You are thinking of making an investment in a new plant. The plant will generate revenues of $$1\mathrm{.}16$ million per year for as long as you maintain it$.$ You expect that the maintenance costs will start at $$67,280$ per year and will increase $5\%$ per year thereafter. Assume that all revenue and maintenance costs occur at the end of the year. You intend to run the plant as long as it continues to make a positive cash flow $($as long as the cash generated by the plant exceeds the maintenance costs$).$ The plant can be built and become operational immediately and the interest rate is $6\%$ per year.

a$.$ What is the present value of the revenues?

b$.$ What is the present value of the maintenance costs?

c$.$ If the plant costs $$11\mathrm{.}6$ million to build, should you invest in the plant?