Williams Industries has decided to borrow money by issuing perpetual bonds with a coupon rate of $7\mathrm{.}5$ percent, payable annually, and a par value of $$1,000.$ The one$-$year interest rate is $7\mathrm{.}5$ percent. Next year, there is a $45$ percent probability that interest rates will increase to $9$ percent and a $55$ percent probability that they will fall to $6$ percent.

a$.$

What will the market value of these bonds be if they are noncallable? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ If the company decides instead to make the bonds callable in one year, what coupon rate 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. $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

c$.$ What will be the value of the call provision to the company? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$