Determining the Present Value of Costs for Building a Truss Bridge

Analysis of Costs for Building a Truss Bridge

Seeing as the state of Georgia is always doing work on the local highways, we'll investigate the cost required to support the development of new truss bridge across a river that will last indefinitely. To build the truss bridge and prepare the approach roads will cost $10.3 Million. There is also the cost of purchasing the right-of-way which is $8.3 Million. The annual maintenance costs are $7,000. The bridge will also have to be painted every 3 years for $18,000, and have to be sandblasted every 10 years at a cost of $55,000.

Calculate the Present Value

Determine how much money you would need now to support this truss bridge. The interest rate is 12%. (Hint: asking for CC(CW) )

Final Answer

To determine the amount of money needed now to support the truss bridge, we need to calculate the present value of all the costs involved. The total amount needed now is approximately $45.2 million.

Explanation

To determine the amount of money needed now to support the truss bridge, we need to calculate the present value of all the costs involved. The present value takes into account the time value of money, considering that money in the future is not worth as much as money in the present. We can use the present value formula: PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods.

The present value of the bridge construction and approach roads cost is $10.3 million. The present value of the right-of-way cost is $8.3 million. The present value of the annual maintenance costs can be calculated by dividing the annual cost by the interest rate (0.12), giving a present value of $58,333.33. The present value of the painting cost can be calculated as $18,000 divided by (1 + 0.12)^3, which is approximately $12,689.48. The present value of the sandblasting cost can be calculated as $55,000 divided by (1 + 0.12)^10, which is approximately $14,540.59.

Adding up all the present values, we get a total amount of approximately $45.2 million needed now to support this truss bridge.