Net Accumulation to the Estate: Meaning and Measurement

Journal of Forensic Economics 20(3), 2007, pp. 227-250 © 2009 by the National Association of Forensic Economics

Net Accumulation to the Estate: Meaning and Measurement Frank Slesnick and Michael J. Piette* I. Introduction In addition to loss of support, wrongful death actions in many states require the estimation of lost net accumulation to the estate or loss of inheritance as a separate element of damages. Conceptually, net estate accumulations are simply a loss of the difference between the value of the estate in the future, had the tort not occurred, compared to the value of the estate at the actual time of death. This approach allows for recovery claims by individuals who were not directly supported by the deceased, including adult children. As a result, these types of actions are sometimes referred to as “survivorship cases” as opposed to “wrongful death cases.” It has been the authors’ experience that in these types of cases, numerous conceptual errors are made in terms of what is meant by net estate accumulation and, most important to the forensic economist, how it is measured. The purpose of this paper is to help clarify the issues surrounding the concept of net estate accumulation and to provide insights regarding the correct calculation of these losses. The paper is organized as follows. Section II focuses on the legal parameters imposed by the courts and the specific guidelines concerning how the economist distinguishes between lost net accumulation to the estate and loss of support. A review of the economics literature is provided in Sections III and IV. In the forensic economics literature, there are few articles written regarding the measurement of lost net accumulation to the estate. On the other hand, there is a significant literature outside of forensic economics that investigates the question of whether Americans adequately save for retirement and the extent to which money is available at the time of death for estate purposes. If, in fact, most Americans do not save enough for retirement, then it is reasonable to conclude that there will be very little passed on through the estate except perhaps for the very wealthy. Section V addresses some common mistakes made by economists when calculating lost net accumulation to the estate. Based upon discussion in this section and review of the literature, an extended example is presented in Section VI. Using simplified assumptions, we indicate the circumstances under which lost net accumulation to the estate estimates are worthwhile. The example can be manipulated to demonstrate how changes in various parameters such as age

*Frank Slesnick, Bellarmine University, Louisville, KY; Michael J. Piette, Analytical Economics, Inc., Tallahassee, FL.

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of the decedent, the savings rate, or the consumption rate in retirement affects the estimate of loss. Summary and conclusions are contained in Section VII. Our main conclusion is that except under unusual circumstances, a net accumulation loss to the estate is a very small portion of total economic losses. Unusual circumstances would include individuals who are relatively young with demonstrable high levels of future income. In these cases, the savings rate would have been relatively high, consumption in retirement low, and the return on investment that would have been earned by the decedent often higher than the return on investment earned by survivors. II. Legal Parameters In the State of Florida, net accumulations are defined in the Florida Wrongful Death Act as ....the part of the decedent’s expected net business or salary income, including pension benefits, the decedent would have retained as savings and left as part of his estate if he had lived his normal life expectancy. “Net business or salary income” is the part of the decedent’s probable gross income after taxes, excluding income from investments continuing beyond death, that remains after deducting the decedent’s personal expenses and support of survivors, excluding contributions in kind. (Florida Statutes, Chapter 768, 2008, p. 1)

In this regard, the net accumulations to the estate are akin to a net worth concept (Williams, 2002). In particular, the loss is the difference between the present value of the estate, had the premature death not occurred, and the current value of the estate that was actually received by survivors. This difference and others are explored more fully in several important cases, including Delta Airlines v. Ageloff (1989). Ageloff was 29-years-old at the time of death and had no dependents. The sole issue in this case relates to the estimation of the lost net accumulation to his estate. Prior to trial, Delta filed a Motion in Limine regarding testimony about returns on any future savings. This motion was denied. But there were several other matters brought up that are of interest. A prominent part of the discussion is related to the assumed discount and investment rates. The plaintiff hired two economists. The first economist assumed that Ageloff would have reinvested 25% of his income back into the family business and that investment would yield a 12.5% return. He then discounted future returns back to the present at 7%. The second plaintiff’s economist assumed that the savings rate would start at 10% of income but rise to 25% within 20 years. Like the first economist, the second economist assumed that savings would be reinvested in the family business but would earn an 8% return rather than a 12.5% return. Future returns were discounted at 7%. The defense economist, not unexpectedly, made more conservative assumptions with regard to the savings rate, the level of income, and the invested rate of return. Interestingly, he was the only economist who calculated consumption during the retirement years. Final calculations showed that the two plaintiff’s

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economists calculated lost net accumulation to the estate in the range of $2 million to $3 million while the defense economist’s estimate was less than $300,000. The jury returned a verdict of $1 million. The plaintiff’s experts’ assumption that the rate of return on investment was greater than the discount rate implies that the investment ability of the decedent was greater than that of the survivors and was no doubt important in calculating the relatively high losses. Defining the return on investment by the deceased as Rd and the return on investment by the survivors as Rs, the plaintiff’s economists assumed that Rd > Rs. The key question: Under what circumstances is it reasonable to assume that these rates are different? As described in the Delta case: They (net accumulations) are supposed to represent what the decedent’s estate would have been worth at death. This sum is reduced to present value so that it can be reinvested by the survivors, with the intention that when the estimated natural death of the decedent occurs the estate will equal what it would have been worth had he not died. (p. 548)

In most situations, it is reasonable to assume that Rd and Rs are equal. This is obvious if the decedent had funds invested in publicly available mutual funds that are accessible to anyone willing to pay the money. If, for example, the decedent was earning on average an 8% return on an indexed portfolio of stocks and bonds, then the survivors could certainly duplicate this portfolio. What sometimes happens, however, is that the economist estimates at the expected return of the invested savings and then compares that to the risk-free return used in most personal injury/wrongful death cases. The critical point is that when comparing Rd and Rs, it is important to compare portfolios of comparable risk. If the increase in return was obtained only by an increase in risk, then assuming different values for Rd and Rs is not correct. The two might be different, for example, if the deceased ran a business and, due to his special skills, was able to obtain above-normal profits for a considerable period of time. Interestingly, the opposite could also be true. For example, the deceased might have received most of his money from an inheritance and subsequently made poor investment decisions. In that case, Rd < Rs and the survivors are actually better off receiving the money early. A second issue raised in the Delta case concerns assets passed on to survivors at the actual time of death. ....income from investments in which the decedent had an interest at his death is passive income which continues to accrue regardless of his skill or efforts. The untimely death deprives neither the decedent’s estate nor his survivors of the income from these investments. (p. 547)

