The director of RCM Inc. is considering launching a new product. The initial investment in equipment and other facilities is $$800,000.$ The project is expected to have a lifespan of $5$ years. First$-$year revenue is projected to be $$600,000,$ and the revenue is expected to remain the same throughout the project's duration. Operating costs for the project are estimated at $$200,000$ per year. If the project is undertaken, the total investment in net working capital will increase by $$100,000$ at the beginning of the project, but the company will recover $50\%$ of its investment in net working capital at the end of the $5$th year. The tax rate is $30\%,$ and the cost of capital depreciation rate is $20\%.$ The equipment can be sold at the end of the project for $$150,000.$ The appropriate discount rate for the project is $9\%.$ Calculate the NPV to determine whether the company should undertake this project or not.