Question

Q.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 $170,087 and an additional cost of $70,087 after 17 years. The annual software maintenance contract cost is $87 for the first 7 years and $131 thereafter. In addition, there is expected to be a recurring major upgrade cost of $17,008 every 14 years. Assume that i = 5% per year for county funds

Answer 1

As per the information given in the question, the cost associated with the software system is as follows

The installed cost (P1) = $170087

Additional cost after 17 years = $70087

The annual software maintenance cost = $87 for first 7 year and $131 thereafter

Major upgrading cost in every 14 years =$17008

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) = $70087(P/F,5%,17) =$70087(0.4362967)=$30578.7268

PW of Annual Maintenance cost (P3)= $87(P/A,5%,7) + $131(P/A,5%,∞)(P/F,5%,7)

PW of Annual Maintenance cost (P3)= $87(P/A,5%,7) + (A/i)(P/F,5%,7)     (A/i=131/0.05=2620)

PW of Annual Maintenance cost (P3)= $87(5.78637) + (2620)(0.710681)

PW of Annual Maintenance cost (P3)= $503.4142 + $1861.9842 =$2365.3984

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

P4 =$17008(A/F,5%,14)(P/A,5%,∞)

P4 =$17008(0.05102)(P/A,5%,∞)      {As (P/A,5%,∞) =A/i}

P4 =$867.74816(P/A,5%,∞) = $867.74816/0.05 = $17354.9632

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

Present Worth (PW)= $170087+$30578.7268+$2365.3984+$17354.9632=$220386.0884

The equivalent value at now (PW) = $220386.0884

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

The equivalent value at now of PW of cost = $220386.0884

A=$220386.0884(A/P,5%,∞) =$220386.0884(0.05) =$11019.3044

The equivalent cost for each year (A)= $11019.3044