Your$$ start$-$up company needs capital. Right$$ now, you own $100\%$ of the firm with $10\mathrm{.}1$ million shares. You have received two offers from venture capitalists. The first offers to invest $3\mathrm{.}02$ million for $1\mathrm{.}02$ million new shares. The second offers $1\mathrm{.}93$ million for $451000$ 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?