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Zorluk: OrtaGovernment, Municipal, and Corporate Bonds

An investor subject to a 32%32\% federal marginal income tax bracket is evaluating a corporate bond offering a 6.25%6.25\% annual yield. What minimum yield (in percent) must a tax-exempt municipal bond offer to provide the exact same after-tax return as the corporate bond?

Cevap: 4.25 %

Cevap

The tax-exempt municipal bond must offer a yield of 4.25%4.25\% to provide the exact same after-tax return as the 6.25%6.25\% corporate bond.
Because municipal bond interest is exempt from federal income taxes, an investor keeps 100%100\% of the interest paid by a qualifying municipal bond. To compare a taxable corporate bond paying 6.25%6.25\% against a tax-free municipal bond, calculate the corporate bond's after-tax yield: After-Tax Yield=Corporate Yield×(1−Tax Rate)\text{After-Tax Yield} = \text{Corporate Yield} \times (1 - \text{Tax Rate}). For an investor in a 32%32\% tax bracket, this yields 6.25%×(1−0.32)=4.25%6.25\% \times (1 - 0.32) = 4.25\%. A municipal bond yielding 4.25%4.25\% delivers the exact same net cash income.

Adım Adım Çözüm

1
Determine the taxable corporate bond yield and the investor's tax rate.
Corporate yield = 6.25%6.25\%, marginal tax rate = 32%32\% (0.320.32).
Taxable fixed-income interest is subject to federal income taxation at the investor's marginal tax bracket.
2
Calculate the percentage of interest retained after federal taxes.
1−0.32=0.681 - 0.32 = 0.68 (or 68%68\% retained).
The investor keeps (1−marginal tax rate)(1 - \text{marginal tax rate}) of any taxable interest earned.
3
Multiply the nominal corporate yield by the retained percentage.
6.25%×0.68=4.25%6.25\% \times 0.68 = 4.25\%.
This calculation determines the net after-tax yield generated by the corporate bond.
4
Equate the after-tax corporate yield to the required municipal bond yield.
Municipal bond yield required = 4.25%4.25\%.
Interest from municipal bonds is exempt from federal income tax, so its nominal yield equals its after-tax yield.

Anahtar Kavram

Municipal Bond After-Tax Yield and Tax-Equivalent Yield
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Konular

Government, Municipal, and Corporate Bonds

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