A bridge will be built which will last for an indefinitely long time. 1-6% per y

Question

A bridge will be built which will last for an indefinitely long time. 1-6% per year. Every year maintenance costs will run 100,000. Every 10 years a major upgrade costs 2 million. A five year cycle of special costs starts at 100,000 in the first year and goes up 30,000 per year each year for five years. This cycle then starts all over again and repeats forever. What is the capitalized cost of this project? (Capitalized cost is present worth as N approaches infinity). (Totally optional Hint: one possible technique for the five year special costs is to find the equivalent uniform cost for the gradient part and consider it as an equivalent yearly cost). 2. The initial cost is 10million.

Explanation / Answer

Let's calculate the annualized cost of major upgrade using PMT function

N = 10, PV = 0, FV = 2,000,000, I/Y = 6% => Compute PMT = $151,735.92

Now, we need to calculate the annualized cost for 5-year cycle, for which we need to calculate the NPV of the cost first.

Insert CF1 = 100,000, CF2 = 130,000, CF3 = 160,000, CF4 = 190,000, CF5 = 220,000, I/Y = 6%

=> Compute NPV = $659,272.84

Now, annualized cost can be calculated using PMT

N = 5, I/Y = 6%, PV = 659,272.84, FV = 0 => Compute PMT = $156,509.00

Total Annualized Cost = 151,735.92 + 156,509.00 = $308,244.92

Present Value of this cost = PMT / Interest Rate = 308,244.92 / 6% = $5,137,415.26

Hence, total capitalized cost = $5,137,415.26 + $10,000,000 = $15,137,415.26

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