Third Inc. wishes to issue a perpetual callable bond. The current interest rate is 6%. Next year, there is a 30% chance that the interest rate will be 4.5% and a 70% chance that the rate will be 8.0%. The bond is callable at $1,000 plus an additional coupon payment and it will be called if the interest rate drops to 4.5%.
a. If the bond sells for par today, what is the coupon?
b. What is the bond's value today if the coupon is set at $70?
c. If the bond is priced at $1,000, what is the cost to Third of the call provision?