Question

The property appraisal district for Marin County has just installed new software to track residential market values for property tax computations. The manager wants to know the total equivalent cost of all future costs incurred when the three county judges agreed to purchase the software system. If the new system will be used for the indefinite future, find the annual worth of the project : The system has an installed cost of $175,350 and an additional cost of $82,323after 10 years. The annual software maintenance contract cost is $9,893 for the first 4 years and $12,386 thereafter. In addition, there is expected to be a recurring major upgrade cost of $24,107 every 13 years. Assume that 5% per year for county funds. The annual cost of Capitalized cost (CC) of the project for ever is

Answer 1

We have the following information

Installation Cost ($)	175,350
Additional Cost after 10 Years ($)	82,323
Annual Software Maintenance Cost for first 4 years ($)	9,893
Annual Software Maintenance Cost after 4 years ($)	12,386
Upgrade Cost after every 13 Years ($)	24,107
Interest Rate	5% or 0.05

Capitalized Cost = 175,350 + 82,323(P/F, 5%, 10) + 9,893(P/A, 5%, 4) + 12,386(A/F, 5%, 5)(P/A, 5%, n=infinite) + 24,107(A/F, 5%, 13)(P/A, 5%, n=infinite)

Capitalized Cost = 175,350 + [82,323/(1 + 0.05)¹⁰] + 9,893[((1+0.05)⁴ – 1)/0.05(1+0.05)⁴] + {12,386 × [0.05/((1 + 0.05)⁵ – 1)] × (1/0.05)} + {24,107 × [0.05/((1 + 0.05)¹³ – 1)] × (1/0.05)}

Capitalized Cost = 175,350 + (82,323 × 0.6139) + (9,893 × 3.546) + (12,386 × 0.1810 × 20) + (24,107 × 0.0565 × 20)

Capitalized Cost = 175,350 + 50,538.09 + 35,080.58 + 44,837.32 + 27,240.91

Capitalized Cost = $333,046.90