The purpose of this question is to ensure you know how to calculate NPV and IRR GIVEN certain structures. You should endeavor to answer these questions ALGEBRAICALLY not by spreadsheet. 

a) A project requires an initial investment of $100M today. The project is expected to produce cash inflows annually, the first of $5.1M occurs in one year, will continue in perpetuity, growing at a rate of 4.0% per year. If the appropriate discount rate is 9.0%, what is the NPV of this project? (Hint, what is the formula for the present value of a growing perpetuity?) 

b) A project requires an initial investment of $25.0M. The project is expected to generate cash inflows annually in perpetuity, beginning at an expected value of $4.8M a year from today, growing at an annual rate of 3.5% thereafter. What is the IRR of this project? 

c) A project requires an initial investment of $35.0M. The project is expected to generate cash inflows of $6.0M in one year - cash flows will continue until year 7, each growing at a rate of 5.0% (CF1 = $6.0M, CF2 = $6.0M x 1.05, CF3 = $6.0M x 1.052, ..., CF7 = $6.0M x 1.056). If the appropriate discount rate for a project of this risk is 8.0%, what is the NPV of this project? (Hint, what is the formula for the present value of a growing annuity?)