A company's $$1000$ par, split$-$coupon bond matures in $15$ years. The bond pays no interest for semiannually years $1-5,$ then pays $12\%$ for years $6-15.$ Comparable yields are $10\%.$

a$.$ Why would a firm construct the terms of a bond in this manner?

b$.$ What is the current price of the bond?

c$.$ If comparable yields decline to $8\%,$ by how much will the price of the bond appreciate?