## Is this calculation on t-bill tax-equivalent return correct

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### Is this calculation on t-bill tax-equivalent return correct

Treasury Direct says the Investment Rate on the 13-week T-Bill is 2.217%
With a state 9.3% tax bracket
Is the tax-equivalent yield 2.217 / (1-0.093) = 2.44%
So that would be the same as a 1-year bank CD with a 2.44% APR (or APY...I'm not concerned about 0.00 decimal places)

mc7
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### Re: Is this calculation on t-bill tax-equivalent return correct

Yep, that's right.

Posts: 82
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### Re: Is this calculation on t-bill tax-equivalent return correct

Thank you.

MotoTrojan
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### Re: Is this calculation on t-bill tax-equivalent return correct

What about federal tax? You’ll pay more of that on the CD at 2.44%. You don’t pay federal tax on the state-tax adjusted yield.

cas
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### Re: Is this calculation on t-bill tax-equivalent return correct

Sat Oct 06, 2018 12:02 am
Treasury Direct says the Investment Rate on the 13-week T-Bill is 2.217%
With a state 9.3% tax bracket
Is the tax-equivalent yield 2.217 / (1-0.093) = 2.44%
So that would be the same as a 1-year bank CD with a 2.44% APR (or APY...I'm not concerned about 0.00 decimal places)
Kevin M has a nice post on how to calculate various TEYs for various bond products here: "Taxable Equivalent Yield (TEY)" viewtopic.php?t=248539

The equation you (OP) are using is accurate for Treasuries if state tax is fully deductible on your federal taxes.

It isn't accurate if you will be using the standard deduction on your federal taxes. Since less people will be able to deduct all their state taxes under the new tax bill, this is probably worth mentioning.

For example, assume a \$10,000 investment in the T-bill or CD and a 22% federal tax rate. (Neither of those really matter. Just for example.) Also assume both CD and T-bill end up earning the given interest rate for a year, to make the math easier. And assume a standard deduction on federal taxes (i.e. no state taxes deducted on federal taxes).

Interest on 2.217% T-bill for a year = \$221.70
Amount left after state tax paid (not state taxable) = \$221.70
Amount left after federal tax paid (22%) = \$221.70 * (1 - .22) = \$172.92 (You pay federal tax on \$221.70)

Interest on 2.44% CD for a year = \$244
After state tax (9.3%) = \$244( 1 - .093) = \$221.30 (So far, so good. You have the same amount in your pocket after state taxes as with the T-bill. I'll assume the \$0.40 difference has to do with decimal place error)
After federal tax (22%) = \$221.30 - (\$244 * (0.22)) = \$167.62 (Whoops! You ended up with less in your pocket after taxes, because you paid federal tax on \$244 rather than on \$221.70)

Kevin M's article above gives (derives) the equations to figure out what CD rate would give you the same amount of money ending up in your pocket after all are taxes paid.

#Cruncher
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### Re: Is this calculation on t-bill tax-equivalent return correct

cas wrote:
Sat Oct 06, 2018 7:39 am
The equation you (OP) are using is accurate for Treasuries if state tax is fully deductible on your federal taxes. It isn't accurate if you will be using the standard deduction on your federal taxes. … Kevin M's article above gives (derives) the equations to figure out what CD rate would give you the same amount of money ending up in your pocket after all are taxes paid.
Here is the calculation for a 22% federal tax rate, assuming state taxes aren't deducted on the federal tax return. It's followed by the general formula.

Code: Select all

``````2.517% = (0.02217 * (1 - 0.22)) / (1 - 0.22 - 0.093) or, more generally,
CDY = (TY      * (1 - f))    / (1 - f    - s) where
CDY = CD equivalent yield
TY = Treasury yield
f = federal tax rate
s = state tax rate``````
Here are the CD equivalent yields for other federal tax rates:

Code: Select all

``````Treasury yield  2.217%
State tax       9.300%
Federal tax   After tax   CD Equiv
-----------   ---------   --------
0%         2.217%     2.444%
10%         1.995%     2.472%
12%         1.951%     2.479%
22%         1.729%     2.517%
24%         1.685%     2.526%
32%         1.508%     2.568%
35%         1.441%     2.587%
37%         1.397%     2.601%``````
By the way, the 2.217% from the original post is the "Investment Rate" from the 10/1/2018 auction results. This converts the T-Bill 2.175% discount rate to the equivalent yield on a coupon-bearing Treasury note or bond.

