Your$$ start$-$up company needs capital. Right$$ now, you own $100\%$ of the firm with $9\mathrm{.}97$ million shares. You have received two offers from venture capitalists. The first offers to invest $$$$3\mathrm{.}03$ million for $1\mathrm{.}09$ million new shares. The second offers $ $1\mathrm{.}96$ million for $478,000$ 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?