The Art Works needs to raise $$6\mathrm{.}2$ million for a new facility. Assuming they issue new equity shares via a general cash offering, they expect to incur administrative costs of $$412,000$ in addition to the underwriting spread of $8\mathrm{.}7$ percent. If the offer price turns out to be $$16$ a share, how many shares need to be sold to finance the new facility?

Multiple Choice

$448,210$ shares

$452,629$ shares

$405,141$ shares

$487,923$ shares

$406,211$ shares