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### Re: Is this calculation on t-bill tax-equivalent return correct

cas wrote:
Sat Oct 06, 2018 7:39 am
Sat Oct 06, 2018 12:02 am
Treasury Direct says the Investment Rate on the 13-week T-Bill is 2.217%
With a state 9.3% tax bracket
Is the tax-equivalent yield 2.217 / (1-0.093) = 2.44%
So that would be the same as a 1-year bank CD with a 2.44% APR (or APY...I'm not concerned about 0.00 decimal places)
Kevin M has a nice post on how to calculate various TEYs for various bond products here: "Taxable Equivalent Yield (TEY)" viewtopic.php?t=248539

The equation you (OP) are using is accurate for Treasuries if state tax is fully deductible on your federal taxes.

It isn't accurate if you will be using the standard deduction on your federal taxes. Since less people will be able to deduct all their state taxes under the new tax bill, this is probably worth mentioning.

For example, assume a \$10,000 investment in the T-bill or CD and a 22% federal tax rate. (Neither of those really matter. Just for example.) Also assume both CD and T-bill end up earning the given interest rate for a year, to make the math easier. And assume a standard deduction on federal taxes (i.e. no state taxes deducted on federal taxes).

Interest on 2.217% T-bill for a year = \$221.70
Amount left after state tax paid (not state taxable) = \$221.70
Amount left after federal tax paid (22%) = \$221.70 * (1 - .22) = \$172.92 (You pay federal tax on \$221.70)

Interest on 2.44% CD for a year = \$244
After state tax (9.3%) = \$244( 1 - .093) = \$221.30 (So far, so good. You have the same amount in your pocket after state taxes as with the T-bill. I'll assume the \$0.40 difference has to do with decimal place error)
After federal tax (22%) = \$221.30 - (\$244 * (0.22)) = \$167.62 (Whoops! You ended up with less in your pocket after taxes, because you paid federal tax on \$244 rather than on \$221.70)

Kevin M's article above gives (derives) the equations to figure out what CD rate would give you the same amount of money ending up in your pocket after all are taxes paid.
Your calculations make sense. I think I need a little more caffeine to get through the thread on Kevin M's original post.
What I'm considering is taking money from a 1.8% savings account and purchasing a \$5,000 13-week T-bill every month for 4 months (roll each bill forward for a total of \$20,000 in T-bills). We likely will not be able to itemize for tax year 2018.
I need to do some more reading and math. But this was helpful, thanks.
Last edited by ladycat on Sat Oct 06, 2018 1:24 pm, edited 1 time in total.

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### Re: Is this calculation on t-bill tax-equivalent return correct

#Cruncher wrote:
Sat Oct 06, 2018 8:48 am
cas wrote:
Sat Oct 06, 2018 7:39 am
The equation you (OP) are using is accurate for Treasuries if state tax is fully deductible on your federal taxes. It isn't accurate if you will be using the standard deduction on your federal taxes. … Kevin M's article above gives (derives) the equations to figure out what CD rate would give you the same amount of money ending up in your pocket after all are taxes paid.
Here is the calculation for a 22% federal tax rate, assuming state taxes aren't deducted on the federal tax return. It's followed by the general formula.

Code: Select all

``````2.517% = (0.02217 * (1 - 0.22)) / (1 - 0.22 - 0.093) or, more generally,
CDY = (TY      * (1 - f))    / (1 - f    - s) where
CDY = CD equivalent yield
TY = Treasury yield
f = federal tax rate
s = state tax rate``````
Here are the CD equivalent yields for other federal tax rates:

Code: Select all

``````Treasury yield  2.217%
State tax       9.300%
Federal tax   After tax   CD Equiv
-----------   ---------   --------
0%         2.217%     2.444%
10%         1.995%     2.472%
12%         1.951%     2.479%
22%         1.729%     2.517%
24%         1.685%     2.526%
32%         1.508%     2.568%
35%         1.441%     2.587%
37%         1.397%     2.601%``````
By the way, the 2.217% from the original post is the "Investment Rate" from the 10/1/2018 auction results. This converts the T-Bill 2.175% discount rate to the equivalent yield on a coupon-bearing Treasury note or bond.
Am I using the wrong T-bill information to do the calculation? I thought the "Investment Rate" was the value I should compare to a CD.

