Question

A city is spending $20 million on a new wastewater treatment plant. The expected life of the system is 40 years, and it will have a market value of $5 million at the end of its useful lifetime. Operating and maintenance expenses for the system are projected to be $1 million per year. If the city’s MARR is 8% per year, what is the annual worth of the system? Express your answer in terms of dollars, rounded to the nearest dollar (e.g., 1234 if you believe the answer to be $1,234.12). Hint: because the only revenue associated with the system is its salvage value, your annual worth should likely be negative.

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this is what I tried:

PV = -$20M - $1M*(P/A, 8%, 40) + $5M*(P/F, 8%, 40)

PV = -20 - (11.9246) + 5*(0.0460) = -31.64946e6

then

AW = PV*(A/P, 8%, 40)

= -31.64946e6*(0.0839) = -2659176.94 -> -2659177

Answer 1

Investment = 20000000,

Salvage revenue = 5000000 after 40 yrs

Annual O&M Cost = 1000000

i=8%

t = 40yrs

Annual worth = -20000000 *(A/P, 8%, 40) - 1000000 + 5000000 * (A/F, 8%, 40)

= -20000000 * 0.083860162 - 1000000 + 5000000 * 0.003860162

= -2,657,902.43