Question

Two different routes for a sewer line are under consideration by a city engineer. Route A is a 20000 foot long gravity line, 8000 foot of this requires tunneling at a cost of $ 250 per linear foot. The remaining 12000 foot will cost $80 per linear foot. The annual maintenance cost is estimated to be $2000. The expected life of the line is 35 years. Route B is a 23000 foot long line requiring a pumping station. The construction of the station costs $840000 and will cost $15000 annually to operate and maintain. The sewer line cost $80 per linear foot and will cost $2100 annually for maintenance. The life of the pumping station is estimated to be 30 years and the line is expected to last for 35 years. Using an interest rate of 8%, and assuming no salvage value, compare the annual cost of both routes.

Answer 1

For both routes, annual cost is measured using Annual worth of costs, as follows.

(a) Route - A

First cost ($) = Digging cost + Non-digging cost = 250 x 8,000 + 80 x 12,000 = 2,000,000 + 960,000 = 2,960,000

Annual cost ($) = 2,960,000 x A/P(8%, 35) + 2,000 = 2,960,000 x 0.0858** + 2,000 = 253,968 + 2,000 = 255,968

(b) Route - B

Annual cost of pump ($) = 840,000 x A/P(8%, 30) + 15,000 = 840,000 x 0.0888 + 15,000 = 74,592 + 15,000

= 89,592

Annual cost of sewer line ($) = 80 x 23,000 x A/P(8%, 35) + 2,100 = 1,840,000 x 0.0858 + 2,100 = 157,872 + 2,100

= 159,972

Total annual cost ($) = Annual cost of pump + Annual cost of sewer line = 89,592 + 159,972 = 249,564

(c) Since Route B has lower annual cost, this is the preferred route.