#Cruncher
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### Re: Is this calculation on t-bill tax-equivalent return correct

Sat Oct 06, 2018 12:43 pm
What I'm considering is ... purchasing a \$5,000 13-week T-bill every month for 4 months (roll each bill forward for a total of \$20,000 in T-bills).
You need to buy them more frequently than every month. For example, if you buy bills every three weeks at week 0, 3, 6, and 9, you'd have a ladder (4 X \$5,000 = \$20,000) maturing at week 13, 16, 19, and 22. Then four weeks later at week 13, you'd roll over the first one to make the ladder mature at week 16, 19, 22, and 26. And so on ...

Code: Select all

``````Mature/Issue  0    3     6     9     13     16     19     etc.
13         New  Old   Old   Old    Mat
16              New   Old   Old    Old    Mat
19                    New   Old    Old    Old    Mat
22                          New    Old    Old    Old
26                                 Roll   Old    Old
29                                        Roll   Old
32                                               Roll
etc.``````
• New = bill purchased with new money
• Old = bill previously purchased
• Mat = maturing bill
• Roll = bill purchased with proceeds from maturing bill

Sat Oct 06, 2018 12:46 pm
#Cruncher wrote:
Sat Oct 06, 2018 8:48 am
… By the way, the 2.217% from the original post is the "Investment Rate" from the 10/1/2018 auction results. This converts the T-Bill 2.175% discount rate to the equivalent yield on a coupon-bearing Treasury note or bond.
Am I using the wrong T-bill information to do the calculation? I thought the "Investment Rate" was the value I should compare to a CD.
No, you aren't using the wrong rate, Ladycat. I was just pointing out where your figure came from. It's not necessary, but to be even more precise, convert the "Investment Rate" (compounded semi-annually) to an annually compounded rate (APY) since that's how CDs are quoted:
2.229% = (1 + 0.02217 / 2) ^ 2 - 1

Posts: 82
Joined: Fri Sep 28, 2018 5:02 pm

### Re: Is this calculation on t-bill tax-equivalent return correct

#Cruncher wrote:
Sat Oct 06, 2018 7:08 pm
Sat Oct 06, 2018 12:43 pm
What I'm considering is ... purchasing a \$5,000 13-week T-bill every month for 4 months (roll each bill forward for a total of \$20,000 in T-bills).
You need to buy them more frequently than every month. For example, if you buy bills every three weeks at week 0, 3, 6, and 9, you'd have a ladder (4 X \$5,000 = \$20,000) maturing at week 13, 16, 19, and 22. Then four weeks later at week 13, you'd roll over the first one to make the ladder mature at week 16, 19, 22, and 26. And so on ...

Code: Select all

``````Mature/Issue  0    3     6     9     13     16     19     etc.
13         New  Old   Old   Old    Mat
16              New   Old   Old    Old    Mat
19                    New   Old    Old    Old    Mat
22                          New    Old    Old    Old
26                                 Roll   Old    Old
29                                        Roll   Old
32                                               Roll
etc.``````
• New = bill purchased with new money
• Old = bill previously purchased
• Mat = maturing bill
• Roll = bill purchased with proceeds from maturing bill

Sat Oct 06, 2018 12:46 pm
#Cruncher wrote:
Sat Oct 06, 2018 8:48 am
… By the way, the 2.217% from the original post is the "Investment Rate" from the 10/1/2018 auction results. This converts the T-Bill 2.175% discount rate to the equivalent yield on a coupon-bearing Treasury note or bond.
Am I using the wrong T-bill information to do the calculation? I thought the "Investment Rate" was the value I should compare to a CD.
No, you aren't using the wrong rate, Ladycat. I was just pointing out where your figure came from. It's not necessary, but to be even more precise, convert the "Investment Rate" (compounded semi-annually) to an annually compounded rate (APY) since that's how CDs are quoted:
2.229% = (1 + 0.02217 / 2) ^ 2 - 1
Ok, thanks. This is the first time I've been looking at treasuries as lower tax alternatives to CDs and I want to be sure I'm understanding correctly.

