how to calculate amortization, constant yield/interest

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 don't understand why you are asking this question as Pub 550 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

compute the YTM.

If your broker doesn't tell you the YTM, one possibility with Excel is to use the template at

TC010421081033.aspx?pid=CT101441121033or 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.]

Actually, it says you __can_choose__ to do so.

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 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").

This procedure is for adjusting the cost basis when you purchase at a premium, not at a discount. In any case ....

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?

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%.

Steve

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.

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.

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).

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.]

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

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?

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

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: &sa=N This one looked good. Its zip file has both xls and ods files: 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.