Answer :
Using Taxable Equivalent Yield, if you are in a 15% tax bracket, at year-end you will owe taxes on this investment equal to 7.18%.
In the given question,
We buy a 9-year $1,000 par value 4.10% annual-payment coupon bond priced to yield 6.10%.
We do not sell the bond at year-end.
If we are in a 15% tax bracket, then we have to calculate at year-end we will owe taxes on this investment equal to.
The face value of bond = $1000
Coupon rate = 4.10%
Yield to Maturity(YTM) = 6.10%
Time(n) = 9 years
Then the amount of coupon = $1000*4.10%
The amount of coupon = $1000*4.10/100
The amount of coupon = $41
Interest rate is always taxed at the investor's tax rate.
We are in 15% tax bracket.
So this investment equal to =$41*15%
=$41*15/100
=$615/100
=$6.15
At the end of the year owe taxes on this investment equal to $6.15 only on interest income not on capital gains.
Taxable Equivalent Yield=Yield on bond/(1−Your Income tax bracket)
Taxable Equivalent Yield=6.10%/(1−15%)
Taxable Equivalent Yield=0.061/(1−0.15)
Taxable Equivalent Yield=0.061/0.85
Taxable Equivalent Yield=0.0718
Taxable Equivalent Yield=7.18%
Hence, if you are in a 15% tax bracket, at year-end you will owe taxes on this investment equal to 7.18%.
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