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**DMFA** · 06-06-2017, 02:24 AM

Those are awesome holding options. You might do well to keep it there.

A "rollover" is like to like, so pretax to pretax or Roth to Roth. So pretax 403(b) to pretax 401(k) is not taxable. Likewise, if you are above the direct Roth contribution limit ($194,000 MFJ), you will want no pretax IRAs to enable backdoor Roth, so you'd do well to rollover the traditional IRA to a 401(k), assuming it accepts incoming rollovers (Vanguard doesn't). Employers can't contribute to *individual* retirement arrangements.

Pretax 403(b) to Roth IRA is not a rollover, it's a "conversion," which is taxable. It is generally ill-advised to do this at a high bracket; cutting the principal by 40% for it to be withdrawn tax-free in a few decades is probably not worth letting the current principal grow and having it taxed at 25% in the future. Now, if you were in the 15-25% brackets (maybe even 28%), then it could be advantageous to convert what you can.

Conversions do not count toward the $5,500 contribution limit since it's not a contribution, it's a conversion.

...why are you capitalizing ROTH? It's an eponym, not an acronym.

**mamaham** · 06-06-2017, 09:46 AM

DMFA wrote:

Those are awesome holding options. You might do well to keep it there.

A “rollover” is like to like, so pretax to pretax or Roth to Roth. So pretax 403(b) to pretax 401(k) is not taxable. Likewise, if you are above the direct Roth contribution limit ($194,000 MFJ), you will want no pretax IRAs to enable backdoor Roth, so you’d do well to rollover the traditional IRA to a 401(k), assuming it accepts incoming rollovers (Vanguard doesn’t). Employers can’t contribute to *individual* retirement arrangements.

Pretax 403(b) to Roth IRA is not a rollover, it’s a “conversion,” which is taxable. It is generally ill-advised to do this at a high bracket; cutting the principal by 40% for it to be withdrawn tax-free in a few decades is probably not worth letting the current principal grow and having it taxed at 25% in the future. Now, if you were in the 15-25% brackets (maybe even 28%), then it could be advantageous to convert what you can.

Conversions do not count toward the $5,500 contribution limit since it’s not a contribution, it’s a conversion.

…why are you capitalizing ROTH? It’s an eponym, not an acronym.

Click to expand...

Thank you for the help with the definitions. We have done all at some point - rollover, conversion, and recharacterization - but I still cannot keep them straight!

Ok, maybe we will keep in the 403(b) then...

One of the posts that I read, which seemed to recommend to convert to Roth for a couple in the 33% bracket (you recommended this too, I believe...)... pretty much says to convert to Roth... https://www.whitecoatinvestor.com/forums/topic/old-403b/

Why is our situation that different? Three responses recommended the 33% couple with a $8,000 403b to convert to a Roth and pay the taxes. I realize that 39% is more tax but not that much more (about $500)... ?

The tIRA is mine, so I want to move it so I can do the backdoor Roth. The husband has nothing blocking his Roth contributions and we do backdoor for him. I moved an old 401k to tIRA before I knew about backdoor Roths... I will have to open a solo 401k as I am a stay-at-home-parent.... Just wanted to check that I should not pay the taxes to have more Roth space...

..."ROTH" is just a bad habit... I write all caps on my retirement summary and it just transferred to here...

**DMFA** · 06-06-2017, 10:49 AM

You could take the tax hit on it and just let it grow tax-free and withdraw it tax-free. That can be a decent idea. It's just better done in a lower bracket, obv, but on small amounts (well, small for someone who makes nearly half a million or more), it's not that big of a deal.

You mentioned reducing the principal. Don't. Just pay an extra $2,800 or so in taxes (you should be able to afford this at that income) for the year you convert instead of withholding from principal at the time of conversion.

Here's an example. Say you make 7% over 30 years. You're at 39.6% now and will retire at 25%. You have $7,000 to consider converting, which would add .396 * 7000 = $2,772 to your tax bill.

