Consider the following premerger information about a bidding firm $($Firm B$)$ and a target firm $($Firm T$).$ Assume that both firms have no debt outstanding.

Firm B Firm T

Shares outstanding $4,8001,800$

Price per share $ $47$ $ $20$

Firm B has estimated that the value of the synergistic benefits from acquiring Firm T is $$9,100.$ Firm T can be acquired for $$22$ per share in cash or by exchange of stock wherein B offers one of its share for every two of T$\text{'}$s shares.

a$.$ Are the shareholders of Firm T better off with the cash offer or the stock offer?

b$.$ At what exchange ratio of B shares to T shares would the shareholders in T be indifferent between the two offers? $($Do not round intermediate calculations and round your answer to $4$ decimal places, e$.$g$.,32\mathrm{.}1616.)$