## CSS Improvement-Change BETR Calculation

### CSS Improvement-Change BETR Calculation

I've been studying and analyzing the concept of break even tax rate (BETR) and how it impacts a Roth conversion vs. no conversion decision. The case study spreadsheet has an estimate for BETR around row 150 on the "Misc. calcs": https://docs.google.com/spreadsheets/d/ ... sp=sharing

I believe the BETR calculation in cell B166 is wrong as discussed with MDM on the Mr. Money Mustache forums here:

https://forum.mrmoneymustache.com/forum ... msg3223883

MDM agrees that the BETR calculation doesn't seem correct and asked me to discuss here. Please read the linked discussion with screenshots and the spreadsheet I used and reply here if you agree or post any corrections to my logic and/or math that you find.

I'm nearly ready with what I believe to be the correct calculation, but would like to start the discussion regarding the errors I see and come to a consensus.

I believe the BETR calculation in cell B166 is wrong as discussed with MDM on the Mr. Money Mustache forums here:

https://forum.mrmoneymustache.com/forum ... msg3223883

MDM agrees that the BETR calculation doesn't seem correct and asked me to discuss here. Please read the linked discussion with screenshots and the spreadsheet I used and reply here if you agree or post any corrections to my logic and/or math that you find.

I'm nearly ready with what I believe to be the correct calculation, but would like to start the discussion regarding the errors I see and come to a consensus.

### Re: CSS Improvement-Change BETR Calculation

Here’s an overview of my understanding of the break even tax rate (BETR) calculation and my thoughts on why the current spreadsheet is wrong.

BETR should be equal to the current ordinary income tax rate at n=0 and go down from there regardless of the cost basis used for the taxable assets.

Per Vanguard, "BETR is that future tax rate at which the after-tax withdrawal value for an investor would be the same in both the no-conversion and conversion scenarios.” Source: https://investor.vanguard.com/investor- ... n-equation

In a conversion scenario, this is pretty simple, the after tax future value of a Roth account is the present value compounded annually by the rate of return. Using the variables assigned on the current spreadsheet calculation for BETR (see screenshot below), we have RothFv = RothPv*(1+i)

In the no conversion scenario when using funds from a taxable account to pay the taxes, it’s necessary to break down the tIRA and taxable account future pretax values, then apply the taxes due at withdrawal.

For the tIRA, this is again simple. Pretax is the same as the Roth, Fv = Pv(1+i)

The taxable account (TA) future value is a bit more complicated. First, let’s define the TA present value. The initial tax bill owed is the taxes paid on the conversion, Pv=T. If the cost basis is less than 100%, there will be additional capital gains (CG) taxes due which requires the adjustment to pretax TA present value. Using CB% for percent cost basis and T2 for the tax on capital gains, this can be calculated as Pv = T/((1-CB%)*(1-T2)).

The taxable account pretax (TAPT) future value isn’t too bad, we compound the present value by the growth return plus the after tax dividend rate, e in the spreadsheet. Taxable account pretax Fv = TAPv*(1+e)

To calculate the taxable account after tax (TAAT) future value, we need to apply the capital gains tax (T2) to the taxable account future value minus the cost basis. The cost basis consists of two parts:

CB1 is the static present value cost basis based on the percent cost basis (CB%), CB1 = TAPv*CB%. Note that the percent cost basis will go down since the taxable account future value grows, but the original cost basis stays the same.

CB2 is the accumulated after tax dividend reinvested. This can’t be expressed as a singe formula as far as I know, but I’m working on an approximation that will provide an accurate BETR with various inputs. Any help with this would be appreciated.

TAATFv = (TAPTFv-CB1-CB2)*(1-T2)

Assuming I haven’t made any typing errors and using the Vanguard definition of BETR above we should have:

RothFv = tIRAFv + TAATFv = (1-BETR)*tIRAPv(1+i)

The error with the current spreadsheet can be seen if we set n=0 and CB% to something other than 100%. This removes any growth and dividends so those can be set to 1 or ignored.

The Roth value is the sum of the present values of the tIRA & taxable accounts after paying taxes, tIRAPv*(1-T) + T/((1-CB%)*(1-T2)).

The future no conversion value after paying taxes without any growth or dividends can be expressed as: tIRAPv*(1-BETR) + T/((1-CB%)*(1-T2))

So we have tIRAPv*(1-T) + T/((1-CB%)*(1-T2)) = tIRAPv*(1-BETR) + T/((1-CB%)*(1-T2)) striking out the taxable account portions since those are the same on both sides.

It can also be shown that the tax drag on the taxable account future value due to taxes on dividends and growth beyond the the present value cost basis will decrease BETR as n increases so that BETR can never be greater than T without changes in capital gains tax rates or using alternate funds to pay future taxes so long as returns are greater than zero.

**Spoiler:**BETR should be equal to the current ordinary income tax rate at n=0 and go down from there regardless of the cost basis used for the taxable assets.

**BETR Definition**Per Vanguard, "BETR is that future tax rate at which the after-tax withdrawal value for an investor would be the same in both the no-conversion and conversion scenarios.” Source: https://investor.vanguard.com/investor- ... n-equation

**Roth Future Value**In a conversion scenario, this is pretty simple, the after tax future value of a Roth account is the present value compounded annually by the rate of return. Using the variables assigned on the current spreadsheet calculation for BETR (see screenshot below), we have RothFv = RothPv*(1+i)

^{n}In the no conversion scenario when using funds from a taxable account to pay the taxes, it’s necessary to break down the tIRA and taxable account future pretax values, then apply the taxes due at withdrawal.

