You are considering purchasing a defunct mine in Africa. Your firm has developed a method to extract valuable rare earth minerals from the mining entrails. The cost of the mine together with the extraction equipment requires an initial investment of \($250\) million. In addition, you have agreed to fund a set of health clinics for the local community at a cost of \($5\) million per year in perpetuity, paid at the end of each year.

Once the agreement is signed and the up-front investment is made, the project is expected to produce revenues of \($35\) million per year for the next 20 years, with operating costs of \($10\) million per year. After 20 years the minerals will be fully extracted and there will be no additional value from the mine, but you will continue to support the community clinics. Calculate the IRR of this opportunity. (Hint : Plot the NPV as a function of the discount rate.)