Innovation Company is thinking about marketing a new software product. Upfront costs to market and develop the product are $$5$ million. The product is expected to generate profits of $$1$ million per year for $10$ years. The company will have to provide product support expected to cost $$100,000$ per year in perpetuity. Assume all profits and expenses occur at the end of the year.

a$)$ What is the NPV of this investment if the cost of capital is $6\%?$ Should the firm undertake the project? Repeat the analysis for discount rates of $2\%$ and $12\%.$

b$)$ How many IRRs does this investment opportunity have?

c$)$ Can the IRR rule be used to evaluate this investment? Explain.