# How to Calculate After Tax Bond Yield

Three Parts:Figuring Out How the Bond is TaxedCalculating After-Tax Bond YieldCalculating Tax-Equivalent Yield

Yield is an investment concept that puts the earnings of an investment vehicle into context. It states earnings as a percentage of the initial investment. After-tax bond yield reflects the earnings of a bond investment, adjusted to account for capital gains taxes levied on the earnings from that bond. Although it may seem like an intimidating concept, it's actually a simple calculation, requiring nothing more advanced than basic algebra.

## Steps

### Part 1 Figuring Out How the Bond is Taxed

- 1
**Determine the type of bond.**Bonds returns are taxed differently based upon the type of bond. There are three major types of bonds: corporate, federal government, and municipal bonds. Corporate bonds are sold by corporations and their returns are taxed like regular income (taxed at all tax levels). Federal government bonds, like treasury bills and bonds, are only taxable at the federal level. Municipal bonds, on the other hand, are tax free if purchased in your own municipality or state.^{[1]} - 2
**Use your income tax bracket for bond returns.**The returns taxed on each type of bond are the coupon payments (interest payments) made to the bondholder throughout the life of the bond. The tax rate used on these payments is the same used to tax your income throughout the year. For example, if you are in the 33 percent tax bracket, returns on a corporate bond that you own would be taxed at 33 percent.^{[2]}- However, you would also need to then calculate your state income tax rate and add in taxes to the state to determine your total tax burden.
^{[3]}

- However, you would also need to then calculate your state income tax rate and add in taxes to the state to determine your total tax burden.
- 3
**Use capital gains tax for gains on trades.**Whenever you sell a bond on the secondary market, you will need to pay capital gains tax on any gains made in the trade. This is true for every type of bond. Capital gains tax is different than income tax, but is still determined by your income. After-tax returns on trades can also be calculated using the after-tax bond yield calculation method described in this article.^{[4]} - 4
**Include any discounts on bonds.**If you buy a bond at a discount, as is typically done with zero-coupon bonds (bond that don't pay interest), you need to report the discount as income. The discount will be spread out evenly over the life of the bond. This discount is then taxed as income at your income tax rate.- Alternately, any bond premiums paid can be deducted from your taxable income. Premiums are any money paid above the par value of a bond.
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- Alternately, any bond premiums paid can be deducted from your taxable income. Premiums are any money paid above the par value of a bond.

### Part 2 Calculating After-Tax Bond Yield

- 1
**Determine the pre-tax yield.**Start by calculating the annual percent return provided by the bond. This is generally spelled out when you purchase the bond. For example, a corporate bond might pay 10 percent annual interest. This can be annual, with one 10 percent payment, semiannual with two 5 percent payments, or any other number of payments throughout the year that total 10 percent of the bond's par value.^{[6]} - 2
**Figure out the tax rate you have paid or will be charged on the bond.**Your tax rate on a bond will depend on the bond's type. See the other part of this article, "figuring out how the bond is taxed," for more information. Add up the relevant taxes for the bond to figure out your total tax rate.^{[7]}- For example, imagine your federal tax bracket is 33 percent. Your state income tax rate is another 7 percent. So, your total tax rate for a corporate bond would be 40 percent (33 percent + 7 percent).

- 3
**Input your data into the after-tax yield equation.**The after-tax yield equation is simply . In the equation, ATY means after-tax yield, r is the pre-tax return, and t is your total tax rate for the bond.^{[8]}- For example, the 10 percent corporate bond would be entered as .
- Note that the percentage return, 10 percent, and the tax rate, 40 percent, were entered in the equation as decimals. This is to simplify calculation. To convert percentages to decimals, simply divide by 100.

- 4
**Solve for after-tax bond yield.**Solve your equation by first subtracting the figures within the parentheses. In the example, this gives . Then, simply multiply the final two numbers to get your answer. This would be 0.06 or 6 percent. So, your after-tax yield for a 10 percent corporate bond at a 40 percent tax rate would be 6 percent.

### Part 3 Calculating Tax-Equivalent Yield

- 1
**Understand tax-equivalent yield.**Tax-equivalent yield is a figure that is used to compare tax-free bond returns to returns from taxable bonds. It converts the untaxed bond's return to an imaginary "pre-tax" return so that it can be easily compared to taxable security returns. This technique is useful for comparing the returns on municipal bonds to federal government and corporate bonds.^{[9]} - 2
**Determine the yield of the untaxed bond.**Check your records for the untaxed bond's yield. For example, imagine that you find a municipal bond that pays 5.5 percent interest annually. This is your return that you will use for return calculations.^{[10]} - 3
**Calculate tax-equivalent yield.**Tax-equivalent yield is calculated using the formula . In the formula, TEY stands for tax-equivalent yield, r represents the bond's annual return in decimal form, and t is your income tax rate, also in decimal form. For example, assuming the 5.5 percent bond described above and a 40 percent total tax rate, you would complete the equation as follows: .^{[11]}- Calculate the answer by first subtracting the numbers on the bottom. Then, divide the remaining numbers to get your answer. Here, this would be 0.055/0.6, which works out to 0.0917 if you round to three decimal places.
- Your 5.5 percent municipal bond offers the same return as a taxable bond with a stated 9.17 percent return.

- 4
**Compare this yield to a taxed security's yield.**This number can now be used to compare the municipal bond's return to taxable bond returns. For example, imagine you were considering a corporate bond that offers 9 percent returns. It may seem like an easy choice to choose the corporate bond over a municipal bond offering 5.5 percent. However, after the calculation, you can see that the municipal bond actually offers a higher return (9.17 percent over 9 percent).

## Tips

- Cashing in a bond often carries a fee for the brokerage or other agent who facilitated the sale. This is not part of taxes, but should be subtracted from the profit like taxes when calculating the real yield of a bond. This is less important when comparing the performance of various bonds handled by the same brokerage, but it can be vital to comparing the performance of bonds sold by different brokers.

## Sources and Citations

- ↑ http://www.investopedia.com/articles/tax/08/bond-tax.asp
- ↑ http://www.investopedia.com/articles/tax/08/bond-tax.asp
- ↑ http://finance.zacks.com/explanation-after-taxequivalent-yield-2431.html
- ↑ http://www.investopedia.com/articles/tax/08/bond-tax.asp
- ↑ http://www.investopedia.com/articles/tax/08/bond-tax.asp
- ↑ http://www.accountingcoach.com/blog/after-tax-cost-of-debt
- ↑ http://finance.zacks.com/explanation-after-taxequivalent-yield-2431.html
- ↑ http://www.investopedia.com/exam-guide/cfa-level-1/fixed-income-investments/after-tax-yield-taxable-security.asp
- ↑ http://www.financeformulas.net/Tax_Equivalent_Yield.html
- ↑ http://www.financeformulas.net/Tax_Equivalent_Yield.html
- ↑ http://www.financeformulas.net/Tax_Equivalent_Yield.html

## Article Info

Categories: Taxes and Fees