An irrigation project costs $1000 to build and will last for 5 years. it will double farmers’ crop yields and increase their sales by $500 a year. the pumps used in the irrigation system use 100 gallons of gasoline a year to operate and require $50 a year to maintain. the domestic price of gasoline is 50 cents a gallon, but it is heavily subsidized and costs the government $2 a gallon to import. assume that for political reasons the government cannot charge farmers for the water. a. if the government’s discount rate is 10%, what is the present value of this project? should the government build it? show and explain all your calculations. b. if the discount rate is 5%, what is the present value? should the government build it? now suppose a private firm can charge $400 per year for the water and can borrow at 10% to finance the project. is it profitable for the private firm to build it?

a. * The government should not invest because it yields a lower than 0 NPV which is -$52.30 . Please see calculations in the explanation part.

b. * If the discount rate is 5%, the government should invest because it yields a higher than 0 NPV which is $82.37. Please see calculations in the explanation part.

   * The private firm should take the project because the profitability or the NPV is $137.24

Explanation:

Because the government is responsible for the increase in common goods of the society while the private firm is not; when calculating NPV for the Government, increase in farmers' sales of corp should be included while it is excluded when doing so for private firm.

Gasoline price should be used domestic price for private firm while for Government, the actual price paid ( import price) is used.

a.

We have the cash flow for the project as followed:

Y0: -1,000; Y1-Y5: Increase in corp sales - Increase in gasoline consumption with price per gallon is calculated at import price - Maintenance cost = 500 - 2 x 100 - 50 = $250

=> NPV = -1,000 + 250/10% x ( 1-1.1^(-5)) = -$52.30

=> Project should not be taken.

b.

* Discount rate for the government is 5%; cash flow in part (a) is remained the same for this scenario:

=> NPV = -1,000 + 250/5% x ( 1-1.05^(-5)) = $82.37

=> Project should be taken.

* The private firm's cash flow is as below:

Y0: -1,000; Y1-Y5: Water charge - Increase in gasoline consumption with price per gallon is calculated at domestic price - Maintenance cost = 400 - 0.5 x 100 - 50 = $300.

=> NPV = -1,000 + 300/10% x ( 1-1.1^(-5)) = $137.24

=> Project should be taken.