**tIRA Future Value**For the tIRA, this is again simple. Pretax is the same as the Roth, Fv = Pv(1+i)

^{n}. Since BETR is defined as the future withdrawal tax rate, we apply that to the above and we get tIRAFv = (1-BETR)*tIRAPv(1+i)^{n}**Taxable Account Future Value**The taxable account (TA) future value is a bit more complicated. First, let’s define the TA present value. The initial tax bill owed is the taxes paid on the conversion, Pv=T. If the cost basis is less than 100%, there will be additional capital gains (CG) taxes due which requires the adjustment to pretax TA present value. Using CB% for percent cost basis and T2 for the tax on capital gains, this can be calculated as Pv = T/((1-CB%)*(1-T2)).

The taxable account pretax (TAPT) future value isn’t too bad, we compound the present value by the growth return plus the after tax dividend rate, e in the spreadsheet. Taxable account pretax Fv = TAPv*(1+e)

^{n}.**Taxes Due on the Taxable Account**To calculate the taxable account after tax (TAAT) future value, we need to apply the capital gains tax (T2) to the taxable account future value minus the cost basis. The cost basis consists of two parts:

CB1 is the static present value cost basis based on the percent cost basis (CB%), CB1 = TAPv*CB%. Note that the percent cost basis will go down since the taxable account future value grows, but the original cost basis stays the same.

CB2 is the accumulated after tax dividend reinvested. This can’t be expressed as a singe formula as far as I know, but I’m working on an approximation that will provide an accurate BETR with various inputs. Any help with this would be appreciated.

TAATFv = (TAPTFv-CB1-CB2)*(1-T2)

Assuming I haven’t made any typing errors and using the Vanguard definition of BETR above we should have:

RothFv = tIRAFv + TAATFv = (1-BETR)*tIRAPv(1+i)

^{n}+ (TAPv*(1+e)^{n}-CB1-CB2)*(1-T2)**Issue with the Current Spreadsheet**The error with the current spreadsheet can be seen if we set n=0 and CB% to something other than 100%. This removes any growth and dividends so those can be set to 1 or ignored.

The Roth value is the sum of the present values of the tIRA & taxable accounts after paying taxes, tIRAPv*(1-T) + T/((1-CB%)*(1-T2)).

The future no conversion value after paying taxes without any growth or dividends can be expressed as: tIRAPv*(1-BETR) + T/((1-CB%)*(1-T2))

So we have tIRAPv*(1-T) + T/((1-CB%)*(1-T2)) = tIRAPv*(1-BETR) + T/((1-CB%)*(1-T2)) striking out the taxable account portions since those are the same on both sides.

**It’s clear that BETR must equal T at n=0 regardless of CB%, but this is not the case with the current version of the spreadsheet.**It can also be shown that the tax drag on the taxable account future value due to taxes on dividends and growth beyond the the present value cost basis will decrease BETR as n increases so that BETR can never be greater than T without changes in capital gains tax rates or using alternate funds to pay future taxes so long as returns are greater than zero.

### Re: CSS Improvement-Change BETR Calculation

It's an interesting issue. In the Simplest situation for Roth vs traditional, say when looking at traditional 401k vs. Roth 401k and the pre-tax amount involved is not more than the IRS maximum, the commutative property of multiplication applies as described in that wiki link. That's the foundation for the usual advice that goes something like "if your future tax rate will be lower, use traditional; if it will be higher, use Roth; if the same, it doesn't matter."murrays wrote: ↑Sun Jan 28, 2024 4:04 pmBETR Definition

Per Vanguard, "BETR is that future tax rate at which the after-tax withdrawal value for an investor would be the same in both the no-conversion and conversion scenarios.” Source: https://investor.vanguard.com/investor- ... n-equation

Things are a little different when taxable money must be considered and there is a "Traditional plus taxable" vs. Roth situation.

There may have been some burying of the lede in this post in Roth 401(k) vs. 401(k) Spreadsheet Attempt - Critique Please: the assumption "there would be 'cash on hand' to pay the tax" in the future.

In that case, one could convert $10K traditional to $10K Roth, and pay the tax (say, $2400) from cash on hand.

If in the present one must sell appreciated assets to raise the funds to pay the tax, more than $2400 must be sold:

Amount sold to pay tax = Converted amount * (conversion tax rate)/(1 - LTGC_rate * (1 - basis_fraction)).

Thus it would be better to keep the money in traditional (i.e., don't convert) unless the future conversion tax rate will be greater than (current conversion tax rate)/(1 - LTGC_rate * (1 - basis_fraction)).

In the extreme case that no taxable funds are presently available, it's not the LTCG rate that applies but instead the ordinary income rate on the conversion amount itself. In other words, one would not want to pay tax now out of the conversion amount if in the future the tax could be paid from cash flow, unless the expected future tax rate would be more than (current rate)/(1 - current rate).

Again, this is based on the assumption that cash flow will be available "in the future" and the math above is why the BETR would be higher than the current conversion tax rate.

As always, different assumptions can lead to different conclusions. Or sometimes any of us can make silly math mistakes and it takes someone else to point out the obvious....

