A company sells for $$20$ million. A preferred investor has the option of taking their capped $(2$x$)$ participating preference of $$10$ million or converting into common shares. The investor owns $500,00$ preferred shares with a $1$:$1$ conversion to common. There are $1,000,000$ existing common shares in the company today. What are the investor$$s proceeds?

a$.$ $$13\mathrm{.}3$ million

b$.$ $$10\mathrm{.}0$ million

c$.$ $$6\mathrm{.}7$ million

d$.$ $$20\mathrm{.}0$ million