Utopia Software Inc. is considering the introduction of a new product that is expected to reach sales of $$10$ million in its first full year, and $$13$ of sales in the second year. Because of intense competition and rapid product obsolescence, sales of the new product were expected to remain unchanged between the second and third years following introduction. Thereafter, annual sales were expected to decline to two thirds of peak annual sales in the fourth year and one third of peak sales in the fifth year. No material levels of revenues or expenses associated with the new product were expected after five years of sales. Based on past experience, cost of sales for the new product were expected to be $60\%$ of total annual sales revenue during each year of its life cycle. Selling, general, and administrative expenses were expected to be $23\mathrm{.}5\%$ of total annual sales. Taxes on profits generated by the new product would be paid at a $40\%$ rate. To launch the new product, Utopia Software would have to incur immediate cash outlays of two types. First, it would have to invest $$500,000$ in specialized new production equipment. This capital investment would be fully depreciated on a straight line basis over the five years anticipated life of the new product. It was not expected to have any material residual value at the end of its depreciable life. No further fixed capital expenditures were required after the initial purchase of the equipment.Second, additional investment in net working capital to support sales would have to be made. Utopia Software generally required $27$ cents of net working capital to support each dollar of sales. As a practical matter, this buildup would have to be made by the beginning the sales year in question $($equivalent to the end of the previous year$).$ As sales grew, further investments in net working capital ahead of sales would have to be made. As sales diminished, net working capital would be liquidated and cash recovered. At the end of the new products life cycle, all remaining net working capital would be liquidated and the cash recovered. Finally, Utopia Software expected to incur tax deductible introductory expenses of $$200,000$ in the first year of the new products sales. These costs would not be recurring over the products life. Approximately $$1\mathrm{.}0$ million had already been spent developing and test marketing the new product. These expenditures were also one$-$time expenses that would not be recurring during the new products life cycle. a$.$ Estimate the new products future sales, profits and cash flows throughout its five year life cycle.b$.$ Assuming a $20\%$ discount rate, what is the products NPV$?$ What is the IRR?c$.$ Should Utopia Software introduce the new product?