### Re: CSS Improvement-Change BETR Calculation

I agree. Unlike the commutative property application to Roth vs tIRA comparisons, moving assets from a taxable account to a Roth, essentially paying taxes from a taxable account, provides a benefit from additional growth beyond the n=0 cost basis plus no tax owed on reinvested dividends.FiveK wrote: ↑Mon Jan 29, 2024 1:39 pmIt's an interesting issue. In the Simplest situation for Roth vs traditional, say when looking at traditional 401k vs. Roth 401k and the pre-tax amount involved is not more than the IRS maximum, the commutative property of multiplication applies as described in that wiki link. That's the foundation for the usual advice that goes something like "if your future tax rate will be lower, use traditional; if it will be higher, use Roth; if the same, it doesn't matter."murrays wrote: ↑Sun Jan 28, 2024 4:04 pmBETR Definition

Per Vanguard, "BETR is that future tax rate at which the after-tax withdrawal value for an investor would be the same in both the no-conversion and conversion scenarios.” Source: https://investor.vanguard.com/investor- ... n-equation

Things are a little different when taxable money must be considered and there is a "Traditional plus taxable" vs. Roth situation.

I gave that some thought. Personally, when RMDs hit and I'm taking SS, I will have the cash on hand to pay the taxes and less need to sell taxable assets.FiveK wrote: ↑Mon Jan 29, 2024 1:39 pmThere may have been some burying of the lede in this post in Roth 401(k) vs. 401(k) Spreadsheet Attempt - Critique Please: the assumption "there would be 'cash on hand' to pay the tax" in the future.

In that case, one could convert $10K traditional to $10K Roth, and pay the tax (say, $2400) from cash on hand.

But, using the Vanguard definition, the future after tax value of the assets used to pay the taxes needs to be accounted for in the no conversion scenario regardless of selling them or not.

It's also possible that income levels drop sufficiently to reduce the CG tax rate which will be accounted for with Future CG Tax Rate. If this is set to zero, then BETR is the same as the current spreadsheet estimate.

Agreed, though I don't see any mistakes in the current BETR estimate, just an assumption that would be better applied as a variable.

I'll post my spreadsheet shortly and would appreciate you having a look and identifying any math or logic errors you see. Ironically, the marginal tax calculation that sent me down this path isn't part of my BETR estimate

Last edited by murrays on Mon Jan 29, 2024 2:52 pm, edited 1 time in total.

### Re: CSS Improvement-Change BETR Calculation

Here's the latest version of my BETR estimating spreadsheet in a couple different versions. I think it should be pretty self explanatory, enter the variables at the top and the results show up in the table below.

The "Calculated Values" row should provide the same results in a single cell vs. the tabulated values above. The calculated values formulas can be used in the current CSS spreadsheet.

Please have a look and let me know if you see any errors or room for improvement.

Excel version via DropBox:

https://www.dropbox.com/scl/fi/ioeu1rw0 ... p0bpz&dl=0

Google Drive version:

https://docs.google.com/spreadsheets/d/ ... sp=sharing

Screenshot:

The "Calculated Values" row should provide the same results in a single cell vs. the tabulated values above. The calculated values formulas can be used in the current CSS spreadsheet.

Please have a look and let me know if you see any errors or room for improvement.

Excel version via DropBox:

https://www.dropbox.com/scl/fi/ioeu1rw0 ... p0bpz&dl=0

Google Drive version:

https://docs.google.com/spreadsheets/d/ ... sp=sharing

Screenshot:

### Re: CSS Improvement-Change BETR Calculation

Yes, definitely, and that's what the decrease in BETR over time shows. With the assumption that one can pay the conversion tax from cash on hand in the future, if such tax-free cash is not available in the present then the BETR starts above the current tax rate on the conversion amount.murrays wrote: ↑Mon Jan 29, 2024 2:17 pmI gave that some thought. Personally, when RMDs hit and I'm taking SS, I will have the cash on hand to pay the taxes and less need to sell taxable assets.FiveK wrote: ↑Mon Jan 29, 2024 1:39 pmThere may have been some burying of the lede in this post in Roth 401(k) vs. 401(k) Spreadsheet Attempt - Critique Please: the assumption "there would be 'cash on hand' to pay the tax" in the future.

In that case, one could convert $10K traditional to $10K Roth, and pay the tax (say, $2400) from cash on hand.

But, using the Vanguard definition, the future after tax value of the assets used to pay the taxes needs to be accounted for in the no conversion scenario regardless of selling them or not.

Agreed.It's also possible that income levels drop sufficiently to reduce the CG tax rate which will be accounted for with Future CG Tax Rate. If this is set to zero, then BETR is the same as the current spreadsheet estimate.

Yes, in hindsight it would have been better to put that assumption up front 2.5 years ago rather than burying it in the last sentence.Agreed, though I don't see any mistakes in the current BETR estimate, just an assumption that would be better applied as a variable.

### Re: CSS Improvement-Change BETR Calculation

Appears that it matches the two tools referenced in the "Traditional plus taxable" vs. Roth wiki section when there isn't a difference in costs to pay the conversion tax, so that's a good sign.

A slightly different situation is behind the table shown in the Typical values section. If you can match those numbers also, it's likely both your spreadsheet and the tool fyre4ce used to generate that table are both correct.

### Re: CSS Improvement-Change BETR Calculation

Thanks for looking and the link!FiveK wrote: ↑Mon Jan 29, 2024 6:09 pmAppears that it matches the two tools referenced in the "Traditional plus taxable" vs. Roth wiki section when there isn't a difference in costs to pay the conversion tax, so that's a good sign.

A slightly different situation is behind the table shown in the Typical values section. If you can match those numbers also, it's likely both your spreadsheet and the tool fyre4ce used to generate that table are both correct.

