The term structure of interest rates is flat at 5%. With equal probability, tomorrow rates will either (1) stay the same, (2) increase to 5.5%, or (3) decrease to 3.5%. Whatever the change, the term structure will remain flat and rates will stay at their new level forever. Consider a callable bond that pays 5.5% coupon (annually), has 8 years to maturity, $1000 par value, and $1050 call price. Assume periodicity of 1.

a.) Assume that the callable bond has no call protection. What should be its price?

b.) Assume that the callable bond has call protection of 3 years. What should be its price?