Two Scenarios Calculating Cost Benefit Analysis

¶ … 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 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.

55,000x10= 550,000 COST

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

35,000x50x3= 5,250,000 COST

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

1,000,000 COST

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.

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 issue that would be taken into account in a real-world scenario -- there is a real human cost to workers being made redundant -- but it is hard to see how they make sense as a potential cost in this accounting. After all, the paying of wages (and the training) for new employees is an expenditure on wages and counts as a cost, not as a benefit to increased employment rates. If we are supposed to consider the wages of the three redundant coal workers as a loss to the overall economy of consumption here, why are the wages of the ten new employees for the windmills not being considered as an addition to it? Therefore the total wages over 3 years of the redundant employees should probably be considered as an overall benefit to the economy, and the three coal workers can be given an edifying pamphlet on Schumpeter's concept of "creative destruction" to read in their ample spare time.

The issue of increased life expectancy is somewhat different. The wording of the problem is somewhat vague as to whether this benefit should be included within the increase in "quality of life" for the town's residents, which does have a cash valuation listed. However, life expectancy is not quality of life. It is probably more accurate to consider the increase in life expectancy as an overall benefit, for 5000 people, that does not have a ready cash valuation provided. But it obviously would provide a substantial benefit. The quality of life benefit for a three-year period is evaluated at 7.5 million, and if we assess the increased life expectancy at a similar rate, the project becomes vastly more attractive. It becomes vastly more attractive even if we consider those 3 lost coal mining jobs to be a cost rather than a benefit.

Of course the single most outrageous fact about the way that this problem is written is that -- despite the invocation of the Sierra Club in terms of evaluating the money saved on pollution damage to buildings and grounds -- there is no mention of the fact that coal-burning causes permanent harm to the whole planet, and windmills do not. Are we supposed to include in our cost benefit analysis that the potential costs of maintaining the coal plant as it exists would include the price-tag for leaving all of southern Florida underwater, or the potential devastation of any coastal cities worldwide which exist at a low elevation, or the devastation of habitats for polar bears, and so forth?