KIC Inc. plans to issue $$5\mathrm{.}1$ million of bonds with a coupon rate of $11$ percent paid semiannually and $31$ years to maturity. The current one$-$year market interest rate on these bonds is $10$ percent. In one year, the interest rate on the bonds will be either $13$ percent or $7$ percent with equal probability. Assume investors are risk neutral. $($The value of the bond should be close to $$1,465)$

a$.$ If the bonds are non$-$callable, what is the price of the bonds today?

b$.$ If the bonds are callable one year from today at $$1,465,$ will their price be greater or less than the price you computed in part $($a$)?$ The answers is Less than!

c$.$ If the bonds are callable one year from today at $$1,465,$ what is the current price of the bond?

d$.$ What is the value of the call provision to the company?