The spreadsheet is pretty close to that table, BETR=20.65% for 24% ordinary tax rate, 15% cap gains/div tax rates and basis set to 100% vs. 20.58% from the table you linked.

If I adjust the dividend tax rate to 15.9% per this: "...yield of 2%, of which 90% is taxed at long-term capital gains rates and 10% as ordinary income", my spreadsheet returns 21.87% for 10 years and 20.58% for 20 which matches exactly which is always nice!

Checking all the tax rates and times, the two seem to deviate at the higher tax rates of 32/18.8%, 37/23.8% & 50.3/37.1%. Worst case at 50.3%/37.1% & 40 years is 26.88% for my spreadsheet vs. 26.79% for the linked table...less than .1% which is probably irrelevant for such a long term estimate, but not the same. Note, this helped me find and fix a slight error in my Calculated Totals when the Div Tax Rate differed from the CG Tax Rate.

So I entered the formulas from the link into a spreadsheet and came up with values that matched mine precisely to whatever number of digits that Excel uses so I suspect there's a rounding error in that table.

Bottom line, my spreadsheet is more precise than the table in Typical values

Thanks for your help! Are there any other resources we should double check?

### Re: CSS Improvement-Change BETR Calculation

While I tend to agree that it is best if you can convert when your tax rate is the lowest, I think you're putting too much emphasis on this. There are other considerations too that make a Roth conversion favorable.

One consideration is if you will need to keep your income low so you can benefit from ACA subsidies before Medicare starts. Another age-related consideration is how many years you have before RMDs start and how big the RMD will then be. If Married, the tax brackets of the future surviving spouse also should be considered.

Less important considerations are future tIRAs which you might inherit which could require withdrawals while you are still converting or other changes in your income or expenses.

One external factor that I benefitted from is doing large conversions during a "down" market. When I converted in 2008 when shares were half their previous price, it was the same as if I had converted for half the tax amount I would have normally paid. I gladly paid a higher tax rate so twice as many shares could be converted. (You don't "see" this benefit until the shares return to their previous value. Then it is as if you paid half price on the taxes.)

But the factor that is most important, in my opinion, is the current and future size of your tax-deferred accounts. They help determine HOW MUCH you should convert before RMDS start. Once RMDs start, it will be harder to convert since you need to remove the RMD first. And there are several reasons someone would want to convert at a higher rate than previously planned (IRMAA, heirs, rate for surviving spouse).

And even if you are trying to take advantage of favorable tax brackets, there's no way to predict how tax laws and brackets will change in the future. Even now, we expect the tax rates to return to 2017 rates when the current tax rates expire after 2025. Historically, Congress makes large changes to the tax code about every 10 years.

A dollar in Roth is worth more than a dollar in a taxable account. A dollar in taxable is worth more than a dollar in a tax-deferred account.

### Re: CSS Improvement-Change BETR Calculation

I agree, this is only one piece in the Roth conversion decision, but I was compelled to look into this in the first place because I felt the existing CSS created a faulty perception that withholding taxes from the conversion amount was better in the short term than selling assets in a taxable account to pay the conversion taxes. I even heard that stated on the Big Picture Retirement podcast. I believe I've shown that's not the case other than if the future CG tax rate is reduced.

And after some additional thought, the assumption that future CG tax rates go away pretty much invalidates the entire current CSS calculation since that means future qualified dividends are not taxed and any reinvested dividend growth is not taxed. In a nutshell, that's nearly the entire benefit of using taxable funds to pay conversion taxes. Of course, there is the situation where my wife and I die and the cost basis is stepped up, but that's a whole other scenario.

### Re: CSS Improvement-Change BETR Calculation

Perhaps you and fyre4cemurrays wrote: ↑Tue Jan 30, 2024 12:22 pm Bottom line, my spreadsheet is more precise than the table in Typical values

could compare notes.

### Re: CSS Improvement-Change BETR Calculation

I think you are forgetting that the NIIT is assessed on non-qualified dividends. In the 50.3/37.1% bracket, the tax rate on qualified dividends is 37.1% (=20%+3.8%+13.3%) and the rate on non-qualified dividends ismurrays wrote: ↑Tue Jan 30, 2024 12:22 pmThanks for looking and the link!FiveK wrote: ↑Mon Jan 29, 2024 6:09 pmAppears that it matches the two tools referenced in the "Traditional plus taxable" vs. Roth wiki section when there isn't a difference in costs to pay the conversion tax, so that's a good sign.

A slightly different situation is behind the table shown in the Typical values section. If you can match those numbers also, it's likely both your spreadsheet and the tool fyre4ce used to generate that table are both correct.

The spreadsheet is pretty close to that table, BETR=20.65% for 24% ordinary tax rate, 15% cap gains/div tax rates and basis set to 100% vs. 20.58% from the table you linked.

If I adjust the dividend tax rate to 15.9% per this: "...yield of 2%, of which 90% is taxed at long-term capital gains rates and 10% as ordinary income", my spreadsheet returns 21.87% for 10 years and 20.58% for 20 which matches exactly which is always nice!

Checking all the tax rates and times, the two seem to deviate at the higher tax rates of 32/18.8%, 37/23.8% & 50.3/37.1%. Worst case at 50.3%/37.1% & 40 years is 26.88% for my spreadsheet vs. 26.79% for the linked table...less than .1% which is probably irrelevant for such a long term estimate, but not the same. Note, this helped me find and fix a slight error in my Calculated Totals when the Div Tax Rate differed from the CG Tax Rate.

So I entered the formulas from the link into a spreadsheet and came up with values that matched mine precisely to whatever number of digits that Excel uses so I suspect there's a rounding error in that table.

