¶ … Value Calculation.
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.
5% discount rate: 1000 / (1+ .05)^2 = 1000 / 1.1025 = 907.03
6% discount rate: 1000 / (1+ .06)^2 = 1000 / 1.1236 = 890.00
7% discount rate: 1000 / (1+ .07)^2 = 1000 / 1.1449 = 873.44
As the interest rate gets higher, the net present value decreases.
It is also worth noting that the differences between each different percentage point per rate in these examples are roughly about 17 dollars per percentage point over the two-year period. We can also observe that Morgan Friedman's inflation calculator calculates a much more substantial rate of inflation over a recent 2-year period than this. If we use Friedman's tool to calculate the inflation rate for 1000 dollars between 2013 and 2015, we learn that "What cost $1,000 in 2013 would cost $1,041.70 in 2015" (Friedman, westegg.com). This is useful to note when we are considering what happens over a two-year period to net present value.
Scenario 2: Cost-Benefit 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:
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.
150,000x50 = 7,500,000 COST
Staff training costs over...
Their hourly wage is $35 per hour and they work 2,080 hours annually.
3x35x2080x3 = 655,200 SEE BELOW
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.
INCREASED LIFE EXPECTANCY = SEE BELOW
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.
5000x1500 = 7,500,000 BENEFIT
The three-year savings on other pollution damage to buildings and grounds, calculated by the Sierra Club, is $7,000,000.
7,000,000 BENEFIT
TOTAL COSTS = 14,300,000
TOTAL BENEFIT = 14,500,000
Discussion:
The basic rule of a benefit cost ratio is that if B/C>1, then the ratio is positive and the project is advantageous. In the calculation offered here, 14,500,000 benefits / 14,300,000 = 1.01, which makes the ratio just positive (although close to a margin of error) and makes the project marginally advantageous.
However, two items from the initial description have been left out of this calculation. The first is the lost wages over three years of the three full-time coal workers who will lose their jobs, which comes to 665,200. The second is the value of increased life expectancy, which should be taken into account in the calculations, but which does not have a dollar amount attached.
The three lost jobs are obviously the sort of…