The argument here is that income accrued at death should be ignored. It must be pointed out, however, that just as future additions to savings might be invested at a higher (risk-adjusted) rate than could be earned by survivors, the same could be said for previously accumulated assets as well. The word “passive” is the key, implying that accumulated funds were not actively invested (at

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least with no superior skill) and hence the return could be duplicated by the survivors. The case description also notes that the defense economist took into account consumption during years of retirement. Although there is no indication that the court approved or disapproved of this calculation, it is apparent that such consumption would have to be considered, given the estate is valued at the time of death. As will be shown in Section VI, consumption in retirement implies that the net loss to the estate will likely be negative the closer death occurs to the age of retirement. As an extreme example, if the deceased died the day he retired, then there are no further additions to retirement savings (although there is interest on existing assets), while the savings are drawn down for self-consumption and support purposes. Another important Florida case is Tobias v. Osorio (1996). One part of the commentary indicates that there was insufficient testimony concerning the savings habits of the deceased to establish any foundation for a claim for lost net accumulation to the estate. In particular, there was no demonstrated propensity to save. It would not be surprising, however, that if the decedent were young there would be no record of prior savings. Studies of life-cycle behavior show that savings are often negative initially but become positive as the person ages. However, based upon the result of this particular case, it is uncertain whether the court would accept this type of evidence. A similar question arose in Synergy Gas Corporation v. Idella Johnson (1993). The commentary stated that: Amounts awarded for loss of net accumulations to estate was not supported by economic expert’s testimony that decedent would have saved six percent of his income per year for the next 26 years where there was no evidence of decedent’s propensity to save or whether he had saved anything at all at time of his death. Clearly, the jury impermissibly based its award of net accumulations on passion, prejudice, corruption or other improper motive. (p. 1872)

Sorting out the amount of savings is often so difficult that the forensic economist may simply lump together support and lost net accumulation to the estate. More specifically, if one subtracts taxes (T) and self-consumption (Cd) from gross income (Y), one is left with funds for support of dependents (Cs) and savings (S). The forensic economist will then calculate Y – T – Cd = Cs + S as an estimate of loss without attempting to distinguish between them. Krueger and Albrecht (2008) expand on this notion in a recent article. For these authors, total loss is defined as the sum of loss of support to the survivors plus lost savings which, in turn, is equal to earned income minus self-consumption of the deceased. Loss is not distinguished between support and net accumulation. This is the same point we made above. As stated by the authors, “This result is important as such allocation would be difficult to reliably measure and it eliminates the need for a separate net estate accumulations calculation.” (p. 40) By assuming that the discount rate and the growth rate of invested savings are equal, Rd = Rs, the authors arrive at the conclusion that the present value of economic loss is simply the sum of loss of support plus savings

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(or investment). As we will point out later herein, the Krueger and Albrecht conclusion (as the authors themselves recognize) does not hold if Rd does not equal Rs. III. Forensic Economics Literature Other than the Krueger and Albrecht article cited above, the forensic economics literature on estate accumulations is limited. One of the first articles on this topic was published by Scott and PonArul (1991) in the Journal of Forensic Economics. The authors provide a straightforward model where loss is equal to the discounted present value of the estate at the expected time of death had premature death not occurred. Of note, their model assumes that the rate of return on invested savings is equal to the discount rate. Thus, using our terminology in this paper, the article assumed that Rd = Rs. The model focuses on additions to savings which, as pointed out above, does not sacrifice accuracy given Rd = Rs. In fact, the authors make this assumption explicitly when they write, “If the discount rate is representative of interest on safe and secure securities, then it is appropriate to assume that this same rate would have been earned on the savings that the individual accumulated.” (p. 227) A numerical example is provided in their article. The estimated loss is extremely small and as a result, the authors imply that this type of calculation may not be worthwhile and can be safely ignored in most cases. More recently, an article by Frasca (2002) offers a framework for estimating how much of the inheritance is lost due to a tort. On this issue, Frasca states, “The lost prospective inheritance should only include that part of a future inheritance that could not be replaced by the reinvestment of the current inheritance received by the plaintiff.” (p. 85) As indicated earlier, that is correct for the usual situation where Rd = Rs. On the other hand, if Rd = 10% and Rs = 7%, then one should include the incremental 3% return on assets already accumulated. In contrast to the Scott and PonArul model, Frasca proposes a model in which survival probabilities are explicitly considered. Savings are assumed to start at $10,000 and are increased by 3% per year until age 65. At retirement, a variety of withdrawals could have been utilized. The one used was designed so that the balance of funds would last until age 100. Of course, the estate would have a positive value as long as death occurred prior to that time. The value of the estate each year is multiplied by the probability of death, which, in turn, is discounted at a rate equal to 5%. The sum of these discounted values is the expected present value of the estate. A second table adds another layer of complication. In particular, individuals cannot receive the money from an inheritance unless they are alive at the time the individual who owns the estate has died. Thus, this consideration estimates a joint probability. If the survivor is fairly young, it will make little difference. Frasca indicates that one could also use this model if the deceased is an adult child. Even with a small probability of the parents collecting, with all the necessary information one could calculate the damages. It should be noted,

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though, that in many cases there are multiple recipients of the estate so calculating such joint probabilities would be extremely difficult. One point that Frasca brings out is that incorporating survival probabilities does increase the estimated loss compared to the certainty model reflected in the Scott and PonArul article. The reason is that in the Frasca model, the survivor could receive the estate at an earlier age before it was largely dissipated through expenditures during the retirement years. As discussed in the next section, one of the primary reasons why estates are left is that they are accidental. That is, individuals save their money for retirement and even if they intend to spend it all in their retirement years, premature death results in a positive estate. The chance of an accidental bequest is what Frasca incorporates into his model. David Jones (unpublished paper, presented at the Eastern Economic Association meetings, 2004) reviewed some of the common errors that are made when calculating lost net accumulation to the estate. One is that the pension fund accumulated over past decades should not be counted. Another error, as noted above, is that one must avoid double counting both loss to the estate and loss of support. For example, if one calculates a complete wrongful death analysis including all of the after-tax income of the deceased (i.e., income less personal consumption), it is not permissible to include savings as loss to the estate. Thus, to some extent, loss of support and loss of accumulation become mutually exclusive. Jones states that physical assets, especially housing, are a large part of any estate. If the house is passed on at the actual time of death, it is unlikely that the house would be part of the loss estimate. One way that might happen is if the deceased was very handy and was planning to significantly improve the value of the house. Jones also points out that much of a person’s wealth cannot be left to the estate. This obviously includes wealth which disappears once the person dies such as Social Security benefits and other life annuities purchased privately. Jones further indicates that the value of the estate is “humped” shaped. It rises to around age 50 or so and then declines. Thus, for the average person over age 50, the loss to the estate is probably negative. The paper also emphasizes that whatever estate is left, the amounts are relatively small. Citing numerous government studies, it is clear that the vast majority of Americans are poor savers and will leave small estates or no estates whatsoever. IV. General Economics Literature The literature pertaining to this topic outside of the field of forensic economics provides valuable information, especially in terms of retirement savings rates and understanding how bequests are made. One of the most useful compendiums in this area is Death and Dollars, The Role of Gifts and Bequests in America (2003). In Chapter 3, Pestieau examines the underlying motives for giving a bequest. One such motive is termed the “altruistic bequest” since parents care about their children. This leads to the hypothesis that parents who are

