Apex Venture Partners, a VC firm, is planning to invest $$7$ million today in a startup entrepreneurial firm, Russel Holdings. The VC expects the firm to have an exit $($IPO$)$ valuation of $$300$ million in four years and has a discount rate of $30\%.$ The number of shares currently outstanding in Russel is $3$ million shares. Calculate the post and pre$-$money valuations, the stock ownership required by the VC$,$ the price per share, and the number of shares the VC will get based on this valuation.

Suppose, modifying the data given in section $($ii$),$ you now assume that, in addition to the current VC financing, Russel Holdings will have to issue another round of private equity financing equal to $50\%$

of the equity outstanding to raise additional private financing just prior to IPO in order to go public and receive the $$300$ million valuation mentioned above, what fraction of equity should Apex demand in return

for its investment of $$7$ million in the firm? Re$-$compute the pre$-$money and post$-$money valuations placed on Russel Holdings today under these revised assumptions.