2. A bridge will be built which will last for an indefinitely long time. The ini
ID: 2792250 • Letter: 2
Question
2. A bridge will be built which will last for an indefinitely long time. The initial cost is 10million 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 equivalent uniform cost for the gradient part and consider it as an equivalent yearly cost).Explanation / Answer
Present worth=-10000000-100000/1.06-130000/1.06^2-160000/1.06^3-190000/1.06^4-220000/1.06^5-100000/1.06^6-130000/1.06^7-160000/1.06^8-190000/1.06^9-220000/1.06^10..............-2000000/1.06^10-2000000/1.06^20
=-10000000-100000/1.06/(1-1/1.06^5)-130000/1.06^2/(1-1/1.06^5)-160000/1.06^3/(1-1/1.06^5)-190000/1.06^4/(1-1/1.06^5)-220000/1.06^5/(1-1/1.06^5)-2000000/1.06^10/(1-1/1.06^10)
=-15137415.26
=-15.13741526 million
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