A highway department is trying to decide whether to patch a section of roadway o

Question

A highway department is trying to decide whether to patch a section of roadway or completely resurface the section. Patching will last two years and require 300 cubic yards of material that costs $700 per cubic yard and $24,000 to improve the roadway shoulders at the same time and another $5,000 per year to maintain the patched up road. Resurfacing the road will cost $850,000 and $2,000 per year to maintain beginning 3 years from now. The useful life of both alternatives is 10 years. At an interest rate of 8% per year, the annual worth of the Patching alternative is closest to $_____ per year.

Explanation / Answer

For Patching:

Material cost = 300 x $700 = $210,000

Initial cost = Material + Improvement cost = $(210,000 + 24,000) = $234,000

Annual worth ($) = 234,000 x A/P(8%, 10)** + 5,000 = 234,000 x 0.15 + 5,000 = 35,100 + 5,000

= 40,100

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