Yuki (age 45 at year-end) has been contributing to a traditional IRA for years (

Question

Yuki (age 45 at year-end) has been contributing to a traditional IRA for years (all deductible contributions), and her IRA is now worth $52,000. She is trying to decide whether she should roll over her traditional IRA into a Roth IRA. Her current marginal tax rate is 25 percent. She plans to withdraw the entire balance of the account in 20 years and she expects to earn a before-tax rate of return of 6.2 percent on her retirement accounts and a 5.2 percent after-tax rate of return on all investments outside of her retirement accounts. For each of the following alternative scenarios, indicate how much more or less Yuki will accumulate after taxes in 20 years if she rolls over her traditional IRA into a Roth IRA. Be sure to include the opportunity cost of having to pay taxes on the rollover. (Round "Future value factor" to 4 decimal places. Round final answers to the nearest whole dollar amount.)

When she withdraws the retirement funds in 20 years, she expects her marginal tax rate to be 35 percent.

accumulation if she keeps funds in a traditional IRA   __________________

acumulation if she rolls funds into an Roth IRA    _____________________

accumulation if she rolls over tradional IRA into a Roth IRA _________________

b.When she withdraws the retirement funds in 20 years, she expects her marginal tax rate to be 20 percent.

accumlation if she keeps funds in a traditonal IRA ____________________

accumlaiton if she rolls funds into a Roth IRA __________________________

accumlation if she rolls tradional IRA into a Roth IRA ________________________

c. Assume the same facts as in part (b), except that she earns a 4.2 percent after-tax rate of return on investments outside of the retirement accounts.

accumaltion is she keeps the funds in a tradioinal IRA ____________________________

accumulation if she rolls the funds into a Roth IRA _______________________________

accumulation if she rolls over tradional IRA into a Roth IRA_________________________________

When she withdraws the retirement funds in 20 years, she expects her marginal tax rate to be 35 percent.

accumulation if she keeps funds in a traditional IRA   __________________

acumulation if she rolls funds into an Roth IRA    _____________________

accumulation if she rolls over tradional IRA into a Roth IRA _________________

b.When she withdraws the retirement funds in 20 years, she expects her marginal tax rate to be 20 percent.

accumlation if she keeps funds in a traditonal IRA ____________________

accumlaiton if she rolls funds into a Roth IRA __________________________

accumlation if she rolls tradional IRA into a Roth IRA ________________________

c. Assume the same facts as in part (b), except that she earns a 4.2 percent after-tax rate of return on investments outside of the retirement accounts.

accumaltion is she keeps the funds in a tradioinal IRA ____________________________

accumulation if she rolls the funds into a Roth IRA _______________________________

accumulation if she rolls over tradional IRA into a Roth IRA_________________________________

Explanation / Answer

Answer a. Accumulation if she keeps funds in traditional IRA: $112566 [$52,000 × 1.06220 × (1 - .35)] Accumulation if she rolls funds into Roth IRA:$137347 $52,000 × 1.06220 = $173178 total accumulation (before considering opportunity cost of tax cost of rolling over) ($13000) × 1.05220 = ($35831) opportunity cost for having to pay tax on rollover (by rolling over traditional IRA, Yuki will have to pay $13000 in taxes ($52,000 × 25%). Because she pays $13000 in taxes with funds that are outside her retirement accounts, she will miss the opportunity of generating a 5.20% after-tax rate of return on the $13000 for 20 years.   Accumulation of Roth IRA net of opportunity cost associated with taxes paid on rollover = $137347 ($173178 - $35831). Roth IRA accumulation $137347 minus traditional IRA accumulation $112566 = $24781 greater accumulation if she rolls over traditional into Roth IRA. Answer b. When she withdraws the retirement funds in 20 years, she expects her marginal tax rate to be 20%. $1196 lower accumulation if she rolls over traditional IRA into Roth IRA (greater accumulation if she does not rollover). See calculations below: Accumulation if she keeps funds in traditional IRA: $138543 [$52,000 × 1.06220 × (1 - .2)] Accumulation if she rolls funds into Roth IRA:$ $52,000 × 1.06220 = $173178 total accumulation (before considering opportunity cost of tax cost of rolling over) ($13000) × 1.05220 = ($35831) opportunity cost for having to pay tax on rollover (by rolling over traditional IRA, Yuki will have to pay $13000 in taxes ($52,000 × 25%). Because she pays $13000 in taxes with funds outside her retirement account, she will miss the opportunity of generating a 5.2% after-tax rate of return on the $13000 for 20 years.   Accumulation of Roth IRA net of opportunity cost associated with taxes paid on rollover = $137347 ($173178 - $35831). Roth IRA accumulation $137347 minus traditional IRA accumulation $138543 = ($1196)smaller accumulation if she rolls over traditional into Roth IRA. That is, she will accumulate $856 more if she does not roll over traditional IRA into Roth. Answer c. Assume the same facts as in b. except that she earns a 4.2% after-tax rate of return on investments outside of the retirement accounts? $5035 greater accumulation if she rolls over traditional IRA into Roth IRA. See calculations below: Accumulation if she keeps funds in traditional IRA: $138543 [$52,000 × 1.06220 × (1 - .2)] Accumulation if she rolls funds into Roth IRA:$110,089 $52,000 × 1.06220 = $173178 total accumulation (before considering opportunity cost of tax cost of rolling over) ($13000) × 1.04220 = ($29600) opportunity cost for having to pay tax on rollover (by rolling over traditional IRA, Yuki will have to pay $13000 in taxes ($52,000 × 25%). Because she pays $13000 in taxes with funds outside her retirement account, she will miss the opportunity of generating a 4.2% after-tax rate of return on the $13000 for 20 years.   Accumulation of Roth IRA net of opportunity cost associated with taxes paid on rollover = $143578 ($173178 - $29600). Roth IRA accumulation $143578 minus traditional IRA accumulation $138543 = $5035greater accumulation if she rolls over traditional into Roth IRA.

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