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wealthier leave larger bequests and parents attempt to equalize children’s incomes so children with lower incomes receive larger bequests. A second motive is the “joy-of-giving or paternalistic bequest.” Parents are motivated by the act of giving itself, often called “warm glow” giving, to individuals or institutions. It is related to a virtuous feeling of sacrifice, a need to help one’s children, or to control their lives. Formally, giving money directly enters the utility function as a consumption expenditure taken later in life. There is also a third motive where bequests are given in exchange for attention to the parents from the children. This is commonly called the “exchange-related motive.” They are not compensatory and do not result in an even distribution between children. The last possibility is no motive at all: it is simply an “accidental bequest.” Whereas the first three are bequests by design and motivation (altruism, joy of giving, or exchange-related), this latter possibility relates to accidental bequests due to life-cycle savings behavior. People die prematurely and hence bequests occur unintentionally. As noted earlier, the Frasca model incorporated this motive by including probabilities of death for each year. Interestingly, even if the estate tax were 100%, there would be no impact upon the amount saved for retirement and given as a bequest if this was the only motive. The literature suggests that there is a great deal of uncertainty regarding the underlying motive for bequests. Orszag, commenting on the chapter by Pestieau, indicates that a combination of the accidental bequest and altruistic motives are primary. Individuals accumulate money as a precaution against uncertainties, especially high medical costs. However, they hope that there is enough left over that they could pass on some funds to their heirs. “Ex-ante, the motivation is thus mixed. Ex-post, the data suggest either a large bequest or not, depending upon whether the person suffered high medical or other expenses at the end of life.” (p. 88) In Chapter 4, Michael Hurd (2003) emphasizes the need to distinguish between retirement assets that can be provided in an estate such as stocks and bonds vs. those that cannot such as Social Security or life annuities. It should also be noted that the house is the largest asset of many people. It is often passed on in the estate for personal reasons. However, from the perspective of calculating lost net accumulation to the estate, it would be unusual if the value of the house would increase in present value relative to the value when passed on at the actual time of death. Hurd sees a relatively weak or no motive for bequests other than an accidental motive. Even with housing, there is evidence of a decline in the value of home ownership as the person ages. In an article written under the auspices of AARP, Mitja Ng-Baumhacki, et. al., (2003) examined the loss of support question of how much the baby boomers might receive as a bequest. Estimates of estates vary greatly depending upon what is considered wealth. Some researchers include gifts during one’s lifetime, the value of social security, and even contributions to human capital such as expenditures on college. Of course, intervivo gifts should be captured in loss of support calculations. There is also a question of the proper unit of measurement—individuals, households or estates. Differences also vary as to bequest motives and family size. Some researchers exclude childless couples, assuming that they are not motivated to provide estates. Others include them on

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the assumption they plan to leave estates to other individuals or entities. Measuring inheritances is also difficult because the data are generally self-reported and matching records is difficult. Despite these uncertainties, there are several factors that influence the size of bequests. Bequests will be larger the greater parental wealth. On the other hand, bequests will be smaller, the longer the life expectancy and the earlier the retirement age. Bequests will be smaller, the greater the chance for unexpected events such as high out-of-pocket medical bills. Bequests will also be smaller, the greater are annuitized assets such as Social Security and certain kinds of company pensions which normally cannot be passed along within the estate. Finally, bequests will be smaller the greater are estate taxes. Based upon the Federal Reserve’s Survey of Consumer Finances (SCF), the article examined both how much individuals had received in the form of bequests and how much they expect to receive in the future. The analysis was broken down between three cohorts—pre-boomers, boomers, and post-boomers. In 2001, only about one-quarter of the respondents indicated they did receive or expected to receive an inheritance. This was true of all three cohorts. Further, these percentages had actually fallen from 1989 through 2001. In 2001, of those who actually received an inheritance, the average amount was $108,885 for pre-boomers, $47,909 for boomers, and $22,167 for post-boomers. One would expect, of course, that the older generation would have received more. It should be noted that this average excludes those who received nothing and also includes the value gifts. Not surprisingly, the vast majority of inheritances in terms of dollars were more than $100,000 and these large inheritances went to wealthy households. Specifically, the top two quintiles in terms of net worth received about twothird of all inheritances. Further, of those inheritances greater than $100,000, 86% went to the top two quintiles. As a concluding comment the AARP article notes, “As of 2001, only 14.9% of boomers expected to receive an inheritance in the future, suggesting that for most people inheritances will remain an elusive, or small, contributor to their retirement security.” (p. 7) Brian K. Bucks, et. al., (2006) draws from the Federal Reserve Board’s SCF between 2001 and 2004, as well as earlier surveys. There is an examination of net worth (wealth), which is the difference between the family’s gross assets and its liabilities. It should be noted that the definition of assets is comprehensive, including both financial and non-financial assets, for both retirement and non-retirement purposes. As expected, net worth displays a “humped pattern” that peaks at age bracket 55-64 and then declines. In particular, the mean value (2004) is $99,200 for ages 35-44, $843,800 for ages 55-64, and $528,100 for ages 75 or more. There is a very large difference between mean and median net worth. For all families, mean net worth is $448,200 while median net worth is $93,100. Net worth for the 25th percentile is -$1,400 and for the 90th percentile it is $3,114,200. As expected, net worth is strongly correlated with education. For households where the head has less than a high school degree, mean net worth is $136,500 while for households where the head has a college degree, mean net worth is $851,300.

