Question: You plan to pay the home renovation expenses of $6500 a year at the end of

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Question:

You plan to pay the home renovation expenses of $6500 a year at the end of the next 3 years. Bonds currently yield 7%.

a. What is the present value and duration of your home renovation obligation? (10points)

b. What maturity zero-coupon bond would immunize your obligation? (3points)

c. Assume that you need to borrow $1000 for paying more renovation expenses at year 1 and plan to pay it back at the end of year 2, given the price of 1-year maturity zero-coupon bonds with face value $1000 is $952.38 and the price of 2-year zeros with $1000 face value is $890. The yield to maturity on the 1-year bond is 5% and on the 2-year bond is 6%. What is the corresponding forward rate for the second year? Can you construct a synthetic 1-year forward loan (apply the forward rate) that starts at t=1 and matures at t=2?

Please explain your strategy and the corresponding cashflows of this synthetic loan.