Bottom line, my spreadsheet is more precise than the table in Typical values

Thanks for your help! Are there any other resources we should double check?

**54.1%**(=37%+3.8%+13.3%). They are taxed at a higher rate than non-investment income like tIRA withdrawals.

Then, the average rate on dividends with 90% qualified would be

**38.8%**(=90% x 37.1% + 10% x 54.1%).

In my Future Value tool, when I change the rate on non-qualified dividends from 54.1% to 50.3% I get a BETR of 26.88% which is what you are reporting from your math.

It would also make sense that this difference would not appear in tax brackets below where the NIIT kicks in, but would appear above it.

Check if this is the issue, and if not, post back and we can look in more detail.

### Re: CSS Improvement-Change BETR Calculation

Yep, that checks out, it was all in my manual calculations of the dividend tax rates. I'm glad we came up with the same answers!fyre4ce wrote: ↑Sat Feb 10, 2024 4:05 pmI think you are forgetting that the NIIT is assessed on non-qualified dividends. In the 50.3/37.1% bracket, the tax rate on qualified dividends is 37.1% (=20%+3.8%+13.3%) and the rate on non-qualified dividends is54.1%(=37%+3.8%+13.3%). They are taxed at a higher rate than non-investment income like tIRA withdrawals.

Then, the average rate on dividends with 90% qualified would be38.8%(=90% x 37.1% + 10% x 54.1%).

In my Future Value tool, when I change the rate on non-qualified dividends from 54.1% to 50.3% I get a BETR of 26.88% which is what you are reporting from your math.

It would also make sense that this difference would not appear in tax brackets below where the NIIT kicks in, but would appear above it.

Check if this is the issue, and if not, post back and we can look in more detail.

Thanks for looking into it!

### Re: CSS Improvement-Change BETR Calculation

One more point about the assumption of funds being available to cover tIRA withdrawal taxes in the future, it seems that assumption only applies to LTCG tax liability present at the time of conversion.

For example, why is there a "Tax rate on capital gains at withdrawal" input on the current spreadsheet and shouldn't that rate apply to the tax liability of funds in the taxable account at the time of conversion for cases where basis < 100%? Put another way, shouldn't the future funds available assumption make that tax rate equal to 0 for all future taxable account LTCG tax liability?

For example, why is there a "Tax rate on capital gains at withdrawal" input on the current spreadsheet and shouldn't that rate apply to the tax liability of funds in the taxable account at the time of conversion for cases where basis < 100%? Put another way, shouldn't the future funds available assumption make that tax rate equal to 0 for all future taxable account LTCG tax liability?

### Re: CSS Improvement-Change BETR Calculation

I didn’t read the whole thread, but I am missing the point about funds to pay the taxes in traditional withdrawals. Traditional withdrawals come out as cash, so you can always use that cash to pay the taxes, whether or not you have other assets.murrays wrote: ↑Sat Feb 10, 2024 5:19 pm One more point about the assumption of funds being available to cover tIRA withdrawal taxes in the future, it seems that assumption only applies to LTCG tax liability present at the time of conversion.

For example, why is there a "Tax rate on capital gains at withdrawal" input on the current spreadsheet and shouldn't that rate apply to the tax liability of funds in the taxable account at the time of conversion for cases where basis < 100%? Put another way, shouldn't the future funds available assumption make that tax rate equal to 0 for all future taxable account LTCG tax liability?

My tool has the capability to use different tax rates at contribution and withdrawal, because you might (for example) be in a different tax bracket and living in a different state, so your LTCG tax rates could be different.

As I said I’m not sure I follow the “future funds available assumption”, but it is important to account for capital gains taxes on taxable withdrawals to do a fair comparison. Remember, the comparison is traditional plus taxable versus Roth, and Roth withdrawals are tax-free, so if withdrawing from the taxable account triggers capital gains, taxes must be paid on those and that needs to be factored in. The best way to account for those capital gains is to assume the taxes get taken out of the withdrawal- that way there is no assumption of other available funds.

Does this help?

### Re: CSS Improvement-Change BETR Calculation

I totally agree. The synopsis I wrote was more a summary of how various people estimate the marginal tax rate and doesn't relate to calculating BETR except for Method 4fyre4ce wrote: ↑Sun Feb 11, 2024 12:10 am I think I know what you're trying to do here - combine all these factors into a single number - but it doesn't work exactly like that. You are trying to calculate a "BETR", which is a constant value for Scenario A, but changes over time for Scenarios B and C.

Outstanding, the numbers from my spreadsheet match exactly out to 40 years! See the screen shots below or the spreadsheet here: https://docs.google.com/spreadsheets/d/ ... sp=sharingfyre4ce wrote: ↑Sun Feb 11, 2024 12:10 amFor Scenario A (paying taxes out of the conversion) the BETR is just the marginal tax rate on the conversion (24%), and doesn't depend on the investments or time.

For B and C, you can use the formula derived here. My results are as follows:

These assumed a 7% total return, 2% yield, 90% qualified yield, 24% current and future marginal tax rate on ordinary income, 18.8% current and future marginal tax rate on LTCG/QD, and 27.8% marginal tax rate on non-qualified dividends.Code: Select all

`Time (yr) Scenario A BETR Scenario B BETR 0 24.00% 24.00% 5 22.64% 23.22% 10 21.58% 22.55% 15 20.71% 21.96% 20 20.00% 21.44% 25 19.40% 20.95% 30 18.88% 20.51% 35 18.41% 20.09% 40 17.99% 19.69%`

As I mentioned in previous posts, the flaw with the current CSS spreadsheet calculation with BETR is the assumption that funds are available in the future to pay the tIRA, but that doesn't change the future tax liability of the taxable account. Also, per my more recent post, that assumption appears to only apply to the tax liability present at the time of conversion.

