Question

A project has an initial cost of $150,000. The annual operating cost is $8000 for the first 10 years and $5000 thereafter. There is a recurring $15000 maintenance cost each 15 years. The equation that represents the capitalized cost of this project at i=10% is:

Group of answer choices

CW(10%)=150,000+8,000(P/A, 10%, 10)+(5000/0.1)(P/F, 10%, 11)+(15000(A/F, 10%, 15))/0.1

CW(10%)=150,000+8,000(P/A, 10%, 10)+(5000/0.1)(P/F, 10%, 10)+(15000(A/F, 10%, 15))/0.1

CW(10%)=150,000+8,000(P/A, 10%, 10)+(5000/0.1)(P/F, 10%, 11)+15000(A/F, 10%, 15)

CW(10%)=150,000+8,000(P/A, 10%, 10)+(5000/0.1)(P/F, 10%, 9)+(15000(A/F, 10%, 15))/0.1

Answer 1

Initial Cost = 150,000

Annual Operating Cost = 8,000 for the first 10 years

And 5,000 per year thereafter for an infinite period

Maintenance Cost = 15,000 at every 15 years

Interest = 10%

The correct equation for capitalized cost will be

C W (10%) =150,000 + 8,000(P/A, 10%, 10) + (5000/0.1) (P/F, 10%, 10) + (15000(A/F, 10%, 15))/0.1

Step 1 – Take the initial cost

Step 2 – Write the expression for the PW of annual operating cost

For the first 10 years = 8,000 (P/A, 10%, 10)

For the period from 11 year to infinity = (5,000 ÷ 0.10) (P/F, 10%, 10)

Step 3 – Write the expression for the PW of periodic maintenance cost at every 15 years

Convert them into yearly maintenance cost and then calculate the PW.

= [15,000 (A/F, 10%, 15)] ÷ 0.10

Therefore, the capitalized worth will be

CW = =150,000 + 8,000(P/A, 10%, 10) + (5000/0.1) (P/F, 10%, 10) + (15000(A/F, 10%, 15))/0.1