Benefit/Cost Analysis

[mei06]

Hello, I'm taking a resource management class and we have delved into B/C analysis. The problem I'm stuck on is below:

The County Council is considering repaving it's parking lots with a new asphalt material. The new pavement has no maintenance costs for 5 years, $20,000 per year for the next 10 years, and $80,000 per year for the following 10 years. The current parking lot has annual pavement costs of $80,000.
1) Assuming a 6% discount rate, what expenditure for the new pavement is justified?
2) How sensitive is the decision to the assumed discount rate?
3) Which alternative would you recommend and why?

I'm confused by the terminology mostly, but also don't know how to begin calculations.
Thank you so much for any help!

 

[tkhunny]

don't know how to begin calculations.

This is a very bad sign, possibly indicating you should not be in this class.

Anyway, learn to use first principles.

If i = 0.06, then v = 1/(1.06).

Having said that:

Cost of New Materials = C

Total Cost of new parking lot = C + 20000*(v^6 + v^7 + ... + v^15) + 80000(v^16 + v^17 + ... + v^25)

Total cost of current parking lot = 80000(v^1 + v^2 + ... + v^25)

The very first thing I notice is that these patterns are EXACTLY equal for the last 10 years. We can just ignore that piece for comparisons.

Comparison Total Cost of new parking lot = C + 20000*(v^6 + v^7 + ... + v^15)

Comparison Total cost of current parking lot = 80000(v^1 + v^2 + ... + v^15)

Can you add those up? You'd be almost done.