Hilton Hotels Corporation has a convertible bond issue outstanding. Each bond, with a face value of $$1,300,$ can be converted into common shares at a rate of $61\mathrm{.}2996$ shares of stock per $$1,300$ face value bond $($the conversion rate$),$ or $$21\mathrm{.}2073$ per share. Hilton's common stock is trading $($on the NYSE$)$ at $$20\mathrm{.}79$ per share and the bonds are trading at $$1,275.$

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.

$\backslash$table$[[],[$a$.,$Conversion value$],[$b$.,$Exercise the conversion option$]]$