Corning issued a zero$-$coupon convertible bond at $\backslash (\backslash$$ $741\mathrm{.}92\backslash )$ per $\backslash (\backslash$$ $1,000\backslash )$ par value on Nov. $8,2000.$ The bond matures in $2015.$ Investors can convert the bond into $8\mathrm{.}3304$ shares of Corning's common stock. In addition, the bond has a call option that allows Corning to call the bond after $2005.$ The bond also carries a put option that lets investors sell the bond back to Corning on Nov. $2005$ and Nov. $2010.$ The bond was rated A by Moody's and S$\backslash$&P$.$ Other A rated, intermediate straight bonds issued by similar companies have an average YTM of $\backslash (7\mathrm{.}9\backslash \%\backslash ).$ a$.$ What is the YTM of the zero$-$coupon bond? Is the YTM higher or lower than similar bond issues and why? b$.$ What should be the price of the bond if it does not contain any embedded option? c$.$ What is the total value of the embedded options in the zero coupon bond? d$.$ Suppose that the value of the embedded call option $($on the bond$)$ is $\backslash (\backslash$$ $284\mathrm{.}98\backslash )$ and the value of the embedded put option is $\backslash (\backslash$$ $166\mathrm{.}25\backslash ).$ What should be the value of the embedded conversion option $($or the call option on the common stock$)?$