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A company wants to sell bonds with $ 100 million par value. The company is considering various alternatives. A non-callable bond has 10 years to maturity. Principal amount of $1,000. Coupon rate is $100 per year (payable at the end of the year but accrued daily). The annual effective yield is 10%.
A callable bond has the same features but the effective yield is 12%. The callable bond is callable at par anytime prior to maturity with payment of accrued interest (in addition to par value). A floating rate bond can be issued at par with LIBOR coupon (the firm has a guarantee from the underwriter that the firm can sell par bonds at LIBOR at any time over the next ten years with maturity not extending beyond ten years from today).
The firm can sell a SWAPTION. If exercised, such a SWAP will require the company to pay 10% fixed rate in return for LIBOR receipts. The swap (regardless of the beginning date) will end 10 years from today. The swaption may be exercised anytime over the next ten years.
Problem 1: Find the price of a callable bond (per $ 1,000 par)
Problem 2: Find the price of a non-callable bond (per $ 1,000 par)
Problem 3: Find the fair market value of a swaption (notional principal $ 100 million).
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