For my personal case, my federal taxes are effectively zero without Roth conversions, but I choose to max out the 24% tax bracket with conversions and then need to liquidate other funds to pay the taxes. Isolating tax rates is challenging since the ordinary rate changes the LTCG rates in a couple ways. It's not a big deal, but I'd appreciate your thoughts.fyre4ce wrote: ↑Sun Feb 11, 2024 12:10 amI would use these rather than try to create some kind of combined "marginal tax rate" on the conversion that includes both ordinary income taxes and capital gains. I'm not sure if that's even possible, but a BETR serves the same purpose and is more accurate and clear how to use.

Thanks for your feedback! It's always helpful to have independent verification. When I get a chance, I'll look a little deeper into your formulas to see how they mesh with mine.

Here's the screenshots of my results:

### Re: CSS Improvement-Change BETR Calculation

Different "assumptions" are not necessarily "flaws".

The difference in free cash flow before SS and RMDs vs. after SS and RMDs makes the assumption that such funds are available in the future to pay taxes applicable to most, although not universal.

### Re: CSS Improvement-Change BETR Calculation

You're right, the assumption isn't flawed, but that shouldn't change the tax liability of LTCG in the taxable account unless the owner(s) die, it just means you don't have to pay the taxes at that moment in time. Step up in basis due to death is certainly a reasonable scenario and easily accounted for by setting the future LTCG rate to 0.

Second, I never saw an explanation to why the step up in basis occurs to the tax liability present at the time of conversion, but not the growth of funds in the taxable account after conversion?

### Re: CSS Improvement-Change BETR Calculation

Yes, that's just a different assumption. Different assumptions may lead to different conclusions.murrays wrote: ↑Sun Feb 11, 2024 11:57 amYou're right, the assumption isn't flawed, but that shouldn't change the tax liability of LTCG in the taxable account unless the owner(s) die, it just means you don't have to pay the taxes at that moment in time. Step up in basis due to death is certainly a reasonable scenario and easily accounted for by setting the future LTCG rate to 0.

Sorry, you've lost me here.Second, I never saw an explanation to why the step up in basis occurs to the tax liability present at the time of conversion, but not the growth of funds in the taxable account after conversion?

### Re: CSS Improvement-Change BETR Calculation

My understanding is that future funds (SS, RMDs, etc.) could be used to pay the ordinary taxes due to tIRA withdrawals which would allow the LTCG taxes of the non 100% basis taxable account to NOT incur future taxes since they don't need to be sold, is that accurate?

If so, why are taxes due on the growth in the taxable account beyond the original basis? Shouldn't the assumption apply to growth in the taxable account in the same manner it's applied to tax liability of selling funds in the conversion scenario?

### Re: CSS Improvement-Change BETR Calculation

I am still not understanding the concern about liquidity to pay taxes on a future pre-tax withdrawal. The money comes out as cash so there should be plenty of liquidity. If I take a $100,000 tIRA withdrawal and owe $24,000 in taxes, I can just take the taxes out of the $100,000 cash now sitting in my checking account. Or, I can withhold it from the withdrawal.murrays wrote: ↑Sun Feb 11, 2024 11:57 amYou're right, the assumption isn't flawed, but that shouldn't change the tax liability of LTCG in the taxable account unless the owner(s) die, it just means you don't have to pay the taxes at that moment in time. Step up in basis due to death is certainly a reasonable scenario and easily accounted for by setting the future LTCG rate to 0.

Second, I never saw an explanation to why the step up in basis occurs to the tax liability present at the time of conversion, but not the growth of funds in the taxable account after conversion?

Likewise, dividends are paid as cash, and any brokerage should let you (1) turn off automatic dividend reinvestment, (2) transfer out the portion of dividends needed to cover the tax bill, and (3) reinvest the remainder. There may be some issues with only being able to buy a whole number of shares, but it's fair to ignore that for this purpose.

The only potential liquidity issue I'm aware of is paying the taxes on the contribution/conversion on the front end, because the money goes into a Roth account, but I believe we've adequately addressed that by considering the options of (1) paying taxes from inside the conversion, (2) paying with cash, and (3) paying with appreciated taxable investments.

You make a fair point that a future step-up in basis at death makes the future effective LTCG rate equal to zero. But, both pre-tax and Roth accounts get a 10-11 year tax-protected stretch, so there are estate planning benefits on both sides. Roth usually has an advantage over pre-tax in this regard, because many/most people inheriting a pre-tax account will spread out the withdrawals over the stretch period, to spread out the taxable income, so they are not getting the full stretch on the whole amount. Exceptions would be (1) small accounts where a withdrawal in 10-11 years won't raise tax rates, (2) heirs who are toward the bottom of tall brackets (eg. the 35% single bracket is ~$360,000 tall), or (3) heirs already in the top bracket. Roth doesn't have these issues, so the default is the leave the money in the full 10-11 years and get the full stretch on the entire account.

At one point I did attempt to reconcile these two benefits. Check out this page (not yet published). It tells you the best order to tap assets in retirement given the possible combinations of tax rates for you and your heirs, considering both a step-up in basis and a 10-year stretch. I assumed that pre-tax account would be withdrawn evenly over the 10 years and a Roth account would be emptied just at the end. You could check and see if my results agree with yours. I believe my spreadsheet is linked there.

