Key terms

After-tax salvage value is the salvage value minus any taxes owed on the capital gain (salvage value minus book value, if positive).

The initial investment in net working capital is typically recaptured at the end of the project, providing a cash inflow.

It is the sum of the final year's differential cash flow and the total terminal cash flow (after-tax salvage value plus NWC recovery).

If the project's risk is similar to the firm's overall risk, the discount rate is set equal to the firm's cost of capital.

Assessing project risk helps determine the appropriate discount rate to use for evaluating the project's cash flows and making a sound investment decision.

NPV = $\sum_{t=0}^{n} \frac{CF_t}{(1+r)^t}$, where $CF_t$ is the cash flow at time $t$, $r$ is the discount rate, and $n$ is the project's life.

The initial outlay is entered as a negative value at time 0, representing a cash outflow.

A positive NPV indicates that the project is expected to increase firm value because the present value of its cash inflows exceeds the present value of its cash outflows.

A negative NPV indicates that the project is expected to decrease firm value because the present value of its cash outflows exceeds the present value of its cash inflows.

The NPV decision rule states that a project with a positive NPV should be accepted, and a project with a negative NPV should be rejected.

The depreciable basis is $610,000 ($587,000 purchase price + $23,000 installation costs).

The total initial outlay is $635,000 ($610,000 depreciable basis + $25,000 increase in NWC).

The annual depreciation expense is $122,000 ($610,000 depreciable basis / 5 years).

The annual differential cash flow is $138,800 (calculated as$16,800 net income + $122,000 depreciation).

The book value is $0, as the entire$610,000 depreciable basis has been depreciated over the 5-year life.

The after-tax cash inflow is $45,000 ($75,000 salvage value - $30,000 tax on capital gain).

The total cash flow at year 5 is $208,800 ($138,800 final year operating cash flow + $70,000 terminal cash flow).

Time 0: -$635,000; Years 1-4:$138,800 each year; Year 5: $208,800.

The NPV is -$134,918.50, calculated using the project's cash flows and a 15% discount rate.

No, the project should be rejected because its NPV is negative, indicating it is expected to destroy firm value.

Yes, strategic or qualitative factors can sometimes influence a decision to accept a project even if its NPV is negative, though the NPV analysis itself suggests rejection.

A taxable gain occurs if the salvage value (sale price) is greater than the book value; the tax is calculated on this difference.

The total cash outflow required at the beginning of a project (time 0), including the asset's purchase price, installation costs, and any increase in net working capital.

The total cost of an asset that can be depreciated for tax purposes, typically including the purchase price and any shipping and installation costs.

The difference between current assets and current liabilities; an increase in NWC represents an investment that needs to be financed but is not depreciated and has no direct tax implications until recaptured.

The annual incremental cash flows generated by a project over its operating life, calculated by considering changes in revenues, operating costs, and the tax shield from depreciation.

A depreciation method that assumes an asset will have zero salvage value at the end of its life, calculating annual depreciation expense as the depreciable basis divided by the asset's useful life.

The increase in a company's earnings before taxes resulting from undertaking a new project, calculated as incremental revenue minus incremental costs and depreciation on the project.

The process of adding back depreciation expense to incremental earnings after taxes (or net income) to arrive at the actual cash flow, as depreciation is a non-cash expense.

The cash flows that occur in the final year of a project, including the last year's differential cash flow, after-tax proceeds from the sale of the asset, and the recapture of net working capital.

The estimated market value of an asset at the end of its useful life, which generates a cash inflow upon sale.

The value of an asset as recorded on a company's balance sheet, calculated as its original cost minus accumulated depreciation.

The difference between an asset's sale price (salvage value) and its book value; a gain is taxable, while a loss can provide a tax shield.

The rate of return required by investors for a given project, used as the discount rate to evaluate project cash flows and determine net present value.

The sum of the present values of all cash inflows and outflows associated with a project, discounted at the cost of capital, used to make accept/reject decisions.

The total cash flow received at the end of a project's life, often including salvage value and recovery of net working capital.

The rate used to discount future cash flows to their present value, reflecting the time value of money and the risk of the investment.