Question

4. Suppose you are an economist on a waste cleanup project.  Engineers on the project have come up with cost estimates. The project is estimated to cost $500 thousand dollars during the first year and an additional $20 thousand in each subsequent year.  The benefits have been estimated at $80 thousand dollars per year.  

1. Calculate the present value of the costs and the benefits over the first 10 years of the project for both a 3% discount rate and a 10% discount rate.
2. Would you recommend that the project proceed?  Why or why not?
3. Which of the two discount rates would you be more likely to use if you were an economist for the Environmental Protection Agency?  What about if you were an economist with DuPont? Why?

Answer 1

(a)

(1) Interest rate = 3%

Present value of costs ($) = 500,000 x P/F(3%, 1) + 20,000 x P/A(3%, 9) x P/F(3%, 1)

= 500,000 x 0.9709** + 20,000 x 7.7861** x 0.9709**

= 485,450 + 151,190

= 636,640

Present value of benefit ($) = 80,000 x P/A(3%, 10)

= 80,000 x 8.5302**

= 682,416

(2) Interest rate = 10%

Present value of costs ($) = 500,000 x P/F(10%, 1) + 20,000 x P/A(10%, 9) x P/F(10%, 1)

= 500,000 x 0.9091** + 20,000 x 5.7590** x 0.9091**

= 454,550 + 104,710

= 559,260

Present value of benefit ($) = 80,000 x P/A(10%, 10)

= 80,000 x 6.1446**

= 491,568

(b)

Net present value (NPV) = Present value of benefits - Present value of costs

NPV with 3% interest rate ($) = 682,416 - 636,640 = 45,776

NPV with 10% interest rate ($) = 491,568 - 559,260 = -67,692

Since NPV > 0 with 3% interest rate, I should recommend to proceed. But since NPV < 0 with 10% interest rate, I should recommend not to proceed.

(c)

As an economist with EPA, I would consider a higher interest (discount) rate (10%) to include the risks of environmental damage caused by the project, which gets reflected in a higher interest rate. But as an economist to DuPont I would not concern myself with any costs and risks to environment, therefore I would consider a lower interest (discount) rate (3%) to project a higher positive NPV.