Williams Industries has decided to borrow money by issuing perpetual bonds with a coupon rate of 6.5%, payable annually, and a par value of $1,000. The 1-year interest rate is 6.5%. Next year, there...

Williams Industries has decided to borrow money by issuing perpetual bonds with a coupon rate of 6.5%, payable annually, and a par value of $1,000.  The 1-year interest rate is 6.5%.  Next year, there is a 35% probability that interest rates will increase to 8% and a 65% probability that they will fall to 5%.

If the company decides instead to make the bonds callable in one year, what coupon will be demanded by the bondholders for the bonds to sell at par?  Assume that the bonds will be called if interest rates fall and that the call premium is equal to the annual coupon.