Question

you are evaluating a capital project with a net investment of $95,000, which includes an increase in net working capital of $5,000. the project has a life of 9 years with an expected salvage value of $3,000. the project will be depreciated via simplified straight-line depreciation. revenues are expected to increase by $20,000 per year and operating expenses by $4,000 per year. the firm's marginal tax rate is 40 percent and the cost of capital for this project is 8%. what is the net present value of this project?

Answer 1

To calculate the NPV of the capital project, we first determine annual cash flows after taxes, considering the increase in revenue, the increase in operating expenses, and the depreciation tax shield. We then discount these cash flows at the firm's cost of capital of 8% and sum them up, including the terminal cash flow from the salvage value.

Step-by-step explanation:

To determine the Net Present Value (NPV) of the capital project, we first need to calculate its cash flows and then discount them back to their present value at the project's cost of capital, which is 8%.

The net investment is $95,000, which is the initial outflow. The simplified straight-line depreciation for the project would be ($95,000 - $3,000 salvage value) ÷ 9 years = $10,222 per year. The project will increase revenues by $20,000 per year and increase operating expenses by $4,000 per year. So the annual operating cash inflow before taxes is $20,000 - $4,000 = $16,000.

Since the firm is subject to a 40% marginal tax rate, we need to calculate the after-tax cash flows. The depreciation tax shield is $10,222 × 40% = $4,089 per year. The annual operating cash flow after taxes is ($16,000 - ($16,000 × 40%)) + depreciation tax shield = $9,600 + $4,089 = $13,689.

To calculate the NPV, we sum the present values of these annual cash inflows, including the terminal cash flow which is the salvage value after taxes at the end of the project's life.

Year 0: -$95,000 (initial investment)

Year 1-9: $13,689 annual cash inflow (after tax)

Year 9: Extra $3,000 salvage value (after tax)

We discount these cash flows back to their present value using the firm's cost of capital, which is 8%.

A comprehensive calculation must be undertaken, adjusting each year's cash flow by the 8% discount rate and then summing them to get the NPV of the project.

If the NPV is positive, it means that the project is expected to generate more in present value terms than its cost, making it a financially viable project. If the NPV is negative, it would suggest the opposite.