Concept explainers
The preference of one alternative out of the three based on economic criteria by using the present worth, equivalent annual cost, benefit-cost ratio and rate of return methods.
Answer to Problem 14P
Alternative 3- Intersection widening
Explanation of Solution
Given:
Analysis period = 20 years
Annual interest rate = 15 percent
Calculation:
Determine the present worth of alternative 1 (Traffic signals):
Determine the present worth of alternative 2 (Intersection widening):
Determine the present worth of alternative 3 (Grade separation):
The project with the highest present worth is alternative 2.
Determine the equivalent annual cost of alternative 1 (Traffic signals):
Determine the equivalent annual cost of alternative 2 (Intersection widening):
Determine the equivalent annual cost of alternative 3 (Grade separation):
The project with the highest equivalent annual costis alternative 2.
Determine the benefit-cost ratioof alternative 1 (Traffic signals):
Determine the benefit-cost ratio of alternative 2 (Intersection widening):
Since BCR >1, we would select Alternative 2.
Determine the benefit-cost ratio of alternative 3 (Grade separation):
Since BCR is less than 1, we would not select Alternative 3
Determine the benefit-cost ratio of alternative 2 with respect to 1:
We reachthe same conclusion as previously, which is to select Alternative 2
Determine the rate of return (ROR)of alternative 1versus 2:
It is very difficult to solve this explicitly for i. By trial and error, we can easily find the i that makes the right side of the equation equal to the left side.
Try
For
Then, we can try
Since ROR is greater than 15 percent, we select Alternative 2
Determine the rate of return (ROR) of alternative 3 versus 1:
By trial and error, we can easily find the i that makes the right side of the equation equal to the left side.
Try
For
By interpolation 11.428 % is the rate of return to make the left side to equal to the right side.
Since the ROR is lower than 15 percent, we discard Alternative 3.
Conclusion:
The second alternative i.e. Intersection widening is selected by using the three economic methods.
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Chapter 13 Solutions
Traffic and Highway Engineering
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