Company A is considering acquiring Company B$.$ The values of the two companies as separate entities are $20$ million and $10$ million respectively. Company A estimates that by merging the two companies, it will reduce its marketing and administrative costs by $500,000$ per year in perpetuity. Company A can offer shares of $50\%$ of the value of the new company. The opportunity cost of capital is $10\%.$ What is the cost of the merger to the stockholders of company A if the merger is done by exchanging shares?