Question

City engineers are considering several plans for building municipal aqueduct tunnels. They use an interest rate of 8%. One plan calls for a full-capacity tunnel that will meet the needs of the city forever. The cost is 3 million now for construction and $0.1 million every 10 years thereafter for repairs. What is the total present worth of the costs of building and maintaining the aqueduct?

Answer 1

The question is solved by calculating net present value of the project.

Net Present Value

The net cash flows are determined and they are discounted back to present values. The project with the highest net present value is selected.

Formula for computing net present value:

NPV=CF0+CF1/1+r)^1+ CF2/1+r)^2……+ CFn/1+r)^n= CFt/(1+r)^t

Where:

CF0= Initial cash investment

CFt= Cash flow in each year

r= Interest rate

This can also be calculated using a financial calculator by inputting the below:

• Press the CF button.
• CF0=0. Since there is no initial cash flow for this question.
• Cash flow for each year should be entered.
• Press Enter and down arrow after inputting each cash flow.
• After entering the last cash flow cash flow, press the NPV button and enter the interest rate.
• Press enter after that. Press the down arrow and CPT buttons to get the net present value.

Given:

Initial investment= $3,000,000

Annual cash flow= $100,000

Interest rate= 8%

Time period= 10 years

The net present value is $3,671,008.

Therefore, the total present worth of the costs of building and maintaining the aqueduct is $3,671,008.

I hope that was helpful :)