A bond with par value of $1,000 has a 10-year maturity and a 10% coupon rate with semi-annual coupon payments. The yield to maturity of this bond currently is 8% per year.

(a) Calculate the value of this bond.

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Suppose that you manage a pension fund with obligations to make perpetual payments of $80,000 per year to beneficiaries, and you plan to fully fund the obligation using 5-year and 20-year maturity zero-coupon bonds. The current interest rate is 8% for all maturities.

(b) How much market value of each of the two zero-coupon bonds is necessary to fund the plan if you decide to take an immunized position?

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(c) If the yield to maturity of a 5-year zero-coupon bond is down by 50 basis points from 8% to 7.5% immediately after the purchase of this bond, what is the percent change in thevalue of this bond?

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(d) Define immunization for managing a bond portfolio and discuss in detail why a bond manager would immunize his or her bond portfolio.