A new bridge across the Allegheny River in Pittsburgh is expected to be permanent and will have an initial cost of $30 million. This bridge must be resurfaced every 5 years at a cost of $1 million. The annual inspection and operating costs are estimated to be $50,000. Determine its equivalent annual worth at an interest rate of 10% per year.

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Viviana Davila

24 September, 08:50

A new bridge across the Allegheny River in Pittsburgh is expected to be permanent and will have an initial cost of $30 million. This bridge must be resurfaced every 5 years at a cost of $1 million. The annual inspection and operating costs are estimated to be $50,000. Determine its equivalent annual worth at an interest rate of 10% per year.

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Rayan Medina · Answer 1

The answer is $32,137,975

Explanation:

Its equivalent annual worth = Initial cost + Present value of annual inspection and operating costs + Present value of resurfaced every 5 years

in which: initial cost = $30 million

- Present value of annual inspection and operating costs = 50,000 / 0.1 = $500,000

- Present value of resurfaced every 5 years = 1,000,000/0.61051 = $1,637,975 (present value factor is calculated as 1 / (1.1^5 - 1) = 1/0.61051)

Thus, equivalent annual worth = 30,000,000 + 500,000 + 1,637,975 = $32,137,975.