## Info

Note: Negative net cash flows represent net cash outlays and are shown within parentheses.

Note: Negative net cash flows represent net cash outlays and are shown within parentheses.

This amount is the sum of column 2 and is equal to the last entry in column 3, which shows the culmination of net cash flows over the life of the project. Net nominal cash flow is a misleading measure of the attractiveness of the project, however, because cash outlays necessary to fund the project must be made substantially before cash inflows are realized. A much more relevant measure of the attractiveness of this project is net cash flow expressed in present-value terms, where each dollar of cash outflow and inflow is converted on a common current-dollar basis. In column 5, net nominal cash flows from column 2 are multiplied by present-value interest factors from column 4 that reflect a 15 percent cost of capital assumption. These present-value interest factors are used to convert the nominal dollar outlays and returns from various periods on a common present-value basis.

The NPV for this investment project is given by the cumulative net discounted cash flow of \$7,732,321 earned over the entire life of the project. This amount is given at the base of column 5 and is the sum of net discounted cash flows over the life of the project. Note also that this amount is given as the last entry in column 6, because it reflects the cumulative net discounted cash flow earned by the end of the project, year 8. Alternatively, NPV is simply the difference between the \$27,987,141 present value of cash inflows from column 5, year 3 through year 8, minus the \$20,254,820 present value of cash outflows from column 5, year 0 through 2. In equation form, the NPV for this project is calculated as follows:

NPV = PV of Cash Inflows - PV of Cash Outflows (15.4) = \$27,987,141 - \$20,254,820

Because dollar inflows received in the future are worth less than necessary dollar outlays at the beginning of the project, the NPV for the project is much less than the \$38,379,720 received in net nominal cash flows (see columns 2 and 3). This divergence between nominal and discounted cash flow figures reflects the time value of money. In present-value terms, the difference between the incremental costs and incremental revenues derived from this project is \$7,732,321. This is a desirable project that if undertaken would increase the value of the firm by this amount.

Firms typically make investments in projects showing positive net present values, reject those with negative net present values, and choose between mutually exclusive investments on the basis of higher net present values. For many capital budgeting problems, the use of the NPV method is far more complex than the preceding description suggests. The capital budgeting problem may require analysis of mutually exclusive projects with different expected lives or with substantially different initial costs. A complication also arises when the size of the firm's capital budget is limited. Under these conditions, a variant of the simple NPV is used to select projects that maximize the value of the firm.

profitability index (PI)

Benefit/cost ratio 