I

Total Revenuet - Total Costt (1 + k)t

In this equation, Net Cash Flowt represents the firm's total after-tax profit plus noncash expenses such as depreciation; k, which is based on an appraisal of the firm's overall riskiness, represents the average cost of capital to the firm. The value of the firm is simply the discounted present value of the difference between total cash inflows and total cash outflows. Any investment project is desirable if it increases the firm's net present value, and it is undesirable if accepting it causes the firm's net present value to decrease.

The use of net present-value analysis in capital budgeting involves the application of the present value model described in Equation 15.2 to individual projects rather than to the firm as a whole. The procedure starts with an estimation of the expected net cash flows. Depending on the nature of the project, these estimates will have a greater or lesser degree of risk. For example, the benefits from replacing a piece of equipment used to produce a stable, established product can be estimated more accurately than those from an investment in equipment to produce a new and untried product. Next, the expected cost or investment outlay of the project must be estimated. This cost estimate will be quite accurate for purchased equipment, because cost equals the invoice price plus delivery and installation charges. Cost estimates for other kinds of projects may be highly uncertain or speculative. The next step involves the determination of an cost of capital appropriate discount rate, or cost of capital, for the project. A high discount rate is used for high-risk projects, and a low discount rate is used for low-risk projects. The cost of capital is considered in detail later in this chapter, but for now it may be thought of as being determined by the riskiness of the project—that is, by the uncertainty of the expected cash flows and the investment outlay. Finally, the present value of expected cash outflows must be subtracted from the present value of expected cash inflows to determine the net present value of the project. If NPV > 0, the project should be accepted. If NPV < 0, the project should be rejected. In equation form, the net present value of an individual project can be written as follows:

Discount rate

where NPV{ is the NPV of the ith project, E(CFit) represents the expected cash inflows of the zth project in the tth year, k is the risk-adjusted discount rate applicable to the th project, and C is the project's investment cost or cash outflow.

To illustrate the NPV method, consider the SVCC capital investment project discussed earlier. Table 15.4 shows net cash flows per year over the entire 8-year planning period in nominal dollars, as well as in dollars discounted using the firm's 15 percent cost of capital. Overall, the net cash flow earned on the project expressed in nominal dollars is $38,379,720.

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