To find out the yield to maturity (YTM) of the taxable bond and then compare it to the yield of a tax-exempt bond, we can use the following steps:
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Calculate the Yield to Maturity (YTM) of the Taxable Bond:
- The bond's coupon payment (C) can be calculated as:
- The bond is currently priced at 98.45% of par value, which means its price (P) is:
- The bond matures in 20 years, which means it has 40 periods of payments (since it pays semi-annually).
We can use a financial calculator or a spreadsheet to solve for YTM, but for illustrative purposes, we can use an approximation formula for YTM:
where: is the coupon payment, is the face value, is the current market price, is the total number of periods.
Plugging in values:
First calculate the terms:
.- So now the YTM formula becomes:
- Calculate the average price:
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Now calculate the YTM:
Since this might come out as annual yield, to find the semi-annual yield, we consider it in its semi-annual format and then multiply by 2. - The bond's coupon payment (C) can be calculated as:
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Adjust for Taxes: The after-tax yield on the taxable bond can be calculated by:
- Given the tax rate of 23%, we have:
- Given the tax rate of 23%, we have:
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Determine Required Yield for Tax-Exempt Bond: Set the after-tax yield of the taxable bond equal to the yield of the tax-exempt bond:
Therefore, the investor would prefer otherwise identical tax-exempt bond if its yield to maturity was more than 1.97%.