Company A plans to invest $$4$ million this year to launch a new product in time for introduction next year. It is anticipated that in the first year of production, it will cost the company $$1$ million dollars to generate $$1\mathrm{.}7$ million in revenue. As Company A$\text{'}$s operations and continuous improvement teams learn how to improve yields and trim waste from the process, it is expected that costs will decrease by $10\%$ each year, while sales are expected to increase by $5\%$ annually over the $5$ year production run.

a$)$ Make a table showing costs, revenues, and net cash flows for the current year and the following $5$ years of production.

b$)$ Using a discount rate of $8\%,$ what is the net present value $($NPV$)$ of this investment?

c$)$ Suppose inflation in wages and materials has made it so that Company A$\text{'}$s costs remain stuck at $$1$ million per year. What is the NPV in this case?

Show your work!!!!