FARO Technologies, whose products include portable $3$D measurement equipment, recently had $34$ million shares outstanding trading at $$50$ a share. Suppose the company announces its intention to raise $$370$ million by selling new shares.

a$.$ How large a loss in dollar terms will existing FARO shareholders experience on the announcement date, based on studies that show losses are $30\%$ of the size of the new issue?

b$.$ What percentage of the value of FARO$$s existing equity prior to the announcement is this expected loss?

c$.$ At what price should FARO expect its existing shares to sell immediately after the announcement?