Forte Bend County is planning to construct a Dam some tens of miles away from th
ID: 2495986 • Letter: F
Question
Forte Bend County is planning to construct a Dam some tens of miles away from the Grand Mission Recreation center to facilitate fishing in the El Rehobatha River Basin. The first cost for the Dam will amount to $8,500,000. Annual maintenance and repairs will amount to $35,000 for each of the first five years, to $40,000 for each of the next ten years, and to $45,000 for each of the next five years. In addition a major overhaul costing $650,000 will be required at the end of the tenth year. Use an interest rate of 8% and determine the equivalent uniform annual cost (EUAC) for a 20year period.
Explanation / Answer
Interest rate ( I ) = 8%, n = 20 years, P = $8,500,000
Annual maintenance cost for the first five years, A1 = $35,000
Annual Maintenance Cost from year 6 through 15, A2 = $40,000
Annual Maintenance Cost from year 16 through 20, A3 = $45,000
Overhaul Costs = $650,000 at year 10.
EUAC = ($8,500,000 + $650,000 (P/F, 8%, 10) (A/P, 8%, 20) + $35,000+ (5000(F/A, 8%, 5) + 5000(F/A, 8%, 15)) (A/F, 8%, 20))
From the compound interest table we find following values-
(P/F, 8%, 10) = 0.4632
(A/P, 8%, 20) = 0.1019
(F/A, 8%, 5) = 5.867
(F/A, 8%, 15) = 27.152
A/F, 8%, 20 = 0.0219
Now, EUAC = ($8,500,000 + $650,000 * 0.4632) (0.1019) + $35000 +( $5000*5.867 + 5000*27.152) (0.0219)
= 896830.52 + 64335 + 2973.144
= $964138.664