### Re: CSS Improvement-Change BETR Calculation

In the future, appreciated taxable investments may or may not *need* to be sold, but the equation we both derived assumes they are both liquidated, because the metric is how much money is available after-tax to you from all accounts at a particular point in time in the future. I think that's a reasonable assumption.murrays wrote: ↑Sun Feb 11, 2024 12:55 pmMy understanding is that future funds (SS, RMDs, etc.) could be used to pay the ordinary taxes due to tIRA withdrawals which would allow the LTCG taxes of the non 100% basis taxable account to NOT incur future taxes since they don't need to be sold, is that accurate?

If so, why are taxes due on the growth in the taxable account beyond the original basis? Shouldn't the assumption apply to growth in the taxable account in the same manner it's applied to tax liability of selling funds in the conversion scenario?

An alternative would be assuming you leave all assets in consideration to heirs. Then you need to account for (1) the step-up in basis, (2) your heir's withdrawal tax rate rather than your own, and (3) the 10-11 year stretch on inherited retirement accounts. As I mentioned, I ran the numbers on that, although from the perspective of which to withdraw, rather than which to contribute to. I think you could reverse the order to decide which to contribute to.

If you want to propose a different assumption, that's totally fine, as long as you state what it is clearly, and derive the numbers consistently based on it.

### Re: CSS Improvement-Change BETR Calculation

So far so good.

I think fyre4ce has already covered this, but in short the assumption is that you are going to spend the money eventually. To get money out of the taxable account, taxes will be due at whatever tax rate applies and you can then spend what is left over....which would allow the LTCG taxes of the non 100% basis taxable account to NOT incur future taxes since they don't need to be sold, is that accurate?

If so, why are taxes due on the growth in the taxable account beyond the original basis? Shouldn't the assumption apply to growth in the taxable account in the same manner it's applied to tax liability of selling funds in the conversion scenario?

### Re: CSS Improvement-Change BETR Calculation

Agree 100%, the question is, why doesn't that future LTCG tax rate apply to the existing tax liability at year 0 (basis < 100%)? That's the difference between your calculations and what fyre4ce and I came up with. Either your future funds available assumption should apply to all capital gains, before and after year 0, or none of the gains if the basis is stepped up at death.

### Re: CSS Improvement-Change BETR Calculation

### Re: CSS Improvement-Change BETR Calculation

Of course, but in the "no conversion scenario", previous gains remain unsold and untaxed. Future rates apply, don't they?

### Re: CSS Improvement-Change BETR Calculation

If you don't convert, you simply start with that amount in your traditional account. When you do take a distribution in the future and spend it, you pay the tax from the cash you have on hand at that time (or so the assumption goes). Whatever basis you do or don't have in taxable accounts becomes irrelevant because that plays no part in your results (again, under these assumptions).murrays wrote: ↑Sun Feb 11, 2024 3:39 pmOf course, but in the "no conversion scenario", previous gains remain unsold and untaxed. Future rates apply, don't they?

### Re: CSS Improvement-Change BETR Calculation

Ok, I get that, the question is why don't you apply thatFiveK wrote: ↑Sun Feb 11, 2024 4:43 pmIf you don't convert, you simply start with that amount in your traditional account. When you do take a distribution in the future and spend it, you pay the tax from the cash you have on hand at that time (or so the assumption goes).Whatever basis you do or don't have in taxable accounts becomes irrelevant because that plays no part in your results(again, under these assumptions).

**same assumption**to taxable gains that happen after year 0? Shouldn't those be equally "irrelevant" as gains that exist at year 0 per the assumption?

### Re: CSS Improvement-Change BETR Calculation

If you are talking about the tax drag that occurs when you have to compare traditional plus taxable versus Roth as fyre4ce noted in that post (or the "Traditional plus taxable" vs. Roth section of the wiki), then what will happen in the taxable account is very relevant.murrays wrote: ↑Sun Feb 11, 2024 4:52 pmOk, I get that, the question is why don't you apply thatFiveK wrote: ↑Sun Feb 11, 2024 4:43 pmIf you don't convert, you simply start with that amount in your traditional account. When you do take a distribution in the future and spend it, you pay the tax from the cash you have on hand at that time (or so the assumption goes).Whatever basis you do or don't have in taxable accounts becomes irrelevant because that plays no part in your results(again, under these assumptions).same assumptionto taxable gains that happen after year 0? Shouldn't those be equally "irrelevant" as gains that exist at year 0 per the assumption?

### Re: CSS Improvement-Change BETR Calculation

I get that, probably way better than most; it's a pretty simple question: Why are gains before year zero treated differently than gains after year zero with your assumption? Either both should be taxed at future withdrawal rates or neither should be taxed at future withdrawal rates.FiveK wrote: ↑Sun Feb 11, 2024 5:21 pmIf you are talking about the tax drag that occurs when you have to compare traditional plus taxable versus Roth as fyre4ce noted in that post (or the "Traditional plus taxable" vs. Roth section of the wiki), then what will happen in the taxable account is very relevant.

### Re: CSS Improvement-Change BETR Calculation

I don't get your question. Perhaps rephrase, or wait for someone else to rephrase, or...?murrays wrote: ↑Sun Feb 11, 2024 10:57 pmI get that, probably way better than most; it's a pretty simple question: Why are gains before year zero treated differently than gains after year zero with your assumption? Either both should be taxed at future withdrawal rates or neither should be taxed at future withdrawal rates.FiveK wrote: ↑Sun Feb 11, 2024 5:21 pmIf you are talking about the tax drag that occurs when you have to compare traditional plus taxable versus Roth as fyre4ce noted in that post (or the "Traditional plus taxable" vs. Roth section of the wiki), then what will happen in the taxable account is very relevant.

