Question

A city is spending $20 million on a new sewage system. The expected life of the system is 40 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 $0.6 million per year. If the city's MARR is 8% per year, what is the capitalized worth of the system?

Answer 1

Answer:

Capitalized worth =$13475000

Explanation:

Given data;

Cost of sewage system = $20

Expected life = 40 years

Maintenance expenses = $0.6 million per year

MARR = 8%

Capitalized worth is calculated by using the formula;

Capitalized worth = Annual worth/Interest rate---------1

But

Annual worth = Initial cost(A/P, 8%, 40) - annual cost----2

From discrete compounding table, the value of (A/P, 8%, 40) at 8% interest rate = 0.0839

Substitute into equation 2, we have

Annual worth =  (20,000,000 * 0.0839) -600,000

                      = 1678000-600,000

                    = $1078000

Substituting the values into equation 1, we have

Capitalized worth = Annual worth/Interest rate

                              = $1078000/0.08

                              =$13475000

Answer 2

Answer:

−$28,475,000

Explanation:

AW = −$20,000,000 (A/P, 8%, 40) $600,000= −$2,278,000

CW = −$2,278,000 / 0.08

= −$28,475,000

Therefore If the city's MARR is 8% per year, the capitalized worth of the system is

−$28,475,000