Problem
A firm wishes to issue a perpetual callable bond with semi-annual coupon payment. The par value is $1000. The current interest rate is 7%. Suppose that at the end of the next year, the interest rate will be 6.5% or 8.5% with equal probability. The bond is callable at $1,075, and it will be called if the interest rate drops to 6.5%. Given the above assumption, what should the coupon rate of the callable bond be so that the callable bond can be issued at par value?