Question

Use PWs to calculate the benefit/cost ratio of i=5% for a highway project. The first cost is $150,000 and the O&M costs are $5000 per year. There is no salvage value after 20 years. Time savings to users are worth $35,000 per year, and neighborhood disruption is a disbenefit of $10,000 per year. Is this project attractive?

Answer 1

Question

First cost = $150,000

Annual O&M cost = $5,000

Calculate the PW of annual O&M cost -

PW = Annual O&M cost(P/A, i, n)

PW = $5,000(P/A, 5%, 20)

PW = $5,000 * 12.4622

PW = $62,311

The PW of annual O&M cost is $62,311

Annual benefits = $35,000

Calculate the PW of annual benefits -

PW = Annual benefits(P/A, i, n)

PW = $35,000(P/A, 5%, 20)

PW = $35,000 * 12.4622

PW = $436,177

The PW of annual benefits is $436,177

Annual disbenefits = $10,000

Calculate the PW of annual disbenefits -

PW = annual disbenefit (P/A, i, n)

PW = $10,000(P/A, 5%, 20)

PW = $10,000 * 12.4622

PW = $124,622

The PW of annual disbenefit is $124,622

calculate the benefit/cost ratio -

B/C ratio = [PW of benefit - PW of disbenefits]/[First cost + PW of O&M costs]

B/C ratio = [436,177 - 124,622]/[150,000 + 62,311]

B/C ratio = 311,555/212,311

B/C ratio = 1.47

The B/C ratio is 1.47

When B/C ratio is equal to or greater than 1, project can be selected.

So,

This project is attractive and should be executed.