Say you meet the earned income eligibility and you do not exceed the AGI limits for a $5,000 contribution. Should you contribute to a deductible IRA or a non-deductible Roth IRA? Assume the following:
- A marginal tax rate of 33%, which will stay the same over the holding period.
- An 8.5% annual rate of return for 30 years.
What will be the value of these investments if they are both liquidated at the end of the holding period?
Step 1 – Calculate the value of the Roth IRA and the cost of paying taxes today.
n = 30; i = 8.5; PV = ($5,000); FV = $57,791 value of Roth
n = 30; i = 8.5; PV = ($1,650) [$5,000 x 33% tax]; FV = $19,071 the opportunity cost of paying $1,650 to the IRS at time of contribution
The FV after tax is the $57,791 tax-free balance – $19,071 lost savings/opportunity cost of paying the government with a nondeductible contribution = $38,720 after tax
Step 2 – Calculate the value of the taxable IRA.
n = 30; i = 8.5; PV = ($5,000); FV = $57,791 before tax value of deductible IRA
FV after tax = $57,791 – ($57,791 x 33%) = $38,720 after tax value of deductible IRA
Note: The above calculations show that the two will equal $38,720. The step most people miss is to subtract the future value of the lost savings by paying the IRS with a nondeductible contribution. Notice that if the IRA is subject to a marginal rate of 25%, there is a savings. Step one is still computed as $38,720. However, in step two, the value is $43,343, as calculated below.
Step 2 (Alt.) – Calculate the value of the taxable IRA.
n = 30; i = 8.5; PV = ($5,000); FV = $57,791 before tax value of deductible IRA
FV after tax = $57,791 – ($57,791 x 25%) = $43,343
Notice the savings is $4,623 ($43,343 value at a 25% marginal rate – $38,720 value at a 33% marginal rate) or just $57,791 x (33% – 25%) = $4,623 savings.
Posted by Boston Institute of Finance at 10:27 AM, October 1, 2009