how to calculate amortization, constant yield/interest
removep...@yahoo.com
interest method for bonds purchased after 9/28/1985.
But what is the constant interest method? Is it the YTM (yield to
maturity)?
And how to calculate the YTM? At http://www.moneychimp.com/articles/finworks/fmbondytm.htm
they present a mathematical expression which can only be solved by a
computer. The calculation will be approximate, though to at least 10
decimal places if using a good computer program.
And what if the annual coupon payment minus the annual amortization is
less than zero (which could happen with a bond purchased at
discount)? You have to increase the cost basis, right? And what
about the true interest payment; it would be a negative number, so is
it deductible on Schedule B or Schedule A?
--
<< ------------------------------------------------------- >>
<< The foregoing was not intended or written to be used, >>
<< nor can it used, for the purpose of avoiding penalties >>
<< that may be imposed upon the taxpayer. >>
<< >>
<< The Charter and the Guidelines for submitting posts >>
<< to this newsgroup as well as our anti-spamming policy >>
<< are at www.asktax.org. >>
<< Copyright (2007) - All rights reserved. >>
<< ------------------------------------------------------- >>
Alan
> Publication 550 says to amortize the bond premium using the constant
> interest method for bonds purchased after 9/28/1985.
>
> But what is the constant interest method? Is it the YTM (yield to
> maturity)?
>
> And how to calculate the YTM? At http://www.moneychimp.com/articles/finworks/fmbondytm.htm
> they present a mathematical expression which can only be solved by a
> computer. The calculation will be approximate, though to at least 10
> decimal places if using a good computer program.
>
> And what if the annual coupon payment minus the annual amortization is
> less than zero (which could happen with a bond purchased at
> discount)? You have to increase the cost basis, right? And what
> about the true interest payment; it would be a negative number, so is
> it deductible on Schedule B or Schedule A?
>
tells you to use the Constant Yield Method to amortize the bond
premium (nothing here about buying the bond at a discount);
describes the three steps to make the calculation; and provides
an example.
You are going to need the YTM by obtaining it from the seller or
utilizing your own calculator or computer. Personally, I use my
trusty HP-12C from 1981... still the best financial calculator on
the planet.
I recommend
http://www.money-zine.com/Calculators/Investment-Calculators/Bond-Yield-Calculator/
to compute the YTM.
pomegranate-man
If your broker doesn't tell you the YTM, one possibility with Excel is to
use the template at
http://office.microsoft.com/en-us/templates/
TC010421081033.aspx?pid=CT101441121033
or modify it to your taste.
First fill in cells F2:F5 as the labels indicate.
To compute the YTM, use
Tools > Goal Seek
In the Goal Seek dialog box, put
Set cell: the last filled-in cell in the "carrying amount" column
To value: the face value of the bond
By changing cell: F6
Using Goal Seek this way calculates the YTM and the amortization schedule
as Publication 550 describes.
This doesn't answer all your questions, but hopefully it's a start.
[Disclaimer: I'm not a tax pro.]
joeu2004
gro...@yahoo.com> wrote:
> Publication 550 says to amortize the bond premium using
> the constant interest method for bonds purchased after
> 9/28/1985.
Actually, it says you __can_choose__ to do so.
> And how to calculate the YTM? At
> http://www.moneychimp.com/articles/finworks/fmbondytm.htm
> they present a mathematical expression which can only be
> solved by a computer.
You can use the IRR function of a business calculator.
You can also you the Excel IRR function. These are
the same as the MoneyChimp formula.
Consider the example in Pub 550 (pg 34). The cash
flows are: -110000, 10000 (6 times), and 110000
(10000+100000). In Excel, if you put those values
into A1:A8, then =IRR(A1:A8) results in about
8.074387%.
> The calculation will be approximate, though to at
> least 10 decimal places if using a good computer
> program.
