Question

4. El Paso Water Utilities (EPWU) purchases surface water for treatment and distribution to EPWU customers from El Paso County Water Improvement District during the irrigation season. A new contract between the two entities resulted in a reduction in future price increases in the cost of the water from 8% per year to 4% per year for the next 20 years. If the cost of water next year (which is year 1 of the new contract) will be $260 per acre- foot, what is the present worth of the savings (in $/acre-ft) to the utility between the old and the new contracts? Let the interest rate equal 6% per year.

Please show work using formulas

Answer 1

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

Present worth when increase in rate is 8% = 260 * [1 - (1+0.08)^20 / (1+0.06)^20] / (0.06-0.08)

= 260 * [1 - (1.08)^20 / (1.06)^20] / (-0.02)

= 260 * 22.665423

= 5893.01

Present worth when increase in rate is 4% = 260 * [1 - (1+0.04)^20 / (1+0.06)^20] / (0.06-0.04)

= 260 * [1 - (1.04)^20 / (1.06)^20] / (0.02)

= 260 * 15.839872

= 4118.37

Present worth of savings = 5893.01 - 4118.37 = 1774.64