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Letter to the EditorLetter to the Editor

To the Editor: There seems to be an error in the calculations of The Net, Net Gift by Michael S. Arlein & William H. Frazier (August 2008) specifically the article's calculations of the actuarial present value of the additional federal estate tax that would be payable if the donor died within three years of the gift and the gift tax paid on the net gift were included in the donor's gross estate under

November 1, 2008

6 Min Read
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To the Editor:

There seems to be an error in the calculations of “The Net, Net Gift” by Michael S. Arlein & William H. Frazier (August 2008) — specifically the article's calculations of the actuarial present value of the additional federal estate tax that would be payable if the donor died within three years of the gift and the gift tax paid on the net gift were included in the donor's gross estate under Internal Revenue Code Section 2035. The formulas used in the piece depart from the formulas used by the Internal Revenue Service under Section 7520 in two respects:

  1. The mortality probabilities are not calculated correctly and overstate the probability of death within three years for the hypothetical donor age 86.

    In determining the probabilities of death for each year of the three years, the article shows the probabilities of death within one year for persons age 86, 87 and 88. But what is needed are the probabilities of a person age 86 dying in the first year, the second year, and the third year, which is a different calculation.

    By basing the probability of death in the second and third years based on the ages at the beginning of those years, the formula used in the article implicitly assumes a 100 percent probability of surviving to those ages and fails to take into account the probability of death for an 86-year-old before reaching those ages.

    The correct probability of death in the second year is the probability of death within two years minus the probability of death within one year, and the probability of death within the third year is the probability of death within three years minus the probability of death within two years.

    Using those formulas, the three probabilities will add up to the probability of death within three years, which under Table 90CM is 1-19783/28687, or .31038 (31 percent). The article shows three probabilities that add up to 34.94 percent, which is almost 4 percentage points too high.

  2. The present value discount factors are for one whole year, two whole years and three whole years, which would be correct if you knew for certain that the donor was going to die at the end of the year. But the donor's death could be at the beginning or end of the year or anywhere in between. The IRS formula for calculating remainder factors (that is to say, the value of money payable at death) assumes that the measuring life dies in the middle of the year, which is done by multiplying the discount by 1 i/2, where “i” is the Section 7520 discount rate. So the IRS “PV Factor” would be (1 i/2)/(1 i)^n and not 1/(1 i)^n as stated in the article.

As a result of those variances from IRS formulas, the actuarial valuation presented in the article differs from a valuation in accordance with the tables in IRS Publication 1...

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