[10 points] A water district needs an additional supply of water from a local re
ID: 1163658 • Letter: #
Question
[10 points] A water district needs an additional supply of water from a local reservoir. The engineer has selected two plans for comparison: (a) The “Gravity” plan, where water is diverted at a point 15 miles up-river from the reservoir and carried to the water district by gravity through the pipeline; or (2) the “Pumping” plan, where water is diverted at a point nearer the district and pumped through three miles of pipeline. The pumping station can be built in two stages, part now and part twenty years later.
Use a 50-year analysis period and 6% interest. Salvage values can be ignored. Use the conventional incremental benefit-cost ratio method to select the more economical plan.
Gravity
Pumping
Initial investment
$ 3,000,000
$ 1,500,000
Investment in 20th year
0
$ 300,000
Annual M&O
$ 15,000
$ 25,000
Average annual power cost
First 20 years
0
$ 50,000
Next 30 years
0
$ 100,000
Gravity
Pumping
Initial investment
$ 3,000,000
$ 1,500,000
Investment in 20th year
0
$ 300,000
Annual M&O
$ 15,000
$ 25,000
Average annual power cost
First 20 years
0
$ 50,000
Next 30 years
0
$ 100,000
Explanation / Answer
Here, the beneft of chosing 'Pumping' over 'Gravity' project, would be the lower investment.
So, the benefit = Present value of investments for Gravity - Present value of investments for Pumping
= 3,000,000 - (1,500,000 + (500,000/(1.08^20)))
= 1,392,726
We will use excel formula PV for calculating annuity values of costs for the projects
present value of M&O and power costs for Pumping project = present value of 50 year annuity of 25000 + present value of 20 year annuity of 75000 + present value of 30 year annuity of 150000 starting 20 years from now
= PV(8%,50,-25000) + PV(8%,20,-75000) + PV(8%,30,-150000)/(1.08^20) = 1,404,499
present value of M&O and power costs for Gravity project = present value of 50 year annuity of 25000 = PV(8%,50,-15000) = 183,502
Cost would be the difference of present value of M&O and power costs for Pumping project - present value of M&O and power costs for Gravity project
= 1,404,499- 183,502 = 1,220,996
Benefit/Cost = 1,392,726/1,220,996 = 1.14
Since, Benefit to cost ratio for choosing Pumping project over Gravity prject is more than 1, hence we will select Pumping project.
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