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 $$16\mathrm{.}46,$ with an underwriting discount of $6\mathrm{.}9\%.$ Secondary market investors, however, were paying $$20\mathrm{.}48$ 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$.$ Calc'late the net proceeds for Keros' IPO.

d$.$ Calc$$late market capitalization for Keros' outstanding stock.

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

f$.$ Explain the IPO underpricing for Keros.