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

r = ia = ip. M = 1, K = 1, C = 1, ip = (1+ic)^c – 1 = (1+r/M)^C – 1 = (1+0.10/1)^1 – 1

= 0.10 (10%)

CE SP (Steel Pipeline) = AE SP/ip

AE SP = -$225*10^6(A/P,100%,N-infinity) - $10*10^6 - $50*10^6(A/F,10%,40)

= -$225*10^6[0.10] - $10*10^6 - $50*10^6[0.10/((1+0.10)^40 -1)]

= -$32612970.9

Thus CE SP = -$32612970.9/0.1

= -$326129707 (or around -$326 million)

CE GFC (gravity flow canal) = AE GFC/ip

AE GFC = 350*10^6*0.10 – 0.5*10^6 = -$35500000

CE GFC = -$35500000/0.1 = -$355 million

Thus CE SP (-$326 million)>CE GFC (-$355 million)

Based on the above calculations of the capitalized cost method steel pipeline will be build.