3) A plant that supplies 1 unit of electricity per year, costs $1 billion to build, lasts 25 years, and has an annual operating cost of $0.2 billion;…

3) A plant that supplies 1 unit of electricity per year, costs $1 billion to build, lasts 25 years, and has an annual operating cost of $0.2 billion; it costs $0.1 billion to decommission the plant at the end of its lifetime (25 years). (Assume that the construction costs and the operating costs are paid at the beginning of the period, and that the decommissioning
cost is paid at the end of the life of the plant.) The annual discount rate is r, with discount factor p(roe) = 1/ (1+r) . Write the formula for the present value of the cost of providing 1 unit of electricity for 100 years, including the decommissioning costs. (Hint: First find the present value of providing one unit of electricity for 25 years. Denote this magnitude as Z. Then find the present value of incurring this cost, Z, 4 times: in periods 0, 25, 50, and 75.)
4) A person plans to save $1 for 20 years. They can invest at an annual rate of 10% (r = 0.1). This investment opportunity .compounds annually.(meaning that they receive interest payments at the end of each year). A second investment opportunity pays a return of ~rx100%, compounded every decade. (After one decade, the investment of one
dollar yields 1 + ~r.) For what value of ~r is the person indifferent between these two investments? (Assume that there is no chance that the person wants to cash in the investment before the 20 year period.) Explain the rationale behind your calculation.