A bridge will be built which will last for an indefinitely Ion 1-6% per year. Ev
ID: 2581250 • Letter: A
Question
A bridge will be built which will last for an indefinitely Ion 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 co . g time. The initial cost is 10million. onsider it as an equivalent yearly costExplanation / Answer
Present value of initial investment = 10million
Present value of operational cost = 0.1million/0.06
=1.67million
present value of spspecspspecial cost
present value of 5year cost = 100000*0.943+130000*0.890+160000*0.84+190000*0.792+220000*0.747
=659220
Equated annual value =659220/PVAF(6%,5yrs)
=659220/4.212
=156510or 0.156millions
Present value of special costs = 0.156/0.06 = 2.6millions
Present value of 10 year costs = 2millions /pvf(6%,10yrs)
=2/0.558
=3.584
Total present value of project =10+1.67+2.6+3.584
=17.854
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