Convert to Roth, withhold tax from principal: (7000 - 2772) * 1.07^30 = $32,185

Leave as pretax, pay 25% tax on withdrawal: (7000 * 1.07^30) * (1-.25) = $53,286 * .75 = $39,964

Convert to Roth, pay tax this year with other cash leaving principal intact: (7000 * 1.07^30) - 2772 = $53,286 - 2772 = $50,514

That doesn't even take into account the importance of having more Roth space available for higher-earning and/or less-tax-efficient holdings.

So yes, converting is probably a good idea, but do not reduce your principal when doing so because it negates the purpose.

**mamaham** · 06-06-2017, 11:39 AM

Got it!! Thanks for the help!!! Much appreciated!!!!

**ENT Doc** · 06-06-2017, 07:23 PM

DMFA wrote:

You could take the tax hit on it and just let it grow tax-free and withdraw it tax-free. That can be a decent idea. It’s just better done in a lower bracket, obv, but on small amounts (well, small for someone who makes nearly half a million or more), it’s not that big of a deal.

You mentioned reducing the principal. Don’t. Just pay an extra $2,800 or so in taxes (you should be able to afford this at that income) for the year you convert instead of withholding from principal at the time of conversion.

Here’s an example. Say you make 7% over 30 years. You’re at 39.6% now and will retire at 25%. You have $7,000 to consider converting, which would add .396 * 7000 = $2,772 to your tax bill.

Convert to Roth, withhold tax from principal: (7000 – 2772) * 1.07^30 = $32,185

Leave as pretax, pay 25% tax on withdrawal: (7000 * 1.07^30) * (1-.25) = $53,286 * .75 = $39,964

Convert to Roth, pay tax this year with other cash leaving principal intact: (7000 * 1.07^30) – 2772 = $53,286 – 2772 = $50,514

That doesn’t even take into account the importance of having more Roth space available for higher-earning and/or less-tax-efficient holdings.

So yes, converting is probably a good idea, but do not reduce your principal when doing so because it negates the purpose.

Click to expand...

I like this, except for the fact that the numbers in the last example are comparing apples to oranges. The $7000*1.07^30 is future value at T=30 while the $2772 is PV. Compound that $2772 by 7% over 30 years and it won't look so rosy.

**DMFA** · 06-06-2017, 08:14 PM

ENT Doc wrote:

I like this, except for the fact that the numbers in the last example are comparing apples to oranges. The $7000*1.07^30 is future value at T=30 while the $2772 is PV. Compound that $2772 by 7% over 30 years and it won’t look so rosy.

Click to expand...

If you invested that same sum in taxable, then you'd be pulling it out at LTCG. You'd also get some, albeit small, tax drag from dividends; VTSAX gets about 2% per year, taxed at QD rate in 39.6% bracket is 20%, so you lose about 0.4% of your gain per year you're in that bracket.

2772*1.066^30 is $18,859, minus 15% LTCG assuming you draw it in the 25-35% brackets is $16,030. Adding that to what you'd get if you left it pretax from the above example, that ends up as $55,994, so assuming you actually invested that additional sum, it's better than leaving it in a pretax account...assuming it isn't an IRA that prevents you from tax-advantaging future years' IRA contributions (i.e. backdoor Roth).

**ENT Doc** · 06-06-2017, 09:49 PM

DMFA wrote:

ENT Doc wrote:

I like this, except for the fact that the numbers in the last example are comparing apples to oranges. The $7000*1.07^30 is future value at T=30 while the $2772 is PV. Compound that $2772 by 7% over 30 years and it won’t look so rosy.

Click to expand…

If you invested that same sum in taxable, then you’d be pulling it out at LTCG. You’d also get some, albeit small, tax drag from dividends; VTSAX gets about 2% per year, taxed at QD rate in 39.6% bracket is 20%, so you lose about 0.4% of your gain per year you’re in that bracket.