The computation is "exact" within the accuracy of
the computer program -- much more precision that
the 4 decimal places required by the IRS ("at least
two decimal places when expressed as a percentage").
> And what if the annual coupon payment minus the
> annual amortization is less than zero (which could
> happen with a bond purchased at discount)?
This procedure is for adjusting the cost basis when
you purchase at a premium, not at a discount. In
any case ....
> You have to increase the cost basis, right? And
> what about the true interest payment; it would be
> a negative number, so is it deductible on Schedule B
> or Schedule A?
See the section "How to Report Amortization",
especially the subsection "Bond premium amortization
more than interest" on pg 35 of Pub 550. Then post
back with what is unclear about that?
Steve Pope
normally stated on a 6-monthly basis, whereas the example
in P550 uses an annual basis (that is to say, a one-year
accrual interval).
A bond with a yield to maturity of 4% as stated by a bond broker
actually has an annual yield of 4.04%.
Steve
pomegranate-man
>> the constant interest method for bonds purchased after
>> 9/28/1985.
> Actually, it says you __can_choose__ to do so.
This is a key point. For taxable bonds, you can choose whether not to
amortize premiums. There may be some advantage in amortizing, but dealing
with the calculation and extra record-keeping can be a pain.
joeu2004
> It's worth noting that in the bond industry, yields are
> normally stated on a 6-monthly basis, whereas the example
> in P550 uses an annual basis (that is to say, a one-year
> accrual interval).
>
> A bond with a yield to maturity of 4% as stated by a bond
> broker actually has an annual yield of 4.04%.
While I quibble with your generalization and
terminology, it is worth noting that the Excel
IRR function returns a periodic rate. So if the
cash flows are semiannual, for example, the YTM
would be computed by (1+IRR(...))^2 - 1.
An adjustment might also need to be made if you
purchase the bond on a date other than the
anniversary of a cash flow.
All of this can be simplified by using the Excel
XIRR function. The result differs slightly from
the equivalent IRR formulation. But the
difference is usually small, and often the two
results will be the same within 2 decimal points
of a percentage, which is all the accuracy that
the IRS requires according to Pub 550.
removep...@yahoo.com
wrote:
> >> Publication 550 says to amortize the bond premium using
> >> theconstantinterest method for bonds purchased after
> >> 9/28/1985.
> > Actually, it says you __can_choose__ to do so.
>
> This is a key point. For taxable bonds, you can choose whether not to
> amortize premiums. There may be some advantage in amortizing, but dealing
> with the calculation and extra record-keeping can be a pain.
My case is a muni bond, so I have to do amortization. For taxable
bonds, I'm not sure if amortization also gives a better result, and
the answer probably depends on circumstances and random factors (such
as your income in a future year).
pomegranate-man
If a muni bond is held to maturity, the premium is all amortized away, so
there's no need to calculate the amortization for capital-gain reporting.
In my case, the intention is to hold bonds to maturity, so I defer thinking
about amortization until/unless I end up selling a muni bond before
maturity (which has never happened).
Strictly speaking (really *really* strictly) the amortization might have a
minor affect on Form 1040 line 8b ("tax-exempt interest"). This would
almost never have any impact on the tax due, however (IMO). Except for
people with large portfolios of tax-exempt bonds, I'd be surprised if
somebody goes to the trouble of doing this calculation, but, hey, what do I
know?
If a retiree has income near a threshold value, line 8b can affect (a) what
fraction of Social Security benefits are taxable, and (b) the Medicare Part
B premium. There are probably other effects as well.
[Disclaimer: I'm not a tax pro.]
--
Steve Pope
>> My case is a muni bond, so I have to do amortization.
>Strictly speaking (really *really* strictly) the amortization might have a
>minor affect on Form 1040 line 8b ("tax-exempt interest"). This would
>almost never have any impact on the tax due, however (IMO). Except for
>people with large portfolios of tax-exempt bonds, I'd be surprised if
>somebody goes to the trouble of doing this calculation, but, hey, what do I
>know?
