Initial Public Offering. A biotechnology company, Keros Therapeutics, completed its IPO on April $8,2020,$ and listed on the Nasdaq.

Keros sold $6,000,000$ shares of stock to primary market investors at an IPO offer price of $$17\mathrm{.}81,$ with an underwriting discount of $6\mathrm{.}3\%.$

Secondary market investors, however, were paying $$20\mathrm{.}18$ per share for Keros' $19,189,391$ shares of stock outstanding $($which includes

the newly$-$issued shares$).$

a$.$ Calculate the total proceeds for Keros' IPO.

b$.$ Calculate the dollar amount of the underwriting fee for Keros' IPO.

c$.$ Calculate the net proceeds for Keros' IPO.

d$.$ Calculate market capitalization for Keros' outstanding stock.

e$.$ Calculate IPO underpricing for Keros' IPO.

f$.$ Explain the IPO underpricing for Keros.