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The survey looks at the holdings of various financial assets. Of particular interest are retirement accounts. For the age group 55-64, an age where one would expect such accounts to be owned, only 62.9% own such an account (of any size). The median value of such accounts for the same age group is $83,000, while the accounts average $80,000 for the age bracket 65-74 and $30,000 for the age bracket 75 or more. It should be noted that the definition of retirement accounts used in the SCF relate to portable accounts such as IRAs, employersponsored accounts such as 401(k) and 403(b) plans, and thrift savings plans. It does not include Social Security or pension (defined benefit) plans. On the other hand, these sources of retirement income normally cannot be passed on as an inheritance. One of the most comprehensive analyses of bequests was authored by Michael Hurd and James Smith (2002). Based upon data from the Health and Retirement Study (HRS), as well as several companion surveys, the authors examine both the bequests that individuals actually leave and bequests they intend to leave. A focus of this study, like the study cited above by Mitja NgBaumhacki, et. al., is to compare different cohorts in reference to these issues. One table examined the actual bequests made by the oldest cohort, those households where one member was born in 1923 or earlier, given a member died between 1992 and 1998. One in five had no estate value, the mean value was $104,500, and the median value was $62,200. Some respondents indicated they were left relatively large estates: 5% were left in excess of $300,000, and 3% were left in excess of $600,000. A second table indicated that most financial inheritances are bequeathed to members of the immediate family. A surviving spouse will get about threefourths of the estate, with one-fourth going to the children. At the death of the surviving spouse, the children will get 90% of the estate. All other beneficiaries receive very little money. The study also showed that, consistent with other studies, parents give equal financial inheritances to their children. Of interest, the study further examined the estate provided each child. Forensic economists often have cases where the beneficiaries are the adult children. The median intended inheritance per child of the oldest cohort was $7,700 while for the youngest cohort it was $19,200. Nineteen thousands dollars is still a modest sum, the flow from which can only finance small additional consumption flows over a lifetime. In spite of the large secular increases in estate values and in the amount of resources transferred at death, most adult children of parents the generations 1947 and earlier can not expect to receive much help from their parents in the form of inheritances. As far as the distribution of inheritances is concerned, we estimate that inheritances by children will become more unequal in the future than they were in the past. (p. 17)

The study also compared the actual wealth of a cohort and the amount individuals predicted they would leave in their estate. Given these predictions are reasonable estimates of what will actually happen, the numbers imply that most respondents anticipate a significant amount of dissaving during their

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years in retirement. In particular, the rate of dissaving is a function of a number of variables including whether the household is single or a couple, and the ages of the household members. Dissaving is relatively small until the household is in its 70s. By the time the household members are 85 and older, the annual rate is almost 10%. This result supports the conclusion that consumption in retirement should be incorporated into the analysis when the forensic economist estimates economic loss. A great deal of research indicates that Americans do not satisfactorily prepare for retirement and do not properly take into account the information that is available. However, other studies indicate that falling below what is “optimal” depends upon what we mean by that term. It could very well be that lowsaving workers can fall back on Social Security or public assistance to support minimal compensation in old age. Further, the decline in consumption after retirement may have been “rationally” anticipated by workers. Surveys show, in fact, that for many people there is not a drop in well-being despite the lower levels of consumption. See, for example, Burtless (2004) and Lowenstein, et. al. (1999). This indicates that spending needs have also decreased. All of this does not prove that workers are rational in terms of retirement planning. It only suggests that it is hard to rule out this possibility, given the evidence available. The traditional life-cycle hypothesis indicates that consumption over a lifetime should be fairly smooth. We expect that early in a person’s career and, given family expenses, savings will be negative, eventually becoming positive as earnings rise and other expenses such as children fall. At retirement, a fund has been accumulated, to be drawn down until death. Wealth is clearly maximized at the time of retirement. There is compelling evidence, however, that a significant number of individuals enter retirement with very little savings, while others with assets actually add to them during retirement. Both of these results are difficult to integrate into the life-cycle hypothesis. There is no doubt many individuals have almost no savings when they retire. Burtless cites data indicating that those in the lowest 25th percentile had little wealth, averaging $28,000 in 1992 dollars (2004). Despite this, however, the optimal amount of savings at retirement may be zero. Since some of these workers may not be eligible for public assistance unless their liquid savings are very low, it may make no sense to accumulate pre-retirement wealth. The availability of Social Security, public assistance, and company provided pensions mean that the amount of savings depends critically on individual circumstances. (pp. 23-24)

The other problem with the life-cycle hypothesis is that consumption declines 15-20% in retirement. However, Burtless believes workers largely anticipate the decline. Thus, worker’s retirement plans may be rational, given expectations that spending needs will eventually decline. In sum, entering retirement with few assets and reducing consumption during retirement may be a rational response to lower expenditure needs and a publicly available safety net. Hence, there is little reason to believe that savings habits will necessarily change in the future based merely upon a call to be more “rational” or “forward-looking” in planning for retirement. This suggests

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that barring major social policy changes, there is no reason to be optimistic that savings will increase significantly in the near future. V. Some Common Mistakes In this section, we examine some of the most common mistakes made when calculating lost net accumulation to the estate. These mistakes are based upon the economic literature and reports reviewed by the authors in the past. The Rate of Return on Investment Is Different From the Discount Rate In Delta Airlines v. Ageloff, the plaintiff’s economists assumed that the rate of return on investment (Rd) was greater than the discount rate (Rs). In order for this to be true, one would have to show that the decedent could earn more than the survivors at comparable risk. An example might be if the deceased had owned a business where above-average returns were fairly assured. But ownership of a real estate firm in Florida, where returns were calculated from 2003 through 2005, would not be adequate proof that above average investment returns were warranted. One might, in fact, propose a null hypothesis that unless significant evidence is presented to the contrary, it is reasonable to assume that Rd and Rs are equal. Certainly if the deceased had owned a passively managed portfolio such as a 401(k) invested in broad-based mutual funds, there should be no difference between Rd and Rs. Even ownership of physical assets such as a house provides no guarantee that ownership by the deceased would have produced larger increases in value than if held by survivors. In fact, the value of the most important physical asset, the family home, often declines in terms of net worth if the owner takes out a reverse mortgage. Counting Assets Previously Accumulated The Delta case makes it very clear that one should not count “passive income” that would continue even after death. Basically, this means that only savings arising from future income should be counted. However, as discussed above one may need to look at previously accumulated assets if Rd and Rs are different. If Rd > Rs, then premature death has lowered the value of the estate to the survivors while the opposite is true if Rd < Rs. Manipulating the Division of Family Income This error can be explained by example. John Smith made $100,000 per year after taxes. There is also trust income of $200,000 per year. Assume there is evidence that consumption of the Smith family prior to his death was $200,000, $50,000 for each member of the family. The forensic economist states that due to Smith’s death, lost net accumulation to the estate is $100,000 per year since all of Smith’s income was saved. That is, the trust income was sufficient to provide for all the family’s consumption needs.

