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 equivalent value (a) now and (b) for each year hereafter. The system has an installed cost of $2,500,000 and an additional cost of $700,000 at year 8. The annual software maintenance contract cost is $75,000 for the first 4 years, $100,000 for the second 4 years, $125,000 for the third 4 years, and $125,000 thereafter. In addition, there is expected to be a recurring major upgrade cost of $100,000 every 14 years. Assume that i= 7% per year for county funds

Answer 1

As per the details given above,

Installation Cost = $2500000

Present Value of Additional Cost:
= $700000 / (1 + 0.7)8
= $700000 * 0.62275
= $435924.82

The computation of Annual Software Maintenance Costs in coming years is as under:

For first 4 Years:
= $75000 * PVAF (7%, 4)
= $75000 * 3.3872
= $254040.84

For Second 4 Years:
= $100000 * PVAF (7%, 4) * PVF (7%, 4)
= $100000 * 3.3872 * 0.7629
= $258408.72

For third 4 Years:
= $125000 * PVAF (7%, 4) * PVF (7%, 8)
= $125000 * 3.3872 * 0.582
= $246423.47

For after 12 Years:
= ($125000/7%) * PVF (7%, 12)
= $1785714.29 * 0.444
= $792878.50

Thus, Total Present Value of Annual Software Maintenance:
= $254040.84 + $258408.72 + $246423.47 + $792878.50
= $1551751.54

Present Value of major upgrade cost:
= $100000 / [(1 + 0.07)14 - 1]
= $100000/1.5785
= $63349.91

Thus, as per above calculations,

(a) Equivalent Value:
= $2500000 + $435924.82 + $1551751.54 + $63349.91
= $4551026.27

(b) Value for each Year:
= $4551026.27 * 7%
= $318571.84