Question

Case The city of Flinth, Arizona needs a new water delivery system from Lake Not There Yet. The two options proposed by the city engineers are the following. Given the pace of remediation, the city assumes that this delivery system is not going to be too temporary a fix. • Option one is a water delivery system using the laws of nature and ingenuity of its designers, similar to the East Maui irrigation system in Hawaii. The initial investment is estimated at $3.5 million. The canals need annual maintenance, estimated at $15,000. The water transport system lasts 30 years. Option two is a similar pipeline system used to transport water from neighboring states to California. The initial investment is estimated at $2.5 million. The power cost is estimated to be $30,000 for the first year of operation with a 6.5% increase in the following years. At year 8, an overhaul of $200,000 is expected. The pipeline is expected to last 20 years. The annual operation and maintenance are estimated to cost the city an extra $25,000. You were hired by the city council to audit the proposed plans and make a recommendation. After your inquiry, you learned that the city's MARR is 5.5%.

Answer 1

Equivalent annual cost of option one = 3500000 * (A/P, 5.5%,30) + 15000

= 3500000 * 0.068805 + 15000

= 255818.86 ~ 255819 (Nearest Dollar)

For option two

Present value of geometric series = A * [1 - (1+g)^n / (1+i)^n] / (i-g)

We need to find present value of power cost for 20 yrs

Present value of power cost =  30000 * [1 - (1+0.065)^20 / (1+0.055)^20] / (0.055-0.065)

=  30000 * [1 - (1.065)^20 / (1.055)^20] / (-0.01)

= 30000 * 20.76552198

= 622965.66

Equivalent annual cost of option two = (2500000 + 200000 * (P/F, 5.5%,8) + 622965.66) *(A/P, 5.5%,20) + 25000

= (2500000 + 200000 * 0.651599 + 622965.66) * 0.083679 + 25000

= 297232.75 ~ 297233 (Nearest Dollar)

As Equivalent annual cost of option one is lower it should be selected