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This approach ignores the fact that under normal circumstances specific categories of spending cannot be traced to specific sources of income so it is necessary to consider consumption of the deceased. The proper approach is to analyze the family’s losses and what it needs to be made whole. In this example, prior to Mr. Smith’s death, family consumption was $200,000 and savings were $100,000. Now the surviving family members require $150,000 to provide for the consumption of the three family members and $100,000 in savings for a total of $250,000. That means the compensation required is $50,000 since they still have the $200,000 from the trust income. Of course, this same amount could have been calculated by taking Smith’s income of $100,000 and then subtracting his self-consumption equal to $50,000. VI. An Extended Example In this section we shall provide an example to study a number of questions concerning estimation of lost net accumulation to the estate. In particular, we ask the question: under what circumstances is it likely that there will be a loss? When considering this issue, it is important to note that not only must there be a sizable estate left at the expected time of death had the tort not occurred, but that estate must be greater (in present value terms) than the amount passed on at the actual time of death. As a general comment, the basic assumptions of the example (listed below) are designed so that loss to the estate is more likely. Nevertheless, as will be shown, the amount of loss is relatively small. The assumptions are as follows. (1) The individual who has died prematurely was a male with a Master’s Degree who entered the workforce at age 25. This assumption implies that the analysis focuses on an individual with earnings significantly higher than average. (2) The individual was married and there were no children. Any money available in the estate would be passed on to the wife. (3) Three different ages are examined. First, it is assumed that death occurs at the time the person first entered the workforce, age 25. Also, ages 40 and 60 are examined to reflect death occurring in the middle and towards the end of work life. All deaths occur in the year 2006. (4) The rate of increase in earnings is based upon two factors – life-cycle earnings and across-the-board increases based upon changes in the general economy. In particular, life-cycle earnings are adapted from Full-Time Earnings in the United States, 2006 Edition (2007). The across-the-board increase in earnings is set equal to 4%. This reflects the rate of increase in wages forecasted by the Social Security Administration (2007). (5) For simplicity, taxes are ignored.

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(6) The annual contribution towards retirement and any bequest is assumed to be 15% of earnings. This is overly generous based upon the savings habits of Americans; it is used only for this example and not for realism. That rate will be changed to test the sensitivity of this assumption in determining economic loss. (7) It is assumed that the rate of return on invested funds is 8%, roughly in line with the return on a mixed portfolio of stocks and bonds. Since the portfolio reflects passive investment and could be duplicated by heirs, it is further assumed that the discount rate also equals 8%. There will also be an analysis where the investment rate and discount rate are not equal. (8) It is assumed that we can calculate the rate of consumption for both the husband and wife during retirement. One of the guidelines utilized when planning for expenditures during retirement years is that prospective retirees should try to have sufficient funds to spend a certain percent of their earnings received in the last years of work. Utilizing this simple rule of thumb, it is assumed that consumption in the first year of retirement is a percentage of earnings in the last year worked. Initially, that percentage will be set equal to 50%. Alternatively, it is assumed that the percentage is 100% and 0%. Clearly, a constraint is that there must be sufficient funds available to pay for all of the expenditures in retirement. The various percentages indicated would represent differences based upon how large a fund had been accrued at the time of death, what alternative sources of retirement income were available such as Social Security and private pensions, and the desire to leave a bequest. After the first year, it is assumed that consumption in retirement increases at the rate of inflation, which is set equal to 3%. This assumption will also be altered. (9) Finally, it is assumed that had the tort not occurred, the individuals would have retired on their 65th birthday and death would have occurred on their 80th birthday. Thus, there is no uncertainty concerning worklife or life expectancy. Further, life expectancy and worklife expectancy are fixed irrespective of how many years the person has worked and lived. Appendix Tables 1 and 2 detail the calculations of lost net estate accumulations for the initial set of assumptions and given death occurred at either age 25 or age 40. At this point, our explanation will focus on Table 1. The top part of the table shows the basic assumptions. Rates of increase in earnings by age brackets include both life-cycle factors and the across-the-board changes equal to 4% per year. The initial loss of nominal earnings is $45,972, a figure derived from FullTime Earnings in the United States, 2006 Edition (2007). Subsequent increases

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are based upon the values indicated at the top of the table. Savings (5th column) is simply nominal earnings times the savings rate equal to 15%. The beginning balance for age 25 is set equal to zero. Interest income (4th column) is equal to the beginning balance times the invested rate of return equal to 8%. The ending balance (last column) is equal to the beginning balance plus interest income plus savings minus consumption in retirement. This last amount is equal to zero until age 65. This process of adding interest earned plus savings to the beginning balance continues until retirement at age 65. At that point, income and hence savings equals zero. Consumption in the first year of retirement is $159,165, which is equal to 50% of the last year’s earned income equal to $318,329. After age 65, consumption is increased at 3% each year. The process of reinvesting the remaining balance and subtracting out consumption expenditures continues until the end of the 79th year. The ending balance in the final year is $8,730,608. Given that death occurred at age 25, this appears to be an enormous sum. Nevertheless reduction to present value results in a figure of $126,689 as lost net accumulation to the estate. This is indicated at the top of the table. Table 2 illustrates the same basic analysis, but in this case assumes that death occurs at age 40 instead of age 25. Nominal earnings the first year (age 40) is now equal to $80,240—a figure obtained from Full-Time Earnings in the United States, 2006 Edition (2007). Earnings are increased according to information given at the top of the table. As in Table 1, the beginning balance for each year earns interest. To this figure is added annual savings, and the ending balance is carried forward to the next year. At age 65, income ceases and consumption in retirement draws down the available funds. The ending balance in the final year is $1,085,683, reduced to just $49,975 in present value terms. Table 2 starts with a beginning balance of $0 at age 40. This is certainly not correct given the individual would have accumulated retirement funds between ages 25 and 40. Given an assumption that the basic shape of the life-cycle curve remains the same over time and simply shifts up at the rate of increase in across-the-board earnings, it can easily be shown that the beginning balance for our 40 year-old would be $197,312. (In the same manner, the beginning balance for a 60 year-old would be $753,831.) However, with the same set of initial assumptions, putting in $197,312 instead of $0 for a beginning balance at age 40 produces the same loss, $49,975. In fact, given the investment rate (Rd) and the discount rate (Rs) are equal, any number can be used for a beginning balance. The reason is that the beginning balance is first invested and then discounted at the same rate. This justifies the conclusion arrived at in Delta Airlines v. Ageloff—namely, passive income accruing from previously invested assets should be ignored. This can be seen in Figure 1. The present value of accumulated funds from the perspective of age 40, the assumed time of death, is shown on the Y- axis as a function of age. The lower curve labeled B1 begins with a value of $0 at age 40, reaches a maximum value of $181,055 at age 65 and falls to $49,975 at age 80 when death was expected to occur. The estimated loss is the present value at age 80 minus the beginning balance, which is just $49,975.

