Two largescale conduits are under consideration by a large m

Two large-scale conduits are under consideration by a large municipal utility district (MUD). The first involves construction of a steel pipeline at a cost of $225 million. Portions of the pipeline will have to be replaced every 40 years at a cost of $50 million. The pumping and other operating costs are expected to be $10 million per year. Alternatively, a gravity flow canal can be constructed at a cost of $350 million. The M&O costs for the canal are expected to be $0.5 million per year. If both conduits are expected to last forever, which should be built at an interest rate of 10% per year? can someone answer this question using CAPITAL COST METHOD? PLEASE SHOW STEPS

Solution

In the capital cost method, we calculate the net present value of all the costs involved in both alternatives and they select the alternative that has the lowest net present value of costs

OPTION 1: Construction of a steel pipeline

Initial Cost = 225 Million

Present value of maintenance costs = FV /r = 10,000,000/0.10 = 100,000,000 = 100 Million

The effective interest rate for replacement every 40 years = 1.10^40 -1 = 44.25925557

The present value of replacement costs = 50,000,000/44.25925577 = 1.13 Million

Total costs = 225 +100 + 1.13 = 326.13 Million

OPTION 2: Construction of a Gravity Flow canal

Initial cost = 350 Million

Present value of maintenance = 0.5/0.10 = 5 Million

Total cost in today’s\' value =350 +5 = 355 Million

Since the total capital cost in today’s value is lower for option 1, we should construct a steel pipeline