Question

Consider three bonds with 6.40% coupon rates, all making annual coupon payments and all selling at face value. The short-term bond has a maturity of 4 years, the intermediate-term bond has a maturity of 8 years, and the long-term bond has a maturity of 30 years.
a. What will be the price of the 4-year bond if its yield increases to 7.40%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)


b. What will be the price of the 8-year bond if its yield increases to 7.40%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

Answer:

a. The price of the 4-year bond if its yield increases to 7.40%: $966.43

b.  The price of the 8-year bond if its yield increases to 7.40%: $941.20

Explanation:

The price of the bond will be equal to the present value discounted at yield to maturity of all the cash flows generating by the bonds including annual coupon payments and face value repayment at the maturity.

a.

4-year bond has the cash flow as followed: 4 annual coupon repayments, $64 each and face value repayment of 1,000 at maturity.

=> Price of the bond = (64/0.074) x [ 1 - 1.074^-4 ] + 1,000/1.074^4 = $966.43

b.

8-year bond has the cash flow as followed: 8 annual coupon repayments, $64 each and face value repayment of 1,000 at maturity.

=> Price of the bond = (64/0.074) x [ 1 - 1.074^-8 ] + 1,000/1.074^8 = $941.20