Question

7. 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

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%