Is this calculation on tbill taxequivalent return correct
Is this calculation on tbill taxequivalent return correct
Treasury Direct says the Investment Rate on the 13week TBill is 2.217%
With a state 9.3% tax bracket
Is the taxequivalent yield 2.217 / (10.093) = 2.44%
So that would be the same as a 1year bank CD with a 2.44% APR (or APY...I'm not concerned about 0.00 decimal places)
With a state 9.3% tax bracket
Is the taxequivalent yield 2.217 / (10.093) = 2.44%
So that would be the same as a 1year bank CD with a 2.44% APR (or APY...I'm not concerned about 0.00 decimal places)
Re: Is this calculation on tbill taxequivalent return correct
Yep, that's right.

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Re: Is this calculation on tbill taxequivalent 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 statetax adjusted yield.
Re: Is this calculation on tbill taxequivalent return correct
Kevin M has a nice post on how to calculate various TEYs for various bond products here: "Taxable Equivalent Yield (TEY)" viewtopic.php?t=248539ladycat wrote: ↑Sat Oct 06, 2018 12:02 amTreasury Direct says the Investment Rate on the 13week TBill is 2.217%
With a state 9.3% tax bracket
Is the taxequivalent yield 2.217 / (10.093) = 2.44%
So that would be the same as a 1year bank CD with a 2.44% APR (or APY...I'm not concerned about 0.00 decimal places)
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 Tbill or CD and a 22% federal tax rate. (Neither of those really matter. Just for example.) Also assume both CD and Tbill 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% Tbill 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 Tbill. 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.
Re: Is this calculation on tbill taxequivalent return correct
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.cas wrote: ↑Sat Oct 06, 2018 7:39 amThe 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.
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
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%
Re: Is this calculation on tbill taxequivalent return correct
Your calculations make sense. I think I need a little more caffeine to get through the thread on Kevin M's original post.cas wrote: ↑Sat Oct 06, 2018 7:39 amKevin M has a nice post on how to calculate various TEYs for various bond products here: "Taxable Equivalent Yield (TEY)" viewtopic.php?t=248539ladycat wrote: ↑Sat Oct 06, 2018 12:02 amTreasury Direct says the Investment Rate on the 13week TBill is 2.217%
With a state 9.3% tax bracket
Is the taxequivalent yield 2.217 / (10.093) = 2.44%
So that would be the same as a 1year bank CD with a 2.44% APR (or APY...I'm not concerned about 0.00 decimal places)
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 Tbill or CD and a 22% federal tax rate. (Neither of those really matter. Just for example.) Also assume both CD and Tbill 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% Tbill 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 Tbill. 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.
What I'm considering is taking money from a 1.8% savings account and purchasing a $5,000 13week Tbill every month for 4 months (roll each bill forward for a total of $20,000 in Tbills). 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.
Re: Is this calculation on tbill taxequivalent return correct
Am I using the wrong Tbill information to do the calculation? I thought the "Investment Rate" was the value I should compare to a CD.#Cruncher wrote: ↑Sat Oct 06, 2018 8:48 amHere 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.cas wrote: ↑Sat Oct 06, 2018 7:39 amThe 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 are the CD equivalent yields for other federal tax rates: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
By the way, the 2.217% from the original post is the "Investment Rate" from the 10/1/2018 auction results. This converts the TBill 2.175% discount rate to the equivalent yield on a couponbearing Treasury note or bond.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%
Re: Is this calculation on tbill taxequivalent return correct
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
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 semiannually) to an annually compounded rate (APY) since that's how CDs are quoted:ladycat wrote: ↑Sat Oct 06, 2018 12:46 pmAm I using the wrong Tbill information to do the calculation? I thought the "Investment Rate" was the value I should compare to a CD.#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 TBill 2.175% discount rate to the equivalent yield on a couponbearing Treasury note or bond.
2.229% = (1 + 0.02217 / 2) ^ 2  1
Re: Is this calculation on tbill taxequivalent return correct
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.#Cruncher wrote: ↑Sat Oct 06, 2018 7:08 pmYou 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
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 semiannually) to an annually compounded rate (APY) since that's how CDs are quoted:ladycat wrote: ↑Sat Oct 06, 2018 12:46 pmAm I using the wrong Tbill information to do the calculation? I thought the "Investment Rate" was the value I should compare to a CD.#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 TBill 2.175% discount rate to the equivalent yield on a couponbearing Treasury note or bond.
2.229% = (1 + 0.02217 / 2) ^ 2  1
Re: Is this calculation on tbill taxequivalent return correct
To do this I correctly, based on the tentative treasury auction schedule#Cruncher wrote: ↑Sat Oct 06, 2018 7:08 pmYou 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
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 semiannually) to an annually compounded rate (APY) since that's how CDs are quoted:ladycat wrote: ↑Sat Oct 06, 2018 12:46 pmAm I using the wrong Tbill information to do the calculation? I thought the "Investment Rate" was the value I should compare to a CD.#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 TBill 2.175% discount rate to the equivalent yield on a couponbearing Treasury note or bond.
2.229% = (1 + 0.02217 / 2) ^ 2  1
https://www.treasury.gov/resourcecente ... ctions.pdf
Do i set the week number (0, 3, 6, 9) to the auction settlement date?
Re: Is this calculation on tbill taxequivalent return correct
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 13week bills to be issued 11/1/2018:
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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.
* For example, the "13week" 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 13week bill will be issued.
Re: Is this calculation on tbill taxequivalent 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.