2772*1.066^30 is $18,859, minus 15% LTCG assuming you draw it in the 25-35% brackets is $16,030. Adding that to what you’d get if you left it pretax from the above example, that ends up as $55,994, so assuming you actually invested that additional sum, it’s better than leaving it in a pretax account…assuming it isn’t an IRA that prevents you from tax-advantaging future years’ IRA contributions (i.e. backdoor Roth).

Click to expand...

Why are you adding back the opportunity cost to the "convert to Roth and pay tax with cash flow" scenario? This is the only scenario that required use of additional funds (lost opportunity) that needs to be subtracted in future value terms. You calculated this reasonably at $16,030. I would subtract this from the "keep in pretax" decision since that takes into account all costs associated with the "convert and pay tax with cash flow" decision. It ends up being the worst decision of all 3, given the tax rates and assumptions you made.

**DMFA** · 06-06-2017, 10:21 PM

ENT Doc wrote:

DMFA wrote:

ENT Doc wrote:

I like this, except for the fact that the numbers in the last example are comparing apples to oranges. The $7000*1.07^30 is future value at T=30 while the $2772 is PV. Compound that $2772 by 7% over 30 years and it won’t look so rosy.

Click to expand…

If you invested that same sum in taxable, then you’d be pulling it out at LTCG. You’d also get some, albeit small, tax drag from dividends; VTSAX gets about 2% per year, taxed at QD rate in 39.6% bracket is 20%, so you lose about 0.4% of your gain per year you’re in that bracket.

2772*1.066^30 is $18,859, minus 15% LTCG assuming you draw it in the 25-35% brackets is $16,030. Adding that to what you’d get if you left it pretax from the above example, that ends up as $55,994, so assuming you actually invested that additional sum, it’s better than leaving it in a pretax account…assuming it isn’t an IRA that prevents you from tax-advantaging future years’ IRA contributions (i.e. backdoor Roth).

Click to expand…

Why are you adding back the opportunity cost to the “convert to Roth and pay tax with cash flow” scenario? This is the only scenario that required use of additional funds (lost opportunity) that needs to be subtracted in future value terms. You calculated this reasonably at $16,030. I would subtract this from the “keep in pretax” decision since that takes into account all costs associated with the “convert and pay tax with cash flow” decision. It ends up being the worst decision of all 3, given the tax rates and assumptions you made.

Click to expand...

I don't understand. Withholding tax from the amount converted, such as the first example, is also lost opportunity which was subtracted from future value, is it not?

And if the money is kept in pretax, then there is no additional cost, but if you were to invest what you would otherwise pay, then why is the amount you'd *not* pay end up being *subtracted* instead of added? Are you saying that it's a missed opportunity to invest additional money?

**ENT Doc** · 06-06-2017, 10:59 PM

DMFA wrote:

ENT Doc wrote:

DMFA wrote:

ENT Doc wrote:

I like this, except for the fact that the numbers in the last example are comparing apples to oranges. The $7000*1.07^30 is future value at T=30 while the $2772 is PV. Compound that $2772 by 7% over 30 years and it won’t look so rosy.

Click to expand…

If you invested that same sum in taxable, then you’d be pulling it out at LTCG. You’d also get some, albeit small, tax drag from dividends; VTSAX gets about 2% per year, taxed at QD rate in 39.6% bracket is 20%, so you lose about 0.4% of your gain per year you’re in that bracket.

2772*1.066^30 is $18,859, minus 15% LTCG assuming you draw it in the 25-35% brackets is $16,030. Adding that to what you’d get if you left it pretax from the above example, that ends up as $55,994, so assuming you actually invested that additional sum, it’s better than leaving it in a pretax account…assuming it isn’t an IRA that prevents you from tax-advantaging future years’ IRA contributions (i.e. backdoor Roth).

