$(**)$ Fall $2007$ Exam $4$ #$18.$ Assume that $10$ years ago $($Year $-10)$ a firm issued $30-$year bonds that had an annual coupon rate of $12$ percent $($paid $$60$ every six months$),$ a par value of $$1,000,$ and were sold at par. These bonds now $($Year $0)$ have $20$ years until they mature, but the firm has run into financial difficulty. The bondholders have agreed to the following terms:

$.$ The firm will make no coupon payments for the next $10$ years. Rather, the coupons that would have been paid will be assumed to be earnini$]$ accrued interest at a rate of $20$ percent per year $(10$ percent every six months$),$ and these coupons, plus accrued interest, will be paid to the bondholders when the bonds mature in Year $20.$

The firm will resume paying interest in Years $11$ through $20$ of $$60$ every six months.

Investors now see these bonds as being very risky and have an annual nominal required rate of return $($yield to maturity$)$ of $24$ percent.

Therefore, investors will receive $$60$ every six months in Years $11$ through $20(20$ payments$),$ will receive the maturity value of $$1,000$ in Year $20,$ and will receive the future value of the coupons foregone in Years $1$ through $10(20$ payments$)$ that have been accruing interest at an annual rate of $20$ percent, in Year $20.$

Given this information, determine what the price of these bonds should be today.

A$.$ $$156\mathrm{.}61$

B$.$ $$193\mathrm{.}87$

C$.$ $$231\mathrm{.}13$

D$.$ $$268\mathrm{.}40$

E$.$ $$305\mathrm{.}66$