Your start$-$up company needs capital. Right now, you own $100\%$ of the firm with $9\mathrm{.}8$ million

shares. You have received two offers from venture capitalists. The first offers to invest $$2\mathrm{.}92$

million for $1\mathrm{.}16$ million new shares. The second offers $$2\mathrm{.}05$ million for $482,000$ new shares.

a$.$ What is the first offer's post$-$money valuation of the firm?

b$.$ What is the second offer's post$-$money valuation of the firm?

c$.$ What is the difference in the percentage dilution caused by each offer?

d$.$ What is the dilution per dollar invested for each offer?