Suppose that a local community is deciding whether to implement an irrigation and drainage system. The associated life span of the project is effectively 6 years, when including in our count the present year. However over the life of the project, because of water pollution, the system requires yearly water treatment and experiences some types of damages due to, say, buildup of certain sediments and possible erosion and/or corrosion caused by certain types of materials in the water. These damages and costs of treatment are expressed in dollar terms and are represented by the variable P, where t refers to the period in which the costs are incurred and experienced in. In addition, because of the pollution, some work is necessary to partially restore the system midway through its life, in period 2. This means that in addition to incurring an initial outlay of Co to construct the irrigation and drainage system, irrespective of the level of water pollution, the community must incur a cost of R in period 2 to restore it, because of the detrimental effects of pollution. The schedule of annual benefits, damages, and costs are as follows: Benefits Yearly damages & costs due to pollution Construction Costs Restoration Costs Current Pd Bo Po Co Period 1 B P Period 2 B P R Period 3 B3 P3 Period 4 B4 P4 Period 5 B5 Ps (3.A) Express the Net Present Value (NPV) of the project. Assume that the interest/discount rate is expressed by the variable i (3.B) Assuming that the project is undertaken, i.e. the NPV of the irrigation system is positive, how much would the community be willing to pay to have the local water supply cleaned? (Hint: This is similar to the problem we did in class concerning housing prices and the willingness to pay to live in an area with improved environmental quality. If this doesn't help, what is the NPV of the project without all the associated costs of pollution? Then take the difference between this and the one you found above.)