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Yield Calculations for Municipal Securities

Instructor: Yusuf Abdullah

Yusuf has taught Science and Mathematics at school level and Finance and Economics at University level. He has recently earned his Ph.D in Financial Econometrics.

The lesson deals with different yield measures for municipal bonds. You'll learn how to calculate the yields and adjust the yields for tax rate and for the call option.

Municipal Bonds (Munis)

Municipal bonds are issued by local or state governments to fund infrastructural projects and other expenses. A considerable number of municipal bonds are tax-exempt and hence attract a large number of investors. One such investor is Phoebe, who has recently bought a Muni or a municipal bond because the bond interest payments are not taxable. She has approached her friend Joey who is a financial advisor to learn more about these bonds. Phoebe describes the characteristic of the bonds as:

5 year bond with an annual coupon of 4%, priced at $985.00 and callable in 2 years at $1,025.00

Joey asks Phoebe about her tax bracket as this is required for yield calculations. Phoebe says that she is in a 30% tax bracket. Phoebe tells Joey that although she is happy with the tax exemption on the muni, she is slightly dejected about the coupon rate which is low. Phoebe asks Joey if 4% is the rate that she is actually earning. Joey replies that the actual rate that she earns equals the yield to maturity. Joey punches in the numbers on his Texas BA II calculator to calculate the yield to maturity (YTM).


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Taxable Equivalent Yield (TEY)

Phoebe says that she requires a return of at least 5% to meet her financial objectives. Joey informs her that since the municipal bonds are not taxed, her effective yield would be higher. Joey further states that the calculation of taxable equivalent yield (TEY) will provide an effective rate earned.


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The calculation of TEY for Phoebe's bond is:


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Phoebe is happy that she is earning a higher effective yield. Joey tells her that the TEY is the after-tax return on taxable security that equals the return on tax-exempt security. TEY is higher for higher tax brackets, and this can be ascertained by looking up at the formula. The higher the tax rate, the lower the denominator and higher the TEY.

Net Yield After Capital Gains Tax

Phoebe asks Joey about tax consequences when the security pays par value after 10 years. Joey replies that only the increase from the purchase price of $985.00 would be taxable. Phoebe inquires if this will affect her total return. Joey tells her that yes, it will. Phoebe asks Joey the return earned if the capital gains taxes are incorporated at 10% capital gains rate. Joey performs the previous calculations with slight variations.
The increase in price is $1,000 - $985.00 = $15.00. The capital gains tax is:
$15.00 * 10%
=$1.50
The net value received after tax for the bond par value is $1,000 - $1.50
=$998.50


Joey calculates the yield after adjusting for the capital gains tax:


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Net yield after capital gains tax is 4.31%. Therefore, net yield after capital gains tax is the yield to maturity that adjusts the selling price or the par value for the capital gains tax. It is worth noting that net yield after capital gains tax will differ from the yield to maturity only if there is an increase in value. A decrease in value would not result in capital gains taxes.

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