To decrease the costs of operating a lock in a large river a

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.)

Solution

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.