Question

A new wastewater treatment plant was built to treat the wastewater flow 800,000 gpd. The capital cost to build the wastewater treatment plant was $6,000,000. The annual operation and maintenance costs of operating the plant is $700,000/year. Estimate the cost of treating 1000 gallons of wastewater ($/1000 gallon). Assume the design life as 20 years and interest rate of 4%.

Answer 1

Wastewater treatment plant capacity= 800000 gpd

Design life= 20 years

Interest rate = 4%

Capital cost = $6000000

Annual maintenance = $700000/years

• Total cost of plant for 20 years =

(Capital cost + interest cost for 20 years) + (Maintenance cost for 20 years + compound interest cost for over 20 years)

• Capital cost= $ 6,000,000
• Interest cost for 20 years = ($ 6000000 * 0.04) * 20 = $ 48, 00, 000

• Maintenance cost for 20 years + compound interest cost for over 20 years =

A = B/C {(1+C) ⁿ – 1}

Where, A = Maintenance cost for 20 years + compound interest cost for over 20 years

            B= Yearly maintenance cost = $ 7, 00,000

            C = Interest rate = 4% = 0.04

            n= Number of years = 20

Therefore, A = (7, 00,000/0.04) {(1+ 0.04)²⁰ – 1}

        = (7, 00,000/0.04) * 1.19

        = $ 2, 08, 25,000

Total cost of plant for 20 years = ($ 6,000,000 + $ 48, 00, 000) + ($ 2, 08, 25, 000)

                                              = $ 31, 36, 50, 000

• Total amount of water processed over 20 years = (Daily capacity of plant) * 365 * 20

     = 8, 00, 000 * 365 * 20

     = 58 40 000 000 gallon

• Cost per gallon = (Total cost of plant for 20 years) / (Total amount of water processed over 20 years)

      = ($31, 36, 50, 000) / (58, 40, 000, 000 gallon)

      = $ 0.00542 /gallon

Cost per 1000 gallon = $ 0.00542 * 1000 = $5.42 / gallon