The following is a letter that I received from a local city engineer:
Dear Professor Park:
Thank you for taking the time to assist with this problem. I'm really embarrassed at not being able to solve it myself, since it seems rather straightforward. The situation is as follows:
A citizen of Opelika paid for concrete drainage pipe approximately 20 years ago to be installed on his property. (We have a policy that if drainage trouble exists on private property and the owner agrees to pay for the material, city crews will install it.) That was the case in this problem. Therefore, we are dealing with only material costs, disregarding labor. However, this past year, we removed the pipe purchased by the citizen, due to a larger area drainage project. He thinks, and we agree, that he is due some refund for salvage value of the pipe due to its remaining life. Problem:
• Known: 80' of 48" pipe purchased 20 years ago. Current quoted price of 48"pipe = $52.60/foot, times 80 feet = $4,208 total cost in today's dollars.
• Unknown: Original purchase price.
• Assumptions: 50-year life; therefore, assume 30 years of life remaining at removal after 20 years. A 4% price increase per year, average, over 20 years.
Thus, we wish to calculate the cost of the pipe 20 years ago. Then we will calculate, in today's dollars, the present salvage value after 20 years' use, with 30 years of life remaining. Thank you again for your help. We look forward to your reply. Charlie Thomas, PE. Director of Engineering City of Opelika After reading this letter, recommend a reasonable amount of compensation to the citizen for the replaced drainage pipe.