Click to expand…

Why are you adding back the opportunity cost to the “convert to Roth and pay tax with cash flow” scenario? This is the only scenario that required use of additional funds (lost opportunity) that needs to be subtracted in future value terms. You calculated this reasonably at $16,030. I would subtract this from the “keep in pretax” decision since that takes into account all costs associated with the “convert and pay tax with cash flow” decision. It ends up being the worst decision of all 3, given the tax rates and assumptions you made.

Click to expand…

I don’t understand. Withholding tax from the amount converted, such as the first example, is also lost opportunity which was subtracted from future value, is it not?

And if the money is kept in pretax, then there is no additional cost, but if you were to invest what you would otherwise pay, then why is the amount you’d *not* pay end up being *subtracted* instead of added? Are you saying that it’s a missed opportunity to invest additional money?

Click to expand...

No, in the 1st scenario you subtracted the present value payment outflow (appropriately) from the initial amount invested (PV), and then compounded. Nothing wrong with that since both the $7000 and $2772 were in PV terms. We are measuring things (appropriately so IMO) at the FV=30 mark to compare the ideal decision, so all of these decisions need to be compared at that FV. The first two situations as you laid out do just that. The 3rd scenario does not, because that involved an additional PV cash flow that you now don't have to invest, thus reducing your after-tax future wealth. Thus, it's FV=30 needs to be subtracted from the "let the pre-tax ride and pay 25% tax on withdrawal" decision. Does that help?

**ENT Doc** · 06-06-2017, 11:14 PM

DMFA wrote:

ENT Doc wrote:

DMFA wrote:

ENT Doc wrote:

I like this, except for the fact that the numbers in the last example are comparing apples to oranges. The $7000*1.07^30 is future value at T=30 while the $2772 is PV. Compound that $2772 by 7% over 30 years and it won’t look so rosy.

Click to expand…

If you invested that same sum in taxable, then you’d be pulling it out at LTCG. You’d also get some, albeit small, tax drag from dividends; VTSAX gets about 2% per year, taxed at QD rate in 39.6% bracket is 20%, so you lose about 0.4% of your gain per year you’re in that bracket.

2772*1.066^30 is $18,859, minus 15% LTCG assuming you draw it in the 25-35% brackets is $16,030. Adding that to what you’d get if you left it pretax from the above example, that ends up as $55,994, so assuming you actually invested that additional sum, it’s better than leaving it in a pretax account…assuming it isn’t an IRA that prevents you from tax-advantaging future years’ IRA contributions (i.e. backdoor Roth).

Click to expand…

Why are you adding back the opportunity cost to the “convert to Roth and pay tax with cash flow” scenario? This is the only scenario that required use of additional funds (lost opportunity) that needs to be subtracted in future value terms. You calculated this reasonably at $16,030. I would subtract this from the “keep in pretax” decision since that takes into account all costs associated with the “convert and pay tax with cash flow” decision. It ends up being the worst decision of all 3, given the tax rates and assumptions you made.

Click to expand…

I don’t understand. Withholding tax from the amount converted, such as the first example, is also lost opportunity which was subtracted from future value, is it not?

And if the money is kept in pretax, then there is no additional cost, but if you were to invest what you would otherwise pay, then why is the amount you’d *not* pay end up being *subtracted* instead of added? Are you saying that it’s a missed opportunity to invest additional money?

Click to expand...

Also, more simply, you accounted for the lost opportunity in the first example by compounding a lower PV over 30 years.

**DMFA** · 06-07-2017, 02:06 AM

ENT Doc wrote:

DMFA wrote:

ENT Doc wrote:

DMFA wrote:

ENT Doc wrote:

I like this, except for the fact that the numbers in the last example are comparing apples to oranges. The $7000*1.07^30 is future value at T=30 while the $2772 is PV. Compound that $2772 by 7% over 30 years and it won’t look so rosy.

