***I JUST NEED THE ANSWER TO QUESTION NUMBER 4, THE OTHER QUESTIONS ARE JUST FOR CONTEXT!!!***

1. Consider the expected value of a three-year continuously compounded coupon bond with interest rate uncertainty. Interest rate the first year is 6% and it increases randomly (50% higher, 50% lower) each year. The bond has a face value of $100 and a coupon rate of 5% of face. What is the expected present value and the yield to maturity? Yes, this is the problem from the last assignment. It is our baseline case. 2. Consider a bond as in question 1 but where the probability of interest rates changing are 60% higher and 40% lower. What is the expected present value and the yield to maturity? 3. Consider a bond as in question 1 (50% higher and 50% lower) but where there is a 1% probability of default. A default may occur anytime during the year. A default means that the issuer makes no further payments on the loan. No principle and no coupon. For example, a default during the first year means that the owner receives nothing: not the first coupon of S5 not the second coupon of $5 and not the final payment of $105. What is the expected present value and the yield to maturity? 4. Consider a bond as in question 1 (50% higher and 50% lower, no default) but where the issuer can call the bond. Assume the issuer calls the bond at the start of any year when it is revealed that the interest rate is above the 6% initial rate. When the bond is called, the issuer makes the coupon payment for the preceding year and makes the payment of the face amount. Draw the binomial tree incorporating the call behavior of the issuer. Clearly indicate the payments made at each point in time. What is the expected present value and the yield to maturity of this bond? a. b