Question

Chapel Hill, North Carolina, has decided to build a 15-mile raw water pipeline to allow it to purchase water from Hillsborough, North Carolina, during times of drought. The engineer has recommended that a 16-in pipeline be built. The basis for the decision is as follows: Cost of Capital Expected Pipe in the cost of Annual Diameter Ground Pumping Power Interest rate is 8%; ($/ft) Station Cost Expected life is 20 yr. $150,000 $10,000 145.000 8,000 140,000 7.000 120,000 6,000 (in) a. Compare the four alternatives based on annual cost and present worth analysis.

Answer 1

a) As 1 mile = 5280 foot

The total cost of 15 mile pipe in the ground

1. For 8 inch diameter pipe = $ 5280*15*5 =$396000

2. For 10 inch diameter pipe = $ 5280*15*8 =$633600

3. For 12 inch diameter pipe = $ 5280*15*12 =$950400

4. For 16 inch diameter pipe = $ 5280*15*14 =$1108800

So, For 8 inch Diameter pipe

PW= -396000-150000 - 10000/0.08*(1-1/1.08^20) = -$644181.47

Annual Cost (A) is given by

-644181.47 = A/0.08* (1-1/1.08^20)

A = -$65611.31

For 10 inch Diameter pipe

PW= -633600-145000 - 8000/0.08*(1-1/1.08^20) = -$857145.18

Annual Cost (A) is given by

-857145.18 = A/0.08* (1-1/1.08^20)

A = -$87302.13

For 12 inch Diameter pipe

PW= -950400-140000 - 7000/0.08*(1-1/1.08^20) = -$1159127.03

Annual Cost (A) is given by

-1159127.03 = A/0.08* (1-1/1.08^20)

A = -$118059.65

For 16 inch Diameter pipe

PW= -1108800-120000 - 6000/0.08*(1-1/1.08^20) = -$1287708.88

Annual Cost (A) is given by

-1287708.88 = A/0.08* (1-1/1.08^20)

A = -$131155.99

So, the PW and the Annual Costs increase as one moves from 5 inch pipe to the 16 inch pipe. If there is no other consideration regarding the performance of the pipe, one should chose the 5 inch pipe as its PW and the Annual Cost are the lowest.