Reference no: EM133175461

Question - In May 2020, the U.S. Treasury issued 30-year bonds with a coupon rate of 6.25%, paid semi-annually. A bond with a face value of $1,000 pays $31.25 (1,000 × 0.0625 / 2) every six months for the next 30 years; in May 2050, the bond also repays the principal amount, $1,000.

a) What is the price of the bond at the time of issue in May 2020 assuming the 30-year interest rate is increased to 7.5% (nominal rate with semi-annual compounding)?

b) What is the price of the bond at the time of issue in May 2020 assuming the 30-year interest rate is decreased to 5% (nominal rate with semi-annual compounding)?

c) Show how the value of the bond changes as the interest rate changes (plot the value as a function of the interest rate). At what interest rate is the value of the bond equal to its face value of $1,000?

d) Assume that the 30-year interest rate remains at 6.25% (nominal rate with semi-annual compounding) at the time of issue in May 2020. If your required rate of return is 6.30% effective, will you buy the bond?

e) Assume that the 30-year interest rate remains at 6.25% (nominal rate with semi-annual compounding) at the time of issue in May 2020. Further, assume that you need to pay for a transaction cost of $15 per bond. If your required rate of return is 6.30% effective, will you buy the bond?