1. A contractor needs water at a remote construction site for a five year project. A...

1. A contractor needs water at a remote construction site for a five year project. A pipeline from a river,six miles away, will supply the water. The cost of the pipeline and the cost of pumping the water will vary with pipe size. See table below. The contractor uses a MARR of 7%. The contractor plans to work 2000 hours per year, and that is the time the pump will run each year. At the end of five years the salvage value of the pipeline will equal the cost of its demolition.
Part A. (20 points) Which pipe diameter should she select? [Copy pertinent values before you start Part B.

Part B. (5 points) The contractor may work overtime, so the work year has more than 2000 hours. How many hours must they work so that the costs of the 3 inch and 4 inch options are equal?


	Pipe Diameter
	2 inch	3 inch	4 inch	6 inch
Cost of pipeline and pump	$22,000.00	$23,000.00	$25,000.00	$30,000.00
Cost per hour for pumping ($/hr)	$1.20	$0.65	$0.50	$0.40

Solutions

Expert Solution

PART A

Annuity factor of 7% for 5 Years = [1-(1+r)^-n] / r = (1-(1+0.07)^-5) / 0.07 = 4.100197436

Calculation of PV of Cash outflow for all Pipe diameter

	Annuity factor/Muliplier	2 inch	3 inch	4 inch	6 inch
Cost of pipeline and pump	1	22000	23000	25000	30000
Cost per hour for pumping ($/hr)	4.100197436	9840.473846	5330.256667	4100.197436	3280.157949
		(1.220004.100197436)	(0.6520004.100197436)	(0.520004.100197436)	(0.420004.100197436)
Total		31840.47385	28330.25667	29100.19744	33280.15795

As per the above table since PV of 3 inch diameter is the least of all the pipes therefore 3 inch pipe diameter should be selected

Part B

Difference in Fixed Cost of 3 inch and 4 inch pipe = 25000 - 23000 = $2000

Difference in cost per hour for pumping = $0.65 - $0.50 = $0.15

Total per hour cost for pumping for 5 years at PV = 0.15 * 4.10019744 = $0.615029615

Therefore Total hours per year required = DIff in fixed cost/Total per hour cost for pumping for 5 years at PV = 2000/0.615029615 = 3251.875926 hours per year

Therefore the contractor must work for 3251.875926 hours per year so that the cost of 3 inch & 4 inch pipe are equal

jeff jeffy answered 1 year ago

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