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Present Value ($)

241

Figure 1 Rd = Rs = 8%

400000 350000 300000

B2

250000 200000 150000 100000

B1

50000 0 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 Age

The upper curve labeled B2 begins with a value of $197,312 at age 40, reaches a maximum value of $378,367 at age 65, and falls to $247,287 at age 80. The loss is ($247,287 – $197,312) = $49,975 – the same as for curve B1. A higher initial balance simply shifts up the curve in a parallel fashion so the estimated loss does not change. Varying the Percentage of Final Year’s Earnings Consumed in Retirement We now turn our attention to how different variables affect loss of net accumulation to the estate. The results of three different consumption rates are shown below. The figures for ages 25 and 40 given a consumption rate of 50% are shown in Tables 1 and 2 presented in the Appendix. Consumption Rate Out Of Final Earnings

Age 25

Age 40

Age 60

0%

$201,252

$181,055

$ 46,818

50%

$126,689

$ 49,975

($232,085)

100%

$ 52,125

($81,105)

($510,988)

As expected, for a given consumption rate, the estimated loss declines the older is the individual when he dies. As the assumed age of death increases, the

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present value of consumption in retirement increases, which will decrease the estimated loss. Since the example utilized represents a person who earns income significantly higher than average, it is instructive that beyond age 40 there is little or even negative loss unless retirement consumption relative to terminal income is very low. As shown in the previous section, some forensic economists ignore consumption in retirement (i.e. the rate equals 0%). This will often guarantee a relatively large loss. It is important to understand the meaning of the negative values in the table. For example, given a consumption rate out of final earnings equal to 100% and death at age 60, the estimated lost net accumulation to the estate is ($510,988). Assuming a beginning balance of $0, the ending balance at age 80 is ($510,988). This, of course, cannot actually occur unless the person dies in extreme debt. If, however, one incorporates a more realistic beginning balance of $753,831, a figure suggested previously, the ending balance at age 80 is ($753,831 – $510,988) = $242,843. Using a beginning balance of $0 is simply a convenience which under the assumption that Rd = Rs does not affect the analysis. Varying the Rate of Increase in Spending in Retirement The rate of increase in the base case was 3%. Below, the rate is increased and decreased by 3%. The results are as follows: Rate of Spending Increase 0%

Age 25

Age 40

Age 60

$138,541

$70,812

($187,750)

3%

$126,689

$49,975

($232,085)

6%

$111,684

$23,598

($288,209)

As expected, the loss increases the lower the rate of increase in spending in the years of retirement. It should be noted that changes in the rate have little effect if the individual died at an early age. Varying the Savings Rate The savings rate in the base case was 15%. The impact of a change in the savings rate is smaller in later years since there are fewer years for the change to have an impact. Savings Rate

Age 25

Age 40

Age 60

10%

$ 59,605

($10,377)

($247,691)

15%

$126,689

$49,975

($232,085)

20%

$193,773

$110,327

($216,479)

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Changing the Investment Rate, Rd, and the Discount Rate, Rs As long as Rd and Rs are equal, the initial balance in the first period does not affect estimated loss—although it will obviously affect the actual dollars left at the time of death had the tort not occurred. But if the two rates are different, that is not the case. For example, if Rd > Rs then not only will future contributions earn a higher rate than the survivors, but previously accumulated assets also will earn this higher rate in the future. As discussed previously, given our initial set of assumptions, the initial balance at age 40 is $197,312 and $753,831 for age 60. The results given below are based upon these initial values for the beginning balance rather than $0. The first row is the base case where Rd and Rs are equal. Age 25

Age 40

Age 60

Rd = Rs = 8%

$126,689

$ 49,975

($232,085)

Rd = 8%, Rs = 7%

$211,318

$161,445

($125,398)

Rd = 8%, Rs = 6%

$354,178

$324,984

$ 4,427

Rd = 8%, Rs = 5%

$596,531

$565,785

$162,702

Rd = 7%, Rs = 8%

$ 72,851

$ 16,438

($347,449)

It is clear that differences between Rd and Rs have a very large impact when calculating estimated loss. For example, if the forensic economist uses an investment rate of 8% while assuming that the discount rate equals 5% rather than 8%, for death occurring at age 25 estimated loss increases over four-fold from $126,689 to $596,531. The last row shows the result if the investment rate is lower than the discount rate. This could occur if the deceased was not very adept at investing or survivors were particularly skilled. In that case, the true loss is smaller compared to assuming equality between Rd and Rs. Put simply, survivors are better off getting the money early since the deceased was relatively less competent as an investor. As a final point, it was stated earlier that given Rd and Rs were equal, then the initial balance in the first period was irrelevant. Thus, the figures in the first row of the previous table would be unchanged irrespective of the beginning balance. However, that is not true for all the other rows. As an example, consider the situation where Rd = 8% and Rs = 6%, as shown in Figure 2 where it is assumed death occurs at age 40. The lower curve labeled B1 indicates present value of accumulated funds as a function of age given the beginning balance is $0. The curve reaches a maximum value of $288,908 at age 65 and falls to $105,552 at age 80—which implies that estimated loss is $105,552. The upper curve labeled B2 assumes a beginning value of $197,312. It reaches a maximum value of $603,755 at age 65 and falls to $522,296 at age 80. Loss is ($522,296 - $197,312) = $324,984—the figure indicated in the previous table. Thus, raising the initial balance from $0 to $197,312 increases the loss from $105,552 to $324,984. As shown in the Figure, a higher initial balance does not produce a parallel shift upwards. Rather,

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the curve rises more steeply. The result is that the higher the initial balance, the greater the estimated loss. The reason is that given the decedent was skilled at investing relative to his survivors, he would have had existing accumulated assets to invest at the superior rate as well as future accumulated assets. VII. Summary and Conclusions In some states such as Florida, the elements of economic losses in a wrongful death case include calculation of net estate accumulations in addition to support and services. Conceptually, net estate accumulations are the present value of future contributions to the estate calculated at the expected time of death had the tort not occurred. A separate calculation is usually required when there are individuals involved other than those who received direct support from the deceased, including adult children. Another typical case arises when the deceased is a young adult who is single. There are few published articles in the forensic economics literature that address this issue. Perhaps the most comprehensive is Frasca (2001). The approach developed is similar to the one developed in Section VI in this paper except that Frasca adds the additional complication of including the probability of living for each year. The literature reviewed clearly indicates that estimating lost net accumulation to the estate often represents only a small loss both because little is left at the end of one’s life and that amount is often discounted from many years in the future.

