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A municipal bond has a coupon rate of 4.5% and just sold for 104.56. It matures...

  1. A municipal bond has a coupon rate of 4.5% and just sold for 104.56. It matures on December 1, 2023. What is its tax-equivalent yield? Assume a marginal tax rate of 40% and interest is paid June 1 and December 1. ISSUE DATE IS 09/10/2020

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Answer #1

For Simplicity and incomplete data following assumptions are made:

1. Coupon Rate Given in Question related to Yearly Interest rate

2. Bond is purchased by the buyer on December 01, 2020

Details As per Given Question

Coupon rate = 4.5% per Year

CMP of Bond = 104.56

Marginal tax rate = 40%

Now Let us Calculate the Yield to Maturity of This Bond

Date Amount PVF @ 3% PV @ 3% PVF @ 2% PV @ 2%
01-Jun.2021 2.25 0.99 2.22 0.99 2.23
01-Dec.2021 2.25 0.97 2.18 0.98 2.21
01-Jun.2021 2.25 0.96 2.15 0.97 2.18
01-Dec.2021 2.25 0.94 2.12 0.96 2.16
01-Jun.2021 2.25 0.93 2.09 0.95 2.14
01-Dec.2021 102.25 0.91 93.51 0.94 96.32
TOTAL 104.27 107.24

Using Interpolation Method

YTM = 3% - {(3% - 2%) / (107.24 - 104.27)} x (104.56 - 104.27)

= 2.9%

Hence , Tax equivalent Yield = 2.9 % / (1 - 40%)

= 4.83%

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