ABC Co is considering the launch of a new widget. If the product goes directly to the market, there is a $40\%$ chance of success. For $$250,000,$ the manager can conduct a focus group to increase the probability of success to $60\%.$ Alternatively, the manager can pay a consulting firm $$4,000,000$ to research the market and refine the product. The consulting firm successfully launches new products $80\%$ of the time. If the firm successfully launches the widget, the payoff will be $$20$ million. If the product is a failure, the NPV is $$0.$

Calculate the expected NPV if the managers go directly to the market.