Reference no: EM132945130
Question - The prices of a set of zero-coupon government bonds with a face value of £100 and a time-to-maturity of 1, 2, 3, 4 and 5 years are, respectively, £95.24, £91.57, £88.90, £87.14 and £86.26. These bonds can be assumed to be risk-free.
You also observe the prices of a set of zero-coupon corporate bonds, just issued by Manchester plc, each of which has a credit rating of BBB. Each bond has a face value of £100. The prices of the bonds with time-to-maturity of 1, 2, 3, 4 and 5 years are, respectively, £88.50, £78.31, £69.31, £61.33 and £54.28.
a) Using the prices of the zero-coupon government bonds, calculate the price of a coupon-bearing government bond with a face value of £10,000, a coupon rate of 5% per annum, and 5 years till maturity. Coupon payments are made at the end of each year only.
b) Using the prices of the zero-coupon government bonds, calculate the yield-to maturity for each of these five maturities.
c) Comment on the shape of the yield curve. What does this yield curve indicate about the market's prediction of future economic conditions? Explain your answer.
d) Consider the zero coupon government bond with a maturity of 5 years mentioned at the start of the question. Describe how the Dirty Price of this bond will change through time, until maturity. Assume that its Yield to Maturity stays constant at all times.
e) Calculate the default risk premium between the BBB yield curve and the government bond yield curve, for each maturity from 1 to 5 years.
f) What would happen to the prices of the zero coupon corporate bonds issued by Manchester plc, if all the corporate bonds' credit ratings were downgraded to CCC from BBB? Assume the yield to maturity of all the zero-coupon government bonds remain the same.
g) Liverpool plc today issues a coupon bond with a time to maturity of 5 years, a face value of £10,000, and which pays a semi-annual coupon. Its coupon rate is 6% in annualized terms, and its yield to maturity is 6% in annualized terms. What is its current price?
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