Final answer:
The present worth of the cost and benefits can be calculated using net present value (NPV). The higher voltage line is not recommended due to negative present worth. Consider both economic and non-economic factors before making a decision.
Step-by-step explanation:
To determine the present worth of the cost and benefits for each estimated value, we can use the concept of net present value (NPV). NPV takes into account the time value of money by discounting future cash flows to their present value. The NPV is calculated as follows: NPV = Benefits - Initial Cost / (1+interest rate)^year. For the optimistic projection, the present worth would be $20,000 - $250,000 / (1+0.06)^0 = -$250,000. For the most likely projection, the present worth would be $15,000 - $250,000 / (1+0.06)^0 = -$250,000. For the pessimistic projection, the present worth would be $8,000 - $250,000 / (1+0.06)^0 = -$250,000.
To calculate the mean annual savings, we can take the average of the optimistic, most likely, and pessimistic projections. Mean annual savings = ($20,000 + $15,000 + $8,000) / 3 = $14,333.33. To determine the present worth using the range of estimates, we can use the same NPV formula but with the mean annual savings. Present worth = $14,333.33 - $250,000 / (1+0.06)^0 = -$250,000.
Now, let's consider the recommendation. From an economic perspective, the present worth for all estimated values and the range of estimates is negative, indicating that the higher voltage line is not financially beneficial. The initial cost outweighs the potential savings. From a non-economic perspective, factors such as safety regulations, environmental impacts, and future scalability should also be considered. It is recommended to consult with experts and conduct a thorough analysis before making a final decision.