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

Maturity (years)	Yield to Maturity (%)	Market Value
1	7.5	100
2	7.6	100
3	7.7	100

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.

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

Year	Spot Rate (%)	One-Year Forward Rate (%)
1
2
3

(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 s), show that if s is assumed to be 10%, the lower one-year forward rate one year from now for two-year 7.6% bond traded in par cannot be 7%.

(e) 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.