A company is considering the development of a new product. The first step would be to do a feasibility study, which would cost $$50,000$ today. If the outcome of the feasibility study is favorable, then the company would build a prototype, which would cost $$600,000$ one year from now. The probability that the feasibility study outcome will be favorable is estimated to be $90\%.$

If the prototype is successful, then the company would build a manufacturing plant, which would cost $$10,000,000$ two years from now. The probability that the prototype will be successful is estimated to be $60\%.$ If the prototype is unsuccessful, then the company would sell it for $$400,000$ two years from now.

If the product is manufactured and offered for sale, the probability that the demand will be high is estimated to be $70\%,$ in which case the present value of the future cash flows is estimated to be $$16,000,000$ three years from now. The probability that the demand will be low is $30\%,$ in which case the present value of the future cash flows is estimated to be $$8,000,000$ three years from now.

If the company's weighted average cost of capital is $12\%$ per year, what is the expected NPV of this product?