# Question

The current on-the-run yields for the Ramsey Corporation are as follows:

Assume that each bond is an annual-pay bond. Each bond is trading at par, so its coupon rate is equal to its yield to maturity.

Answer the below questions.

(a) Using the bootstrapping methodology, complete the following table:

(b) Using the spot rates, what would be the value of an 8.5% option-free bond of this issuer?

(c) Using the one-year forward rates, what would be the value of an 8.5% coupon option-free bond of this issuer?

(d) Using the binomial model (which assumes that one-year rates undergo a lognormal random walk with volatility (), show that if ( is assumed to be 10%, the lower one-year forward rate one year from now cannot be 7%.

(e) Demonstrate that if σ is assumed to be 10%, the lower one-year forward rate one year from now is 6.944%.

(f) Demonstrate that if σ is assumed to be 10%, the lower one-year forward rate two years from now is approximately 6.437%.

(g) Show the binomial interest-rate tree that should be used to value any bond of this issuer.

(h) Determine the value of an 8.5% coupon option-free bond for this issuer using the binomial interest-rate tree given in part g.

(i) Determine the value of an 8.5% coupon bond that is callable at par (100) assuming that the issue will be called if the price exceeds par.

Assume that each bond is an annual-pay bond. Each bond is trading at par, so its coupon rate is equal to its yield to maturity.

Answer the below questions.

(a) Using the bootstrapping methodology, complete the following table:

(b) Using the spot rates, what would be the value of an 8.5% option-free bond of this issuer?

(c) Using the one-year forward rates, what would be the value of an 8.5% coupon option-free bond of this issuer?

(d) Using the binomial model (which assumes that one-year rates undergo a lognormal random walk with volatility (), show that if ( is assumed to be 10%, the lower one-year forward rate one year from now cannot be 7%.

(e) Demonstrate that if σ is assumed to be 10%, the lower one-year forward rate one year from now is 6.944%.

(f) Demonstrate that if σ is assumed to be 10%, the lower one-year forward rate two years from now is approximately 6.437%.

(g) Show the binomial interest-rate tree that should be used to value any bond of this issuer.

(h) Determine the value of an 8.5% coupon option-free bond for this issuer using the binomial interest-rate tree given in part g.

(i) Determine the value of an 8.5% coupon bond that is callable at par (100) assuming that the issue will be called if the price exceeds par.

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