Assume a firm has assets worth $100,and that σ = 30%, r = 8%, and the firm makes no payouts prior to the maturity date ofthe debt.

(a) Construct a binomial lattice withthree periods, representing asset values over each year.

(b) Value the equity of the firmassuming that there exists a three year zero coupon bond with face value 50.

(c) Value the debt of the firm at eachnode in the lattice over the three years.

(d) Assume a two year call optionexists on the risky debt. The strike price of the call option on the bond is42. Compute the price of the call option.

(e) Assume the firm issued a callablebond instead of a straight bond. The terms of the call option are in (d). Thatis the firm retains the right to retire the debt at 42 dollars in the first twoyears. What would be the price of the callable bonds, and what would the equityprice be.

(f) Explain why the callable bonds arecheaper than the otherwise equivalent callable bonds. Also explain when thecall option would be exercised. Can you tell today exactly when the maturitydate is for the callable bond?

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