Difference between revisions of "User talk:Fyre4ce/Roth conversion"

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(Added contribution/conversion math)
 
(Added estate tax math)
 
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--[[User:Fyre4ce|Fyre4ce]] 23:10, 10 March 2020 (UTC)
 
--[[User:Fyre4ce|Fyre4ce]] 23:10, 10 March 2020 (UTC)
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==Conversions on estates subject to estate tax==
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Define variables:
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<math>
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\begin{align}
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R & = \text{Roth balance} \\
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T & = \text{Traditional balance} \\
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A & = \text{After-tax balance} \\
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C & = \text{Roth-converted amount} \\
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V_h & = \text{Total value of estate to heirs after-tax} \\
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MTR_n & = \text{marginal tax rate now} \\
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MTR_e & = \text{marginal tax rate on estate} \\
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MTR_h & = \text{marginal tax rate on heirs} \\
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\end{align}
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</math>
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When a Roth conversion is performed on assets, during the owner's life on assets expected to be subject to estate tax, and the taxes can be paid from after-tax assets, the net effect on types of assets are as follows:
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<math>\Delta T = -C</math>
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<math>\Delta R = +C</math>
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<math>\Delta A = -C \cdot MTR_n \cdot (1 - MTR_e)</math>
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The change in after-tax value of the estate to heirs will be as follows:
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<math>\Delta V_h = \Delta T \cdot (1 - MTR_h) + \Delta R + \Delta A = -C \cdot (1 - MTR_h) + C - C \cdot MTR_n \cdot (1 - MTR_e)</math>
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<math>\Delta V_h = C \cdot ((MTR_h - 1) + 1 + MTR_n \cdot (MTR_e - 1)) = C \cdot (MTR_h + MTR_n \cdot (MTR_e - 1))</math>
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It follows that Roth conversions increase the value of the after-tax value of the estate if:
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<math>MTR_h + MTR_n \cdot (MTR_e - 1) > 0</math>
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or
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<math>MTR_e > 1 - \frac{MTR_h}{MTR_n}</math>
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--[[User:Fyre4ce|Fyre4ce]] 04:44, 10 December 2020 (UTC)

Latest revision as of 00:44, 10 December 2020

Relative value of contributions and conversions

Define variables:

The overall value of a change to tax-advantaged space is equal to:

Consider a given after-tax investment that can be contributed to a traditional account, a Roth account, or used to pay the taxes on a Roth conversion. When making a traditional contribution, the change in traditional balance is:

Therefore, the change in value when making a traditional contribution is:

When making a Roth contribution, the change in Roth balance is simply:

Therefore, the change in value when making a Roth contribution is:

When making a Roth conversion, the converted amount is:

Therefore, the change in value when making a Roth conversion is:

When (current marginal tax rate is less than predicted future marginal tax rate),

When (current marginal tax rate equals predicted future marginal tax rate),

When (current marginal tax rate is greater than predicted future marginal tax rate),

--Fyre4ce 23:10, 10 March 2020 (UTC)

Conversions on estates subject to estate tax

Define variables:

When a Roth conversion is performed on assets, during the owner's life on assets expected to be subject to estate tax, and the taxes can be paid from after-tax assets, the net effect on types of assets are as follows:

The change in after-tax value of the estate to heirs will be as follows:

It follows that Roth conversions increase the value of the after-tax value of the estate if:

or

--Fyre4ce 04:44, 10 December 2020 (UTC)