in Petition of Marina Mercante Nicaraguense, S.A., 248 F. Supp. 15, 27 (S.D.N.Y.1965), modified on other grounds, 364 F.2d 118 (2d Cir.1966), cert. denied, 385 U.S. 1005, 87 S. Ct. 710, 17 L. Ed. 2d 544 (1967). Though the 50 percent deduction has been used by other fact-finders, see In re Marine Sulphur Transport Corp., 1974 A.M.C. 1504 (S.D.N.Y.1974), and may frequently be appropriate, it is not a rule of law. Judge Carter weighed the fact that Duffy's normal schedule took him to sea for extensive portions of the year and concluded that a consumption deduction of approximately 25 percent was sufficient. That is a finding of fact, and it is not clearly erroneous.

Because of the need to reconsider the prejudgment interest rate, we vacate the judgment of the District Court and remand for further consideration in light of this opinion.