Hilton Hotels Corporation has a convertible bond issue outstanding. Each bond, with a face value of $$1,200,$ can be converted into

common shares at a rate of $61\mathrm{.}2999$ shares of stock per $$1,200$ face value bond $($the conversion rate$),$ or $$19\mathrm{.}5759$ per share. Hilton's

common stock is trading $($on the NYSE$)$ at $$19\mathrm{.}16$ per share and the bonds are trading at $$1,175.$

a$.$ Calculate the conversion value of each bond. $($Round your answer to $2$ decimal places. $($e$.$g$.,32\mathrm{.}16))$

b$.$ State whether it is currently profitable for bond holders to convert their bonds into shares of Hilton Hotels common stock.

a$.$ Conversion value

b$.$ Exercise the conversion option