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 theindefinite future, find the present worth  (or capitalized cost) of the system.

The system has an installed cost of $225,793 and an additional cost of $54,878after 10 years. The annual software maintenance contract cost is $7,032 for the first 4 years and $11,184 thereafter. In addition, there is expected to be a recurring major upgrade cost of $16,845 every 13 years. Assume that 5% per year for county funds.

The Capitalized cost (CC) of the project is

Answer 1

Capitalized Cost is also known as the present worth of a constant annual cost over an infinite period of time. The cost of an item is capitalized if the company expects it to use over a long period of time like fixed assets. But other assets like labor, transportation, sales, materials can also be included.

In this the new software is the asset. Initial non recurring cost = $ 225,793 and overall interest per year = 5%

CC1 = Present worth of $225,793 now and $ 54,878 in year 10 at 5%

= - 225,793 - 54,878(P/F, 5,10) where P/F is present worth P = F(1 + i)^(-n)

= -225,793 - 33,870.70 = -259,664 (Approx)

Next, the recurring cost of $16,845 every 13 years is converted to annual cost for first 13 years

A1 = -16,845(A/F, 5%,13) where A/F is sinking fund A = F[i / {(1+i)^n -1}]

= -951.69 = - 952 (Approx)

The capitalized cost for the two annual maintenance cost series will be done by taking a series of $ 7032 from

now to infinity plus a series of $4152 (11184-7032) from year 5 on wards.

So, annual cost forever A2 = -7032

CC2 = -4152/.05 [P/F, 5%,4]

= -51,252

The CC2 value is calculated using n=4 because the present worth of the annual $4152 cost is located in year 4, one period ahead of the first. Then the two annual cost series is converted into capital cost CC3

CC3 = A1 + A2 / i = -19,186

TOTAL capitalized cost CCT= CC1 + CC2 + CC3

CCT = - 19,186 - 51,252 - 259,664 = 330,102

The total capitalized cost for Marin Officials is $330,102.

The annual value forever is A = 330,102(0.05) = $ 16,505

Correctly interpreted, this means Marin County officials have committed the equivalent of $16,505 forever to operate and maintain the property appraisal software.

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