Scenario 1: Present-Value Calculation
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 two years discounted at 10%:
$1,000 = $1,000 = $1,000 = $826.44
(1+10%)
2
(1.1)2
1.21
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.
Scenario 1 tasks:
 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’s Fiscal Administration on cost-benefit and cost-effectiveness
© 2016 Laureate Education, Inc. Page 2 of 2
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 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.
Scenario 2 tasks:
 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?