### Calculate the present value at each interest rate

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Application: Time-Value Formulas and Cost-Benefit Analysis

Governments are concerned primarily with real prices rather than "shadow prices," or prices that have been "assigned" to intangible costs and benefits. A major budget management function is cost-benefit analysis. When coupled with the use of time-value formulas, decision making related to operational expenditures is facilitated. Cost-benefit analysis is a means of evaluating all costs on a dollar basis, even those costs that do not have a dollar value attached to them. After all other calculations have been made, the analysis needs to conclude with the calculation of the ratio between costs and benefits. The results aid decision makers in considering multiple avenues for expenditure. This week, you practice the principles and related formulas of time- (present) value and cost-benefit analysis.

Scenario 1: Present-Value Calculation

Using the present value time-value formulas to calculate the future cost of goods and services is one way to produce more realistic prices. In this Application, you practice using a time-value formula to determine future prices.

The following simple, present-value formula shows the effect of discounting on the cost of a public policy. In the formula, the discount rate will be set at:
(1 + r)time where:
1= a constant
r = a selected interest rate
time = a period of time, usually a year
The formula is:
Cost or Benefit
(1+r)time
The calculation occurs like this example of \$1,000 over 2 years discounted at 10%:

 \$1,000 (1+10%)2 = \$1,000 (1.1)2 = \$1,000 1.21 = \$826.44

Consider the following scenario:

A city wants to open a recycling center aimed at reducing waste. The total benefits of the program are valued at \$1,000,000. Three different discount rates are estimated at 5%, 6%, and 7%. The time period for receiving the benefits of the program is two years.

- Calculate the present value at each interest rate.

- Note and discuss what happens to the present value at each interest rate.

Scenario 2: Cost-Benefit Analysis

Note: Scenario 2 is a separate calculation. Scenario 2 is not influenced by the results of Scenario 1.

In doing the following exercise, please refer to the discussion in pages 319-333 of Chapter 7 from Mikesell'sFiscal Administration on cost-benefit and cost-effectiveness analysis. Cost-benefit analysis is a technique that assumes all costs and benefits can have a dollar value attached to them. It is a tool and should not be used as the sole basis for decision making. The result of a calculation is a ratio between costs and benefits. After all other calculations have been made, the analysis needs to conclude with the calculation of the ratio between costs and benefits. If the ratio costs exceed benefits, the project advice is to not accept the project and to consider accepting the project if benefits exceed costs.

Consider the following example from the fictitious Swobodaville's efforts to build a Community Windmill Renewable Energy Project. The following has been agreed upon:

1. Land is already owned. The price of a new is windmill is \$150,000. A minimum of 50 windmills are needed to achieve desired efficiency compared to the current coal-burning method.

2. Staff training costs over three years when considering direct costs, including loss of productive hours while in training, will be \$55,000 for each of the 10 specialists to be hired.

3. The annual operating and maintenance costs of the machine in the three-year period will be \$35,000 per windmill.

4. The cost of shutting down a portion of the coal plant to achieve the same energy production as the windmills is \$1,000,000.

5. Three full-time coal workers will lose their jobs as a result of the transition. Their hourly wage is \$35 per hour and they work 2,080 hours annually.

6. As a widely supported community project with an investment in every aspect of the community's well being, quality of life expected from reductions in pollution is considered in the cost calculation. The medical center that conducted an analysis has concluded that the value of increased life expectancy should be included as a benefit to the community. The quality of life of 5,000 residents is expected to be increased by an average of dollars over three years. The average benefit of a resident (including all men, women, and children) over a three-year period is estimated to be \$1,500.

7. The three-year savings on other pollution damage to buildings and grounds, calculated by the Sierra Club, is \$7,000,000.

- Calculate the cost-benefit ratio.
- Explain whether the ratio is positive or negative.
- If positive, explain if you would replace a portion of the coal-burning operation or the whole operation? Why or why not?

Support your Assignment with specific references to all resources used in its preparation. Be sure to follow APA guidelines when citing your sources.

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