Question

1. 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 $174515 and an additional cost of $74515 after 17 years. The annual software maintenance contract cost is $4515 for the first 7 years and $6772.5 thereafter. In addition, there is expected to be a recurring major upgrade cost of $17451 every 14 years. Assume that i = 5% per year for county funds.

Answer 1

As per the information given in the question, the cost related to software system for property tax computation is as follows

The installed cost (P1) = $174515

Additional cost after 17 years = $74515

The annual software maintenance contract cost = $4515 for first 7 year and $6772.5 thereafter

Major upgrading cost in every 14 years is =$17451

Rate of interest (i) =5% =0.05

Useful life (N) = ∞ (Infinite)

(A)The equivalent value at now or Present Worth (PW)=?

PW of Additional cost after 17 years (P2) = $74515(P/F,5%,17) =$74515(0.4362967)=$32510.6486

PW of Annual Maintenance cost (P3)= $4515(P/A,5%,7) + $6772.5(P/A,5%,∞)(P/F,5%,7)

P3= $4515(P/A,5%,7) + $6772.5(A/i)(P/F,5%,7)     (A/i=6772.5/0.05=135450)

P3= $4515(5.78637) + (135450)(0.710681)

P3= $26125.4606 + $96261.7415 =$122387.2021

PW of Major upgrading cost in every 14 years (P4)

P4 =$17451(A/F,5%,14)(P/A,5%,∞)

P4 =$17451(0.05102)(P/A,5%,∞)      {As (P/A,5%,∞) =A/i}

P4 =$890.35(P/A,5%,∞) = $890.35/0.05 = $17807

Present Worth (PW)= P1+P2+P3+P4

Present Worth (PW)= $174515+$32510.6486 +$122387.2021+$17807=$347219.8507

The equivalent value at now (PW) = $347219.8507

(B)The equivalent cost for each year (A)=?

The equivalent value at now of PW of cost = $347219.8507

A=$347219.8507(A/P,5%,∞) =$347219.8507(0.05) =$17360.9925  

The equivalent cost for each year (A)= $17360.9925