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# Cost benefit analysis Examining Present-Values

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

Let's say a large community-wide animal shelter wants to open a new suburban center aimed at rehabilitating dogs from puppy mills and dog-fighting operations. 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: Cost-Benefit Analysis

In doing the following exercise, please refer to the discussion in the course text 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. In the ratio, if the costs exceed benefits, the advice is to not accept the project and to consider accepting the project if benefits exceed costs. Consider the following example from the fictitious Knotfer Prophet Agency 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. This was calculated using the \$55 average hourly rate of the ten specialized staff; the total number of hours over the three-year period is 450. Three current coal plant workers will lose their jobs at a wage of \$35 per hour. 6.
6. The three year savings on other pollution damage to buildings and grounds, calculated by the Sierra Club, is \$7,000,000.

The assignment (2-3 pages):

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 coal-burning operation or the whole operation? Why or why not?

#### Solution Preview

See the attached file. Thanks

Scenario 1:
A large community-wide animal shelter wants to open a new suburban center aimed at rehabilitating dogs from puppy mills and dog-fighting operations. The total benefits of the program are valued at \$1,000,000 and will be received at the end of two years from now. The objective of this exercise is to see how the present worth of this payment will change if the interest rate (discount rate) expected in the next two years change.
The present value of a payment to be received after n years from now at a discount rate r, is given by the formula
PV=C/(1+r)^n
Where C= payment to be received at the end of nth year
r= discount rate (interest rate)
n=number of years

The present value when the estimated discount rate is 5% is
=\$1,000,000/(1+5%)^2= \$907,029.48

Similarly, the present value when the estimated discount rate is 6% is
=\$1,000,000/(1+6%)^2= \$ 889,996.44

Similarly, the ...

#### Solution Summary

The solution creates a cost-benefit analysis to examine present values.

\$2.19