Present Value ($)

Figure 2 Rd = 8%, Rs = 6%

700000 600000

B2

500000 400000 300000 200000

B1

100000 0 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 Age

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The idea that only small amounts are left in estates is reinforced in the general economics literature. Americans do not save very much and what they save is largely spent. Further, such behavior is not necessarily irrational. The data concerning the dollar value of estates indicate a highly skewed distribution with most individuals leaving little or nothing, while a few leave sizable estates. Thus, unless the case involves a person of significant wealth, this category of loss will likely have negligible value. The authors have reviewed numerous reports where lost net accumulation to the estate was calculated. Many reports make common mistakes that we believe should be avoided. One typical mistake is to assume that invested return and the discount rate are different. That assumption is true only in very limited circumstances. Another common mistake is to include previously accumulated assets. This is not valid except when the return on investment is different than the discount rate. Finally, some reports attempt to separate the sources of income, when, in fact, income is fungible in most situations. Finally, a straightforward example was developed. The base case assumed an individual who would earn a relatively high income. Several parameters were manipulated to determine their impact on the estimate of lost net accumulation to the estate. Changing spending during retirement can have a large impact on the estimate, especially when death occurs at an older age. Changes in the savings rate also has an effect, which increases when death occurs at a younger age since there are more years in which wealth will be accumulated. However, the assumption that the investment rate, Rd, and the discount rate, Rs, were different had by far the largest effect on estimated loss. Given Rd equals 8%, reducing Rs from 8% to 5% increases estimated loss 4.7 times when death occurs at age 25 and 11.3 times when death occurs at age 40. Certainly, the forensic economist must scrutinize this and all other assumptions very carefully. A case-by-case approach is highly recommended when estimates of net accumulation to the estate are required under the law. References Bucks, Brian, et. al., “Recent Changes in U.S. Family Finances: Evidence from the 2001 and 2004 Survey of Consumer Finances,” Federal Reserve Bulletin, 2006. Burtless, Gary, “Social Norms, Rules of Thumb, and Retirement: Evidence for Rationality in Retirement Planning,” the Brookings Institution, CSED Working Paper No. 37, November 2004. Death and Dollars, The Role of Gifts and Bequests in America, edited by Alicia Munnell and Annika Sunden, Washington, DC: Brookings Institution Press, 2003. Frasca, Ralph, “An Economic Model for Calculating Prospective Inheritance,” Journal of Legal Economics, 2002, 12(1), 83-98. Hurd, Michael and James Smith, “Expected Bequests and Their Distribution,” Working Paper 9142, National Bureau of Economic Research, September 2002. _______, “Bequests: By Accident or by Design?,” in Death and Dollars: The Role of Gifts and Bequests in America, Munnell and Sunden, eds., 2003, 93-118. Jones, David, “Savings, Wealth, and Potential Estate Accumulations in Wrongful Death Actions,” unpublished paper presented at the Eastern Economic Association Annual Meetings, June 2004.

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Krueger, Kurt V. and Gary A. Albrecht, “The Present Value of Lost Financial Support Due to Wrongful Death,” Journal of Legal Economics, 2008, 15(1), 35-42. Lowenstein, George, Drazen Prelec and Roberto Weber, “What Me Worry? A Psychological Perspective on Economic Aspects of Retirement,” in Behavioral Dimensions of Retirement Economics, H. J. Aaron, editor, Brookings Institution Press, 1999, 215-246. Ng-Baumhacki, Mitja, et. al., “Pennies From Heaven: Will Inheritances Bail Out the Boomers?,” AARP Public Policy Institute, 2003. Orszag, Peter, comment on paper by Pierre Pestieau, “The Role of Gift and Estate Transfer in the United States and in Europe,” in Death and Dollars: The Role of Gifts and Bequests in America, Munnell and Sunden, eds., 2003, 86-90. Pestieau, Pierre, “The Role of Gift and Estate Transfer in the United States and in Europe,” in Death and Dollars: The Role of Gifts and Bequests in America, Munnell and Sunden, eds., 2003, 64-85. Scott, R. Haney and Richard PonArul, “Appropriate Formulae for Calculation of the Present Value of a Future Estate,” Journal of Forensic Economics, 1991, 4(2), 225-232. Williams, David, “Assessing Economic Damages in Personal Injury and Wrongful Death Litigation: The State of Florida,” Journal of Forensic Economics, 2002, 15(3), 357-367. Full-Time Earnings in the United States: American Community Survey Analysis, Expectancy Data, 2007. The 2007 Annual Report of the Board of Trustees of the Federal Old-Age and Survivors Insurance and Federal Disability Insurance Trust Funds.

Cases Delta Air Lines v. Ageloff 552 So.2d 1089 (1989) Synergy Gas Corporation v. Johnson 627 So.2d 539,540-41 (1993) Tobias v. Osorio 681 So.2d905 (1996)

Statutes Florida Statutes, Title XLV, Torts, Chapter 768.16 to 768.27, 2008

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Appendix Table 1 Calculating Net Estate Accumulations Assuming Death At Age 25

Rate of Increase, 21-30 Rate of Increase, 31-40 Rate of Increase, 41-50 Rate of Increase, 51-60 Rate of Increase, 61-70

9.20% 7.33% 4.14% 3.32% 1.40%

Savings Rate Investment Rate Discount Rate Increase in Spending in Retirement Percentage of Last Years' Income Spent in Retirement Across-the-board earnings increase

15.00% 8.00% 8.00% 3.00% 50.00%

PV of Loss, Age 25 $126,689

4.00%

Age

Nominal Earnings

Beginning Balance

Interest Income

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

$45,972 50,201 54,820 59,863 65,371 71,385 76,616 82,230 88,256 94,724 101,665 109,115 117,111 125,693 134,904 144,789 150,777 157,012

