In: Finance
Problem 4.3 part 2
On October 5, 2015, you purchase a $10,000 T-note that matures on August 15, 2027. (Settlement occurs two dayws after purchase, so you receive actual ownership of the bond on October 7, 2015). The coupon rate on the T-note is 4.375% and the current price quoted on the bond is 105.250%. The last coupon payment occurred on May 15, 2015 (145 days before settlement) and the next coupon payment will be paid on November 15, 2015 (39 days from settlement).
A) Calculate the annual yield to maturity (based on the clean price) for the bond purchased on October 7, 2013, and maturing on August 15, 2024 (or in 10.8603 years).
B) Explain in an essay of at least one full paragraph exactly why the bond in this problem is selling at a premium (ignore the accrued interest). That is, explain exactly why investors would be willing to pay more than face value for this bond, and in your answer address the issue of how newly issued bonds compete with this bond, which is being sold in the secondary market as a previously issued bond.
Using the excel yield function, Yield(Settlement date, maturity date, annual coupon rate, price of bond per $100, redemption amount, interest frequency (2 for semi annual), basis= actual/actual)
Yield is 3.8198% i.e 3.82%
The bond is selling at a premium because the market rate of interest is less than the coupon rate on the bond, i.e the annual yield in the market is less than 4.375%.
Investors are willing to pay more than face value because the annual return they are getting is more than what the market provides. Thus, this increases the demand for the bond, which increases it's price, therefore pushing down the yield till the market yield is equal to the yield on the bond.
In case of a newly issued bond, the price will depend on many factor such as maturity, coupon payment, etc. In a well performing capital market, the issue price must be such that it provides a yield that is equal to the market rate of yield.