You have started a company and are in luck$$a venture capitalist has offered to invest. You own $100\%$ of the company with $5\mathrm{.}07$ million shares. The VC offers $$1\mathrm{.}13$ million for $840,000$ new shares.

a$.$ What is the implied price per$$ share?

b$.$ What is the$$ post$-$money valuation?

c$.$ What fraction of the firm will you own after the$$ investment?