Question

A Transportation Authority has just installed a new software to charge and track toll fees. The director wants to know the total equivalent cost of all future costs incurred to purchase the software system. If the new system will be used for the indefinite future, find the equivalent cost (a) now, a CC value, and (b) for each year hereafter, an AW value. - The system has an installed cost of $100,000 and an additional cost of $20,000 after 6 years, and $50,000 after 10 years. - The annual software maintenance contract cost is $5000 for the first 6 years and $8000 thereafter. - In addition, there is expected to be a recurring major upgrade cost of $15,000 every 12 years. Assume that i = 5% per year for county funds. --Good Luck

Answer 1

a)

The new software system has a non repeating cost of $100,000 now, $ 20,000 in year 6 and $ 50,000 in year 10.

Non recurring capitalized cost = - $100,000 - $20,000 $\times$ (P/F, 5%, 6 years) - $ 50,000 $\times$ (P/F, 5%, 10 years)

Non recurring capitalized cost = - $100,000 - $20,000 $\times$ 0.7462 - $ 50,000 $\times$ 0.6139 = $ - 145619

The new system has a major upgrade cost of $ 15,000 every 12 years

Recurring capitalized cost = (- $ 15000 $\div$ 0.05 ) $\times$ (A/F, 5% , 12 years) = (- $ 15000 $\div$ 0.05 ) $\times$ 0.0628

Recurring capitalized cost = $ - 18,840

The annual maintenance contract for indefinite period should be converted present value.

Capitalized cost annual maintenance contract = - $5000 $\div$ 0.05 - ($3000 $\div$ 0.05) $\times$ (P/F, 5%, 6 years)

Capitalized cost annual maintenance contract = $ - 100,000 - ($3000 $\div$ 0.05) $\times$ 0.7462 = $ - 144,772

Total capitalized cost = - $ 145,619 - $ 18,840 - $ 144,772

Total capitalized cost = $ - 309,231

-----------------------------------------------------------------------------------------------

b)

Annual worth = Total capitalized cost $\times$ i = $ 309,231 $\times$ 0.05

Annual worth = $ 15,461.55 $\approx$ $ 15,462