ABC is also interested in buying some corporate bonds for its investment account

Question

ABC is also interested in buying some corporate bonds for its investment account. Suppose these bonds have identical coupon rates of 7.75% but one issue matures in 3 years, one in 8 years, and the third in 13 years. Assume that a coupon payment was made yesterday and they are all issued by the same company.

a)     The yield to maturity for all three is 6.55%, what is the fair price of each bond?  

b)    Suppose that the yield to maturity for all of these bonds changed instantaneously to 5%. What is the fair price of each bond now?

c)     Suppose that the yield to maturity for all of these bonds changed instantaneously again, this time to 9%. Now what is the fair price of each bond?

d)    Based on the fair prices at the various yields to maturity is interest-rate risk the same, higher, or lower for longer- versus shorter-maturity bonds.  

Explanation / Answer

The par value is not given, so am assuming it is $1000. The frequency of coupon payments is not mentioned, so am assuming it is annual. If either of these assumptions change, the answers given below will also need to be changed. The below PV formulas are to be used in Excel.

a. Bond price 1 is =PV(6.55%,3,-77.5,-1000). This is 1031.75

Bond price 2 is =PV(6.55%,8,-77.5,-1000). This is 1072.92

Bond price 3 is =PV(6.55%,13,-77.5,-1000). This is 1102.90

b. Bond price 1 is =PV(5%,3,-77.5,-1000). This is 1074.89

Bond price 2 is =PV(5%,8,-77.5,-1000). This is 1177.74

Bond price 3 is =PV(5%,13,-77.5,-1000). This is 1258.32

c. Bond price 1 is =PV(9%,3,-77.5,-1000). This is 968.36

Bond price 2 is =PV(9%,8,-77.5,-1000). This is 930.81

Bond price 3 is =PV(9%,13,-77.5,-1000). This is 906.41

d. As we can see, the longer maturity bond (the 13-year bond or Bond 3) changes in price more drastically as compared to the shorter maturity bonds with changes in interest rates. So the interest rate risk is higher for longer maturity bonds as compared to shorter maturity bonds.

Hope this helped ! Let me know in case of any queries.

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