Question

A city is spending ​$19.6 million on a new sewage system. The expected life of the system is 50 ​years, and it will have no market value at the end of its life. Operating and maintenance expenses for the system are projected to average ​$0.7 million per year. If the​ city's MARR is 10​% per​ year, what is the capitalized worth of the​ system? The study period is 100 years.

Answer 1

We can solve this by first converting the cash flow into present value then into annual worth and at the last into capitalized cost

PW = - 19.6 - 0.7 (P/A,10%,100) - 19.6(P/F,10%,50)

PW = - 19.6 - 0.7 × 9.999 - 19.6/1.1⁵⁰

PW = - 19.6 - 6.999 - 0.16696

PW = - $ 26.7664556 million

Now convert it to annual worth

AW = PW(A/P,10%,100)

AW = - 26.7664556 × 0.100007257

AW = - $ 2.676839 million

Capitalized cost = - 2.676839/0.1 = - $ 26.76839 million

Or we can solve this type of problem

CC = - $ 26.696 million

The difference e in values is due to approximation. I have solved it using the two methods you can use any one of them. Please contact if having any query will be obliged to you for your generous support. Please help me it mean a lot to me. Thank you.