Halcyon Lines is considering the purchase of a new bulk carrier for $$20$ million. The forecasted revenues are $$10$ million a year and operating costs are $$7$ million. Assume the revenues and costs occur at the end of each year. A major refit costing $$5$ million will be required at the end of the eighth year. After $12$ years, the ship is expected to be sold for scrap at $$4$ million. The cost of capital is $11\%.$ a$.$ What is the NPV of this project? b$.$ According to the rule of signs, what is the maximum number of positive IRRs for this project?