Posts: 82
Joined: Fri Sep 28, 2018 5:02 pm

### Re: Is this calculation on t-bill tax-equivalent return correct

#Cruncher wrote:
Sat Oct 06, 2018 7:08 pm
Sat Oct 06, 2018 12:43 pm
What I'm considering is ... purchasing a \$5,000 13-week T-bill every month for 4 months (roll each bill forward for a total of \$20,000 in T-bills).
You need to buy them more frequently than every month. For example, if you buy bills every three weeks at week 0, 3, 6, and 9, you'd have a ladder (4 X \$5,000 = \$20,000) maturing at week 13, 16, 19, and 22. Then four weeks later at week 13, you'd roll over the first one to make the ladder mature at week 16, 19, 22, and 26. And so on ...

Code: Select all

``````Mature/Issue  0    3     6     9     13     16     19     etc.
13         New  Old   Old   Old    Mat
16              New   Old   Old    Old    Mat
19                    New   Old    Old    Old    Mat
22                          New    Old    Old    Old
26                                 Roll   Old    Old
29                                        Roll   Old
32                                               Roll
etc.``````
• New = bill purchased with new money
• Old = bill previously purchased
• Mat = maturing bill
• Roll = bill purchased with proceeds from maturing bill

Sat Oct 06, 2018 12:46 pm
#Cruncher wrote:
Sat Oct 06, 2018 8:48 am
… By the way, the 2.217% from the original post is the "Investment Rate" from the 10/1/2018 auction results. This converts the T-Bill 2.175% discount rate to the equivalent yield on a coupon-bearing Treasury note or bond.
Am I using the wrong T-bill information to do the calculation? I thought the "Investment Rate" was the value I should compare to a CD.
No, you aren't using the wrong rate, Ladycat. I was just pointing out where your figure came from. It's not necessary, but to be even more precise, convert the "Investment Rate" (compounded semi-annually) to an annually compounded rate (APY) since that's how CDs are quoted:
2.229% = (1 + 0.02217 / 2) ^ 2 - 1
To do this I correctly, based on the tentative treasury auction schedule
https://www.treasury.gov/resource-cente ... ctions.pdf
Do i set the week number (0, 3, 6, 9) to the auction settlement date?

#Cruncher
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Location: New York City
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### Re: Is this calculation on t-bill tax-equivalent return correct

Wed Oct 10, 2018 11:47 pm
Do i set the week number (0, 3, 6, 9) to the auction settlement date?
Yes. 4, 13, and 26 week Treasury Bills are scheduled so that every week a new one is issued (i.e., the settlement date) on the same day an old one matures. (Normally this is on Thursday, but will be Friday if Thursday is a holiday like Thanksgiving. [*]) So here is an example of how you could build up a four rung ladder starting with the 13-week bills to be issued 11/1/2018:

Code: Select all

``````           Issued                          Roll Over
Week    (Settlement)       Matures        Bill Issued
----   --------------   --------------   --------------
0   Thu 11/01/2018   Thu 01/31/2019
3   Fri 11/23/2018   Thu 02/21/2019
6   Thu 12/13/2018   Thu 03/14/2019
9   Thu 01/03/2019   Thu 04/04/2019
13   Thu 01/31/2019   Thu 05/02/2019   Thu 11/01/2018
16   Thu 02/21/2019   Thu 05/23/2019   Fri 11/23/2018
19   Thu 03/14/2019   Thu 06/13/2019   Thu 12/13/2018
22   Thu 04/04/2019   Thu 07/04/2019   Thu 01/03/2019
26   Thu 05/02/2019   Thu 08/01/2019   Thu 01/31/2019
etc.``````
At TreasuryDirect you can schedule purchase of 13-week T Bills up to about nine weeks in advance. You can also specify that each bill be automatically reinvested up to eight times (two years). On the other hand, I believe most brokers only accept orders during the small window between when the auction is officially announced and the auction. Check with your broker to see if you can specify automatic reinvestment.

* For example, the "13-week" bill issued Thursday 8/23/2018 has a term of 92 days instead of the normal 91 so that it will mature on Friday 11/23/2018, the day a new 13-week bill will be issued.

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### Re: Is this calculation on t-bill tax-equivalent return correct

Thanks. I arrived at a similar result starting with the first purchase on 11/18/18. But I did it old school with a calendar and pencil and matched it up against the treasury settlement dates. Tedious, but effective.