U13LO6: Compute the tax-equivalent yield of municipal bonds

How to calculate tax-equivalent yield: -Assume an investor has $2,000 to invest. -If he purchases, at par, one corporate or government bond of standard size ($1,000) w/ a 10% nominal (coupon) yield, he would receive $100 per year paid by two semiannual interest checks of $50.

-For purposes of this example, assume that he is in the 28% federal income tax bracket. -An individual in the 28% tax bracket pays tax on any additional income earned at a rate of 28%. -Therefore, on the $100 in interest received, he would pay the IRS $28 (28%) and keep the other $72.

How to calculate tax-equivalent yield: Example Continued: The other $1,000 he had available to invest was used to purchase a $1,000 par-value municipal bond with a 7.5% nominal yield. -He would receive $75 annually on that bond paid by two semiannual interest checks of $37.50

-Of the $75 interest received none of it is taxed

How to calculate tax-equivalent yield: Example Continued: A client in the 28% bracket should purchase 7.5% municipals before 10% corporates

-The taxable equivalent yield of a 7.5% tax-free bond for this investor in the 28% tax bracket would be: the tax-free yield / *100% - tax bracket **In this case, 7.5 / (100-28), or .72 = 10.42% **The 7.5% municipal bond will provide a higher after tax return

2 ways to work with the tax-equivalent yield (TEY)

1. Given the coupon on a municipal bond and the investors tax bracket then: coupon / (100-tax bracket) to determine what a taxable security would have to pay to give the same after tax return 2. We might know the taxable security's coupon and the investors tax bracket, and we want to know what the tax-free bond must yield to give us an equivalent yield.

Tax Equivalent Yield Formula, what the tax free bond must yield to give an equivalent yield

Example: A taxable bond is paying 8% interest and the investor is in the 30% tax bracket. -The investor will pay taxes equal to 2.4% (30% of the 8%) -After paying taxes the investor will keep the other 5.6% (8% - 2.4%) -So, a tax-free bond paying 5.6% will offer a TEY equal to the 8% one

Answer C *The formula for computing tax equivalent yield is: nominal (coupon) yield / (1-federal income tax rate) 0.045 / (1-0.27) = 6.16%

SAMPLE TEST QUESTION: If an investor in the 27% federal income tax bracket invests in municipal general obligation bonds selling at par with a coupon of 4.5%, what is the tax equivalent yield? A. 3.29% B. 5.72% C. 6.16 % D. 16.67%

higher TEY to a resident of that state due to the "Double" tax exemption

TEST TOPIC ALERT: The TEY for a municipal bond issued by an entity within a state with a state income tax will have a:

Municipal Bond coupon / (100% - investors tax bracket) **If the coupon rate (nominal yield) of the municipal bond is 4.2% and the investor is in the 40% tax bracket -You would: 4.2% / (100 - 40%) or 4.2% / 60% = a TEY of 7% **In order to receive the same after-tax benefit, investor would have to purchase a taxable bond (corp. or gov't) w/ a coupon of 7%. ****TO PROVE: TAKE THE 7% YIELD AND REDUCE IT BY THE 40% TAX WHICH IS: 7% - 2.8% = 4.2% TAX

The formula for computing TEY is:

Interest received from Municipal bonds

is free of federal income tax; and if investor resides in the issuer's state, it is generally free of state income tax as well.

interest on Treasury debt

is only taxable on the federal level

Interest on corporate bonds

is taxed as ordinary income on both state and federal tax returns