To decrease the costs of operating a lock in a large river, a new system of oper
ID: 2824678 • Letter: T
Question
To decrease the costs of operating a lock in a large river, a new system of operation is proposed. The system will cost $830,000 to design and build. It is estimated that it will have to be reworked every 10 years at a cost of $120,000. In addition, an expenditure of $80,000 will have to be made at the end of the fifth year for a new type of gear that will not be available until then. Annual operating costs are expected to be $70,000 for the first 15 years and $100,000 a year thereafter. Compute the capitalized cost of perpetual service at i-7%. Click the icon to view the interest factors for discrete compounding when ,-7% per year. The capitalized cost of perpetual service is thousand. (Round to the nearest whole number.)Explanation / Answer
Capitalized Cost of Perpetual Services refers to the total present value of all the project related cash outflows.
i = 7 % per annum
Annual Operating Costs = $ 70000 for the first 15 years and $ 100000 thereafter to perpetuity.
PV of Annual Operating Costs = 70000 x (1/0.07) x [1-{1/(1.07)^(15)}] + (100000/0.07) x 1/(1.07)^(15) = $ 1155334.008
PV of One Time Expenditure = 80000 / (1.07)^(5) = $ 57038.894
PV of Reworking Cost Every 10 years = 120000 / (1.07)^(10) + 120000 / (1.07)^(20) +...... = 120000 / [(1.07)^(10) - 1] = $ 116058.163
Initial Design and Building Cost = $ 830000
Total PV of all costs = 830000 + 116058.163 + 57038.894 + 1155334.008 = $ 2158431.065 or $ 2158431 approximately.
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