Click to expand…

If you invested that same sum in taxable, then you’d be pulling it out at LTCG. You’d also get some, albeit small, tax drag from dividends; VTSAX gets about 2% per year, taxed at QD rate in 39.6% bracket is 20%, so you lose about 0.4% of your gain per year you’re in that bracket.

2772*1.066^30 is $18,859, minus 15% LTCG assuming you draw it in the 25-35% brackets is $16,030. Adding that to what you’d get if you left it pretax from the above example, that ends up as $55,994, so assuming you actually invested that additional sum, it’s better than leaving it in a pretax account…assuming it isn’t an IRA that prevents you from tax-advantaging future years’ IRA contributions (i.e. backdoor Roth).

Click to expand…

Why are you adding back the opportunity cost to the “convert to Roth and pay tax with cash flow” scenario? This is the only scenario that required use of additional funds (lost opportunity) that needs to be subtracted in future value terms. You calculated this reasonably at $16,030. I would subtract this from the “keep in pretax” decision since that takes into account all costs associated with the “convert and pay tax with cash flow” decision. It ends up being the worst decision of all 3, given the tax rates and assumptions you made.

Click to expand…

I don’t understand. Withholding tax from the amount converted, such as the first example, is also lost opportunity which was subtracted from future value, is it not?

And if the money is kept in pretax, then there is no additional cost, but if you were to invest what you would otherwise pay, then why is the amount you’d *not* pay end up being *subtracted* instead of added? Are you saying that it’s a missed opportunity to invest additional money?

Click to expand…

No, in the 1st scenario you subtracted the present value payment outflow (appropriately) from the initial amount invested (PV), and then compounded. Nothing wrong with that since both the $7000 and $2772 were in PV terms. We are measuring things (appropriately so IMO) at the FV=30 mark to compare the ideal decision, so all of these decisions need to be compared at that FV. The first two situations as you laid out do just that. The 3rd scenario does not, because that involved an additional PV cash flow that you now don’t have to invest, thus reducing your after-tax future wealth. Thus, it’s FV=30 needs to be subtracted from the “let the pre-tax ride and pay 25% tax on withdrawal” decision. Does that help?

Click to expand...

No, I still think we're looking at it differently. Assuming that there is no other money at play here other than the $7,000 currently in a pretax account and the $2,772 that would have to be paid as tax on the conversion, I don't think there's a way to have both $7,000 in Roth *and* $2,772 in taxable in this scenario, meaning I think you might be adding a bit much to the lost opportunity cost.

The best way to illustrate the sunk opportunity cost that you're mentioning is the first scenario, basically taking the tax out of the principal. a*([1+r]^t) - b*([1+r]^t) = (a-b)*([1+r]^t).

The only way to have *both* the $7,000 and $2,772 invested is option 2, to pay nothing in tax now leaving the $7,000 in pretax, and instead investing what would be paid into the taxable; that's the second scenario, in which case they'd be additive. I don't understand why you're subtracting. This would actually be how to have the most available; you don't lose anything in 2017, and instead of losing $2,772 to tax in 2017, you invest it, pay tax on your QDs, and pay LTCG at drawing it.

The third scenario is converting to Roth and paying cash on the conversion tax, losing $2,772 in 2017 dollars that isn't invested. Any other calculation, such as what if it were in taxable, brings in other money that wasn't originally considered in the scenario. It's not reasonable to create an additional pile of the same amount gaining in a taxable account along with it because you can't reasonably subtract the possible gains from $2,772 in taxable from $7,000 in Roth because if you had that tax money invested, you couldn't also have the full Roth principal invested because tax has to be paid to keep the Roth principal at that level.

You are right in that I don't really have a great means to express the opportunity cost of paying that money in taxes in 2017 dollars compared to what it could become in 30 years other than removing it from the principal as per the first example...maybe just expressing it after 30 years of inflation, I'm not sure.

