Question

There are 2 routes for a sewer line are under consideration.

Route A is a 20,000 ft gravity line, 8,000 ft of this line requires digging. The digging costs $ 250 per foot. The remaining12,000 ft will cost $80 per foot. The annual maintenance cost is $2000. the line has a 35 year life.

Route B is a 23,000 ft line that needs a pumping station. The construction of the station costs $840,000 and will cost $15,000 annually for maintanance. On the other hand, the sewer line costs $80 per foot and will cost $2100 annually for maintenance. The life of the pumping station is estimated to be 30 years and the sewer 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

Route - A

Initial cost ($) = Cost of digging + Non-digging cost = 250 x 8,000 + 80 x (20,000 - 8,000) = 2,000,000 + 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

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 ($) = 89,592 + 159,972 = 249,564