# Public finance – cost and benefits analysis

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Cost benefit at the local level often uses a simple tool for calculating potential benefits of a project. It is the simple payback time. That is if a project costs \$100,000 to do but will save \$25,000 per year, then the simple payback time is 4 years (100,000/25,000). This is not the method Anderson describes in the text, which employs a method to calculate the time value of money: discounting. I have added a PowerPoint to the content area entitled Cost-Benefit Analysis, which reviews this tool again, but the last slide has a project to assess whether or not to proceed. The project is buying new garbage trucks for \$400,000 with the estimated annual savings of \$90,000; the trucks would last 4 years and would be sold for \$100,000. A simple payback analysis would show a payback of 4.4 years (400,000/90,000); however, the residual value of \$100,000 was not included; adding that in gives a payback of 3.33 years (400,000-100,000/90,000). Would you make the decision to do this project? Of course, there is a flaw in the simple payback: it does not account for the time value of money. A dollar today is worth more than a dollar 4 years from now.

Also in the Content area is a spreadsheet entitled Discountinggarbage trucks. This spreadsheet has computed the net present value of this proposal using a 7% discount rate; note that it is negative (-\$18,861). (Negative numbers are often shown in parentheses in Excel.) With a negative number, you would not recommend doing this project. Since the spreadsheet is set up for you, I would like you to play around with the discount rate until you get the smallest possible positive number next to Net Present Value. Tell me what this number is. Then explain 1) who might want to use a higher discount rate (you should see a negative number) and 2) who might use a lower number than the one you found ( a positive result), and why. That’s it.

For those of you who are new to Excel (I hope you use it, since it is the primary budget and finance tool used at all levels of government), you simply type over the number in the cell next to the one labeled Discount Rate to change the rest of the spreadsheet, particularly the net present value number.

Note: to do this more correctly, you would also have to include an inflation factor in the formula; we will not do so for this exercise.

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