Part II - Computation Methods

Trial and Substitution Method

The Trial and Substitution method requires a series of computations to reach the correct result. For the Federal estate tax computations, the first trial is computed based on reducing the deductible interest by only those taxes, penalties, and certain allowable administrative expenses that are constant; in other words, all taxes, penalties, and certain allowable expenses that are variable are assumed to be $0.00. The second trial computation is made based on the taxes, penalties, and certain allowable administrative expenses figured in the first trial computation. The third trial computation is based on the taxes, penalties, and certain allowable administrative expenses figured in the second trial computation, and so on. The computations continue until two successive computations are equal. When two successive computations produce the same result, the last computation is the correct computation of the estate tax.

Note: The spreadsheet-based Trial and Substitution Method calculation results are displayed to 2 digits whereas the internal calculations use more than 2 digits. As a result, the displayed numbers may show results that are slightly different from the internally calculated results. For example, in Estate Tax Example 3, Trial 2, Part 2, the example displays the “Trial SDTD” result as $11,707,861.15 whereas the formula result is $11,707,861.1456.

As stated above, for gift tax purposes, an interrelated computation is required if the person receiving the gift agrees to pay the gift tax on the gifted property resulting in a “net gift.” Like the estate tax computation, the Trial and Substitution method for the gift tax continues until the amount of the gift tax paid by the donee equals the amount of the gift tax due.

Under the Trial and Substitution method, there are two options to use when computing either the estate tax or the gift tax - the conventional option or the alternate option.

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Estate and Gift Tax Interrelated Computations

The conventional option is illustrated below:

Conventional Option

Taxable Interests .......................................................... $100,000,000.00

Step 1 Minus: Bracket from Table A, Column A ....................... 1,000,000.00

Excess ......................................................................... $99,000,000.00

Step 2 Times: Marginal Rate from Table A, Column D ........... x 0.40

Product ......................................................................... $39,600,000.00

Step 3 Plus: Tax on bracket from Table A, Column C .............. 345,800.00

Tax on taxable interest ................................................. $39,945,800.00

Step 1 – For taxable interests greater than $1,000,000.00, subtract the amount shown in Table A, Column A from the taxable interests, i.e., $100,000,000.00 – 1,000,000.00 = $99,000,000.00,

Step 2 – Multiply the excess from Step 1 by the tax rate shown in Table A, Column D, i.e., $99,000,000.00 x .40 = $39,600,000.00, and

Step 3 – Add the amount from Column C that corresponds to the taxable amount in Column A to the amount from Step 2, i.e., $39,600,000.00 + 345,800.00 = $39,945,800.00.

The Unified Rate Schedule, Table A shown above, has five columns instead of the usual four because the additional column, Column E, allows for the alternate option. The first four columns in Table A, Columns A, B, C, and D are used to figure the tax using the conventional option and columns A, B, D, and E are used to compute the tax using the alternate option. As with the conventional option, the alternate option also requires a series of computations to reach the correct answer. However, the alternate option has two advantages over the conventional option. First, it requires fewer steps to figure the tax, and second, it eliminates certain negative numbers when figuring the trial estate tax in interrelated computations.

The alternate option is illustrated below:

Alternate Option

Taxable Interests ......................................................... $100,000,000.00

Step 1 Times: Marginal Rate from Table A, Column D ............ x 0.40

Product ......................................................................... $40,000,000.00

Step 2 Minus: Subtractive terms from Table A, Column E ....... 54,200.00

Product ......................................................................... $39,945,800.00

Step 1 – Multiply the taxable interests by the marginal tax rate from Column D that corresponds to the taxable interest amount from Column A, $100,000,000.00 x .40 = $40,000,000.00, and

Step 2 – Subtract the amount shown in Column E corresponding to the Column A amount from Step 1, $40,000,000.00 – 54,200.00 = $39,945,800.00.

The Part III examples include illustrations using the Trial and Substitution method to compute the estate tax. Part IV shows examples of the Trial and Substitution method for computing net gifts.

Estate and Gift Tax Interrelated Computations

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Algebraic Method

The Algebraic method uses a linear algebraic equation to determine the deduction and the tax. The linear equation is a simple equation that takes the general form of ax=b or stated another way, (a * x) = b, where “ a ” and “ b ” are determined values and “ x ” is an undetermined value. The linear equation may be used to solve most interrelated estate tax computation problems that do not involve tax apportionment, second limitation gift tax credit, or second limitation foreign death tax credit. The Algebraic method is a shorter method for figuring the taxes. However, as more elements of the computation become interrelated, this method becomes more difficult to use. In the Algebraic method, the deductible interest is figured based on an unknown amount of tax. The tax is then figured based on a variable deduction and algebra is used to solve for the unknown value. Round the coefficients to a commensurate number of places comparable to the amount of tax owed. Additionally, only the final tax figures are rounded to two digits in both the estate tax calculations and the gift tax calculations.

Both the Part III and Part IV examples include illustrations using the Algebraic method.

Note: If the Algebraic method proof does not provide the same answer as the original computation, there are two potential reasons:

1. An incorrect tax bracket for trial taxable interests was used, or

2. A mathematical error was made.

To resolve the error, first check to make sure you used the correct bracket. Compare the tax bracket used in the trial computation with the tax bracket used in the proof. If these two figures are different, an incorrect bracket was selected. You must select the bracket based on an estimate of the taxable interests after taxes and recompute the steps in the problem. Second, if the correct bracket was selected, check the entire computation for mathematical and rounding errors.