E.g.,

- Gains in a taxable account that play no part in a Roth conversion...play no part in a Roth conversion, so...?

- Any gains realized to pay tax on a current conversion will be taxed at current rates not future rates.

- Anything that happened before year zero is "sunk cost" so it's unclear why we could consider that (except for establishing the basis if one sells in a taxable account to pay conversion tax).

### Re: CSS Improvement-Change BETR Calculation

Let's try it with real numbers...FiveK wrote: ↑Sun Feb 11, 2024 11:24 pmI don't get your question. Perhaps rephrase, or wait for someone else to rephrase, or...?

E.g.,

- Gains in a taxable account that play no part in a Roth conversion...play no part in a Roth conversion, so...?

- Any gains realized to pay tax on a current conversion will be taxed at current rates not future rates.

- Anything that happened before year zero is "sunk cost" so it's unclear why we could consider that (except for establishing the basis if one sells in a taxable account to pay conversion tax).

Let's use the old example

$10k in a tIRA,

50% basis fund in the taxable account,

24% ordinary income tax rare,

18.8% current and future LTCG tax rate,

5% capital return and no dividend return for this example.

If we convert the tIRA and pay all taxes out of the taxable account, we have:

$10k in the Roth under the conversion scenario and

$10k in the tIRA and $2649 unsold funds in the taxable account with $2649*50% =

**$1324.50 cost basis**in the no-conversion scenario.

Under your assumption, at Year 0, the taxable account isn't sold and BETR = 2649/10000 = 26.49%

Are we in agreement so far?

Now go forward 20 years at 5% growth, no dividends.

Roth & pretax tIRA values are both $26,533 and the taxable account pretax value is $7,029.

Under your assumption, the taxable account isn't sold so no tax is taken out and we have:

BETR = 1-(26533-7029)/26533 = 26.49% See row A) in the screenshot below

Or we can apply the tax liability due on the taxable account in the no conversion scenario:

$7029 value, cost basis remains at $1324.50 from year zero because no dividends were added and 18.8% LTCG rate

Tax due = (7029 - 1324.50)*.188 = $1072

BETR = 1-(26533-(7029-1072))/26533 = 22.45% which matches my spreadsheet, see row B) below.

The current spreadsheet doesn't match either one of these. For some reason, it steps up the cost basis at year zero AND does't apply your future funds assumption to growth beyond year 0 by applying the future tax rate to those gains.

Tax due = (7029 - 2649)*.188 = $823

BETR = 1-(26533-(7029-823))/26533 = 23.39% which matches the current spreadsheet, see row C) below.

So the current spreadsheet uses your assumption on the cost basis at year 0, but does NOT use your assumption on growth after year zero. It's Schrodinger's assumption, it both applies and doesn't apply at the same time

Again, I don't disagree that your assumption may apply in some cases, but it makes no sense to only use it on some of the growth in the taxable account, it has to apply to all of the taxable growth.

Here's a screenshot that puts it all together:

### Re: CSS Improvement-Change BETR Calculation

The exact ratio will vary, and "in the library" might now be better said "on the internet" but "A month in the laboratory can often save an hour in the library." remains apt.

Going all the way back to dodonnell's original post regarding Formula for dividend tax drag?, we find

If we

Thanks again to dodonnell for getting it right in the first place, and murrays for raising the issue recently. I expect MDM will have no problem making that simple modification.

And some other wiki modifications are in order as well....

Going all the way back to dodonnell's original post regarding Formula for dividend tax drag?, we find

**FVIFtaxable = ( 1 + r* )^n (1 - T*) + T* - (1 - B )Tcg**

...

(B is original cost basis, which can be set to 1, eliminating this term...

(B is original cost basis, which can be set to 1, eliminating this term

If we

*eliminate that term - which of course we never should have eliminated in the first place - and add that to the CSS calculation in B161,***don't***voilà*we get a result I think all can agree on.Thanks again to dodonnell for getting it right in the first place, and murrays for raising the issue recently. I expect MDM will have no problem making that simple modification.

And some other wiki modifications are in order as well....

### Re: CSS Improvement-Change BETR Calculation

Well done! That seems far more simple than the formulas I came up with and yes, after plugging it in, it appears to match the output that I get.FiveK wrote: ↑Mon Feb 12, 2024 5:25 pm The exact ratio will vary, and "in the library" might now be better said "on the internet" but "A month in the laboratory can often save an hour in the library." remains apt.

Going all the way back to dodonnell's original post regarding Formula for dividend tax drag?, we find

FVIFtaxable = ( 1 + r* )^n (1 - T*) + T* - (1 - B )Tcg

...

(B is original cost basis, which can be set to 1, eliminating this term

If weeliminate that term - which of course we never should have eliminated in the first place - and add that to the CSS calculation in B161,don'tvoilàwe get a result I think all can agree on.

Thanks again to dodonnell for getting it right in the first place, and murrays for raising the issue recently. I expect MDM will have no problem making that simple modification.

And some other wiki modifications are in order as well....

The formula I entered into B161 is:

Code: Select all

`=(((1 + B157)^B160 * (1 - B159) + B159)-(1-B164)*B158) / (1 + B155)^B160`