Determine Which Route Should Be Selected For A New Interstat

Question

Determine which route should be selected for a new interstate highway Two different routes are under consideration for a new interstate highway: The "Long" route and the Transmountain shortcut. The long route is 22 miles long, with a first cost of $21 million and annual upkeep costs of $140,000. The shortcut is 10 miles, with a first cost of $45 million and annual upkeep costs of $165,000. Both routes are expected to carry 400,000 cars per year, with vehicles operating at $0.25 per mile. The roads have a 40-year lifespan, and the interest rate is 10%. Calculate the annualized cost for each route, including initial investment and upkeep, to determine which route should be selected.

Dr. Jack HW Helper · Accepted Answer

To determine which route to select for the new interstate highway, we need to evaluate the total annual cost of each route, incorporating both the initial capital investment (first cost) and the annual operation and maintenance costs. This comprehensive cost analysis allows decision-makers to select the route that provides the most economical solution over the project's lifespan, considering the time value of money with a specified interest rate of 10% over 40 years. First, we assess the annual costs associated with vehicle operation, which is based on the volume of traffic, the length of the route, and the cost per mile per vehicle. Then, the capital costs are annualized using the Capital Recovery Factor (A/P) factor, which accounts for the interest rate and lifespan of the project. Operational Costs Calculation For the long route, the annual user operating costs are calculated as follows: Annual User Cost (Long Route) = Length × Cost per mile × Number of cars per year = 22 miles × $0.25 × 400,000 cars = $2,200,000 Similarly, for the shortcut: Annual User Cost (Shortcut) = 10 miles × $0.25 × 400,000 cars = $1,000,000 Capital Cost Annualization The initial costs are spread over the 40-year life using the Capital Recovery Factor (A/P) at 10% interest: For the long route: A/P = [i(1 + i)^N] / [(1 + i)^N – 1], where i = 0.10 and N = 40 Calculating A/P: A/P = [0.10 × (1 + 0.10)^40] / [(1 + 0.10)^40 – 1] A/P ≈ 0.10 × 57.275 / 56.275 ≈ 0.1014 Annualized First Cost (Long Route) = $21 million × 0.1014 ≈ $2,129,400 Adding the annual upkeep: Total Annual Capital Cost (Long Route) = $2,129,400 + $140,000 ≈ $2,269,400 For the shortcut: Annualized First Cost = $45 million × 0.1014 ≈ $4,563,000 Total Annual Capital Cost (Shortcut) = $4,563,000 + $165,000 ≈ $4,728,000 Total Annual Costs Adding operational and capital costs: Long route: Total Annual Cost = Operational + Capital = $2,200,000 + $2,269,400 ≈ $4,469,400 Shortcut: Total Annual Cost = $1,000,000 + $4,728,000 ≈ $5,728,000

Determine Which Route Should Be Selected For A New Interstat

Determine which route should be selected for a new interstate highway

Paper For Above instruction

Operational Costs Calculation

Capital Cost Annualization

Total Annual Costs

Conclusion

References