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. The system has an installation cost of $150,000 and an additional cost of $50,000 at year 10. The annual software maintenance cost is $5,000 for the first 4 years and $8,000 thereafter. If the new system will be used for the indefinite future, find the equivalent present value at a discount rate of 5%.

Equivalent annual cost = $16,502.89

Explanation:

Equivalent annual cost = Present Value of cost / Annuity factor

Present value of cost:

PV of additional cost  =50,000 ×1.05^(-10)=30,695.66

PV of maintenance cost

First four years= 5,000×  (1-1.05^(-4))/0.05=17,729.75

From year 5 to infinity = (8,000/0.05)× 1.05^(-4)=131,632.39

PV of maintenance cost =  17,729.75  + 131,632.396= 149,362.14

PV of costs = 150,000 + 30,695.66 + 149,362.14= 330,057.8112

Annuity factor = 1/r = 1/0.05= 20

Equivalent annual cost = 330,057.8112 /20=$16,502.89

Equivalent annual cost = $16,502.89

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