Problem 2: Discounting Mechanics Suppose that at the start of year 0 , you are considering installing solar panels on your roof and the cost of the panels and installation is $20,000. In years 0,1,2,3 and 4 due to the panels carbon dioxide and other pollutants are reduced causing an annual external benefit of $4000 /year and are saving you $2000/y in electricity and heating costs. All the above values are in the current values of the year produced. Draw a time line to illustrate the timing of these costs and benefits. For simplicity assume the world ends at the end of year 4 and you know this. a) Assume a discount rate of 1.5%(0.015) and calculate the present value of each of the 7 costs and benefits listed above and put under the time line. Aggregate these present values to calculate the net present value (NPV) of the project. b) Repeat the calculation for a discount rate of 5%(0.05). c) Suppose the decision rule is to install the panels if the NPV is positive. Given this, would you install the panels under each of the two discount rates? Explain the reason behind differences in the NPV under the two calculations