Dotcom, Inc. went public in $2001.$ The offer price was $$60.$ Furthermore, the first quoted price amounted to $$63\mathrm{.}5.$ Overall, $833,000$ shares were sold, of which $93,000$ were sold by original shareholders. None of the original shareholders bought shares in the IPO. The total number of shares outstanding after the capital increase and IPO amounted to $2,000,000.$

a$)$ How much money did Dotcom Inc. leave on the table?

b$)$ The direct costs of the IPO had been estimated not to surpass $3\mathrm{.}5$ million $ in the prospectus. What are the total costs of going public as a percentage of capital inflows to the firm?

c$)$ One year after the IPO, Dotcom needs to issue $500,000$ new shares at a price of $$35$ in order to finance future investments. The current stock price right before the SEO is $$75.$ What is the rights ratio $("$Bezugsverh$$ltnis$"),$ Dotcom's stock price right after the SEO, and the value of one subscription right?