As for the other thread I recommended converting to Roth, I don't remember the circumstances, but they may have had it in a traditional IRA needing to be emptied to enable backdoor Roth and may not have had a pretax employer account which accepted incoming rollovers. They were in a slightly lower bracket as it was. And, there's always the possibility that I was wrong then, or am wrong now...either way, if I am, then the fortunately difference is not particularly profound.

**ENT Doc** · 06-07-2017, 06:02 AM

Let me take it back a notch. Go back to your original 3 scenarios you posted about. What were you calculating for comparison in each of those 3 scenarios? PV or FV - and if FV, at what time?

**DMFA** · 06-07-2017, 09:40 AM

ENT Doc wrote:

Let me take it back a notch. Go back to your original 3 scenarios you posted about. What were you calculating for comparison in each of those 3 scenarios? PV or FV – and if FV, at what time?

Click to expand...

Future post-tax value at an arbitrarily-chosen 30 year interval.

I'll re-order them for simplicity. This is assuming the same holdings in each account behaving the same way (which per se might not occur between a tax-deferred and tax-free account).

P = present value of pre-tax account = $7,000

b = current tax bracket = 39.6% = 0.396

c = cost of converting to Roth = P*b = $2,772

r = annual rate of gain = 7% = 0.07 (I chose this arbitrarily)

t = time in years = 30 (I chose this arbitrarily)

a = future retirement tax bracket = 25% (I guessed this, if this is 15% it changes a lot)

Option 1: leave things as is ($7,000 in a pretax account). F = P*(1+r)^t * (1-a) = 7000*1.07^30 * (1-.25) = $53,286 pretax * 0.75 = $39,964 post-tax

Option 2: convert to Roth. This introduces the cost c ($2,772). This can either come out of principal by withholding at transfer (which I'll call 2a) or can keep it in and pay it at tax time which brings in outside cash to the equation (2b).

2a: F = (P-c)*(1+r)^t = (7000-2772)*1.07^30 = 4228*1.07^30 = $32,185 post-tax

2b: I don't really know how to account for the one-time post-tax sunk cost, since the principal is staying the same. Saying that it would be offset by what it could be from being in a taxable isn't totally appropriate since it has to be paid to keep P at 7000. So I just subtracted the one-time cost at the beginning while letting P grow untaxed by doing F = P*(1+r)^t - c, which I know isn't completely appropriate either because it's mixing future and present dollars. That's what I originally put as 7000*1.07^30 = $53,286, then just subtracted c from it to get $50,514

What I think you're saying is to subtract what c would be at the same time frame if invested. I don't think that is a fully reasonable comparison because in this situation one wouldn't have both P in Roth and c invested (prob in taxable); you'd have either P-c in Roth (option 2a), or P in Roth and have paid c.

However, my corollary to try to determine the magnitude of using post-tax c instead of investing it was the other way to have both P and c invested, with the idea being "if converting P to Roth will cost me c, then why don't I just leave P in tax-deferred and invest c in taxable?" Which is why I have what I posted next, which I'll now rename option 3: leave the pretax as it is in option 1, but add in what you'd otherwise pay to convert P to Roth at bracket b, which is c, and invest it in taxable? We'll assume the fund pays a dividend rate of 2%/year, has no turnover, will grow while she is in bracket b (hence QD tax of 20%), and be withdrawn at bracket a (meaning LTCG of 15%).

3: F = Option 1 + c*(1+r-[.02*.2])^t * (1-.15) = $39,964 + 2772*(1.066)^30 * 0.85 = $39,964 + $16,030 = $55,994

Which is greater than what you'd have with all of P in Roth as it is, even before you account for spending c on taxes...which is to say that, given the above circumstances, it wouldn't be advantageous to convert it to Roth.

**ENT Doc** · 06-07-2017, 04:54 PM

DMFA wrote:

ENT Doc wrote:

Let me take it back a notch. Go back to your original 3 scenarios you posted about. What were you calculating for comparison in each of those 3 scenarios? PV or FV – and if FV, at what time?

Click to expand…

Future post-tax value at an arbitrarily-chosen 30 year interval.

