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Technical Appendix for: Roth 2010 Conversion Strategies: Using the AMT to Lock-in Tax Savings

By Paul V. Hamilton, Ph.D.

This is a Technical Appendix to the article, " Roth 2010 Conversion Strategies: Using the AMT to Lock-in Tax Savings."


The spreadsheet model incorporates the major components of the U.S. Federal Tax code for both the regular and AMT tax. However, it is no substitute for a formal and complete analysis by a financial planner and/or tax professional. Assumptions are made regarding household-specific tax exemptions, post-tax investment returns, and inflation indexing. All the inputs and assumptions can be modified in the spreadsheet. 

Inputs:

  • Single or married filing jointly
  • Gross Income
  • AMT exemption = 46,700 (single) and 70,950 (couple); phased out 25 percent when Gross Income minus mutual reductions > 112,500

Assumptions:

  • Regular income brackets and all exemption levels are indexed to inflation
  • Mutual reductions = 20 percent of Gross Income (modifiable)
  • Regular tax only reductions = 10 percent of Gross Income (modifiable)
  • Tax credits are not deducted from the tax liability. Both the regular tax and AMT have similar treatment of tax credits if applicable.
  • TIRA assets earn pre-tax the nominal return.
  • Inflation = 3 percent, real return = 5 percent, nominal return = 8.15 percent.
  • Conversion taxes are paid out of a taxable account with an after tax return of nominal return*(1-capital gains tax rate) = 8.15 percent*(1-.15) = 6.8 percent.
  • State taxes are not modeled (e.g. the household is in a state without an income tax).
  • The future tax rate that will apply to TIRA withdrawals is the current regular tax rate prior to Roth conversions.
  • All TIRA balances were created by deductible contributions. here is no tax basis.
  • 20-year investment horizon.

The future value equations are analogous to those described in Horan (2006 a,b). The future value of the TIRA after-tax balance is calculated as:

FV TIRA = (1- Future tax rate)*Value2010 *(1 + nominal return)T
                = (1- Future tax rate)*Value2010 *(1.0815)20


The future value of the Roth balance if taxes are paid in 2010 is:

FV Roth 2010 = Value2010 *(1+nominal return)T - Conversion tax*(1 + after-tax return)T
                           = Value2010 *(1.0815)20 - Conversion tax*(1.068)20

where the conversion tax is the difference in tax liability between the no conversion scenario and the additional tax liability in 2010 due to converting the TIRA to a Roth.


The future value of the Roth balance if taxable income is split between 2011 and 2012 is as follows:

FV Roth 2011/12 =  Value2010 *(1+nominal return)T
       - 0.5*Conversion tax2011*(1 + after-tax return)T-1 - 0.5*Conversion tax2012*(1 + after-tax return)T-2
       = Value2010 *(1.0815)20 - 0.5*Conversion tax2011*(1.068)19- 0.5*Conversion tax2012*(1.068)18

where conversion taxYear is the additional tax liability created in those years by recognizing taxable conversion amounts.


All present values are found by discounting the associated future value at a discount rate equal to the nominal interest rate. The difference between the TIRA and Roth present values relative to the conversion amount is used to compare the two strategies.