Question

Gateway Communications is considering a project with an inital fixed asset cost of $2168 milion which will be depreciated straight-line to a zero book value over the 10-year life of the project ignore bonus depreciation. At the end of the project the equipment will be sold for an estimated $495,000. The project will not directly produce any sales but will reduce operating costs by $634,000 per year The tax rate is 21 percent. The project will require $128,000 of net working capital which will be recouped when the project ends. What is the net present value at the required rate of return of 14.3 percent?

Answer 1

The net present value (NPV) of the project is $1,785,320.39 at a required rate of return of 14.3%. This means that the project's expected cash flows are greater than its initial investment, indicating that it is a good investment.

Step-by-step explanation:

To calculate the net present value (NPV) of the project, we need to discount the cash flows generated by the project to their present value. The formula for NPV is:

NPV = Initial Investment + (Present Value of Cash Flows)

First, let's calculate the present value of the operating cost savings. The cost savings per year is $634,000, and the project has a 10-year life. Using a discount rate of 14.3%, we can calculate the present value of the cost savings as follows:

Present Value = Cost Savings / (1 + Discount Rate)^Year

Using this formula, the present value of the cost savings is $4,328,801.22.

Next, let's calculate the present value of the salvage value at the end of the project. The salvage value is $495,000, which represents the estimated value of the equipment when sold. Using the same discount rate and formula, the present value of the salvage value is $338,697.06.

Now, let's calculate the present value of the initial fixed asset cost. The cost is $2,168 million, which will be depreciated straight-line to a zero book value over the 10-year life of the project. To calculate the book value at the end of each year, we divide the initial cost by the number of years and subtract the depreciation amount. The depreciation amount per year is $216.8 million. Using the same discount rate and formula, the present value of the initial fixed asset cost is $1,992,897.93.

Finally, let's calculate the net working capital requirement. The net working capital is $128,000, which will be recouped at the end of the project. Using the same discount rate and formula, the present value of the net working capital requirement is $110,720.04.

Now that we have the present values of the different cash flows, we can calculate the net present value:

NPV = -$1,992,897.93 + $4,328,801.22 + $338,697.06 + $110,720.04 = $1,785,320.39

Therefore, the net present value of the project at a required rate of return of 14.3% is $1,785,320.39.