I’ll re-order them for simplicity. This is assuming the same holdings in each account behaving the same way (which per se might not occur between a tax-deferred and tax-free account).

P = present value of pre-tax account = $7,000

b = current tax bracket = 39.6% = 0.396

c = cost of converting to Roth = P*b = $2,772

r = annual rate of gain = 7% = 0.07 (I chose this arbitrarily)

t = time in years = 30 (I chose this arbitrarily)

a = future retirement tax bracket = 25% (I guessed this, if this is 15% it changes a lot)

Option 1: leave things as is ($7,000 in a pretax account). F = P*(1+r)^t * (1-a) = 7000*1.07^30 * (1-.25) = $53,286 pretax * 0.75 = $39,964 post-tax

Option 2: convert to Roth. This introduces the cost c ($2,772). This can either come out of principal by withholding at transfer (which I’ll call 2a) or can keep it in and pay it at tax time which brings in outside cash to the equation (2b).

2a: F = (P-c)*(1+r)^t = (7000-2772)*1.07^30 = 4228*1.07^30 = $32,185 post-tax

2b: I don’t really know how to account for the one-time post-tax sunk cost, since the principal is staying the same. Saying that it would be offset by what it could be from being in a taxable isn’t totally appropriate since it has to be paid to keep P at 7000. So I just subtracted the one-time cost at the beginning while letting P grow untaxed by doing F = P*(1+r)^t – c, which I know isn’t completely appropriate either because it’s mixing future and present dollars. That’s what I originally put as 7000*1.07^30 = $53,286, then just subtracted c from it to get $50,514

What I think you’re saying is to subtract what c would be at the same time frame if invested. I don’t think that is a fully reasonable comparison because in this situation one wouldn’t have both P in Roth and c invested (prob in taxable); you’d have either P-c in Roth (option 2a), or P in Roth and have paid c.

However, my corollary to try to determine the magnitude of using post-tax c instead of investing it was the other way to have both P and c invested, with the idea being “if converting P to Roth will cost me c, then why don’t I just leave P in tax-deferred and invest c in taxable?” Which is why I have what I posted next, which I’ll now rename option 3: leave the pretax as it is in option 1, but add in what you’d otherwise pay to convert P to Roth at bracket b, which is c, and invest it in taxable? We’ll assume the fund pays a dividend rate of 2%/year, has no turnover, will grow while she is in bracket b (hence QD tax of 20%), and be withdrawn at bracket a (meaning LTCG of 15%).

3: F = Option 1 + c*(1+r-[.02*.2])^t * (1-.15) = $39,964 + 2772*(1.066)^30 * 0.85 = $39,964 + $16,030 = $55,994

Which is greater than what you’d have with all of P in Roth as it is, even before you account for spending c on taxes…which is to say that, given the above circumstances, it wouldn’t be advantageous to convert it to Roth.

Click to expand...

Your 2c calculation became invalidated when you mixed FV and PV. You can't do that. This is the same person. In options 1 and 2a they had money on the side (at least $2772) to create the option 2b to pull in that money from the outside. You have to account for that lost opportunity of investment in 2c in FV=30 terms. Because in options 1 and 2a that money was presumably being used for investment and wasn't just sitting under the mattress for 30 years. If your assumption is that she puts the money under the mattress for 30 years then I agree with subtracting the $2772. But that doesn't realistically assess the opportunity of that money in an alternative investment of the same risk. This is why your taxable account scenario is appropriate. The risk and growth is the same (7%), it's just that there happens to be a 3rd party involved along the way pulling money out. What you calculated in the second half of your option 3 calculates the opportunity cost of that marginal $2772 over 30 years. That money is what she had sitting on the side in options 1 and 2a. Option 2b has lost that opportunity and doesn't have that money sitting on the side, thus it needs to be subtracted from the 7000*(1+0.07)^30 term which has no assessment of lost opportunity.

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