$0,000 6,896 14,978 24,399 35,330 47,962 62,507 79,000 97,655 118,705 142,410 169,053 198,945 232,427 269,875 311,700 358,355 409,640

$0,000 552 1,198 1,952 2,826 3,837 5,001 6,320 7,812 9,496 11,393 13,524 15,916 18,594 21,590 24,936 28,668 32,771

Savings

Consumption in Retirement

Ending Balance

$6,896 7,530 8,223 8,980 9,806 10,708 11,492 12,335 13,238 14,209 15,250 16,367 17,567 18,854 20,236 21,718 22,617 23,552

$0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000

$6,896 14,978 24,399 35,330 47,962 62,507 79,000 97,655 118,705 142,410 169,053 198,945 232,427 269,875 311,700 358,355 409,640 465,963

(continued)

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JOURNAL OF FORENSIC ECONOMICS Table 1 (continued) Calculating Net Estate Accumulations Assuming Death At Age 25

Age

Nominal Earnings

Beginning Balance

Interest Income

43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79

163,504 170,266 177,307 184,639 192,274 200,225 208,504 217,126 224,344 231,801 239,506 247,467 255,693 264,192 272,974 282,047 291,423 301,110 305,325 309,600 313,934 318,329 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000

465,963 527,765 595,526 669,765 751,041 839,966 937,197 1,043,448 1,159,493 1,285,904 1,423,546 1,573,356 1,736,345 1,913,606 2,106,323 2,315,775 2,543,344 2,790,525 3,058,934 3,349,447 3,663,843 4,004,041 4,372,113 4,562,718 4,763,796 4,976,041 5,200,201 5,437,076 5,687,527 5,952,478 6,232,924 6,529,933 6,844,654 7,178,323 7,532,268 7,907,918 8,306,813

37,277 42,221 47,642 53,581 60,083 67,197 74,976 83,476 92,759 102,872 113,884 125,868 138,908 153,088 168,506 185,262 203,468 223,242 244,715 267,956 293,107 320,323 349,769 365,017 381,104 398,083 416,016 434,966 455,002 476,198 498,634 522,395 547,572 574,266 602,581 632,633 664,545

Savings


Ending Balance

24,526 25,540 26,596 27,696 28,841 30,034 31,276 32,569 33,652 34,770 35,926 37,120 38,354 39,629 40,946 42,307 43,713 45,166 45,799 46,440 47,090 47,749 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000

0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 159,165 163,940 168,858 173,923 179,141 184,515 190,051 195,752 201,625 207,674 213,904 220,321 226,931 233,739 240,751

527,765 595,526 669,765 751,041 839,966 937,197 1,043,448 1,159,493 1,285,904 1,423,546 1,573,356 1,736,345 1,913,606 2,106,323 2,315,775 2,543,344 2,790,525 3,058,934 3,349,447 3,663,843 4,004,041 4,372,113 4,562,718 4,763,796 4,976,041 5,200,201 5,437,076 5,687,527 5,952,478 6,232,924 6,529,933 6,844,654 7,178,323 7,532,268 7,907,918 8,306,813 8,730,608

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Table 2 Calculating Net Estate Accumulations Assuming Death At Age 40

Rate of Increase, 21-30 Rate of Increase, 31-40 Rate of Increase, 41-50 Rate of Increase, 51-60 Rate of Increase, 61-70

9.20% 7.33% 4.14% 3.32% 1.40%

Savings Rate Investment Rate Discount Rate Increase in Spending in Retirement Percentage of Last Years' Income Spent in Retirement Across-the-board earnings increase

15.00% 8.00% 8.00% 3.00% 50.00%

Age

Nominal Earnings

40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

$80,240 83,558 87,013 90,612 94,359 98,260 102,324 106,555 110,961 115,550 120,328 124,328 128,460 132,730 137,142 141,701 146,411 151,278

PV of Loss, Age 40 $49,975

4.00%

Consumption Beginning Interest in Ending Balance Income Savings Retirement Balance $0,000 12,036 25,533 40,627 57,469 76,220 97,057 120,170 145,767 174,073 205,331 239,807 277,640 319,121 364,560 414,296 468,695 528,152

$0,000 963 2,043 3,250 4,598 6,098 7,765 9,614 11,661 13,926 16,426 19,185 22,211 25,530 29,165 33,144 37,496 42,252

(continued)

$12,036 12,534 13,052 13,592 14,154 14,739 15,349 15,983 16,644 17,332 18,049 18,649 19,269 19,910 20,571 21,255 21,962 22,692

$0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000

$12,036 25,533 40,627 57,469 76,220 97,057 120,170 145,767 174,073 205,331 239,807 277,640 319,121 364,560 414,296 468,695 528,152 593,096

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JOURNAL OF FORENSIC ECONOMICS Table 2 (continued) Calculating Net Estate Accumulations Assuming Death At Age 40

Age

Nominal Earnings

Beginning Balance

Interest Income

58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79

156,306 161,502 166,870 169,206 171,575 173,977 176,413 $0,000 $0,000 $0,000 $0,000 $0,000 $0,000 $0,000 $0,000 $0,000 $0,000 $0,000 $0,000 $0,000 $0,000 $0,000

593,096 663,989 741,334 825,671 917,106 1,016,210 1,123,604 1,239,954 1,250,944 1,260,167 1,267,402 1,272,408 1,274,924 1,274,662 1,271,312 1,264,534 1,253,960 1,239,187 1,219,780 1,195,264 1,165,124 1,128,799

47,448 53,119 59,307 66,054 73,368 81,297 89,888 99,196 100,075 100,813 101,392 101,793 101,994 101,973 101,705 101,163 100,317 99,135 97,582 95,621 93,210 90,304

Savings


Ending Balance

23,446 24,225 25,031 25,381 25,736 26,097 26,462 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000

0,000 0,000 0,000 0,000 0,000 0,000 0,000 88,206 90,853 93,578 96,386 99,277 102,255 105,323 108,483 111,737 115,089 118,542 122,098 125,761 129,534 133,420

663,989 741,334 825,671 917,106 1,016,210 1,123,604 1,239,954 1,250,944 1,260,167 1,267,402 1,272,408 1,274,924 1,274,662 1,271,312 1,264,534 1,253,960 1,239,187 1,219,780 1,195,264 1,165,124 1,128,799 1,085,683