Problem $7$

Gentherm Inc. has a convertible bond issue outstanding. Each bond, with a face value of $$1,000,$ can be converted into common shares at a rate of $42\mathrm{.}25$ shares of stock per $$1,000$ face value bond $($the conversion rate$),$ or $$19\mathrm{.}85$ per share. Gentherm's common stock is trading $($on the NYSE$)$ at $$19\mathrm{.}85$ per share and the bonds are trading at $$1,025.$

a$.$ Calculate the conversion value of each bond.

b$.$ Determine if it is currently profitable for bond holders to convert their bonds into shares of Gentherm common stock.