Mr$.$ Duncan has decided to eliminate preferred stock as one of the alternatives and focus on the others. EduSoft$$s investment banker estimates that EduSoft could issue a bond$-$with$-$warrants package consisting of a $20-$year bond and $27$ warrants. Each warrant would have a strike price of $$25$ and $10$ years until expiration. It is estimated that each warrant, when detached and traded separately, would have a value of $$5.$ The coupon on a similar bond but without warrants would be $10\%.$

$($C$1)-$ What coupon rate should be set on the bond with warrants if the total package is to sell at par $($$$1,000)?$

$($C$2)-$ When would you expect the warrants to be exercised? What is a stepped$-$up exercise price?