Question

Suppose a municipality is proposing to upgrade its municipal water treatment plant to reduce pesticide contamination of its water supply to a level that does not adversely affect human health. The new plant would be constructed over the course of the initial year (year “0”) at a cost of $15 million. Once the plant begins operating in year “1”, estimated operating and maintenance costs of $3 million will be incurred per year for the life of the plant which is 12 years, and estimated accrued benefits will be $5 million per year. Conduct a benefit-cost analysis to determine whether this project should be considered feasible at a discount rate of 5%. What about a discount rate of 10%? Use Excel to save much time and effort. I have provided a template that you could use. If you prefer to do calculations manually you can complete the table below. Year Benefits Costs Net Benefits in Current Values Net Benefits in Present Values

Answer 1

Present value of initial cost is $15 million

Present value of annual cost of $3 million for 12 years at 5% will be PV = P*(1-(1+r)^-n)/r

= 3*(1-(1+5%)^-12)/5%

= 3*(1-(1.05)^-12)/0.05

= 3*(1-0.5568)/0.05

=3*(0.4432)/0.05

= $26.59

Hence total Present Value of cost = 15+26.59 = $41.59

Present value of annual benefit of $5 million for 12 years at 5% will be PV = P*(1-(1+r)^-n)/r

= 5*(1-(1+5%)^-12)/5%

= 5*(1-(1.05)^-12)/0.05

= 5*(1-0.5568)/0.05

=5*(0.4432)/0.05

= $44.32

Hence Present value of Total Benefits = $44.32

Hence Benefit Cost Ratio = Benefits/ Costs = 44.32/41.59 = 1.066

Since Benefit cost ratio is more than 1 project is feasible for discount rate of 5%

Present value of annual cost of $3 million for 12 years at 10% will be PV = P*(1-(1+r)^-n)/r

= 3*(1-(1+10%)^-12)/10%

= 3*(1-(1.1)^-12)/0.10

= 3*(1-0.3186)/0.10

=3*(0.6814)/0.10

= $20.44

Hence total Present Value of cost = 15+20.44 = $35.44

Present value of annual benefit of $5 million for 12 years at 10% will be PV = P*(1-(1+r)^-n)/r

= 5*(1-(1+10%)^-12)/10%

= 5*(1-(1.1)^-12)/0.10

= 5*(1-0.3186)/0.10

=5*(0.6814)/0.10

= $34.06

Hence Present value of Total Benefits = $34.06

Hence Benefit Cost Ratio = Benefits/ Costs = 34.06/35.44 = 0.96

Since Benefit cost ratio is less than 1 project is not feasible at discount rate of 10%