To finance a new project, JPE Inc. will issue a $10-$year, $12\%$ coupon callable bond $($For simplicity, assume coupons are paid annually$).$ The current required yield is $12\%.$ At the end of year $3,$ there is a $30\%$ probability that the yield will be $5\%$ and $70\%$ probability that the yield will be $16\%.$ The bond will be called at $$1,000($the par value$)$ plus one additional coupon payment if the bond price is higher than the call price.

a$)$ What is the callable bond price?

b$)$ If JPE wants to issue the callable bond at $$1,050,$ what must the coupon rate be$?$

c$)$ Assume that the yield changes to $5\%$ at the end of year $3,$ JPE replaces the bond $($in part a$)$ with a new $7-$year bond $($issued at par$).$ The flotation cost is $$80$ per bond. The new bond will be parked in the money market to earn $2\%($per year$)$ interest during the $30-$day overlap period. The tax rate is $40\%.$ What is the NPV of the bond refund? plz show steps