The use of the word "must" twice in the following passage in
Pub 550 suggests to me people do it:
"If the bond yields tax-exempt interest, you must amortize the
premium. This amortized amount is not deductible in determining
taxable income. However, each year you must reduce your basis
in the bond (and tax-exempt interest otherwise reportable on
Form 1040, line 8b) by the amortization for the year."
Steve
removep...@yahoo.com
wrote:
> If a muni bond is held to maturity, the premium is all amortized away, so
> there's no need to calculate the amortization for capital-gain reporting.
If a muni bond is held to call, and the bond is called at face value,
then there is also nothing to worry about. What if the bond is called
at something other than par value?
pomegranate-man
> Pub 550 suggests to me people do it:
>
> "If the bond yields tax-exempt interest, you must amortize the
> premium. This amortized amount is not deductible in determining
> taxable income. However, each year you must reduce your basis
> in the bond (and tax-exempt interest otherwise reportable on
> Form 1040, line 8b) by the amortization for the year."
I see your point.
To satisfy my curiosity, could professional tax preparers out there answer,
"Do you routinely reduce Form 1040 line 8b by the amortized tax-exempt
interest for all your clients to which the above rule applies?" Thanks!
Steve Pope
>> The use of the word "must" twice in the following passage in
>> Pub 550 suggests to me people do it:
>> "If the bond yields tax-exempt interest, you must amortize the
>> premium. This amortized amount is not deductible in determining
>> taxable income. However, each year you must reduce your basis
>> in the bond (and tax-exempt interest otherwise reportable on
>> Form 1040, line 8b) by the amortization for the year."
>I see your point.
>To satisfy my curiosity, could professional tax preparers out there answer,
>"Do you routinely reduce Form 1040 line 8b by the amortized tax-exempt
>interest for all your clients to which the above rule applies?" Thanks!
I'm interested in this as well.
Another oddity: the line 8b reporting applies when you buy a muni
bond above par, but it doesn't apply when you buy a zero-coupon
muni that, while trading below par, is trading above its OID-adjusted
price. This seems to suggest people in the special tax situations where
8b affects taxation should avoid the zero.
Steve
DF2
>
>
>And how to calculate the YTM? At http://www.moneychimp.com/articles/finworks/fmbondytm.htm
>they present a mathematical expression which can only be solved by a
>computer. The calculation will be approximate, though to at least 10
>decimal places if using a good computer program.
I did this search:
http://www.google.com/search?hl=en&q=%22Bond+Yield+Calculator%22+schedule&start=10&sa=N
This one looked good. Its zip file has both xls and ods files:
http://www.my-install.com/prog/Business-Calculators-Converters/23268/Bond-Yield-Calculator.html
I did launch the application, but I did not enable macros. I am sure
what is safe and what is not. I would like to think that Microsoft
Excel and Open Office Calc (both native spreadsheets are in the
download) would not do unsafe things, but I am pretty sure they are
not smart enough for that... or they are too smart for my own good.
I suspect it is perfectly safe. There is a misspelling/malapropism
of "Greatest Common Devisor" for "Greatest Common Divisor".
But it looks really good in that it knows to deal with days in the
"First 'Odd' Period". If somebody could inspect the macros for
safety, I expect this would be found to be worthwhile.
On a different note, bonds can have a Yield to Call that is less
than the Yield to Maturity. Imagine a 10% bond that matures in 20
years, but is callable in 1 year. You fully expect that it will be
called. You pay $1050 for a $1000 bond for a yield to call of 5%.
Your yield to maturity would be about 9.52% per year if it were
never called. Basis would amortized down by $2.50 per year to $1000
after 20 years. Could you claim $100 in tax free interest and take a
$47.50 capital loss when the bond gets called in a year? I doubt
it, but I have not seen this part discussed. Please ignore small
differences in my simple calculations. I am asking about the
concept.