A corporate bond with remaining maturity of 20 years pays 6% annual coupon interest and has a par value of $1,000. If the bond is currently trading at a $80 premium over par value in the market, what is the yield to maturity of the bond?Question 13Select one:a.6.00%b.5.56%c.5.34%d.6.74%
Question
A corporate bond with remaining maturity of 20 years pays 6% annual coupon interest and has a par value of 80 premium over par value in the market, what is the yield to maturity of the bond?Question 13Select one:a.6.00%b.5.56%c.5.34%d.6.74%
Solution
To calculate the yield to maturity (YTM) of the bond, we need to use the formula for YTM, which is the interest plus the difference between the face value and the purchase price, divided by the average of the face value and the purchase price.
Here are the steps:
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Identify the given values:
- Coupon payment (C) = 6% of 60
- Face value (F) = $1,000
- Purchase price (P) = Face value + Premium = 80 = $1,080
- Number of years to maturity (n) = 20 years
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Plug these values into the YTM formula:
YTM = [(C + (F - P) / n) / ((F + P) / 2)] * 100%
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Calculate the YTM:
YTM = [(60 + (1000 - 1080) / 20) / ((1000 + 1080) / 2)] * 100% = [(60 - 4) / 1040] * 100% = [56 / 1040] * 100% = 5.38%
So, the yield to maturity of the bond is approximately 5.38%. The closest answer in the options is 5.34%, so the answer is c. 5.34%.
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