1. Callable bond and call premium. Edward has just purchased a callable bond and wants to set up the bond’s potential payoff price if it is called at any time during its callable life. The callable bond is a twenty-year semiannual bond that an issuer can call starting at year ten. It is callable every six months on the coupon payment date. The call price is declining and starts out as one extra year’s coupon (a full annual coupon payment). It reduces each period (every six months by 1/20th of the annual coupon payment) until—at the bond’s maturity—there is no call premium price. If the original bond is an 8% semiannual coupon bond with a par value of $1,000 and an original yield to maturity of 6.5%, what is the bond price today at each potential callable date (coupon payment date) given no change in its original yield to maturity? Edward wants to compare the callable bond price at each callable date with that of a noncallable bond that is identical in every way other than the call feature (same yield to maturity, same coupon rate, and same maturity date). The difference between the callable bond price and the noncallable bond price is the call premium if called on that date. Find the call premium for each potential call date.


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