Question

A water utility is trying to decide between an investment of doing infiltration and inflow correction for the cost of $5,000,000 or do nothing a pay the additional amount for treating the infiltration at their plant. The additional annual operating costs for the do-nothing alternative is $1,500,000 while the additional annual operating costs associated with the inflow correction is estimated at $150,000. The cost of money criteria for the investment (capital bond for municipal utility) is 3.5% and the time frame for the analysis is 20 years. Which approach is best? (the value for P/A, 3.5%, 20 years is 14.2124)

Answer 1

We have the following information

	Inflow Correction	Do Nothing
Initial Cost ($)	5,000,000
Annual Operating Cost ($)	150,000	1,500,000
Interest Rate (i)	3.5% or 0.035	3.5% or 0.035
Life (n)	20 years	20 years

We will use Present Worth Analysis for Comparing the Alternatives

Inflow Correction Option

PW(3.5%) = Initial Cost + Annual Cost(P/A, i, n)

PW(3.5%) = 5,000,000 + 150,000(P/A, 3.5%, 20)

PW(3.5%) = 5,000,000 + 150,000[((1+0.035)²⁰ – 1)/0.035(1+0.035)²⁰]

PW(3.5%) = 5,000,000 + (150,000 × 14.212)

PW(3.5%) = 5,000,000 + 2,131,860.50

PW(3.5%) = $7,131,860.50

Do Nothing Option

PW(3.5%) = Annual Cost(P/A, i, n)

PW(3.5%) = 1,500,000(P/A, 3.5%, 20)

PW(3.5%) = 1,500,000[((1+0.035)²⁰ – 1)/0.035(1+0.035)²⁰]

PW(3.5%) = 1,500,000 × 14.212

PW(3.5%) = $21,318,604.95

Since, the Present Worth of Inflow Correction Option is lower as compared to Do Nothing Option, so Inflow Correction Option should be selected.