$3.$ Velcro Saddles is contemplating the acquisitions of Pogo Ski Sticks. Inc. The values of the two companies as separate entities are $$20$ million and $$10$ Million, respectively. Velcro Saddles estimates that by combining the two companies, it will reduce after tax marketing and administrative costs by $$500,000$ per year in perpetuity. Velcro Saddles is willing to pay $$14$ million cash for Pogo. The opportunity cost of capital is $8\%$ and the tax rate is $30\%.$

a$.$ What would be the gain from the merger?

b$.$ What is the cost of the cash offer?

c$.$ What is the NPV of the acquisition under the cash offer?