# Time-Value Formulas and Cost-Benefit Analysis

Time-Value Formulas and Cost-Benefit Analysis
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 2 years discounted at
10%:
\$1,000 = \$1,000 = \$1,000 = \$826.44
(1+10 percent)2 (1.1)2 1.21
Let’s say 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 2
In doing the following exercise, please refer to the discussion in the designated
pages of Chapter of Fiscal 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 the ratio between costs and
benefits. If in 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 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 fifty 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 ten
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. There will be a decrease in staff productivity compared to coal burning
operations. It was calculated on the average hourly rate of the ten specialized
staff of \$55 and the number of hours added over the three year-period, 450.
Three current coal plant workers who will lose their jobs is three at a wage of \$35
per hour.
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 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 \$1500.
7. The three year savings on other pollution damage to buildings and grounds
calculated by the Sierra Club is \$7,000,000.
Scenario 1:
• Calculate the present value at each interest rate.
• Note and discuss what happens to the present value at each interest
rate.
Scenario 2:
• Calculate the cost-benefit ratio.
• Determine whether the ratio is positive or negative.
• If positive, would you go ahead and replace a portion of the coalburning
operation or the whole operation? Why or why not?
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