2. A damn will be built which will last for an indefinitely long time. The initi

Question

2. A damn will be built which will last for an indefinitely long time. The initial cost is 2 milion. Every year maintenance costs will run 200,000. Every 5 years a major upgrade costs 1 million. ten year cycle of special costs starts at 100,000 in the first year and goes up 20,000 pery each year for ten years. This cycle then starts all over again and repeats forever ear . What is the italized cost of this project? (Capitalized cost is present worth as N approaches infinity) y optional Hint: one possible technique for the ten year special costs is to find the 6 ( equivalent uniform cost for the gradient part and consider it as an equivalent yearly cost).

Explanation / Answer

Let's calculate the annual cost for major upgrade using PMT function on a calculator

N = 5, PV = 0, I/Y = 6%, FV = 1,000,000 => Compute PMT = 177,396.40

Now, let's calculate the present value of ten cycle cost using NPV function on a calculator

CF1 = 100,000, CF2 = 120,000...CF10 = 300,000 and I/Y = 6%

=> Compute NPV = $1,486,091.39

Now its annualized cost can be calculated using PMT function

N = 10, I/Y = 6%, PV = 1,486,091.39, FV = 0 => Compute PMT = $201,912.20

Total annual cost = 201,912.20 + 177,396.40 + 200,000 = $579,308.60

Capitalized cost = Initial Cost + Annual Cost / Interest rate = 2,000,000 + 579,308.60 / 6% = $11,655,143.39

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