Problem $15-10$ Valuing Callable Bonds

Bandon Manufacturing intends to issue callable, perpetual bonds with annual coupon payments and a par value of $$1,000.$ The bonds are callable at $$1,180.$ One$-$year interest rates are $8$ percent. There is a $60$ percent probability that long$-$term interest rates one year from today will be $9$ percent, and a $40$ percent probability that they will be $7$ percent. Assume that if interest rates fall the bonds will be called. What coupon rate should the bonds have in order to sell at par value? $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$